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Functions
FLA_Hess_UT_vars.h File Reference

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Functions

FLA_Error FLA_Hess_UT_unb_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_blk_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_unb_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_unb_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_blk_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_unb_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_unb_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_blk_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_unb_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_unb_var4 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_blk_var4 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_unb_var4 (FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T)
FLA_Error FLA_Hess_UT_unb_var5 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_blk_var5 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_unb_var5 (FLA_Obj A, FLA_Obj U, FLA_Obj Z, FLA_Obj T)
FLA_Error FLA_Hess_UT_opt_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_opt_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ops_var1 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opd_var1 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opc_var1 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opz_var1 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_opt_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_opt_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ops_var2 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opd_var2 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opc_var2 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opz_var2 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_opt_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_opt_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ops_var3 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opd_var3 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opc_var3 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opz_var3 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_opt_var4 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_opt_var4 (FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ops_var4 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_Y, int rs_Y, int cs_Y, float *buff_Z, int rs_Z, int cs_Z, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opd_var4 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_Y, int rs_Y, int cs_Y, double *buff_Z, int rs_Z, int cs_Z, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opc_var4 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_Y, int rs_Y, int cs_Y, scomplex *buff_Z, int rs_Z, int cs_Z, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opz_var4 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_Y, int rs_Y, int cs_Y, dcomplex *buff_Z, int rs_Z, int cs_Z, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_opt_var5 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_opt_var5 (FLA_Obj A, FLA_Obj U, FLA_Obj Z, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ops_var5 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_U, int rs_U, int cs_U, float *buff_Z, int rs_Z, int cs_Z, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opd_var5 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_U, int rs_U, int cs_U, double *buff_Z, int rs_Z, int cs_Z, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opc_var5 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_U, int rs_U, int cs_U, scomplex *buff_Z, int rs_Z, int cs_Z, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_opz_var5 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_U, int rs_U, int cs_U, dcomplex *buff_Z, int rs_Z, int cs_Z, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_ofu_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofu_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofs_var1 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofd_var1 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofc_var1 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofz_var1 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_ofu_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofu_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofs_var2 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofd_var2 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofc_var2 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofz_var2 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_ofu_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofu_var3 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofs_var3 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofd_var3 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofc_var3 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofz_var3 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_ofu_var4 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofu_var4 (FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T)
FLA_Error FLA_Hess_UT_step_ofs_var4 (int m_A, int m_T, float *buff_A, int rs_A, int cs_A, float *buff_Y, int rs_Y, int cs_Y, float *buff_Z, int rs_Z, int cs_Z, float *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofd_var4 (int m_A, int m_T, double *buff_A, int rs_A, int cs_A, double *buff_Y, int rs_Y, int cs_Y, double *buff_Z, int rs_Z, int cs_Z, double *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofc_var4 (int m_A, int m_T, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_Y, int rs_Y, int cs_Y, scomplex *buff_Z, int rs_Z, int cs_Z, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Hess_UT_step_ofz_var4 (int m_A, int m_T, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_Y, int rs_Y, int cs_Y, dcomplex *buff_Z, int rs_Z, int cs_Z, dcomplex *buff_T, int rs_T, int cs_T)
FLA_Error FLA_Fused_Ahx_Ax_ops_var1 (int m_A, int n_A, float *buff_A, int rs_A, int cs_A, float *buff_x, int inc_x, float *buff_v, int inc_v, float *buff_w, int inc_w)
FLA_Error FLA_Fused_Ahx_Ax_opd_var1 (int m_A, int n_A, double *buff_A, int rs_A, int cs_A, double *buff_x, int inc_x, double *buff_v, int inc_v, double *buff_w, int inc_w)
FLA_Error FLA_Fused_Ahx_Ax_opc_var1 (int m_A, int n_A, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_x, int inc_x, scomplex *buff_v, int inc_v, scomplex *buff_w, int inc_w)
FLA_Error FLA_Fused_Ahx_Ax_opz_var1 (int m_A, int n_A, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_x, int inc_x, dcomplex *buff_v, int inc_v, dcomplex *buff_w, int inc_w)
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_ops_var1 (int m_A, int n_A, float *buff_alpha, float *buff_u, int inc_u, float *buff_y, int inc_y, float *buff_z, int inc_z, float *buff_A, int rs_A, int cs_A, float *buff_x, int inc_x, float *buff_v, int inc_v, float *buff_w, int inc_w)
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_opd_var1 (int m_A, int n_A, double *buff_alpha, double *buff_u, int inc_u, double *buff_y, int inc_y, double *buff_z, int inc_z, double *buff_A, int rs_A, int cs_A, double *buff_x, int inc_x, double *buff_v, int inc_v, double *buff_w, int inc_w)
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_opc_var1 (int m_A, int n_A, scomplex *buff_alpha, scomplex *buff_u, int inc_u, scomplex *buff_y, int inc_y, scomplex *buff_z, int inc_z, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_x, int inc_x, scomplex *buff_v, int inc_v, scomplex *buff_w, int inc_w)
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_opz_var1 (int m_A, int n_A, dcomplex *buff_alpha, dcomplex *buff_u, int inc_u, dcomplex *buff_y, int inc_y, dcomplex *buff_z, int inc_z, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_x, int inc_x, dcomplex *buff_v, int inc_v, dcomplex *buff_w, int inc_w)
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_ops_var1 (int m_U, int n_U, float *buff_delta, float *buff_U, int rs_U, int cs_U, float *buff_Y, int rs_Y, int cs_Y, float *buff_Z, int rs_Z, int cs_Z, float *buff_u, int inc_u, float *buff_y, int inc_y, float *buff_z, int inc_z)
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_opd_var1 (int m_U, int n_U, double *buff_delta, double *buff_U, int rs_U, int cs_U, double *buff_Y, int rs_Y, int cs_Y, double *buff_Z, int rs_Z, int cs_Z, double *buff_u, int inc_u, double *buff_y, int inc_y, double *buff_z, int inc_z)
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_opc_var1 (int m_U, int n_U, scomplex *buff_delta, scomplex *buff_U, int rs_U, int cs_U, scomplex *buff_Y, int rs_Y, int cs_Y, scomplex *buff_Z, int rs_Z, int cs_Z, scomplex *buff_u, int inc_u, scomplex *buff_y, int inc_y, scomplex *buff_z, int inc_z)
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_opz_var1 (int m_U, int n_U, dcomplex *buff_delta, dcomplex *buff_U, int rs_U, int cs_U, dcomplex *buff_Y, int rs_Y, int cs_Y, dcomplex *buff_Z, int rs_Z, int cs_Z, dcomplex *buff_u, int inc_u, dcomplex *buff_y, int inc_y, dcomplex *buff_z, int inc_z)

Function Documentation

FLA_Error FLA_Fused_Ahx_Ax_opc_var1 ( int  m_A,
int  n_A,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_x,
int  inc_x,
scomplex buff_v,
int  inc_v,
scomplex buff_w,
int  inc_w 
)

References bli_cdot(), bli_csetv(), F77_caxpy(), and FLA_ZERO.

Referenced by FLA_Fused_Ahx_Ax_opt_var1(), FLA_Hess_UT_step_ofc_var2(), FLA_Hess_UT_step_ofc_var3(), and FLA_Hess_UT_step_ofc_var4().

{
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  int       i;

  bli_csetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    scomplex* a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    scomplex* nu1      = buff_v + (i  )*inc_v;
    scomplex* x        = buff_x;
    scomplex* chi1     = buff_x + (i  )*inc_x;
    scomplex* w        = buff_w;

    /*------------------------------------------------------------*/

    bli_cdot( BLIS_CONJUGATE,
              m_A,
              a1, rs_A,
              x,  inc_x,
              nu1 );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_caxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Ahx_Ax_opd_var1 ( int  m_A,
int  n_A,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_x,
int  inc_x,
double *  buff_v,
int  inc_v,
double *  buff_w,
int  inc_w 
)

References bli_dsetv(), F77_daxpy(), F77_ddot(), and FLA_ZERO.

Referenced by FLA_Fused_Ahx_Ax_opt_var1(), FLA_Hess_UT_step_ofd_var2(), FLA_Hess_UT_step_ofd_var3(), and FLA_Hess_UT_step_ofd_var4().

{
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  int       i;

  bli_dsetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    double*   a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    double*   nu1      = buff_v + (i  )*inc_v;
    double*   x        = buff_x;
    double*   chi1     = buff_x + (i  )*inc_x;
    double*   w        = buff_w;

    /*------------------------------------------------------------*/

    // bli_ddot( BLIS_CONJUGATE,
    //           m_A,
    //           a1, rs_A,
    //           x,  inc_x,
    //           nu1 );
    *nu1 = F77_ddot( &m_A,
                     a1, &rs_A,
                     x,  &inc_x );

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_daxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );

    /*------------------------------------------------------------*/

  }


  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Ahx_Ax_ops_var1 ( int  m_A,
int  n_A,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_x,
int  inc_x,
float *  buff_v,
int  inc_v,
float *  buff_w,
int  inc_w 
)

References bli_ssetv(), F77_saxpy(), F77_sdot(), and FLA_ZERO.

Referenced by FLA_Fused_Ahx_Ax_opt_var1(), FLA_Hess_UT_step_ofs_var2(), FLA_Hess_UT_step_ofs_var3(), and FLA_Hess_UT_step_ofs_var4().

{
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  int       i;

  bli_ssetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    float*    a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    float*    nu1      = buff_v + (i  )*inc_v;
    float*    x        = buff_x;
    float*    chi1     = buff_x + (i  )*inc_x;
    float*    w        = buff_w;

    /*------------------------------------------------------------*/

    // bli_sdot( BLIS_CONJUGATE,
    //           m_A,
    //           a1, rs_A,
    //           x,  inc_x,
    //           nu1 );
    *nu1 = F77_sdot( &m_A,
                     a1, &rs_A,
                     x,  &inc_x );

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_saxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );

    /*------------------------------------------------------------*/

  }


  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Ahx_Ax_opz_var1 ( int  m_A,
int  n_A,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_x,
int  inc_x,
dcomplex buff_v,
int  inc_v,
dcomplex buff_w,
int  inc_w 
)

References bli_zdot(), bli_zsetv(), F77_zaxpy(), and FLA_ZERO.

Referenced by FLA_Fused_Ahx_Ax_opt_var1(), FLA_Hess_UT_step_ofz_var2(), FLA_Hess_UT_step_ofz_var3(), and FLA_Hess_UT_step_ofz_var4().

{
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  int       i;

  bli_zsetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    dcomplex* a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    dcomplex* nu1      = buff_v + (i  )*inc_v;
    dcomplex* x        = buff_x;
    dcomplex* chi1     = buff_x + (i  )*inc_x;
    dcomplex* w        = buff_w;

    /*------------------------------------------------------------*/

    bli_zdot( BLIS_CONJUGATE,
              m_A,
              a1, rs_A,
              x,  inc_x,
              nu1 );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_zaxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_opc_var1 ( int  m_U,
int  n_U,
scomplex buff_delta,
scomplex buff_U,
int  rs_U,
int  cs_U,
scomplex buff_Y,
int  rs_Y,
int  cs_Y,
scomplex buff_Z,
int  rs_Z,
int  cs_Z,
scomplex buff_u,
int  inc_u,
scomplex buff_y,
int  inc_y,
scomplex buff_z,
int  inc_z 
)

References bli_cdot(), and F77_caxpy().

Referenced by FLA_Fused_Gemv_Uhu_Yhu_Zhu_opt_var1(), and FLA_Hess_UT_step_ofc_var4().

{
  int       i;

  for ( i = 0; i < n_U; ++i )
  {
    scomplex* u1       = buff_U + (i  )*cs_U + (0  )*rs_U;
    scomplex* y1       = buff_Y + (i  )*cs_Y + (0  )*rs_Y;
    scomplex* z1       = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    scomplex* delta    = buff_delta;
    scomplex* u        = buff_u;
    scomplex* y        = buff_y;
    scomplex* z        = buff_z;
    scomplex  alpha;
    scomplex  beta;
    scomplex  gamma;

    /*------------------------------------------------------------*/

    bli_cdot( BLIS_CONJUGATE,
              m_U,
              u1, rs_U,
              u,  inc_u,
              &alpha );

    bli_cdot( BLIS_CONJUGATE,
              m_U,
              z1, rs_Z,
              u,  inc_u,
              &beta );

    bli_cdot( BLIS_CONJUGATE,
              m_U,
              y1, rs_Y,
              u,  inc_u,
              &gamma );

    bli_cscals( delta, &alpha );
    bli_cscals( delta, &beta );
    bli_cscals( delta, &gamma );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             y1, rs_Y,
    //             y,  inc_y );
    F77_caxpy( &m_U,
               &alpha,
               y1, &rs_Y,
               y,  &inc_y );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &beta,
    //             u1, rs_U,
    //             y,  inc_y );
    F77_caxpy( &m_U,
               &beta,
               u1, &rs_U,
               y,  &inc_y );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             z1, rs_Z,
    //             z,  inc_z );
    F77_caxpy( &m_U,
               &alpha,
               z1, &rs_Z,
               z,  &inc_z );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &gamma,
    //             u1, rs_U,
    //             z,  inc_z );
    F77_caxpy( &m_U,
               &gamma,
               u1, &rs_U,
               z,  &inc_z );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_opd_var1 ( int  m_U,
int  n_U,
double *  buff_delta,
double *  buff_U,
int  rs_U,
int  cs_U,
double *  buff_Y,
int  rs_Y,
int  cs_Y,
double *  buff_Z,
int  rs_Z,
int  cs_Z,
double *  buff_u,
int  inc_u,
double *  buff_y,
int  inc_y,
double *  buff_z,
int  inc_z 
)

References F77_daxpy(), and F77_ddot().

Referenced by FLA_Fused_Gemv_Uhu_Yhu_Zhu_opt_var1(), and FLA_Hess_UT_step_ofd_var4().

{
  int       i;

  for ( i = 0; i < n_U; ++i )
  {
    double*   u1       = buff_U + (i  )*cs_U + (0  )*rs_U;
    double*   y1       = buff_Y + (i  )*cs_Y + (0  )*rs_Y;
    double*   z1       = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    double*   delta    = buff_delta;
    double*   u        = buff_u;
    double*   y        = buff_y;
    double*   z        = buff_z;
    double    alpha;
    double    beta;
    double    gamma;

    /*------------------------------------------------------------*/

    // bli_ddot( BLIS_CONJUGATE,
    //           m_U,
    //           u1, rs_U,
    //           u,  inc_u,
    //           &alpha );
    alpha = F77_ddot( &m_U,
                      u1, &rs_U,
                      u,  &inc_u );

    // bli_ddot( BLIS_CONJUGATE,
    //           m_U,
    //           z1, rs_Z,
    //           u,  inc_u,
    //           &beta );
    beta  = F77_ddot( &m_U,
                      z1, &rs_Z,
                      u,  &inc_u );

    // bli_ddot( BLIS_CONJUGATE,
    //           m_U,
    //           y1, rs_Y,
    //           u,  inc_u,
    //           &gamma );
    gamma = F77_ddot( &m_U,
                      y1, &rs_Y,
                      u,  &inc_u );

    // bli_dscals( delta, &alpha );
    // bli_dscals( delta, &beta );
    // bli_dscals( delta, &gamma );
    alpha *= *delta;
    beta  *= *delta;
    gamma *= *delta;

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             y1, rs_Y,
    //             y,  inc_y );
    F77_daxpy( &m_U,
               &alpha,
               y1, &rs_Y,
               y,  &inc_y );

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &beta,
    //             u1, rs_U,
    //             y,  inc_y );
    F77_daxpy( &m_U,
               &beta,
               u1, &rs_U,
               y,  &inc_y );

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             z1, rs_Z,
    //             z,  inc_z );
    F77_daxpy( &m_U,
               &alpha,
               z1, &rs_Z,
               z,  &inc_z );

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &gamma,
    //             u1, rs_U,
    //             z,  inc_z );
    F77_daxpy( &m_U,
               &gamma,
               u1, &rs_U,
               z,  &inc_z );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_ops_var1 ( int  m_U,
int  n_U,
float *  buff_delta,
float *  buff_U,
int  rs_U,
int  cs_U,
float *  buff_Y,
int  rs_Y,
int  cs_Y,
float *  buff_Z,
int  rs_Z,
int  cs_Z,
float *  buff_u,
int  inc_u,
float *  buff_y,
int  inc_y,
float *  buff_z,
int  inc_z 
)

References F77_saxpy(), and F77_sdot().

Referenced by FLA_Fused_Gemv_Uhu_Yhu_Zhu_opt_var1(), and FLA_Hess_UT_step_ofs_var4().

{
  int       i;

  for ( i = 0; i < n_U; ++i )
  {
    float*    u1       = buff_U + (i  )*cs_U + (0  )*rs_U;
    float*    y1       = buff_Y + (i  )*cs_Y + (0  )*rs_Y;
    float*    z1       = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    float*    delta    = buff_delta;
    float*    u        = buff_u;
    float*    y        = buff_y;
    float*    z        = buff_z;
    float     alpha;
    float     beta;
    float     gamma;

    /*------------------------------------------------------------*/

    // bli_sdot( BLIS_CONJUGATE,
    //           m_U,
    //           u1, rs_U,
    //           u,  inc_u,
    //           &alpha );
    alpha = F77_sdot( &m_U,
                      u1, &rs_U,
                      u,  &inc_u );

    // bli_sdot( BLIS_CONJUGATE,
    //           m_U,
    //           z1, rs_Z,
    //           u,  inc_u,
    //           &beta );
    beta  = F77_sdot( &m_U,
                      z1, &rs_Z,
                      u,  &inc_u );

    // bli_sdot( BLIS_CONJUGATE,
    //           m_U,
    //           y1, rs_Y,
    //           u,  inc_u,
    //           &gamma );
    gamma = F77_sdot( &m_U,
                      y1, &rs_Y,
                      u,  &inc_u );

    // bli_sscals( delta, &alpha );
    // bli_sscals( delta, &beta );
    // bli_sscals( delta, &gamma );
    alpha *= *delta;
    beta  *= *delta;
    gamma *= *delta;

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             y1, rs_Y,
    //             y,  inc_y );
    F77_saxpy( &m_U,
               &alpha,
               y1, &rs_Y,
               y,  &inc_y );

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &beta,
    //             u1, rs_U,
    //             y,  inc_y );
    F77_saxpy( &m_U,
               &beta,
               u1, &rs_U,
               y,  &inc_y );

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             z1, rs_Z,
    //             z,  inc_z );
    F77_saxpy( &m_U,
               &alpha,
               z1, &rs_Z,
               z,  &inc_z );

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &gamma,
    //             u1, rs_U,
    //             z,  inc_z );
    F77_saxpy( &m_U,
               &gamma,
               u1, &rs_U,
               z,  &inc_z );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gemv_Uhu_Yhu_Zhu_opz_var1 ( int  m_U,
int  n_U,
dcomplex buff_delta,
dcomplex buff_U,
int  rs_U,
int  cs_U,
dcomplex buff_Y,
int  rs_Y,
int  cs_Y,
dcomplex buff_Z,
int  rs_Z,
int  cs_Z,
dcomplex buff_u,
int  inc_u,
dcomplex buff_y,
int  inc_y,
dcomplex buff_z,
int  inc_z 
)

References bli_zdot(), and F77_zaxpy().

Referenced by FLA_Fused_Gemv_Uhu_Yhu_Zhu_opt_var1(), and FLA_Hess_UT_step_ofz_var4().

{
  int       i;

  for ( i = 0; i < n_U; ++i )
  {
    dcomplex* u1       = buff_U + (i  )*cs_U + (0  )*rs_U;
    dcomplex* y1       = buff_Y + (i  )*cs_Y + (0  )*rs_Y;
    dcomplex* z1       = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    dcomplex* delta    = buff_delta;
    dcomplex* u        = buff_u;
    dcomplex* y        = buff_y;
    dcomplex* z        = buff_z;
    dcomplex  alpha;
    dcomplex  beta;
    dcomplex  gamma;

    /*------------------------------------------------------------*/

    bli_zdot( BLIS_CONJUGATE,
              m_U,
              u1, rs_U,
              u,  inc_u,
              &alpha );

    bli_zdot( BLIS_CONJUGATE,
              m_U,
              z1, rs_Z,
              u,  inc_u,
              &beta );

    bli_zdot( BLIS_CONJUGATE,
              m_U,
              y1, rs_Y,
              u,  inc_u,
              &gamma );

    bli_zscals( delta, &alpha );
    bli_zscals( delta, &beta );
    bli_zscals( delta, &gamma );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             y1, rs_Y,
    //             y,  inc_y );
    F77_zaxpy( &m_U,
               &alpha,
               y1, &rs_Y,
               y,  &inc_y );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &beta,
    //             u1, rs_U,
    //             y,  inc_y );
    F77_zaxpy( &m_U,
               &beta,
               u1, &rs_U,
               y,  &inc_y );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &alpha,
    //             z1, rs_Z,
    //             z,  inc_z );
    F77_zaxpy( &m_U,
               &alpha,
               z1, &rs_Z,
               z,  &inc_z );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_U,
    //             &gamma,
    //             u1, rs_U,
    //             z,  inc_z );
    F77_zaxpy( &m_U,
               &gamma,
               u1, &rs_U,
               z,  &inc_z );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_opc_var1 ( int  m_A,
int  n_A,
scomplex buff_alpha,
scomplex buff_u,
int  inc_u,
scomplex buff_y,
int  inc_y,
scomplex buff_z,
int  inc_z,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_x,
int  inc_x,
scomplex buff_v,
int  inc_v,
scomplex buff_w,
int  inc_w 
)

References bli_cdot(), bli_csetv(), F77_caxpy(), and FLA_ZERO.

Referenced by FLA_Fused_Gerc2_Ahx_Ax_opt_var1(), and FLA_Hess_UT_step_ofc_var3().

{
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  int       i;

  bli_csetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    scomplex* a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    scomplex* nu1      = buff_v + (i  )*inc_v;
    scomplex* x        = buff_x;
    scomplex* chi1     = buff_x + (i  )*inc_x;
    scomplex* psi1     = buff_y + (i  )*inc_y;
    scomplex* u        = buff_u;
    scomplex* upsilon1 = buff_u + (i  )*inc_u;
    scomplex* w        = buff_w;
    scomplex* z        = buff_z;
    scomplex* alpha    = buff_alpha;
    scomplex  temp1;
    scomplex  temp2;
    scomplex  conj_psi1;
    scomplex  conj_upsilon1;

    /*------------------------------------------------------------*/

    bli_ccopyconj( psi1, &conj_psi1 );
    bli_cmult3( alpha, &conj_psi1, &temp1 );

    bli_ccopyconj( upsilon1, &conj_upsilon1 );
    bli_cmult3( alpha, &conj_upsilon1, &temp2 );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp1,
    //             u,  inc_u,
    //             a1, rs_A );
    F77_caxpy( &m_A,
               &temp1,
               u,  &inc_u,
               a1, &rs_A );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp2,
    //             z,  inc_z,
    //             a1, rs_A );
    F77_caxpy( &m_A,
               &temp2,
               z,  &inc_z,
               a1, &rs_A );

    bli_cdot( BLIS_CONJUGATE,
              m_A,
              a1, rs_A,
              x,  inc_x,
              nu1 );

    // bli_caxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_caxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_opd_var1 ( int  m_A,
int  n_A,
double *  buff_alpha,
double *  buff_u,
int  inc_u,
double *  buff_y,
int  inc_y,
double *  buff_z,
int  inc_z,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_x,
int  inc_x,
double *  buff_v,
int  inc_v,
double *  buff_w,
int  inc_w 
)

References bli_dsetv(), F77_daxpy(), F77_ddot(), and FLA_ZERO.

Referenced by FLA_Fused_Gerc2_Ahx_Ax_opt_var1(), and FLA_Hess_UT_step_ofd_var3().

{
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  int       i;

  bli_dsetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    double*   a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    double*   nu1      = buff_v + (i  )*inc_v;
    double*   x        = buff_x;
    double*   chi1     = buff_x + (i  )*inc_x;
    double*   psi1     = buff_y + (i  )*inc_y;
    double*   u        = buff_u;
    double*   upsilon1 = buff_u + (i  )*inc_u;
    double*   w        = buff_w;
    double*   z        = buff_z;
    double*   alpha    = buff_alpha;
    double    temp1;
    double    temp2;

    /*------------------------------------------------------------*/

    // bli_dcopyconj( psi1, &conj_psi1 );
    // bli_dmult3( alpha, &conj_psi1, &temp1 );
    temp1 = *alpha * *psi1;

    // bli_dcopyconj( upsilon1, &conj_upsilon1 );
    // bli_dmult3( alpha, &conj_upsilon1, &temp2 );
    temp2 = *alpha * *upsilon1;

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp1,
    //             u,  inc_u,
    //             a1, rs_A );
    F77_daxpy( &m_A,
               &temp1,
               u,  &inc_u,
               a1, &rs_A );

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp2,
    //             z,  inc_z,
    //             a1, rs_A );
    F77_daxpy( &m_A,
               &temp2,
               z,  &inc_z,
               a1, &rs_A );

    // bli_ddot( BLIS_CONJUGATE,
    //           m_A,
    //           a1, rs_A,
    //           x,  inc_x,
    //           nu1 );
    *nu1 = F77_ddot( &m_A,
                     a1, &rs_A,
                     x,  &inc_x );

    // bli_daxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_daxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_ops_var1 ( int  m_A,
int  n_A,
float *  buff_alpha,
float *  buff_u,
int  inc_u,
float *  buff_y,
int  inc_y,
float *  buff_z,
int  inc_z,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_x,
int  inc_x,
float *  buff_v,
int  inc_v,
float *  buff_w,
int  inc_w 
)

References bli_ssetv(), F77_saxpy(), F77_sdot(), and FLA_ZERO.

Referenced by FLA_Fused_Gerc2_Ahx_Ax_opt_var1(), and FLA_Hess_UT_step_ofs_var3().

{
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  int       i;

  bli_ssetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    float*    a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    float*    nu1      = buff_v + (i  )*inc_v;
    float*    x        = buff_x;
    float*    chi1     = buff_x + (i  )*inc_x;
    float*    psi1     = buff_y + (i  )*inc_y;
    float*    u        = buff_u;
    float*    upsilon1 = buff_u + (i  )*inc_u;
    float*    w        = buff_w;
    float*    z        = buff_z;
    float*    alpha    = buff_alpha;
    float     temp1;
    float     temp2;

    /*------------------------------------------------------------*/

    // bli_scopyconj( psi1, &conj_psi1 );
    // bli_smult3( alpha, &conj_psi1, &temp1 );
    temp1 = *alpha * *psi1;

    // bli_scopyconj( upsilon1, &conj_upsilon1 );
    // bli_smult3( alpha, &conj_upsilon1, &temp2 );
    temp2 = *alpha * *upsilon1;

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp1,
    //             u,  inc_u,
    //             a1, rs_A );
    F77_saxpy( &m_A,
               &temp1,
               u,  &inc_u,
               a1, &rs_A );

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp2,
    //             z,  inc_z,
    //             a1, rs_A );
    F77_saxpy( &m_A,
               &temp2,
               z,  &inc_z,
               a1, &rs_A );

    // bli_sdot( BLIS_CONJUGATE,
    //           m_A,
    //           a1, rs_A,
    //           x,  inc_x,
    //           nu1 );
    *nu1 = F77_sdot( &m_A,
                     a1, &rs_A,
                     x,  &inc_x );

    // bli_saxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_saxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );
    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Fused_Gerc2_Ahx_Ax_opz_var1 ( int  m_A,
int  n_A,
dcomplex buff_alpha,
dcomplex buff_u,
int  inc_u,
dcomplex buff_y,
int  inc_y,
dcomplex buff_z,
int  inc_z,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_x,
int  inc_x,
dcomplex buff_v,
int  inc_v,
dcomplex buff_w,
int  inc_w 
)

References bli_zdot(), bli_zsetv(), F77_zaxpy(), and FLA_ZERO.

Referenced by FLA_Fused_Gerc2_Ahx_Ax_opt_var1(), and FLA_Hess_UT_step_ofz_var3().

{
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  int       i;

  bli_zsetv( n_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    dcomplex* a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    dcomplex* nu1      = buff_v + (i  )*inc_v;
    dcomplex* x        = buff_x;
    dcomplex* chi1     = buff_x + (i  )*inc_x;
    dcomplex* psi1     = buff_y + (i  )*inc_y;
    dcomplex* u        = buff_u;
    dcomplex* upsilon1 = buff_u + (i  )*inc_u;
    dcomplex* w        = buff_w;
    dcomplex* z        = buff_z;
    dcomplex* alpha    = buff_alpha;
    dcomplex  temp1;
    dcomplex  temp2;
    dcomplex  conj_psi1;
    dcomplex  conj_upsilon1;

    /*------------------------------------------------------------*/

    bli_zcopyconj( psi1, &conj_psi1 );
    bli_zmult3( alpha, &conj_psi1, &temp1 );

    bli_zcopyconj( upsilon1, &conj_upsilon1 );
    bli_zmult3( alpha, &conj_upsilon1, &temp2 );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp1,
    //             u,  inc_u,
    //             a1, rs_A );
    F77_zaxpy( &m_A,
               &temp1,
               u,  &inc_u,
               a1, &rs_A );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             &temp2,
    //             z,  inc_z,
    //             a1, rs_A );
    F77_zaxpy( &m_A,
               &temp2,
               z,  &inc_z,
               a1, &rs_A );

    bli_zdot( BLIS_CONJUGATE,
              m_A,
              a1, rs_A,
              x,  inc_x,
              nu1 );

    // bli_zaxpyv( BLIS_NO_CONJUGATE,
    //             m_A,
    //             chi1,
    //             a1, rs_A,
    //             w,  inc_w );
    F77_zaxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_blk_var1 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemm_external(), FLA_Hess_UT_step_opt_var1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Triangularize(), FLA_Trsm_external(), and FLA_ZERO.

Referenced by FLA_Hess_UT_internal().

{
  FLA_Obj  ATL,   ATR,      A00, A01, A02, 
           ABL,   ABR,      A10, A11, A12,
                            A20, A21, A22;
  FLA_Obj  UT,              U0,
           UB,              U1,
                            U2;
  FLA_Obj  ZT,              Z0,
           ZB,              Z1,
                            Z2;
  FLA_Obj  TL,    TR,       T0, T1, T2; 

  FLA_Obj  U, Z;
  FLA_Obj  ABR_l;
  FLA_Obj  UB_l;
  FLA_Obj  T1_tl;
  FLA_Obj  WT_l;
  FLA_Obj  none, none2, none3;
  FLA_Obj  UB_tl,
           UB_bl;
  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg, b, bb;

  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &U );
  FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &Z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x1( U,    &UT, 
                      &UB,            0, FLA_TOP );
  FLA_Part_2x1( Z,    &ZT, 
                      &ZB,            0, FLA_TOP );
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT ); 

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) )
  {
    b = min( FLA_Obj_length( ABR ), b_alg );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );
    FLA_Repart_2x1_to_3x1( UT,                &U0, 
                        /* ** */            /* ** */
                                              &U1, 
                           UB,                &U2,        b, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( ZT,                &Z0, 
                        /* ** */            /* ** */
                                              &Z1, 
                           ZB,                &Z2,        b, FLA_BOTTOM );
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &T2,
                           b, FLA_RIGHT );

    /*------------------------------------------------------------*/

    FLA_Part_2x2( T1,     &T1_tl, &none,   
                          &none2, &none3,   b, b, FLA_TL ); 

    bb = min( FLA_Obj_length( ABR ) - 1, b_alg );

    FLA_Part_1x2( ABR,    &ABR_l, &none,    bb, FLA_LEFT ); 
    FLA_Part_1x2( UB,     &UB_l,  &none,    bb, FLA_LEFT ); 

    // [ ABR, T1 ] = FLA_Hess_UT_step_unb_var1( ABR, T1, b );
    //FLA_Hess_UT_step_unb_var1( ABR, T1_tl );
    FLA_Hess_UT_step_opt_var1( ABR, T1_tl );

    // Build UB from ABR, with explicit unit subdiagonal and zeros.
    FLA_Copy_external( ABR_l, UB_l );
    FLA_Part_2x1( UB_l,   &UB_tl, 
                          &UB_bl,            1, FLA_TOP );
    FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_UNIT_DIAG, UB_bl );
    FLA_Obj_set_to_scalar( FLA_ZERO, UB_tl );

    // ATR = ATR - ATR * UB * inv( triu( T1 ) ) * UB' );
    if ( FLA_Obj_length( ATR ) > 0 )
    {
      // NOTE: We use ZT as temporary workspace.
      FLA_Part_1x2( ZT,     &WT_l,  &none,    bb, FLA_LEFT ); 
      FLA_Part_2x2( T1,     &T1_tl, &none,   
                            &none2, &none3,   bb, bb, FLA_TL ); 

      // WT_l = ATR * UB_l * inv( triu( T1 ) ).
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_ONE, ATR, UB_l, FLA_ZERO, WT_l );
      FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
                         FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, WT_l );

      // ATR = ATR - WT_l * UB_l'
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                         FLA_MINUS_ONE, WT_l, UB_l, FLA_ONE, ATR );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &UT,                U0, 
                                                  U1, 
                            /* ** */           /* ** */
                              &UB,                U2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &ZT,                Z0, 
                                                  Z1, 
                            /* ** */           /* ** */
                              &ZB,                Z2,     FLA_TOP );
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ T2,
                              FLA_LEFT );
  }

  FLA_Obj_free( &U );
  FLA_Obj_free( &Z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_blk_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemm_external(), FLA_Hess_UT_step_opt_var2(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Triangularize(), FLA_Trsm_external(), and FLA_ZERO.

Referenced by FLA_Hess_UT_internal().

{
  FLA_Obj  ATL,   ATR,      A00, A01, A02, 
           ABL,   ABR,      A10, A11, A12,
                            A20, A21, A22;
  FLA_Obj  UT,              U0,
           UB,              U1,
                            U2;
  FLA_Obj  ZT,              Z0,
           ZB,              Z1,
                            Z2;
  FLA_Obj  TL,    TR,       T0, T1, T2; 

  FLA_Obj  U, Z;
  FLA_Obj  ABR_l;
  FLA_Obj  UB_l;
  FLA_Obj  T1_tl;
  FLA_Obj  WT_l;
  FLA_Obj  none, none2, none3;
  FLA_Obj  UB_tl,
           UB_bl;
  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg, b, bb;

  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &U );
  FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &Z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x1( U,    &UT, 
                      &UB,            0, FLA_TOP );
  FLA_Part_2x1( Z,    &ZT, 
                      &ZB,            0, FLA_TOP );
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT ); 

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) )
  {
    b = min( FLA_Obj_length( ABR ), b_alg );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );
    FLA_Repart_2x1_to_3x1( UT,                &U0, 
                        /* ** */            /* ** */
                                              &U1, 
                           UB,                &U2,        b, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( ZT,                &Z0, 
                        /* ** */            /* ** */
                                              &Z1, 
                           ZB,                &Z2,        b, FLA_BOTTOM );
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &T2,
                           b, FLA_RIGHT );

    /*------------------------------------------------------------*/

    FLA_Part_2x2( T1,     &T1_tl, &none,   
                          &none2, &none3,   b, b, FLA_TL ); 

    bb = min( FLA_Obj_length( ABR ) - 1, b_alg );

    FLA_Part_1x2( ABR,    &ABR_l, &none,    bb, FLA_LEFT ); 
    FLA_Part_1x2( UB,     &UB_l,  &none,    bb, FLA_LEFT ); 

    // [ ABR, T1 ] = FLA_Hess_UT_step_unb_var2( ABR, T1, b );
    //FLA_Hess_UT_step_unb_var2( ABR, T1_tl );
    //FLA_Hess_UT_step_ofu_var2( ABR, T1_tl );
    FLA_Hess_UT_step_opt_var2( ABR, T1_tl );

    // Build UB from ABR, with explicit unit subdiagonal and zeros.
    FLA_Copy_external( ABR_l, UB_l );
    FLA_Part_2x1( UB_l,   &UB_tl, 
                          &UB_bl,            1, FLA_TOP );
    FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_UNIT_DIAG, UB_bl );
    FLA_Obj_set_to_scalar( FLA_ZERO, UB_tl );

    // ATR = ATR - ATR * UB * inv( triu( T1 ) ) * UB' );
    if ( FLA_Obj_length( ATR ) > 0 )
    {
      // NOTE: We use ZT as temporary workspace.
      FLA_Part_1x2( ZT,     &WT_l,  &none,    bb, FLA_LEFT ); 
      FLA_Part_2x2( T1,     &T1_tl, &none,   
                            &none2, &none3,   bb, bb, FLA_TL ); 

      // WT_l = ATR * UB_l * inv( triu( T1 ) ).
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_ONE, ATR, UB_l, FLA_ZERO, WT_l );
      FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
                         FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, WT_l );

      // ATR = ATR - WT_l * UB_l'
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                         FLA_MINUS_ONE, WT_l, UB_l, FLA_ONE, ATR );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &UT,                U0, 
                                                  U1, 
                            /* ** */           /* ** */
                              &UB,                U2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &ZT,                Z0, 
                                                  Z1, 
                            /* ** */           /* ** */
                              &ZB,                Z2,     FLA_TOP );
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ T2,
                              FLA_LEFT );
  }

  FLA_Obj_free( &U );
  FLA_Obj_free( &Z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_blk_var3 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemm_external(), FLA_Hess_UT_step_opt_var3(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Triangularize(), FLA_Trsm_external(), and FLA_ZERO.

Referenced by FLA_Hess_UT_internal().

{
  FLA_Obj  ATL,   ATR,      A00, A01, A02, 
           ABL,   ABR,      A10, A11, A12,
                            A20, A21, A22;
  FLA_Obj  UT,              U0,
           UB,              U1,
                            U2;
  FLA_Obj  ZT,              Z0,
           ZB,              Z1,
                            Z2;
  FLA_Obj  TL,    TR,       T0, T1, T2; 

  FLA_Obj  U, Z;
  FLA_Obj  ABR_l;
  FLA_Obj  UB_l;
  FLA_Obj  WT_l;
  FLA_Obj  T1_tl;
  FLA_Obj  none, none2, none3;
  FLA_Obj  UB_tl,
           UB_bl;
  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg, b, bb;

  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, m_A,    b_alg, 0, 0, &U );
  FLA_Obj_create( datatype_A, m_A,    b_alg, 0, 0, &Z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x1( U,    &UT, 
                      &UB,            0, FLA_TOP );
  FLA_Part_2x1( Z,    &ZT, 
                      &ZB,            0, FLA_TOP );
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT ); 

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) )
  {
    b = min( FLA_Obj_length( ABR ), b_alg );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );
    FLA_Repart_2x1_to_3x1( UT,                &U0, 
                        /* ** */            /* ** */
                                              &U1, 
                           UB,                &U2,        b, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( ZT,                &Z0, 
                        /* ** */            /* ** */
                                              &Z1, 
                           ZB,                &Z2,        b, FLA_BOTTOM );
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &T2,
                           b, FLA_RIGHT );

    /*------------------------------------------------------------*/

    FLA_Part_2x2( T1,     &T1_tl, &none,   
                          &none2, &none3,   b, b, FLA_TL ); 

    bb = min( FLA_Obj_length( ABR ) - 1, b_alg );

    FLA_Part_1x2( ABR,    &ABR_l, &none,    bb, FLA_LEFT ); 
    FLA_Part_1x2( UB,     &UB_l,  &none,    bb, FLA_LEFT ); 

    // [ ABR, T1 ] = FLA_Hess_UT_step_unb_var3( ABR, T1, b );
    //FLA_Hess_UT_step_unb_var3( ABR, T1_tl );
    //FLA_Hess_UT_step_ofu_var3( ABR, T1_tl );
    FLA_Hess_UT_step_opt_var3( ABR, T1_tl );

    // Build UB from ABR, with explicit unit subdiagonal and zeros.
    FLA_Copy_external( ABR_l, UB_l );
    FLA_Part_2x1( UB_l,   &UB_tl, 
                          &UB_bl,            1, FLA_TOP );
    FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_UNIT_DIAG, UB_bl );
    FLA_Obj_set_to_scalar( FLA_ZERO, UB_tl );

    // ATR = ATR - ATR * UB * inv( triu( T1 ) ) * UB' );
    if ( FLA_Obj_length( ATR ) > 0 )
    {
      // NOTE: We use ZT as temporary workspace.
      FLA_Part_1x2( ZT,     &WT_l,  &none,    bb, FLA_LEFT ); 
      FLA_Part_2x2( T1,     &T1_tl, &none,   
                            &none2, &none3,   bb, bb, FLA_TL ); 

      // WT_l = ATR * UB_l * inv( triu( T1 ) ).
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_ONE, ATR, UB_l, FLA_ZERO, WT_l );
      FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
                         FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, WT_l );

      // ATR = ATR - WT_l * UB_l'
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                         FLA_MINUS_ONE, WT_l, UB_l, FLA_ONE, ATR );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &UT,                U0, 
                                                  U1, 
                            /* ** */           /* ** */
                              &UB,                U2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &ZT,                Z0, 
                                                  Z1, 
                            /* ** */           /* ** */
                              &ZB,                Z2,     FLA_TOP );
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ T2,
                              FLA_LEFT );
  }

  FLA_Obj_free( &U );
  FLA_Obj_free( &Z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_blk_var4 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemm_external(), FLA_Hess_UT_step_opt_var4(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Triangularize(), FLA_Trsm_external(), and FLA_ZERO.

Referenced by FLA_Hess_UT_internal().

{
  FLA_Obj  ATL,   ATR,      A00, A01, A02, 
           ABL,   ABR,      A10, A11, A12,
                            A20, A21, A22;
  FLA_Obj  UT,              U0,
           UB,              U1,
                            U2;
  FLA_Obj  YT,              Y0,
           YB,              Y1,
                            Y2;
  FLA_Obj  ZT,              Z0,
           ZB,              Z1,
                            Z2;
  FLA_Obj  TL,    TR,       T0, T1, T2; 

  FLA_Obj  U, Y, Z;
  FLA_Obj  ABR_l;
  FLA_Obj  UB_l, U2_l;
  FLA_Obj  YB_l, Y2_l;
  FLA_Obj  ZB_l, Z2_l;
  FLA_Obj  WT_l;
  FLA_Obj  T1_tl;
  FLA_Obj  none, none2, none3;
  FLA_Obj  UB_tl,
           UB_bl;
  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg, b, bb;

  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, m_A,    b_alg, 0, 0, &U );
  FLA_Obj_create( datatype_A, m_A,    b_alg, 0, 0, &Y );
  FLA_Obj_create( datatype_A, m_A,    b_alg, 0, 0, &Z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x1( U,    &UT, 
                      &UB,            0, FLA_TOP );
  FLA_Part_2x1( Y,    &YT, 
                      &YB,            0, FLA_TOP );
  FLA_Part_2x1( Z,    &ZT, 
                      &ZB,            0, FLA_TOP );
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT ); 

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) )
  {
    b = min( FLA_Obj_length( ABR ), b_alg );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );
    FLA_Repart_2x1_to_3x1( UT,                &U0, 
                        /* ** */            /* ** */
                                              &U1, 
                           UB,                &U2,        b, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( YT,                &Y0, 
                        /* ** */            /* ** */
                                              &Y1, 
                           YB,                &Y2,        b, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( ZT,                &Z0, 
                        /* ** */            /* ** */
                                              &Z1, 
                           ZB,                &Z2,        b, FLA_BOTTOM );
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &T2,
                           b, FLA_RIGHT );

    /*------------------------------------------------------------*/

    FLA_Part_2x2( T1,     &T1_tl, &none,   
                          &none2, &none3,   b, b, FLA_TL ); 

    bb = min( FLA_Obj_length( ABR ) - 1, b_alg );

    FLA_Part_1x2( ABR,    &ABR_l, &none,    bb, FLA_LEFT ); 
    FLA_Part_1x2( UB,     &UB_l,  &none,    bb, FLA_LEFT ); 
    FLA_Part_1x2( YB,     &YB_l,  &none,    bb, FLA_LEFT ); 
    FLA_Part_1x2( ZB,     &ZB_l,  &none,    bb, FLA_LEFT ); 

    FLA_Part_2x1( UB_l,   &none,
                          &U2_l,             b, FLA_TOP );
    FLA_Part_2x1( YB_l,   &none,
                          &Y2_l,             b, FLA_TOP );
    FLA_Part_2x1( ZB_l,   &none,
                          &Z2_l,             b, FLA_TOP );

    // [ ABR, YB, ZB, T1 ] = FLA_Hess_UT_step_unb_var4( ABR, YB, ZB, T1, b );
    //FLA_Hess_UT_step_unb_var4( ABR, YB, ZB, T1_tl );
    //FLA_Hess_UT_step_ofu_var4( ABR, YB, ZB, T1_tl );
    FLA_Hess_UT_step_opt_var4( ABR, YB, ZB, T1_tl );

    // Build UB from ABR, with explicit unit subdiagonal and zeros.
    FLA_Copy_external( ABR_l, UB_l );
    FLA_Part_2x1( UB_l,   &UB_tl, 
                          &UB_bl,            1, FLA_TOP );
    FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_UNIT_DIAG, UB_bl );
    FLA_Obj_set_to_scalar( FLA_ZERO, UB_tl );

    // ATR = ATR - ATR * UB * inv( triu( T ) ) * UB' );
    if ( FLA_Obj_length( ATR ) > 0 )
    {
      // NOTE: We use ZT as temporary workspace.
      FLA_Part_1x2( ZT,     &WT_l,  &none,    bb, FLA_LEFT ); 
      FLA_Part_2x2( T1,     &T1_tl, &none,   
                            &none2, &none3,   bb, bb, FLA_TL ); 

      // WT_l = ATR * UB_l * inv( triu( T ) ).
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_ONE, ATR, UB_l, FLA_ZERO, WT_l );
      FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
                         FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, WT_l );

      // ATR = ATR - WT_l * UB_l'
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                         FLA_MINUS_ONE, WT_l, UB_l, FLA_ONE, ATR );
    }

    // A22 = A22 - U2 * Y2' - Z2 * U2';
    FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                       FLA_MINUS_ONE, U2_l, Y2_l, FLA_ONE, A22 );
    FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                       FLA_MINUS_ONE, Z2_l, U2_l, FLA_ONE, A22 );

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &UT,                U0, 
                                                  U1, 
                            /* ** */           /* ** */
                              &UB,                U2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &YT,                Y0, 
                                                  Y1, 
                            /* ** */           /* ** */
                              &YB,                Y2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &ZT,                Z0, 
                                                  Z1, 
                            /* ** */           /* ** */
                              &ZB,                Z2,     FLA_TOP );
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ T2,
                              FLA_LEFT );
  }

  FLA_Obj_free( &U );
  FLA_Obj_free( &Y );
  FLA_Obj_free( &Z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_blk_var5 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Apply_Q_UT(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemm_external(), FLA_Hess_UT_step_opt_var5(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trsm_external(), and FLA_ZERO.

Referenced by FLA_Hess_UT_internal().

{
  FLA_Obj  ATL,   ATR,      A00, A01, A02, 
           ABL,   ABR,      A10, A11, A12,
                            A20, A21, A22;
  FLA_Obj  UT,              U0,
           UB,              U1,
                            U2;
  FLA_Obj  ZT,              Z0,
           ZB,              Z1,
                            Z2;
  FLA_Obj  TL,    TR,       T0, T1, W12; 

  FLA_Obj  U, Z;
  FLA_Obj  UB_l;
  FLA_Obj  ZB_l;
  FLA_Obj  WT_l;
  FLA_Obj  T1_tl;
  FLA_Obj  none, none2, none3;
  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg, b, bb;

  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &U );
  FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &Z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x1( U,    &UT, 
                      &UB,            0, FLA_TOP );
  FLA_Part_2x1( Z,    &ZT, 
                      &ZB,            0, FLA_TOP );
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT ); 

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) )
  {
    b = min( FLA_Obj_length( ABR ), b_alg );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );
    FLA_Repart_2x1_to_3x1( UT,                &U0, 
                        /* ** */            /* ** */
                                              &U1, 
                           UB,                &U2,        b, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( ZT,                &Z0, 
                        /* ** */            /* ** */
                                              &Z1, 
                           ZB,                &Z2,        b, FLA_BOTTOM );
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &W12,
                           b, FLA_RIGHT );

    /*------------------------------------------------------------*/

    FLA_Part_2x2( T1,     &T1_tl, &none,   
                          &none2, &none3,    b, b, FLA_TL ); 

    bb = min( FLA_Obj_length( ABR ) - 1, b_alg );

    FLA_Part_1x2( UB,     &UB_l,  &none,    bb, FLA_LEFT ); 
    FLA_Part_1x2( ZB,     &ZB_l,  &none,    bb, FLA_LEFT ); 

    // [ ABR, UB, ZB, T1 ] = FLA_Hess_UT_step_unb_var5( ABR, UB, ZB, T1, b );
    //FLA_Hess_UT_step_unb_var5( ABR, UB, ZB, T1_tl );
    FLA_Hess_UT_step_opt_var5( ABR, UB, ZB, T1_tl );

    // ATR = ATR - ATR * UB * inv( triu ( T1 ) ) * UB' );
    if ( FLA_Obj_length( ATR ) > 0 )
    {
      // NOTE: We use ZT as temporary workspace.
      FLA_Part_1x2( ZT,     &WT_l,  &none,    bb, FLA_LEFT ); 
      FLA_Part_2x2( T1,     &T1_tl, &none,   
                            &none2, &none3,   bb, bb, FLA_TL ); 

      // WT_l = ATR * UB_l * inv( triu( T1 ) ).
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_ONE, ATR, UB_l, FLA_ZERO, WT_l );
      FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR, 
                         FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, WT_l );

      // ATR = ATR - WT_l * UB_l'
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
                         FLA_MINUS_ONE, WT_l, UB_l, FLA_ONE, ATR );
    }

    //  / A12 \  =  Q11' * / / A12 \ - / Z1 \ * inv( triu( T1 ) ) * U2' \
    //  \ A22 /            \ \ A22 /   \ Z2 /                           /
    //
    //   where Q11 corresponds to the block Householder transformation
    //   associated with UB and T1.
    if ( FLA_Obj_width( A12 ) > 0 )
    {
      FLA_Obj ABR2, ABR2_b;
      FLA_Obj UB_b;

      // NOTE: Since A12.n > 0, we are guaranteed to not be at an edge case,
      // namely the case where bb = b - 1 = ABR.m - 1, thus we are free to use
      // the "full" matrix partitions in this scope block (ie: ZB instead of
      // ZB_l).

      // W12 = U2'
      // W12 = inv( triu( T1 ) ) * W12;
      FLA_Copyt_external( FLA_CONJ_TRANSPOSE, U2, W12 );
      FLA_Trsm_external( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE,
                         FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, W12 );

      FLA_Merge_2x1( A12,
                     A22,   &ABR2 );

      //  / A12 \  =  / A12 \  -  / Z1 \ * W12
      //  \ A22 /     \ A22 /     \ Z2 / 
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_MINUS_ONE, ZB, W12, FLA_ONE, ABR2 );

      // Omit the top row of UB so it has [implicit] unit diagonal, allowing us
      // to use FLA_Apply_Q_UT() to apply the block Householder transformation
      // corresponding to UB and T1. This trick is valid since the top row of
      // ABR2 would normally be unchanged by the transformation (ie: multiplied
      // by identity).
      FLA_Part_2x1( UB,     &none,   
                            &UB_b,     1, FLA_TOP );
      FLA_Part_2x1( ABR2,   &none,   
                            &ABR2_b,   1, FLA_TOP );

      // Apply Q11' to A12 and A22 from the left:
      //
      //   / A12 \  =  / I - / U1 \ * inv( triu( T1 ) ) * / U1 \' \' / A12 \
      //   \ A22 /     \     \ U2 /                       \ U2 /  /  \ A22 /
      //
      FLA_Apply_Q_UT( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                      UB_b, T1_tl, W12, ABR2_b );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &UT,                U0, 
                                                  U1, 
                            /* ** */           /* ** */
                              &UB,                U2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &ZT,                Z0, 
                                                  Z1, 
                            /* ** */           /* ** */
                              &ZB,                Z2,     FLA_TOP );
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ W12,
                              FLA_LEFT );
  }

  FLA_Obj_free( &U );
  FLA_Obj_free( &Z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_ofu_var1 ( FLA_Obj  A,
FLA_Obj  T 
)
FLA_Error FLA_Hess_UT_ofu_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_ofu_var2().

{
  return FLA_Hess_UT_step_ofu_var2( A, T );
}
FLA_Error FLA_Hess_UT_ofu_var3 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_ofu_var3().

{
  return FLA_Hess_UT_step_ofu_var3( A, T );
}
FLA_Error FLA_Hess_UT_ofu_var4 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_ofu_var4(), FLA_Obj_create_conf_to(), and FLA_Obj_free().

{
  FLA_Error r_val;
  FLA_Obj   Y, Z;

  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Y );
  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );

  r_val = FLA_Hess_UT_step_ofu_var4( A, Y, Z, T );

  FLA_Obj_free( &Y );
  FLA_Obj_free( &Z );

  return r_val;
}
FLA_Error FLA_Hess_UT_opt_var1 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opt_var1().

Referenced by FLA_Hess_UT_internal().

{
  return FLA_Hess_UT_step_opt_var1( A, T );
}
FLA_Error FLA_Hess_UT_opt_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opt_var2().

Referenced by FLA_Hess_UT_internal().

{
  return FLA_Hess_UT_step_opt_var2( A, T );
}
FLA_Error FLA_Hess_UT_opt_var3 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opt_var3().

Referenced by FLA_Hess_UT_internal().

{
  return FLA_Hess_UT_step_opt_var3( A, T );
}
FLA_Error FLA_Hess_UT_opt_var4 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opt_var4(), FLA_Obj_create_conf_to(), and FLA_Obj_free().

Referenced by FLA_Hess_UT_internal().

{
  FLA_Error r_val;
  FLA_Obj   Y, Z;

  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Y );
  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );

  r_val = FLA_Hess_UT_step_opt_var4( A, Y, Z, T );

  FLA_Obj_free( &Y );
  FLA_Obj_free( &Z );

  return r_val;
}
FLA_Error FLA_Hess_UT_opt_var5 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opt_var5(), FLA_Obj_create_conf_to(), and FLA_Obj_free().

Referenced by FLA_Hess_UT_internal().

{
  FLA_Error r_val;
  FLA_Obj   U, Z;

  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &U );
  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );

  r_val = FLA_Hess_UT_step_opt_var5( A, U, Z, T );

  FLA_Obj_free( &U );
  FLA_Obj_free( &Z );

  return r_val;
}
FLA_Error FLA_Hess_UT_step_ofc_var1 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_T,
int  rs_T,
int  cs_T 
)
FLA_Error FLA_Hess_UT_step_ofc_var2 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_caxpyv(), bli_cdot(), bli_cgemv(), bli_cger(), bli_cscalv(), FLA_free(), FLA_Fused_Ahx_Ax_opc_var1(), FLA_Househ2_UT_l_opc(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var2().

{
  scomplex* buff_2  = FLA_COMPLEX_PTR( FLA_TWO );
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );

  scomplex  first_elem;
  scomplex  dot_product;
  scomplex  beta, conj_beta;
  scomplex  inv_tau11;
  scomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  scomplex* buff_y = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_z = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* y0       = buff_y + (0  )*inc_y;
    scomplex* y2       = buff_y + (i+1)*inc_y;

    scomplex* z2       = buff_z + (i+1)*inc_z;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_cdiv3( buff_1, tau11, &inv_tau11 );
      bli_cneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      FLA_Fused_Ahx_Ax_opc_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y2,  inc_y,
                                 z2,  inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_cdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_cinvscals( buff_2, &beta );
      bli_ccopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_cscals( &minus_inv_tau11, &conj_beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_cscals( &minus_inv_tau11, &beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_cdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_cscals( &minus_inv_tau11, &dot_product );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofc_var3 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_caxpyv(), bli_ccopyv(), bli_cdot(), bli_cgemv(), bli_cger(), bli_cscalv(), FLA_free(), FLA_Fused_Ahx_Ax_opc_var1(), FLA_Fused_Gerc2_Ahx_Ax_opc_var1(), FLA_Househ2_UT_l_opc(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var3().

{
  scomplex* buff_2  = FLA_COMPLEX_PTR( FLA_TWO );
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );

  scomplex  first_elem;
  scomplex  dot_product;
  scomplex  beta, conj_beta;
  scomplex  inv_tau11;
  scomplex  minus_inv_tau11;
  scomplex  minus_upsilon1, minus_conj_upsilon1;
  scomplex  minus_psi1, minus_conj_psi1;
  scomplex  minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  scomplex* buff_u = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_y = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_z = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_v = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_w = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* upsilon1 = buff_u + (i  )*inc_u;
    scomplex* u2       = buff_u + (i+1)*inc_u;

    scomplex* y0       = buff_y + (0  )*inc_y;
    scomplex* psi1     = buff_y + (i  )*inc_y;
    scomplex* y2       = buff_y + (i+1)*inc_y;

    scomplex* zeta1    = buff_z + (i  )*inc_z;
    scomplex* z2       = buff_z + (i+1)*inc_z;

    scomplex* v2       = buff_v + (i+1)*inc_v;

    scomplex* w2       = buff_w + (i+1)*inc_w;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_cmult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_ccopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_cmult3( buff_m1, psi1, &minus_psi1 );
      bli_ccopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_cmult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_caxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_caxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_cdiv3( buff_1, tau11, &inv_tau11 );
      bli_cneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Gerc2_Ahx_Ax_opc_var1( m_ahead,
                                       n_ahead,
                                       buff_m1,
                                       u2,  inc_u,
                                       y2,  inc_y,
                                       z2,  inc_z,
                                       A22, rs_A, cs_A,
                                       a21, rs_A,
                                       v2,  inc_v,
                                       w2,  inc_w );
    }
    else if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Ahx_Ax_opc_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 v2,  inc_v,
                                 w2,  inc_w );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_cdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_cinvscals( buff_2, &beta );
      bli_ccopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_cscals( &minus_inv_tau11, &conj_beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_cscals( &minus_inv_tau11, &beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_cdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_cscals( &minus_inv_tau11, &dot_product );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofc_var4 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_Y,
int  rs_Y,
int  cs_Y,
scomplex buff_Z,
int  rs_Z,
int  cs_Z,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_caxpyv(), bli_cdot(), bli_cgemv(), bli_cger(), bli_cscalv(), bli_csetm(), FLA_free(), FLA_Fused_Ahx_Ax_opc_var1(), FLA_Fused_Gemv_Uhu_Yhu_Zhu_opc_var1(), FLA_Househ2_UT_l_opc(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var4().

{
  scomplex* buff_2  = FLA_COMPLEX_PTR( FLA_TWO );
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );

  scomplex  first_elem, last_elem;
  scomplex  dot_product;
  scomplex  beta, conj_beta;
  scomplex  inv_tau11;
  scomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  scomplex* buff_e = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_e  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_csetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_csetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    scomplex* Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    scomplex* y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    scomplex* z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    scomplex* Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    scomplex* z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* e0       = buff_e + (0  )*inc_e;

    scomplex* a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    scomplex* ABL      = a10t;
    scomplex* ZBL      = z10t;

    scomplex* a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_cgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_cgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_cgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_cgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_cdiv3( buff_1, tau11, &inv_tau11 );
      bli_cneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      FLA_Fused_Ahx_Ax_opc_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y21, rs_Y,
                                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      FLA_Fused_Gemv_Uhu_Yhu_Zhu_opc_var1( m_ahead,
                                           n_behind,
                                           buff_m1,
                                           A20, rs_A, cs_A,
                                           Y20, rs_Y, cs_Y,
                                           Z20, rs_Z, cs_Z,
                                           a21, rs_A,
                                           y21, rs_Y,
                                           z21, rs_Z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_cdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_cinvscals( buff_2, &beta );
      bli_ccopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_cscals( &minus_inv_tau11, &conj_beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_cscals( &minus_inv_tau11, &beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_cdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_cscals( &minus_inv_tau11, &dot_product );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &e );
  FLA_free( buff_e );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofd_var1 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_T,
int  rs_T,
int  cs_T 
)
FLA_Error FLA_Hess_UT_step_ofd_var2 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_daxpyv(), bli_ddot(), bli_dgemv(), bli_dger(), bli_dscalv(), FLA_free(), FLA_Fused_Ahx_Ax_opd_var1(), FLA_Househ2_UT_l_opd(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var2().

{
  double*   buff_2  = FLA_DOUBLE_PTR( FLA_TWO );
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );

  double    first_elem;
  double    dot_product;
  double    beta, conj_beta;
  double    inv_tau11;
  double    minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  double*   buff_y = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_z = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    double*   A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    double*   y0       = buff_y + (0  )*inc_y;
    double*   y2       = buff_y + (i+1)*inc_y;

    double*   z2       = buff_z + (i+1)*inc_z;

    double*   a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    double*   a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_ddiv3( buff_1, tau11, &inv_tau11 );
      bli_dneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      FLA_Fused_Ahx_Ax_opd_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y2,  inc_y,
                                 z2,  inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_ddot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_dinvscals( buff_2, &beta );
      bli_dcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_dscals( &minus_inv_tau11, &conj_beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_dscals( &minus_inv_tau11, &beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_ddot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_dscals( &minus_inv_tau11, &dot_product );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofd_var3 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_daxpyv(), bli_dcopyv(), bli_ddot(), bli_dgemv(), bli_dger(), bli_dscalv(), FLA_free(), FLA_Fused_Ahx_Ax_opd_var1(), FLA_Fused_Gerc2_Ahx_Ax_opd_var1(), FLA_Househ2_UT_l_opd(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var3().

{
  double*   buff_2  = FLA_DOUBLE_PTR( FLA_TWO );
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );

  double    first_elem;
  double    dot_product;
  double    beta, conj_beta;
  double    inv_tau11;
  double    minus_inv_tau11;
  double    minus_upsilon1, minus_conj_upsilon1;
  double    minus_psi1, minus_conj_psi1;
  double    minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  double*   buff_u = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_y = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_z = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_v = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_w = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    double*   A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    double*   alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    double*   upsilon1 = buff_u + (i  )*inc_u;
    double*   u2       = buff_u + (i+1)*inc_u;

    double*   y0       = buff_y + (0  )*inc_y;
    double*   psi1     = buff_y + (i  )*inc_y;
    double*   y2       = buff_y + (i+1)*inc_y;

    double*   zeta1    = buff_z + (i  )*inc_z;
    double*   z2       = buff_z + (i+1)*inc_z;

    double*   v2       = buff_v + (i+1)*inc_v;

    double*   w2       = buff_w + (i+1)*inc_w;

    double*   a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    double*   a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_dmult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_dcopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_dmult3( buff_m1, psi1, &minus_psi1 );
      bli_dcopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_dmult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_daxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_daxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_ddiv3( buff_1, tau11, &inv_tau11 );
      bli_dneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Gerc2_Ahx_Ax_opd_var1( m_ahead,
                                       n_ahead,
                                       buff_m1,
                                       u2,  inc_u,
                                       y2,  inc_y,
                                       z2,  inc_z,
                                       A22, rs_A, cs_A,
                                       a21, rs_A,
                                       v2,  inc_v,
                                       w2,  inc_w );
    }
    else if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Ahx_Ax_opd_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 v2,  inc_v,
                                 w2,  inc_w );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_ddot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_dinvscals( buff_2, &beta );
      bli_dcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_dscals( &minus_inv_tau11, &conj_beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_dscals( &minus_inv_tau11, &beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_ddot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_dscals( &minus_inv_tau11, &dot_product );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofd_var4 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_Y,
int  rs_Y,
int  cs_Y,
double *  buff_Z,
int  rs_Z,
int  cs_Z,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_daxpyv(), bli_ddot(), bli_dgemv(), bli_dger(), bli_dscalv(), bli_dsetm(), FLA_free(), FLA_Fused_Ahx_Ax_opd_var1(), FLA_Fused_Gemv_Uhu_Yhu_Zhu_opd_var1(), FLA_Househ2_UT_l_opd(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var4().

{
  double*   buff_2  = FLA_DOUBLE_PTR( FLA_TWO );
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );

  double    first_elem, last_elem;
  double    dot_product;
  double    beta, conj_beta;
  double    inv_tau11;
  double    minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  double*   buff_e = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_e  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_dsetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_dsetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    double*   a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    double*   A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    double*   alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    double*   y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    double*   Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    double*   y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    double*   z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    double*   Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    double*   z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    double*   e0       = buff_e + (0  )*inc_e;

    double*   a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    double*   a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    double*   a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    double*   ABL      = a10t;
    double*   ZBL      = z10t;

    double*   a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_dgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_dgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_dgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_dgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_ddiv3( buff_1, tau11, &inv_tau11 );
      bli_dneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      FLA_Fused_Ahx_Ax_opd_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y21, rs_Y,
                                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      FLA_Fused_Gemv_Uhu_Yhu_Zhu_opd_var1( m_ahead,
                                           n_behind,
                                           buff_m1,
                                           A20, rs_A, cs_A,
                                           Y20, rs_Y, cs_Y,
                                           Z20, rs_Z, cs_Z,
                                           a21, rs_A,
                                           y21, rs_Y,
                                           z21, rs_Z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_ddot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_dinvscals( buff_2, &beta );
      bli_dcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_dscals( &minus_inv_tau11, &conj_beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_dscals( &minus_inv_tau11, &beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_ddot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_dscals( &minus_inv_tau11, &dot_product );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &e );
  FLA_free( buff_e );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofs_var1 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_T,
int  rs_T,
int  cs_T 
)
FLA_Error FLA_Hess_UT_step_ofs_var2 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_saxpyv(), bli_sdot(), bli_sgemv(), bli_sger(), bli_sscalv(), FLA_free(), FLA_Fused_Ahx_Ax_ops_var1(), FLA_Househ2_UT_l_ops(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var2().

{
  float*    buff_2  = FLA_FLOAT_PTR( FLA_TWO );
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );

  float     first_elem;
  float     dot_product;
  float     beta, conj_beta;
  float     inv_tau11;
  float     minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  float*    buff_y = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_z = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    float*    A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    float*    y0       = buff_y + (0  )*inc_y;
    float*    y2       = buff_y + (i+1)*inc_y;

    float*    z2       = buff_z + (i+1)*inc_z;

    float*    a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    float*    a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_sdiv3( buff_1, tau11, &inv_tau11 );
      bli_sneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      FLA_Fused_Ahx_Ax_ops_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y2,  inc_y,
                                 z2,  inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_sdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_sinvscals( buff_2, &beta );
      bli_scopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_sscals( &minus_inv_tau11, &conj_beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_sscals( &minus_inv_tau11, &beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_sdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_sscals( &minus_inv_tau11, &dot_product );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofs_var3 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_saxpyv(), bli_scopyv(), bli_sdot(), bli_sgemv(), bli_sger(), bli_sscalv(), FLA_free(), FLA_Fused_Ahx_Ax_ops_var1(), FLA_Fused_Gerc2_Ahx_Ax_ops_var1(), FLA_Househ2_UT_l_ops(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var3().

{
  float*    buff_2  = FLA_FLOAT_PTR( FLA_TWO );
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );

  float     first_elem;
  float     dot_product;
  float     beta, conj_beta;
  float     inv_tau11;
  float     minus_inv_tau11;
  float     minus_upsilon1, minus_conj_upsilon1;
  float     minus_psi1, minus_conj_psi1;
  float     minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  float*    buff_u = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_y = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_z = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_v = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_w = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    float*    A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    float*    alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    float*    upsilon1 = buff_u + (i  )*inc_u;
    float*    u2       = buff_u + (i+1)*inc_u;

    float*    y0       = buff_y + (0  )*inc_y;
    float*    psi1     = buff_y + (i  )*inc_y;
    float*    y2       = buff_y + (i+1)*inc_y;

    float*    zeta1    = buff_z + (i  )*inc_z;
    float*    z2       = buff_z + (i+1)*inc_z;

    float*    v2       = buff_v + (i+1)*inc_v;

    float*    w2       = buff_w + (i+1)*inc_w;

    float*    a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    float*    a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_smult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_scopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_smult3( buff_m1, psi1, &minus_psi1 );
      bli_scopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_smult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_saxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_saxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_sdiv3( buff_1, tau11, &inv_tau11 );
      bli_sneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Gerc2_Ahx_Ax_ops_var1( m_ahead,
                                       n_ahead,
                                       buff_m1,
                                       u2,  inc_u,
                                       y2,  inc_y,
                                       z2,  inc_z,
                                       A22, rs_A, cs_A,
                                       a21, rs_A,
                                       v2,  inc_v,
                                       w2,  inc_w );
    }
    else if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Ahx_Ax_ops_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 v2,  inc_v,
                                 w2,  inc_w );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_sdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_sinvscals( buff_2, &beta );
      bli_scopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_sscals( &minus_inv_tau11, &conj_beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_sscals( &minus_inv_tau11, &beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_sdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_sscals( &minus_inv_tau11, &dot_product );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofs_var4 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_Y,
int  rs_Y,
int  cs_Y,
float *  buff_Z,
int  rs_Z,
int  cs_Z,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_saxpyv(), bli_sdot(), bli_sgemv(), bli_sger(), bli_sscalv(), bli_ssetm(), FLA_free(), FLA_Fused_Ahx_Ax_ops_var1(), FLA_Fused_Gemv_Uhu_Yhu_Zhu_ops_var1(), FLA_Househ2_UT_l_ops(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var4().

{
  float*    buff_2  = FLA_FLOAT_PTR( FLA_TWO );
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );

  float     first_elem, last_elem;
  float     dot_product;
  float     beta, conj_beta;
  float     inv_tau11;
  float     minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  float*    buff_e = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_e  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_ssetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_ssetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    float*    a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    float*    A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    float*    alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    float*    y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    float*    Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    float*    y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    float*    z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    float*    Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    float*    z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    float*    e0       = buff_e + (0  )*inc_e;

    float*    a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    float*    a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    float*    a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    float*    ABL      = a10t;
    float*    ZBL      = z10t;

    float*    a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_sgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_sgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_sgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_sgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_sdiv3( buff_1, tau11, &inv_tau11 );
      bli_sneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      FLA_Fused_Ahx_Ax_ops_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y21, rs_Y,
                                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      FLA_Fused_Gemv_Uhu_Yhu_Zhu_ops_var1( m_ahead,
                                           n_behind,
                                           buff_m1,
                                           A20, rs_A, cs_A,
                                           Y20, rs_Y, cs_Y,
                                           Z20, rs_Z, cs_Z,
                                           a21, rs_A,
                                           y21, rs_Y,
                                           z21, rs_Z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_sdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_sinvscals( buff_2, &beta );
      bli_scopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_sscals( &minus_inv_tau11, &conj_beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_sscals( &minus_inv_tau11, &beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_sdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_sscals( &minus_inv_tau11, &dot_product );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &e );
  FLA_free( buff_e );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofu_var1 ( FLA_Obj  A,
FLA_Obj  T 
)
FLA_Error FLA_Hess_UT_step_ofu_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_ofc_var2(), FLA_Hess_UT_step_ofd_var2(), FLA_Hess_UT_step_ofs_var2(), FLA_Hess_UT_step_ofz_var2(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_ofu_var2().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ofs_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_ofd_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_ofc_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_ofz_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofu_var3 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_ofc_var3(), FLA_Hess_UT_step_ofd_var3(), FLA_Hess_UT_step_ofs_var3(), FLA_Hess_UT_step_ofz_var3(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_ofu_var3().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ofs_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_ofd_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_ofc_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_ofz_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofu_var4 ( FLA_Obj  A,
FLA_Obj  Y,
FLA_Obj  Z,
FLA_Obj  T 
)

References FLA_Hess_UT_step_ofc_var4(), FLA_Hess_UT_step_ofd_var4(), FLA_Hess_UT_step_ofs_var4(), FLA_Hess_UT_step_ofz_var4(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_ofu_var4().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_Y, cs_Y;
  int          rs_Z, cs_Z;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_Y     = FLA_Obj_row_stride( Y );
  cs_Y     = FLA_Obj_col_stride( Y );

  rs_Z     = FLA_Obj_row_stride( Z );
  cs_Z     = FLA_Obj_col_stride( Z );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_Y = FLA_FLOAT_PTR( Y );
      float* buff_Z = FLA_FLOAT_PTR( Z );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ofs_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_Y = FLA_DOUBLE_PTR( Y );
      double* buff_Z = FLA_DOUBLE_PTR( Z );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_ofd_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_Y = FLA_COMPLEX_PTR( Y );
      scomplex* buff_Z = FLA_COMPLEX_PTR( Z );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_ofc_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_Y = FLA_DOUBLE_COMPLEX_PTR( Y );
      dcomplex* buff_Z = FLA_DOUBLE_COMPLEX_PTR( Z );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_ofz_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofz_var1 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)
FLA_Error FLA_Hess_UT_step_ofz_var2 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zaxpyv(), bli_zdot(), bli_zgemv(), bli_zger(), bli_zscalv(), FLA_free(), FLA_Fused_Ahx_Ax_opz_var1(), FLA_Househ2_UT_l_opz(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var2().

{
  dcomplex* buff_2  = FLA_DOUBLE_COMPLEX_PTR( FLA_TWO );
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );

  dcomplex  first_elem;
  dcomplex  dot_product;
  dcomplex  beta, conj_beta;
  dcomplex  inv_tau11;
  dcomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  dcomplex* buff_y = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_z = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    dcomplex* y0       = buff_y + (0  )*inc_y;
    dcomplex* y2       = buff_y + (i+1)*inc_y;

    dcomplex* z2       = buff_z + (i+1)*inc_z;

    dcomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_zdiv3( buff_1, tau11, &inv_tau11 );
      bli_zneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      FLA_Fused_Ahx_Ax_opz_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y2,  inc_y,
                                 z2,  inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_zdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_zinvscals( buff_2, &beta );
      bli_zcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_zscals( &minus_inv_tau11, &conj_beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_zscals( &minus_inv_tau11, &beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_zdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_zscals( &minus_inv_tau11, &dot_product );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofz_var3 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zaxpyv(), bli_zcopyv(), bli_zdot(), bli_zgemv(), bli_zger(), bli_zscalv(), FLA_free(), FLA_Fused_Ahx_Ax_opz_var1(), FLA_Fused_Gerc2_Ahx_Ax_opz_var1(), FLA_Househ2_UT_l_opz(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var3().

{
  dcomplex* buff_2  = FLA_DOUBLE_COMPLEX_PTR( FLA_TWO );
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );

  dcomplex  first_elem;
  dcomplex  dot_product;
  dcomplex  beta, conj_beta;
  dcomplex  inv_tau11;
  dcomplex  minus_inv_tau11;
  dcomplex  minus_upsilon1, minus_conj_upsilon1;
  dcomplex  minus_psi1, minus_conj_psi1;
  dcomplex  minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  dcomplex* buff_u = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_y = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_z = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_v = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_w = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    dcomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    dcomplex* upsilon1 = buff_u + (i  )*inc_u;
    dcomplex* u2       = buff_u + (i+1)*inc_u;

    dcomplex* y0       = buff_y + (0  )*inc_y;
    dcomplex* psi1     = buff_y + (i  )*inc_y;
    dcomplex* y2       = buff_y + (i+1)*inc_y;

    dcomplex* zeta1    = buff_z + (i  )*inc_z;
    dcomplex* z2       = buff_z + (i+1)*inc_z;

    dcomplex* v2       = buff_v + (i+1)*inc_v;

    dcomplex* w2       = buff_w + (i+1)*inc_w;

    dcomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_zmult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_zcopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_zmult3( buff_m1, psi1, &minus_psi1 );
      bli_zcopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_zmult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_zaxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_zaxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_zdiv3( buff_1, tau11, &inv_tau11 );
      bli_zneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Gerc2_Ahx_Ax_opz_var1( m_ahead,
                                       n_ahead,
                                       buff_m1,
                                       u2,  inc_u,
                                       y2,  inc_y,
                                       z2,  inc_z,
                                       A22, rs_A, cs_A,
                                       a21, rs_A,
                                       v2,  inc_v,
                                       w2,  inc_w );
    }
    else if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      FLA_Fused_Ahx_Ax_opz_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 v2,  inc_v,
                                 w2,  inc_w );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_zdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_zinvscals( buff_2, &beta );
      bli_zcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_zscals( &minus_inv_tau11, &conj_beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_zscals( &minus_inv_tau11, &beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_zdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_zscals( &minus_inv_tau11, &dot_product );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ofz_var4 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_Y,
int  rs_Y,
int  cs_Y,
dcomplex buff_Z,
int  rs_Z,
int  cs_Z,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zaxpyv(), bli_zdot(), bli_zgemv(), bli_zger(), bli_zscalv(), bli_zsetm(), FLA_free(), FLA_Fused_Ahx_Ax_opz_var1(), FLA_Fused_Gemv_Uhu_Yhu_Zhu_opz_var1(), FLA_Househ2_UT_l_opz(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_ofu_var4().

{
  dcomplex* buff_2  = FLA_DOUBLE_COMPLEX_PTR( FLA_TWO );
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );

  dcomplex  first_elem, last_elem;
  dcomplex  dot_product;
  dcomplex  beta, conj_beta;
  dcomplex  inv_tau11;
  dcomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  dcomplex* buff_e = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_e  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_zsetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_zsetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    dcomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    dcomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    dcomplex* y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    dcomplex* Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    dcomplex* y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    dcomplex* z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    dcomplex* Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    dcomplex* z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    dcomplex* e0       = buff_e + (0  )*inc_e;

    dcomplex* a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    dcomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    dcomplex* ABL      = a10t;
    dcomplex* ZBL      = z10t;

    dcomplex* a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_zgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_zgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_zgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_zgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_zdiv3( buff_1, tau11, &inv_tau11 );
      bli_zneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      FLA_Fused_Ahx_Ax_opz_var1( m_ahead,
                                 n_ahead,
                                 A22, rs_A, cs_A,
                                 a21, rs_A,
                                 y21, rs_Y,
                                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      FLA_Fused_Gemv_Uhu_Yhu_Zhu_opz_var1( m_ahead,
                                           n_behind,
                                           buff_m1,
                                           A20, rs_A, cs_A,
                                           Y20, rs_Y, cs_Y,
                                           Z20, rs_Z, cs_Z,
                                           a21, rs_A,
                                           y21, rs_Y,
                                           z21, rs_Z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_zdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_zinvscals( buff_2, &beta );
      bli_zcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_zscals( &minus_inv_tau11, &conj_beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_zscals( &minus_inv_tau11, &beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_zdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_zscals( &minus_inv_tau11, &dot_product );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &e );
  FLA_free( buff_e );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opc_var1 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_cgemv(), FLA_Apply_H2_UT_l_opc_var1(), FLA_Apply_H2_UT_r_opc_var1(), FLA_Househ2_UT_l_opc(), FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var1().

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );

  scomplex  first_elem;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;

    scomplex* a21_t    = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* a21_b    = buff_A + (i  )*cs_A + (i+2)*rs_A;

    scomplex* A22_t    = buff_A + (i+1)*cs_A + (i+1)*rs_A;
    scomplex* A22_b    = buff_A + (i+1)*cs_A + (i+2)*rs_A;

    scomplex* A2_l     = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* A2_r     = buff_A + (i+2)*cs_A + (0  )*rs_A;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Apply_H2_UT( FLA_LEFT, tau11, a21_b, A22_t,
      //                                          A22_b );
      FLA_Apply_H2_UT_l_opc_var1( m_ahead - 1,
                                  n_ahead,
                                  tau11,
                                  a21_b, rs_A,
                                  A22_t, cs_A,
                                  A22_b, rs_A, cs_A );

      // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a21_b, A2_l, A2_r );
      FLA_Apply_H2_UT_r_opc_var1( m_A,
                                  n_ahead - 1,
                                  tau11,
                                  a21_b, rs_A,
                                  A2_l,  rs_A,
                                  A2_r,  rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opc_var2 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_caxpyv(), bli_cdot(), bli_cgemv(), bli_cger(), bli_cscalv(), FLA_free(), FLA_Househ2_UT_l_opc(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var2().

{
  scomplex* buff_2  = FLA_COMPLEX_PTR( FLA_TWO );
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );

  scomplex  first_elem;
  scomplex  dot_product;
  scomplex  beta, conj_beta;
  scomplex  inv_tau11;
  scomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  scomplex* buff_y = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_z = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* y0       = buff_y + (0  )*inc_y;
    scomplex* y2       = buff_y + (i+1)*inc_y;

    scomplex* z2       = buff_z + (i+1)*inc_z;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_cdiv3( buff_1, tau11, &inv_tau11 );
      bli_cneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y2, inc_y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_cdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_cinvscals( buff_2, &beta );
      bli_ccopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_cscals( &minus_inv_tau11, &conj_beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_cscals( &minus_inv_tau11, &beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_cdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_cscals( &minus_inv_tau11, &dot_product );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opc_var3 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_caxpyv(), bli_ccopyv(), bli_cdot(), bli_cgemv(), bli_cger(), bli_cscalv(), FLA_free(), FLA_Househ2_UT_l_opc(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var3().

{
  scomplex* buff_2  = FLA_COMPLEX_PTR( FLA_TWO );
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );

  scomplex  first_elem;
  scomplex  dot_product;
  scomplex  beta, conj_beta;
  scomplex  inv_tau11;
  scomplex  minus_inv_tau11;
  scomplex  minus_upsilon1, minus_conj_upsilon1;
  scomplex  minus_psi1, minus_conj_psi1;
  scomplex  minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  scomplex* buff_u = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_y = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_z = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_v = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_w = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  // Initialize some variables (only to prevent compiler warnings).
  first_elem           = *buff_0;
  minus_inv_tau11 = *buff_0;

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* upsilon1 = buff_u + (i  )*inc_u;
    scomplex* u2       = buff_u + (i+1)*inc_u;

    scomplex* y0       = buff_y + (0  )*inc_y;
    scomplex* psi1     = buff_y + (i  )*inc_y;
    scomplex* y2       = buff_y + (i+1)*inc_y;

    scomplex* zeta1    = buff_z + (i  )*inc_z;
    scomplex* z2       = buff_z + (i+1)*inc_z;

    scomplex* v2       = buff_v + (i+1)*inc_v;

    scomplex* w2       = buff_w + (i+1)*inc_w;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_cmult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_ccopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_cmult3( buff_m1, psi1, &minus_psi1 );
      bli_ccopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_cmult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_caxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_caxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_cdiv3( buff_1, tau11, &inv_tau11 );
      bli_cneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 v2, inc_v );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 w2, inc_w );

      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_cdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_cinvscals( buff_2, &beta );
      bli_ccopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_cscals( &minus_inv_tau11, &conj_beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_cscals( &minus_inv_tau11, &beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_cdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_cscals( &minus_inv_tau11, &dot_product );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opc_var4 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_Y,
int  rs_Y,
int  cs_Y,
scomplex buff_Z,
int  rs_Z,
int  cs_Z,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_caxpyv(), bli_cdot(), bli_cgemv(), bli_cger(), bli_cscalv(), bli_csetm(), FLA_free(), FLA_Househ2_UT_l_opc(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var4().

{
  scomplex* buff_2  = FLA_COMPLEX_PTR( FLA_TWO );
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );

  scomplex  first_elem, last_elem;
  scomplex  dot_product;
  scomplex  beta, conj_beta;
  scomplex  inv_tau11;
  scomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  scomplex* buff_d = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_e = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_f = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_d  = 1;
  int       inc_e  = 1;
  int       inc_f  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_csetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_csetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    scomplex* Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    scomplex* y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    scomplex* z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    scomplex* Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    scomplex* z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* d0       = buff_d + (0  )*inc_d;

    scomplex* e0       = buff_e + (0  )*inc_e;

    scomplex* f0       = buff_f + (0  )*inc_f;

    scomplex* a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    scomplex* ABL      = a10t;
    scomplex* ZBL      = z10t;

    scomplex* a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_cgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_cgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_cgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_cgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_cdiv3( buff_1, tau11, &inv_tau11 );
      bli_cneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 d0,  inc_d );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Y20, rs_Y, cs_Y,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Z20, rs_Z, cs_Z,
                 a21, rs_A,
                 buff_0,
                 f0,  inc_f );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Y20, rs_Y, cs_Y,
                 d0,  inc_d,
                 buff_1,
                 y21, rs_Y );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 f0,  inc_f,
                 buff_1,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 e0,  inc_e,
                 buff_1,
                 z21, rs_Z );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20, rs_Z, cs_Z,
                 d0,  inc_d,
                 buff_1,
                 z21, rs_Z );


      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_cdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_cinvscals( buff_2, &beta );
      bli_ccopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_cscals( &minus_inv_tau11, &conj_beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_cscals( &minus_inv_tau11, &beta );
      bli_caxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_cscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_cdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_cscals( &minus_inv_tau11, &dot_product );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_cger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &d );
  // FLA_Obj_free( &e );
  // FLA_Obj_free( &f );
  FLA_free( buff_d );
  FLA_free( buff_e );
  FLA_free( buff_f );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opc_var5 ( int  m_A,
int  m_T,
scomplex buff_A,
int  rs_A,
int  cs_A,
scomplex buff_U,
int  rs_U,
int  cs_U,
scomplex buff_Z,
int  rs_Z,
int  cs_Z,
scomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_caxpyv(), bli_ccopyv(), bli_cdot(), bli_cdots(), bli_cgemv(), bli_csetm(), bli_ctrmv(), bli_ctrmvsx(), bli_ctrsv(), FLA_free(), FLA_Househ2_UT_l_opc(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var5().

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  scomplex* buff_w = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_w  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, U );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_csetm( m_A,
             b_alg,
             buff_0,
             buff_U, rs_U, cs_U );
  bli_csetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
    scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* U00      = buff_U + (0  )*cs_U + (0  )*rs_U;
    scomplex* u10t     = buff_U + (0  )*cs_U + (i  )*rs_U;
    scomplex* U20      = buff_U + (0  )*cs_U + (i+1)*rs_U;
    scomplex* u21      = buff_U + (i  )*cs_U + (i+1)*rs_U;

    scomplex* Z00      = buff_Z + (0  )*cs_Z + (0  )*rs_Z;
    scomplex* z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    scomplex* Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    scomplex* z01      = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    scomplex* zeta11   = buff_Z + (i  )*cs_Z + (i  )*rs_Z;
    scomplex* z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    scomplex* T00      = buff_T + (0  )*cs_T + (0  )*rs_T;
    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* w0       = buff_w + (0  )*inc_w;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    scomplex* u21_t    = u21    + (0  )*cs_U + (0  )*rs_U;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copyt( FLA_CONJ_TRANSPOSE, u10t, w0 );
      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_ccopyv( BLIS_CONJUGATE,
                  m_behind,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_ctrsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_NO_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, z10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, w0, FLA_ONE, a21 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_behind,
                 buff_m1,
                 Z00,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a01,  rs_A );
      bli_cdots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 z10t, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a21,  rs_A );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_ONE, U00, a01, FLA_ZERO, w0 );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, alpha11, u10t, w0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, a21, FLA_ONE, w0 );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_behind,
                  a01, rs_A,
                  w0,  inc_w );
      bli_ctrmv( BLIS_LOWER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 U00, rs_U, cs_U,
                 w0,  inc_w );
      bli_caxpyv( BLIS_CONJUGATE,
                  m_behind,
                  alpha11,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 a21, rs_A,
                 buff_1,
                 w0,  inc_w );

      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_ctrsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_MINUS_ONE, U00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, u10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, U20, w0, FLA_ONE, a21 );
      bli_ctrmvsx( BLIS_LOWER_TRIANGULAR,
                   BLIS_NO_TRANSPOSE,
                   BLIS_NONUNIT_DIAG,
                   m_behind,
                   buff_m1,
                   U00, rs_U, cs_U,
                   w0,  inc_w,
                   buff_1,
                   a01, rs_A );
      bli_cdots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 u10t, cs_U,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 U20, rs_U, cs_U,
                 w0,  inc_w,
                 buff_1,
                 a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opc( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21, u21 );
      bli_ccopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u21, rs_U );

      // FLA_Obj_set_to_scalar( FLA_ONE, u21_t );
      *u21_t = *buff_1;

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, u21, FLA_ZERO, z01 );
      // FLA_Dot( a12t, u21, zeta11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, u21, FLA_ZERO, z21 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z01, rs_Z );
      bli_cdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                u21,  rs_U,
                zeta11 );
      bli_cgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, u21, FLA_ZERO, t01 );
      bli_cgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 u21, rs_U,
                 buff_0,
                 t01, rs_T );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &w );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opd_var1 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_dgemv(), FLA_Apply_H2_UT_l_opd_var1(), FLA_Apply_H2_UT_r_opd_var1(), FLA_Househ2_UT_l_opd(), FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var1().

{
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );

  double    first_elem;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  for ( i = 0; i < b_alg; ++i )
  {
    double*   A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;

    double*   a21_t    = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   a21_b    = buff_A + (i  )*cs_A + (i+2)*rs_A;

    double*   A22_t    = buff_A + (i+1)*cs_A + (i+1)*rs_A;
    double*   A22_b    = buff_A + (i+1)*cs_A + (i+2)*rs_A;

    double*   A2_l     = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   A2_r     = buff_A + (i+2)*cs_A + (0  )*rs_A;

    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Apply_H2_UT( FLA_LEFT, tau11, a21_b, A22_t,
      //                                          A22_b );
      FLA_Apply_H2_UT_l_opd_var1( m_ahead - 1,
                                  n_ahead,
                                  tau11,
                                  a21_b, rs_A,
                                  A22_t, cs_A,
                                  A22_b, rs_A, cs_A );

      // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a21_b, A2_l, A2_r );
      FLA_Apply_H2_UT_r_opd_var1( m_A,
                                  n_ahead - 1,
                                  tau11,
                                  a21_b, rs_A,
                                  A2_l,  rs_A,
                                  A2_r,  rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opd_var2 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_daxpyv(), bli_ddot(), bli_dgemv(), bli_dger(), bli_dscalv(), FLA_free(), FLA_Househ2_UT_l_opd(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var2().

{
  double*   buff_2  = FLA_DOUBLE_PTR( FLA_TWO );
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );

  double    first_elem;
  double    dot_product;
  double    beta, conj_beta;
  double    inv_tau11;
  double    minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  double*   buff_y = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_z = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    double*   A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    double*   y0       = buff_y + (0  )*inc_y;
    double*   y2       = buff_y + (i+1)*inc_y;

    double*   z2       = buff_z + (i+1)*inc_z;

    double*   a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    double*   a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_ddiv3( buff_1, tau11, &inv_tau11 );
      bli_dneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y2, inc_y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_ddot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_dinvscals( buff_2, &beta );
      bli_dcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_dscals( &minus_inv_tau11, &conj_beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_dscals( &minus_inv_tau11, &beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_ddot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_dscals( &minus_inv_tau11, &dot_product );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opd_var3 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_daxpyv(), bli_dcopyv(), bli_ddot(), bli_dgemv(), bli_dger(), bli_dscalv(), FLA_free(), FLA_Househ2_UT_l_opd(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var3().

{
  double*   buff_2  = FLA_DOUBLE_PTR( FLA_TWO );
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );

  double    first_elem;
  double    dot_product;
  double    beta, conj_beta;
  double    inv_tau11;
  double    minus_inv_tau11;
  double    minus_upsilon1, minus_conj_upsilon1;
  double    minus_psi1, minus_conj_psi1;
  double    minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  double*   buff_u = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_y = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_z = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_v = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_w = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  // Initialize some variables (only to prevent compiler warnings).
  first_elem           = *buff_0;
  minus_inv_tau11 = *buff_0;

  for ( i = 0; i < b_alg; ++i )
  {
    double*   A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    double*   alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    double*   upsilon1 = buff_u + (i  )*inc_u;
    double*   u2       = buff_u + (i+1)*inc_u;

    double*   y0       = buff_y + (0  )*inc_y;
    double*   psi1     = buff_y + (i  )*inc_y;
    double*   y2       = buff_y + (i+1)*inc_y;

    double*   zeta1    = buff_z + (i  )*inc_z;
    double*   z2       = buff_z + (i+1)*inc_z;

    double*   v2       = buff_v + (i+1)*inc_v;

    double*   w2       = buff_w + (i+1)*inc_w;

    double*   a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    double*   a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_dmult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_dcopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_dmult3( buff_m1, psi1, &minus_psi1 );
      bli_dcopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_dmult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_daxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_daxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_ddiv3( buff_1, tau11, &inv_tau11 );
      bli_dneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 v2, inc_v );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 w2, inc_w );

      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_ddot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_dinvscals( buff_2, &beta );
      bli_dcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_dscals( &minus_inv_tau11, &conj_beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_dscals( &minus_inv_tau11, &beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_ddot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_dscals( &minus_inv_tau11, &dot_product );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opd_var4 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_Y,
int  rs_Y,
int  cs_Y,
double *  buff_Z,
int  rs_Z,
int  cs_Z,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_daxpyv(), bli_ddot(), bli_dgemv(), bli_dger(), bli_dscalv(), bli_dsetm(), FLA_free(), FLA_Househ2_UT_l_opd(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var4().

{
  double*   buff_2  = FLA_DOUBLE_PTR( FLA_TWO );
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );

  double    first_elem, last_elem;
  double    dot_product;
  double    beta, conj_beta;
  double    inv_tau11;
  double    minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  double*   buff_d = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_e = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  double*   buff_f = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_d  = 1;
  int       inc_e  = 1;
  int       inc_f  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_dsetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_dsetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    double*   a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    double*   A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    double*   alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    double*   y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    double*   Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    double*   y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    double*   z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    double*   Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    double*   z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    double*   d0       = buff_d + (0  )*inc_d;

    double*   e0       = buff_e + (0  )*inc_e;

    double*   f0       = buff_f + (0  )*inc_f;

    double*   a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    double*   a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    double*   a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    double*   ABL      = a10t;
    double*   ZBL      = z10t;

    double*   a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_dgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_dgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_dgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_dgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_ddiv3( buff_1, tau11, &inv_tau11 );
      bli_dneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 d0,  inc_d );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Y20, rs_Y, cs_Y,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Z20, rs_Z, cs_Z,
                 a21, rs_A,
                 buff_0,
                 f0,  inc_f );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Y20, rs_Y, cs_Y,
                 d0,  inc_d,
                 buff_1,
                 y21, rs_Y );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 f0,  inc_f,
                 buff_1,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 e0,  inc_e,
                 buff_1,
                 z21, rs_Z );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20, rs_Z, cs_Z,
                 d0,  inc_d,
                 buff_1,
                 z21, rs_Z );


      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_ddot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_dinvscals( buff_2, &beta );
      bli_dcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_dscals( &minus_inv_tau11, &conj_beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_dscals( &minus_inv_tau11, &beta );
      bli_daxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_dscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_ddot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_dscals( &minus_inv_tau11, &dot_product );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_dger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &d );
  // FLA_Obj_free( &e );
  // FLA_Obj_free( &f );
  FLA_free( buff_d );
  FLA_free( buff_e );
  FLA_free( buff_f );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opd_var5 ( int  m_A,
int  m_T,
double *  buff_A,
int  rs_A,
int  cs_A,
double *  buff_U,
int  rs_U,
int  cs_U,
double *  buff_Z,
int  rs_Z,
int  cs_Z,
double *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_daxpyv(), bli_dcopyv(), bli_ddot(), bli_ddots(), bli_dgemv(), bli_dsetm(), bli_dtrmv(), bli_dtrmvsx(), bli_dtrsv(), FLA_free(), FLA_Househ2_UT_l_opd(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var5().

{
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_0  = FLA_DOUBLE_PTR( FLA_ZERO );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  double*   buff_w = ( double* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_w  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, U );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_dsetm( m_A,
             b_alg,
             buff_0,
             buff_U, rs_U, cs_U );
  bli_dsetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    double*   a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
    double*   alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    double*   A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    double*   U00      = buff_U + (0  )*cs_U + (0  )*rs_U;
    double*   u10t     = buff_U + (0  )*cs_U + (i  )*rs_U;
    double*   U20      = buff_U + (0  )*cs_U + (i+1)*rs_U;
    double*   u21      = buff_U + (i  )*cs_U + (i+1)*rs_U;

    double*   Z00      = buff_Z + (0  )*cs_Z + (0  )*rs_Z;
    double*   z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    double*   Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    double*   z01      = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    double*   zeta11   = buff_Z + (i  )*cs_Z + (i  )*rs_Z;
    double*   z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    double*   T00      = buff_T + (0  )*cs_T + (0  )*rs_T;
    double*   t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    double*   tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    double*   w0       = buff_w + (0  )*inc_w;

    double*   a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    double*   a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    double*   u21_t    = u21    + (0  )*cs_U + (0  )*rs_U;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copyt( FLA_CONJ_TRANSPOSE, u10t, w0 );
      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_dcopyv( BLIS_CONJUGATE,
                  m_behind,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_dtrsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_NO_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, z10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, w0, FLA_ONE, a21 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_behind,
                 buff_m1,
                 Z00,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a01,  rs_A );
      bli_ddots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 z10t, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a21,  rs_A );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_ONE, U00, a01, FLA_ZERO, w0 );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, alpha11, u10t, w0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, a21, FLA_ONE, w0 );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_behind,
                  a01, rs_A,
                  w0,  inc_w );
      bli_dtrmv( BLIS_LOWER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 U00, rs_U, cs_U,
                 w0,  inc_w );
      bli_daxpyv( BLIS_CONJUGATE,
                  m_behind,
                  alpha11,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 a21, rs_A,
                 buff_1,
                 w0,  inc_w );

      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_dtrsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_MINUS_ONE, U00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, u10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, U20, w0, FLA_ONE, a21 );
      bli_dtrmvsx( BLIS_LOWER_TRIANGULAR,
                   BLIS_NO_TRANSPOSE,
                   BLIS_NONUNIT_DIAG,
                   m_behind,
                   buff_m1,
                   U00, rs_U, cs_U,
                   w0,  inc_w,
                   buff_1,
                   a01, rs_A );
      bli_ddots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 u10t, cs_U,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 U20, rs_U, cs_U,
                 w0,  inc_w,
                 buff_1,
                 a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opd( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21, u21 );
      bli_dcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u21, rs_U );

      // FLA_Obj_set_to_scalar( FLA_ONE, u21_t );
      *u21_t = *buff_1;

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, u21, FLA_ZERO, z01 );
      // FLA_Dot( a12t, u21, zeta11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, u21, FLA_ZERO, z21 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z01, rs_Z );
      bli_ddot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                u21,  rs_U,
                zeta11 );
      bli_dgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, u21, FLA_ZERO, t01 );
      bli_dgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 u21, rs_U,
                 buff_0,
                 t01, rs_T );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &w );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ops_var1 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_sgemv(), FLA_Apply_H2_UT_l_ops_var1(), FLA_Apply_H2_UT_r_ops_var1(), FLA_Househ2_UT_l_ops(), FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var1().

{
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );

  float     first_elem;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  for ( i = 0; i < b_alg; ++i )
  {
    float*    A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;

    float*    a21_t    = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    a21_b    = buff_A + (i  )*cs_A + (i+2)*rs_A;

    float*    A22_t    = buff_A + (i+1)*cs_A + (i+1)*rs_A;
    float*    A22_b    = buff_A + (i+1)*cs_A + (i+2)*rs_A;

    float*    A2_l     = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    A2_r     = buff_A + (i+2)*cs_A + (0  )*rs_A;

    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Apply_H2_UT( FLA_LEFT, tau11, a21_b, A22_t,
      //                                          A22_b );
      FLA_Apply_H2_UT_l_ops_var1( m_ahead - 1,
                                  n_ahead,
                                  tau11,
                                  a21_b, rs_A,
                                  A22_t, cs_A,
                                  A22_b, rs_A, cs_A );

      // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a21_b, A2_l, A2_r );
      FLA_Apply_H2_UT_r_ops_var1( m_A,
                                  n_ahead - 1,
                                  tau11,
                                  a21_b, rs_A,
                                  A2_l,  rs_A,
                                  A2_r,  rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ops_var2 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_saxpyv(), bli_sdot(), bli_sgemv(), bli_sger(), bli_sscalv(), FLA_free(), FLA_Househ2_UT_l_ops(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var2().

{
  float*    buff_2  = FLA_FLOAT_PTR( FLA_TWO );
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );

  float     first_elem;
  float     dot_product;
  float     beta, conj_beta;
  float     inv_tau11;
  float     minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  float*    buff_y = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_z = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    float*    A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    float*    y0       = buff_y + (0  )*inc_y;
    float*    y2       = buff_y + (i+1)*inc_y;

    float*    z2       = buff_z + (i+1)*inc_z;

    float*    a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    float*    a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_sdiv3( buff_1, tau11, &inv_tau11 );
      bli_sneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y2, inc_y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_sdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_sinvscals( buff_2, &beta );
      bli_scopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_sscals( &minus_inv_tau11, &conj_beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_sscals( &minus_inv_tau11, &beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_sdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_sscals( &minus_inv_tau11, &dot_product );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ops_var3 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_saxpyv(), bli_scopyv(), bli_sdot(), bli_sgemv(), bli_sger(), bli_sscalv(), FLA_free(), FLA_Househ2_UT_l_ops(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var3().

{
  float*    buff_2  = FLA_FLOAT_PTR( FLA_TWO );
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );

  float     first_elem;
  float     dot_product;
  float     beta, conj_beta;
  float     inv_tau11;
  float     minus_inv_tau11;
  float     minus_upsilon1, minus_conj_upsilon1;
  float     minus_psi1, minus_conj_psi1;
  float     minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  float*    buff_u = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_y = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_z = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_v = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_w = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  // Initialize some variables (only to prevent compiler warnings).
  first_elem           = *buff_0;
  minus_inv_tau11 = *buff_0;

  for ( i = 0; i < b_alg; ++i )
  {
    float*    A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    float*    alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    float*    upsilon1 = buff_u + (i  )*inc_u;
    float*    u2       = buff_u + (i+1)*inc_u;

    float*    y0       = buff_y + (0  )*inc_y;
    float*    psi1     = buff_y + (i  )*inc_y;
    float*    y2       = buff_y + (i+1)*inc_y;

    float*    zeta1    = buff_z + (i  )*inc_z;
    float*    z2       = buff_z + (i+1)*inc_z;

    float*    v2       = buff_v + (i+1)*inc_v;

    float*    w2       = buff_w + (i+1)*inc_w;

    float*    a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    float*    a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_smult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_scopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_smult3( buff_m1, psi1, &minus_psi1 );
      bli_scopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_smult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_saxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_saxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_sdiv3( buff_1, tau11, &inv_tau11 );
      bli_sneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 v2, inc_v );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 w2, inc_w );

      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_sdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_sinvscals( buff_2, &beta );
      bli_scopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_sscals( &minus_inv_tau11, &conj_beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_sscals( &minus_inv_tau11, &beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_sdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_sscals( &minus_inv_tau11, &dot_product );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ops_var4 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_Y,
int  rs_Y,
int  cs_Y,
float *  buff_Z,
int  rs_Z,
int  cs_Z,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_saxpyv(), bli_sdot(), bli_sgemv(), bli_sger(), bli_sscalv(), bli_ssetm(), FLA_free(), FLA_Househ2_UT_l_ops(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var4().

{
  float*    buff_2  = FLA_FLOAT_PTR( FLA_TWO );
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );

  float     first_elem, last_elem;
  float     dot_product;
  float     beta, conj_beta;
  float     inv_tau11;
  float     minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  float*    buff_d = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_e = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  float*    buff_f = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_d  = 1;
  int       inc_e  = 1;
  int       inc_f  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_ssetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_ssetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    float*    a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    float*    A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    float*    alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    float*    y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    float*    Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    float*    y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    float*    z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    float*    Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    float*    z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    float*    d0       = buff_d + (0  )*inc_d;

    float*    e0       = buff_e + (0  )*inc_e;

    float*    f0       = buff_f + (0  )*inc_f;

    float*    a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    float*    a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    float*    a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    float*    ABL      = a10t;
    float*    ZBL      = z10t;

    float*    a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_sgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_sgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_sgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_sgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_sdiv3( buff_1, tau11, &inv_tau11 );
      bli_sneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 d0,  inc_d );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Y20, rs_Y, cs_Y,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Z20, rs_Z, cs_Z,
                 a21, rs_A,
                 buff_0,
                 f0,  inc_f );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Y20, rs_Y, cs_Y,
                 d0,  inc_d,
                 buff_1,
                 y21, rs_Y );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 f0,  inc_f,
                 buff_1,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 e0,  inc_e,
                 buff_1,
                 z21, rs_Z );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20, rs_Z, cs_Z,
                 d0,  inc_d,
                 buff_1,
                 z21, rs_Z );


      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_sdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_sinvscals( buff_2, &beta );
      bli_scopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_sscals( &minus_inv_tau11, &conj_beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_sscals( &minus_inv_tau11, &beta );
      bli_saxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_sscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_sdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_sscals( &minus_inv_tau11, &dot_product );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_sger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &d );
  // FLA_Obj_free( &e );
  // FLA_Obj_free( &f );
  FLA_free( buff_d );
  FLA_free( buff_e );
  FLA_free( buff_f );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_ops_var5 ( int  m_A,
int  m_T,
float *  buff_A,
int  rs_A,
int  cs_A,
float *  buff_U,
int  rs_U,
int  cs_U,
float *  buff_Z,
int  rs_Z,
int  cs_Z,
float *  buff_T,
int  rs_T,
int  cs_T 
)

References bli_saxpyv(), bli_scopyv(), bli_sdot(), bli_sdots(), bli_sgemv(), bli_ssetm(), bli_strmv(), bli_strmvsx(), bli_strsv(), FLA_free(), FLA_Househ2_UT_l_ops(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var5().

{
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_0  = FLA_FLOAT_PTR( FLA_ZERO );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  float*    buff_w = ( float* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_w  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, U );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_ssetm( m_A,
             b_alg,
             buff_0,
             buff_U, rs_U, cs_U );
  bli_ssetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    float*    a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
    float*    alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    float*    A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    float*    U00      = buff_U + (0  )*cs_U + (0  )*rs_U;
    float*    u10t     = buff_U + (0  )*cs_U + (i  )*rs_U;
    float*    U20      = buff_U + (0  )*cs_U + (i+1)*rs_U;
    float*    u21      = buff_U + (i  )*cs_U + (i+1)*rs_U;

    float*    Z00      = buff_Z + (0  )*cs_Z + (0  )*rs_Z;
    float*    z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    float*    Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    float*    z01      = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    float*    zeta11   = buff_Z + (i  )*cs_Z + (i  )*rs_Z;
    float*    z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    float*    T00      = buff_T + (0  )*cs_T + (0  )*rs_T;
    float*    t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    float*    tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    float*    w0       = buff_w + (0  )*inc_w;

    float*    a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    float*    a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    float*    u21_t    = u21    + (0  )*cs_U + (0  )*rs_U;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copyt( FLA_CONJ_TRANSPOSE, u10t, w0 );
      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_scopyv( BLIS_CONJUGATE,
                  m_behind,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_strsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_NO_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, z10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, w0, FLA_ONE, a21 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_behind,
                 buff_m1,
                 Z00,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a01,  rs_A );
      bli_sdots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 z10t, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a21,  rs_A );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_ONE, U00, a01, FLA_ZERO, w0 );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, alpha11, u10t, w0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, a21, FLA_ONE, w0 );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_behind,
                  a01, rs_A,
                  w0,  inc_w );
      bli_strmv( BLIS_LOWER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 U00, rs_U, cs_U,
                 w0,  inc_w );
      bli_saxpyv( BLIS_CONJUGATE,
                  m_behind,
                  alpha11,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 a21, rs_A,
                 buff_1,
                 w0,  inc_w );

      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_strsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_MINUS_ONE, U00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, u10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, U20, w0, FLA_ONE, a21 );
      bli_strmvsx( BLIS_LOWER_TRIANGULAR,
                   BLIS_NO_TRANSPOSE,
                   BLIS_NONUNIT_DIAG,
                   m_behind,
                   buff_m1,
                   U00, rs_U, cs_U,
                   w0,  inc_w,
                   buff_1,
                   a01, rs_A );
      bli_sdots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 u10t, cs_U,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 U20, rs_U, cs_U,
                 w0,  inc_w,
                 buff_1,
                 a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_ops( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21, u21 );
      bli_scopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u21, rs_U );

      // FLA_Obj_set_to_scalar( FLA_ONE, u21_t );
      *u21_t = *buff_1;

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, u21, FLA_ZERO, z01 );
      // FLA_Dot( a12t, u21, zeta11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, u21, FLA_ZERO, z21 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z01, rs_Z );
      bli_sdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                u21,  rs_U,
                zeta11 );
      bli_sgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, u21, FLA_ZERO, t01 );
      bli_sgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 u21, rs_U,
                 buff_0,
                 t01, rs_T );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &w );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opt_var1 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opc_var1(), FLA_Hess_UT_step_opd_var1(), FLA_Hess_UT_step_ops_var1(), FLA_Hess_UT_step_opz_var1(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_blk_var1(), and FLA_Hess_UT_opt_var1().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ops_var1( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_opd_var1( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opc_var1( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opz_var1( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opt_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opc_var2(), FLA_Hess_UT_step_opd_var2(), FLA_Hess_UT_step_ops_var2(), FLA_Hess_UT_step_opz_var2(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_blk_var2(), and FLA_Hess_UT_opt_var2().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ops_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_opd_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opc_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opz_var2( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opt_var3 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opc_var3(), FLA_Hess_UT_step_opd_var3(), FLA_Hess_UT_step_ops_var3(), FLA_Hess_UT_step_opz_var3(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_blk_var3(), and FLA_Hess_UT_opt_var3().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ops_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_opd_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opc_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opz_var3( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opt_var4 ( FLA_Obj  A,
FLA_Obj  Y,
FLA_Obj  Z,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opc_var4(), FLA_Hess_UT_step_opd_var4(), FLA_Hess_UT_step_ops_var4(), FLA_Hess_UT_step_opz_var4(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_blk_var4(), and FLA_Hess_UT_opt_var4().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_Y, cs_Y;
  int          rs_Z, cs_Z;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_Y     = FLA_Obj_row_stride( Y );
  cs_Y     = FLA_Obj_col_stride( Y );

  rs_Z     = FLA_Obj_row_stride( Z );
  cs_Z     = FLA_Obj_col_stride( Z );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_Y = FLA_FLOAT_PTR( Y );
      float* buff_Z = FLA_FLOAT_PTR( Z );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ops_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_Y = FLA_DOUBLE_PTR( Y );
      double* buff_Z = FLA_DOUBLE_PTR( Z );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_opd_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_Y = FLA_COMPLEX_PTR( Y );
      scomplex* buff_Z = FLA_COMPLEX_PTR( Z );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opc_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_Y = FLA_DOUBLE_COMPLEX_PTR( Y );
      dcomplex* buff_Z = FLA_DOUBLE_COMPLEX_PTR( Z );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opz_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opt_var5 ( FLA_Obj  A,
FLA_Obj  U,
FLA_Obj  Z,
FLA_Obj  T 
)

References FLA_Hess_UT_step_opc_var5(), FLA_Hess_UT_step_opd_var5(), FLA_Hess_UT_step_ops_var5(), FLA_Hess_UT_step_opz_var5(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), and FLA_Obj_row_stride().

Referenced by FLA_Hess_UT_blk_var5(), and FLA_Hess_UT_opt_var5().

{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_U, cs_U;
  int          rs_Z, cs_Z;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_U     = FLA_Obj_row_stride( U );
  cs_U     = FLA_Obj_col_stride( U );

  rs_Z     = FLA_Obj_row_stride( Z );
  cs_Z     = FLA_Obj_col_stride( Z );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_U = FLA_FLOAT_PTR( U );
      float* buff_Z = FLA_FLOAT_PTR( Z );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ops_var5( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_U, rs_U, cs_U,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_U = FLA_DOUBLE_PTR( U );
      double* buff_Z = FLA_DOUBLE_PTR( Z );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_opd_var5( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_U, rs_U, cs_U,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_U = FLA_COMPLEX_PTR( U );
      scomplex* buff_Z = FLA_COMPLEX_PTR( Z );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opc_var5( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_U, rs_U, cs_U,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_U = FLA_DOUBLE_COMPLEX_PTR( U );
      dcomplex* buff_Z = FLA_DOUBLE_COMPLEX_PTR( Z );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opz_var5( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_U, rs_U, cs_U,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opz_var1 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zgemv(), FLA_Apply_H2_UT_l_opz_var1(), FLA_Apply_H2_UT_r_opz_var1(), FLA_Househ2_UT_l_opz(), FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var1().

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );

  dcomplex  first_elem;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;

    dcomplex* a21_t    = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* a21_b    = buff_A + (i  )*cs_A + (i+2)*rs_A;

    dcomplex* A22_t    = buff_A + (i+1)*cs_A + (i+1)*rs_A;
    dcomplex* A22_b    = buff_A + (i+1)*cs_A + (i+2)*rs_A;

    dcomplex* A2_l     = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* A2_r     = buff_A + (i+2)*cs_A + (0  )*rs_A;

    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Apply_H2_UT( FLA_LEFT, tau11, a21_b, A22_t,
      //                                          A22_b );
      FLA_Apply_H2_UT_l_opz_var1( m_ahead - 1,
                                  n_ahead,
                                  tau11,
                                  a21_b, rs_A,
                                  A22_t, cs_A,
                                  A22_b, rs_A, cs_A );

      // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a21_b, A2_l, A2_r );
      FLA_Apply_H2_UT_r_opz_var1( m_A,
                                  n_ahead - 1,
                                  tau11,
                                  a21_b, rs_A,
                                  A2_l,  rs_A,
                                  A2_r,  rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opz_var2 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zaxpyv(), bli_zdot(), bli_zgemv(), bli_zger(), bli_zscalv(), FLA_free(), FLA_Househ2_UT_l_opz(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var2().

{
  dcomplex* buff_2  = FLA_DOUBLE_COMPLEX_PTR( FLA_TWO );
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );

  dcomplex  first_elem;
  dcomplex  dot_product;
  dcomplex  beta, conj_beta;
  dcomplex  inv_tau11;
  dcomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  dcomplex* buff_y = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_z = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_y  = 1;
  int       inc_z  = 1;

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    dcomplex* y0       = buff_y + (0  )*inc_y;
    dcomplex* y2       = buff_y + (i+1)*inc_y;

    dcomplex* z2       = buff_z + (i+1)*inc_z;

    dcomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_zdiv3( buff_1, tau11, &inv_tau11 );
      bli_zneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y2, inc_y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_zdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_zinvscals( buff_2, &beta );
      bli_zcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_zscals( &minus_inv_tau11, &conj_beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_zscals( &minus_inv_tau11, &beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_zdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_zscals( &minus_inv_tau11, &dot_product );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                a21, rs_A,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                a21, rs_A,
                A22, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  FLA_free( buff_y );
  FLA_free( buff_z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opz_var3 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zaxpyv(), bli_zcopyv(), bli_zdot(), bli_zgemv(), bli_zger(), bli_zscalv(), FLA_free(), FLA_Househ2_UT_l_opz(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var3().

{
  dcomplex* buff_2  = FLA_DOUBLE_COMPLEX_PTR( FLA_TWO );
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );

  dcomplex  first_elem;
  dcomplex  dot_product;
  dcomplex  beta, conj_beta;
  dcomplex  inv_tau11;
  dcomplex  minus_inv_tau11;
  dcomplex  minus_upsilon1, minus_conj_upsilon1;
  dcomplex  minus_psi1, minus_conj_psi1;
  dcomplex  minus_zeta1;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  dcomplex* buff_u = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_y = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_z = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_v = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_w = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_y  = 1;
  int       inc_z  = 1;
  int       inc_v  = 1;
  int       inc_w  = 1;

  // Initialize some variables (only to prevent compiler warnings).
  first_elem           = *buff_0;
  minus_inv_tau11 = *buff_0;

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    dcomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    dcomplex* upsilon1 = buff_u + (i  )*inc_u;
    dcomplex* u2       = buff_u + (i+1)*inc_u;

    dcomplex* y0       = buff_y + (0  )*inc_y;
    dcomplex* psi1     = buff_y + (i  )*inc_y;
    dcomplex* y2       = buff_y + (i+1)*inc_y;

    dcomplex* zeta1    = buff_z + (i  )*inc_z;
    dcomplex* z2       = buff_z + (i+1)*inc_z;

    dcomplex* v2       = buff_v + (i+1)*inc_v;

    dcomplex* w2       = buff_w + (i+1)*inc_w;

    dcomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon1, minus_upsilon1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );
      bli_zmult3( buff_m1, upsilon1, &minus_upsilon1 );
      bli_zcopyconj( &minus_upsilon1, &minus_conj_upsilon1 );

      // FLA_Copy( psi1, minus_psi1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );
      bli_zmult3( buff_m1, psi1, &minus_psi1 );
      bli_zcopyconj( &minus_psi1, &minus_conj_psi1 );

      // FLA_Copy( zeta1, minus_zeta1 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );
      bli_zmult3( buff_m1, zeta1, &minus_zeta1 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );
      bli_zaxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_upsilon1,
                  psi1,    1,
                  alpha11, 1 );
      bli_zaxpyv( BLIS_CONJUGATE,
                  1,
                  &minus_zeta1,
                  upsilon1, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_upsilon1,
                  y2,   inc_y,
                  a12t, cs_A );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &minus_zeta1,
                  u2,   inc_u,
                  a12t, cs_A );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_psi1,
                  u2,  inc_u,
                  a21, rs_A );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon1,
                  z2,  inc_z,
                  a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_zdiv3( buff_1, tau11, &inv_tau11 );
      bli_zneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;
    }

    if ( m_behind > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 v2, inc_v );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 w2, inc_w );

      // FLA_Copy( a21, u2 );
      // FLA_Copy( v2, y2 );
      // FLA_Copy( w2, z2 );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u2,  inc_u );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  v2, inc_v,
                  y2, inc_y );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  w2, inc_w,
                  z2, inc_z );

      // FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_zdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z2,  inc_z,
                &beta );
      bli_zinvscals( buff_2, &beta );
      bli_zcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y2 );
      // FLA_Scal( inv_tau11, y2 );
      bli_zscals( &minus_inv_tau11, &conj_beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y2, inc_y );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y2, inc_y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z2 );
      // FLA_Scal( inv_tau11, z2 );
      bli_zscals( &minus_inv_tau11, &beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z2, inc_z );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z2, inc_z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_zdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_zscals( &minus_inv_tau11, &dot_product );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y0,  inc_y );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                y0,  inc_y,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    if ( m_behind + 1 == b_alg && m_ahead > 0 )
    {
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                u2,  inc_u,
                y2,  inc_y,
                A22, rs_A, cs_A );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_ahead,
                n_ahead,
                buff_m1,
                z2,  inc_z,
                u2,  inc_u,
                A22, rs_A, cs_A );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &u );
  // FLA_Obj_free( &y );
  // FLA_Obj_free( &z );
  // FLA_Obj_free( &v );
  // FLA_Obj_free( &w );
  FLA_free( buff_u );
  FLA_free( buff_y );
  FLA_free( buff_z );
  FLA_free( buff_v );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opz_var4 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_Y,
int  rs_Y,
int  cs_Y,
dcomplex buff_Z,
int  rs_Z,
int  cs_Z,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zaxpyv(), bli_zdot(), bli_zgemv(), bli_zger(), bli_zscalv(), bli_zsetm(), FLA_free(), FLA_Househ2_UT_l_opz(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var4().

{
  dcomplex* buff_2  = FLA_DOUBLE_COMPLEX_PTR( FLA_TWO );
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );

  dcomplex  first_elem, last_elem;
  dcomplex  dot_product;
  dcomplex  beta, conj_beta;
  dcomplex  inv_tau11;
  dcomplex  minus_inv_tau11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
  dcomplex* buff_d = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_e = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  dcomplex* buff_f = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_d  = 1;
  int       inc_e  = 1;
  int       inc_f  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_zsetm( m_A,
             b_alg,
             buff_0,
             buff_Y, rs_Y, cs_Y );
  bli_zsetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* a10t     = buff_A + (0  )*cs_A + (i  )*rs_A;
    dcomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    dcomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    dcomplex* y10t     = buff_Y + (0  )*cs_Y + (i  )*rs_Y;
    dcomplex* Y20      = buff_Y + (0  )*cs_Y + (i+1)*rs_Y;
    dcomplex* y21      = buff_Y + (i  )*cs_Y + (i+1)*rs_Y;

    dcomplex* z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    dcomplex* Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    dcomplex* z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    dcomplex* d0       = buff_d + (0  )*inc_d;

    dcomplex* e0       = buff_e + (0  )*inc_e;

    dcomplex* f0       = buff_f + (0  )*inc_f;

    dcomplex* a10t_r   = a10t   + (i-1)*cs_A + (0  )*rs_A;

    dcomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    dcomplex* ABL      = a10t;
    dcomplex* ZBL      = z10t;

    dcomplex* a2       = alpha11;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copy( a10t_r, last_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
      last_elem = *a10t_r;
      *a10t_r = *buff_1;
    }

    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    // FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
    bli_zgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ABL,  rs_A, cs_A,
               y10t, cs_Y,
               buff_1,
               a2,   rs_A );
    bli_zgemv( BLIS_NO_TRANSPOSE,
               BLIS_CONJUGATE,
               m_ahead + 1,
               n_behind,
               buff_m1,
               ZBL,  rs_Z, cs_Z,
               a10t, cs_A,
               buff_1,
               a2,   rs_A );

    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    // FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
    bli_zgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               Y20,  rs_Y, cs_Y,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );
    bli_zgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               n_behind,
               buff_m1,
               A20,  rs_A, cs_A,
               z10t, cs_Z,
               buff_1,
               a12t, cs_A );

    if ( m_behind > 0 )
    {
      // FLA_Copy( last_elem, a10t_r );
      *a10t_r = last_elem;
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      // FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      // FLA_Copy( inv_tau11, minus_inv_tau11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
      bli_zdiv3( buff_1, tau11, &inv_tau11 );
      bli_zneg2( &inv_tau11, &minus_inv_tau11 );

      // FLA_Copy( a21_t, first_elem );
      // FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
      first_elem = *a21_t;
      *a21_t = *buff_1;

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 d0,  inc_d );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Y20, rs_Y, cs_Y,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 Z20, rs_Z, cs_Z,
                 a21, rs_A,
                 buff_0,
                 f0,  inc_f );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Y20, rs_Y, cs_Y,
                 d0,  inc_d,
                 buff_1,
                 y21, rs_Y );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 f0,  inc_f,
                 buff_1,
                 y21, rs_Y );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 A20, rs_A, cs_A,
                 e0,  inc_e,
                 buff_1,
                 z21, rs_Z );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20, rs_Z, cs_Z,
                 d0,  inc_d,
                 buff_1,
                 z21, rs_Z );


      // FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      // FLA_Inv_scal( FLA_TWO, beta );
      // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
      bli_zdot( BLIS_CONJUGATE,
                m_ahead,
                a21, rs_A,
                z21, rs_Z,
                &beta );
      bli_zinvscals( buff_2, &beta );
      bli_zcopyconj( &beta, &conj_beta );

      // FLA_Scal( minus_inv_tau11, conj_beta );
      // FLA_Axpy( conj_beta, a21, y21 );
      // FLA_Scal( inv_tau11, y21 );
      bli_zscals( &minus_inv_tau11, &conj_beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &conj_beta,
                  a21, rs_A,
                  y21, rs_Y );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  y21, rs_Y );

      // FLA_Scal( minus_inv_tau11, beta );
      // FLA_Axpy( beta, a21, z21 );
      // FLA_Scal( inv_tau11, z21 );
      bli_zscals( &minus_inv_tau11, &beta );
      bli_zaxpyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &beta,
                  a21, rs_A,
                  z21, rs_Z );
      bli_zscalv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  &inv_tau11,
                  z21, rs_Z );

      // FLA_Dot( a12t, a21, dot_product );
      // FLA_Scal( minus_inv_tau11, dot_product );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
      bli_zdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                a21,  rs_A,
                &dot_product );
      bli_zscals( &minus_inv_tau11, &dot_product );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_ahead,
                  &dot_product,
                  a21,  rs_A,
                  a12t, cs_A );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      // FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 e0,  inc_e );
      bli_zger( BLIS_NO_CONJUGATE,
                BLIS_CONJUGATE,
                m_behind,
                n_ahead,
                &minus_inv_tau11,
                e0,  inc_e,
                a21, rs_A,
                A02, rs_A, cs_A );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 A20, rs_A, cs_A,
                 a21, rs_A,
                 buff_0,
                 t01, rs_T );

      // FLA_Copy( first_elem, a21_t );
      *a21_t = first_elem;
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &d );
  // FLA_Obj_free( &e );
  // FLA_Obj_free( &f );
  FLA_free( buff_d );
  FLA_free( buff_e );
  FLA_free( buff_f );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_opz_var5 ( int  m_A,
int  m_T,
dcomplex buff_A,
int  rs_A,
int  cs_A,
dcomplex buff_U,
int  rs_U,
int  cs_U,
dcomplex buff_Z,
int  rs_Z,
int  cs_Z,
dcomplex buff_T,
int  rs_T,
int  cs_T 
)

References bli_zaxpyv(), bli_zcopyv(), bli_zdot(), bli_zdots(), bli_zgemv(), bli_zsetm(), bli_ztrmv(), bli_ztrmvsx(), bli_ztrsv(), FLA_free(), FLA_Househ2_UT_l_opz(), FLA_malloc(), FLA_MINUS_ONE, FLA_ONE, and FLA_ZERO.

Referenced by FLA_Hess_UT_step_opt_var5().

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_0  = FLA_DOUBLE_COMPLEX_PTR( FLA_ZERO );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  dcomplex* buff_w = ( dcomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_w  = 1;

  // FLA_Obj_set_to_scalar( FLA_ZERO, U );
  // FLA_Obj_set_to_scalar( FLA_ZERO, Z );
  bli_zsetm( m_A,
             b_alg,
             buff_0,
             buff_U, rs_U, cs_U );
  bli_zsetm( m_A,
             b_alg,
             buff_0,
             buff_Z, rs_Z, cs_Z );

  for ( i = 0; i < b_alg; ++i )
  {
    dcomplex* a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
    dcomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    dcomplex* A02      = buff_A + (i+1)*cs_A + (0  )*rs_A;
    dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
    dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    dcomplex* U00      = buff_U + (0  )*cs_U + (0  )*rs_U;
    dcomplex* u10t     = buff_U + (0  )*cs_U + (i  )*rs_U;
    dcomplex* U20      = buff_U + (0  )*cs_U + (i+1)*rs_U;
    dcomplex* u21      = buff_U + (i  )*cs_U + (i+1)*rs_U;

    dcomplex* Z00      = buff_Z + (0  )*cs_Z + (0  )*rs_Z;
    dcomplex* z10t     = buff_Z + (0  )*cs_Z + (i  )*rs_Z;
    dcomplex* Z20      = buff_Z + (0  )*cs_Z + (i+1)*rs_Z;
    dcomplex* z01      = buff_Z + (i  )*cs_Z + (0  )*rs_Z;
    dcomplex* zeta11   = buff_Z + (i  )*cs_Z + (i  )*rs_Z;
    dcomplex* z21      = buff_Z + (i  )*cs_Z + (i+1)*rs_Z;

    dcomplex* T00      = buff_T + (0  )*cs_T + (0  )*rs_T;
    dcomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    dcomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    dcomplex* w0       = buff_w + (0  )*inc_w;

    dcomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    dcomplex* u21_t    = u21    + (0  )*cs_U + (0  )*rs_U;

    int       m_ahead  = m_A - i - 1;
    int       n_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

    /*------------------------------------------------------------*/

    if ( m_behind > 0 )
    {
      // FLA_Copyt( FLA_CONJ_TRANSPOSE, u10t, w0 );
      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_zcopyv( BLIS_CONJUGATE,
                  m_behind,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_ztrsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_NO_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, z10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, w0, FLA_ONE, a21 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_behind,
                 buff_m1,
                 Z00,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a01,  rs_A );
      bli_zdots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 z10t, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 Z20,  rs_Z, cs_Z,
                 w0,   inc_w,
                 buff_1,
                 a21,  rs_A );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_ONE, U00, a01, FLA_ZERO, w0 );
      // FLA_Axpyt( FLA_CONJ_TRANSPOSE, alpha11, u10t, w0 );
      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, a21, FLA_ONE, w0 );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_behind,
                  a01, rs_A,
                  w0,  inc_w );
      bli_ztrmv( BLIS_LOWER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 U00, rs_U, cs_U,
                 w0,  inc_w );
      bli_zaxpyv( BLIS_CONJUGATE,
                  m_behind,
                  alpha11,
                  u10t, cs_U,
                  w0,   inc_w );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 a21, rs_A,
                 buff_1,
                 w0,  inc_w );

      // FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
      //           T00, w0 );
      bli_ztrsv( BLIS_UPPER_TRIANGULAR,
                 BLIS_CONJ_TRANSPOSE,
                 BLIS_NONUNIT_DIAG,
                 m_behind,
                 T00, rs_T, cs_T,
                 w0,  inc_w );

      // FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
      //             FLA_MINUS_ONE, U00, w0, FLA_ONE, a01 );
      // FLA_Dots( FLA_MINUS_ONE, u10t, w0, FLA_ONE, alpha11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, U20, w0, FLA_ONE, a21 );
      bli_ztrmvsx( BLIS_LOWER_TRIANGULAR,
                   BLIS_NO_TRANSPOSE,
                   BLIS_NONUNIT_DIAG,
                   m_behind,
                   buff_m1,
                   U00, rs_U, cs_U,
                   w0,  inc_w,
                   buff_1,
                   a01, rs_A );
      bli_zdots( BLIS_NO_CONJUGATE,
                 m_behind,
                 buff_m1,
                 u10t, cs_U,
                 w0,   inc_w,
                 buff_1,
                 alpha11 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_m1,
                 U20, rs_U, cs_U,
                 w0,  inc_w,
                 buff_1,
                 a21, rs_A );
    }

    if ( m_ahead > 0 )
    {
      // FLA_Househ2_UT( FLA_LEFT,
      //                 a21_t,
      //                 a21_b, tau11 );
      FLA_Househ2_UT_l_opz( m_ahead - 1,
                            a21_t,
                            a21_b, rs_A,
                            tau11 );

      // FLA_Copy( a21, u21 );
      bli_zcopyv( BLIS_NO_CONJUGATE,
                  m_ahead,
                  a21, rs_A,
                  u21, rs_U );

      // FLA_Obj_set_to_scalar( FLA_ONE, u21_t );
      *u21_t = *buff_1;

      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, u21, FLA_ZERO, z01 );
      // FLA_Dot( a12t, u21, zeta11 );
      // FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, u21, FLA_ZERO, z21 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_behind,
                 n_ahead,
                 buff_1,
                 A02, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z01, rs_Z );
      bli_zdot( BLIS_NO_CONJUGATE,
                m_ahead,
                a12t, cs_A,
                u21,  rs_U,
                zeta11 );
      bli_zgemv( BLIS_NO_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_ahead,
                 buff_1,
                 A22, rs_A, cs_A,
                 u21, rs_U,
                 buff_0,
                 z21, rs_Z );

      // FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, u21, FLA_ZERO, t01 );
      bli_zgemv( BLIS_CONJ_TRANSPOSE,
                 BLIS_NO_CONJUGATE,
                 m_ahead,
                 n_behind,
                 buff_1,
                 U20, rs_U, cs_U,
                 u21, rs_U,
                 buff_0,
                 t01, rs_T );
    }

    /*------------------------------------------------------------*/

  }

  // FLA_Obj_free( &w );
  FLA_free( buff_w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_unb_var1 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Apply_H2_UT(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Gemv(), FLA_Househ2_UT(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), and FLA_ZERO.

Referenced by FLA_Hess_UT_unb_var1().

{
  FLA_Obj  ATL,   ATR,      A00,  a01,     A02, 
           ABL,   ABR,      a10t, alpha11, a12t,
                            A20,  a21,     A22;
  FLA_Obj  AL,    AR,       A0,   a1,      A2;
  FLA_Obj  TTL,   TTR,      T00,  t01,   T02, 
           TBL,   TBR,      t10t, tau11, t12t,
                            T20,  t21,   T22;
           
  FLA_Obj  a21_t,
           a21_b;

  FLA_Obj  A22_t,
           A22_b;

  FLA_Obj  A2_l, A2_r;

  FLA_Obj  first_elem;

  dim_t        b_alg;
  FLA_Datatype datatype_A;


  b_alg      = FLA_Obj_length( T );
  datatype_A = FLA_Obj_datatype( A );

  FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_1x2( A,    &AL,  &AR,         0, FLA_LEFT );
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );

  while ( FLA_Obj_length( ATL ) < b_alg )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    FLA_Repart_1x2_to_1x3( AL,  /**/ AR,        &A0, /**/ &a1, &A2,
                           1, FLA_RIGHT );

    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************** */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );

    /*------------------------------------------------------------*/

    if ( FLA_Obj_length( A22 ) > 0 )
    {
      FLA_Part_2x1( a21,    &a21_t,
                            &a21_b,        1, FLA_TOP );

      FLA_Part_2x1( A22,    &A22_t,
                            &A22_b,        1, FLA_TOP );

      FLA_Part_1x2( A2,     &A2_l, &A2_r,        1, FLA_LEFT );

      // [ u21, tau11, a21 ] = House( a21 );
      FLA_Househ2_UT( FLA_LEFT,
                      a21_t,
                      a21_b, tau11 );

      // Save first element of a21_t and set it to one so we can use a21 as
      // u21 in subsequent computations. We will restore a21_t later on.
      FLA_Copy( a21_t, first_elem );
      FLA_Obj_set_to_scalar( FLA_ONE, a21_t );

      // A22 = ( I - inv( tau ) * u21 * u21' ) * A22;
      FLA_Apply_H2_UT( FLA_LEFT, tau11, a21_b, A22_t,
                                               A22_b );

      // A02  = A02  * ( I - inv( tau ) * u21 * u21' );
      // a12t = a12t * ( I - inv( tau ) * u21 * u21' );
      // A22  = A22  * ( I - inv( tau ) * u21 * u21' );
      FLA_Apply_H2_UT( FLA_RIGHT, tau11, a21_b, A2_l, A2_r );

      // t01 = U20' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );

      // Restore first element of a21.
      FLA_Copy( first_elem, a21_t );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );

    FLA_Cont_with_1x3_to_1x2( &AL,  /**/ &AR,        A0, a1, /**/ A2,
                              FLA_LEFT );

    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ************************ */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
  }

  FLA_Obj_free( &first_elem );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_unb_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Axpy(), FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dotc(), FLA_Gemv(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_unb_var2().

{
  FLA_Obj  ATL,   ATR,      A00,  a01,     A02, 
           ABL,   ABR,      a10t, alpha11, a12t,
                            A20,  a21,     A22;
  FLA_Obj  TTL,   TTR,      T00,  t01,   T02, 
           TBL,   TBR,      t10t, tau11, t12t,
                            T20,  t21,   T22;
  FLA_Obj  yT,              y0,
           yB,              psi1,
                            y2;
  FLA_Obj  zT,              z0,
           zB,              zeta1,
                            z2;
  FLA_Obj  y, z;
           
  FLA_Obj  inv_tau11;
  FLA_Obj  minus_inv_tau11;
  FLA_Obj  first_elem;
  FLA_Obj  beta;
  FLA_Obj  conj_beta;
  FLA_Obj  dot_product;

  FLA_Obj  a21_t,
           a21_b;

  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg;


  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &first_elem );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &conj_beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &dot_product );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
  FLA_Part_2x1( y,    &yT, 
                      &yB,            0, FLA_TOP );
  FLA_Part_2x1( z,    &zT, 
                      &zB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < b_alg )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************** */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
    FLA_Repart_2x1_to_3x1( yT,                &y0, 
                        /* ** */            /* **** */
                                              &psi1, 
                           yB,                &y2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( zT,                &z0, 
                        /* ** */            /* ***** */
                                              &zeta1, 
                           zB,                &z2,        1, FLA_BOTTOM );

    /*------------------------------------------------------------*/

    if ( FLA_Obj_length( A22 ) > 0 )
    {
      FLA_Part_2x1( a21,    &a21_t,
                            &a21_b,        1, FLA_TOP );

      // [ u21, tau11, a21 ] = House( a21 );
      FLA_Househ2_UT( FLA_LEFT,
                      a21_t,
                      a21_b, tau11 );

      // inv_tau11            =  1 / tau11;
      // minus_inv_tau11      = -1 / tau11;
      FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      FLA_Copy( inv_tau11, minus_inv_tau11 );
      FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );

      // Save first element of a21_t and set it to one so we can use a21 as
      // u21 in subsequent computations. We will restore a21_t later on.
      FLA_Copy( a21_t, first_elem );
      FLA_Obj_set_to_scalar( FLA_ONE, a21_t );

      // y21 = A22' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );

      // z21 = A22 * u21;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );

      // beta      = u21' * z21 / 2;
      // conj_beta = conj(beta);
      FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      FLA_Inv_scal( FLA_TWO, beta );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );

      // y21' = ( y21' - beta / tau * u21' ) / tau;
      // y21  = ( y21 - conj(beta) / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, conj_beta );
      FLA_Axpy( conj_beta, a21, y2 );
      FLA_Scal( inv_tau11, y2 );

      // z21 = ( z21 - beta / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, beta );
      FLA_Axpy( beta, a21, z2 );
      FLA_Scal( inv_tau11, z2 );

      // a12t = a12t * ( I - u21 * u21' / tau );
      //      = a12t - ( a12t * u21 ) * u21' / tau;
      FLA_Dot( a12t, a21, dot_product );
      FLA_Scal( minus_inv_tau11, dot_product );
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );

      // A02 = A02 * ( I - u21 * u21' / tau );
      //     = A02 - ( A02 * u21 ) * u21' / tau;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );

      // A22 = A22 - u21 * y21' - z21 * u21';
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );

      // t01 = U20' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );

      // Restore first element of a21.
      FLA_Copy( first_elem, a21_t );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ************************ */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &yT,                y0, 
                                                  psi1, 
                            /* ** */           /* **** */
                              &yB,                y2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &zT,                z0, 
                                                  zeta1, 
                            /* ** */           /* ***** */
                              &zB,                z2,     FLA_TOP );
  }

  FLA_Obj_free( &inv_tau11 );
  FLA_Obj_free( &minus_inv_tau11 );
  FLA_Obj_free( &first_elem );
  FLA_Obj_free( &beta );
  FLA_Obj_free( &conj_beta );
  FLA_Obj_free( &dot_product );
  FLA_Obj_free( &y );
  FLA_Obj_free( &z );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_unb_var3 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Axpy(), FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dotc(), FLA_Gemv(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_unb_var3().

{
  FLA_Obj  ATL,   ATR,      A00,  a01,     A02, 
           ABL,   ABR,      a10t, alpha11, a12t,
                            A20,  a21,     A22;
  FLA_Obj  TTL,   TTR,      T00,  t01,   T02, 
           TBL,   TBR,      t10t, tau11, t12t,
                            T20,  t21,   T22;
  FLA_Obj  uT,              u0,
           uB,              upsilon1,
                            u2;
  FLA_Obj  yT,              y0,
           yB,              psi1,
                            y2;
  FLA_Obj  zT,              z0,
           zB,              zeta1,
                            z2;
  FLA_Obj  vT,              v0,
           vB,              nu1,
                            v2;
  FLA_Obj  wT,              w0,
           wB,              omega1,
                            w2;
  FLA_Obj  u, y, z, v, w;

  FLA_Obj  inv_tau11;
  FLA_Obj  minus_inv_tau11;
  FLA_Obj  first_elem;
  FLA_Obj  beta;
  FLA_Obj  conj_beta;
  FLA_Obj  dot_product;
  FLA_Obj  minus_upsilon1;
  FLA_Obj  minus_conj_upsilon1;
  FLA_Obj  minus_psi1;
  FLA_Obj  minus_conj_psi1;
  FLA_Obj  minus_zeta1;

  FLA_Obj  a21_t,
           a21_b;

  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg;


  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &first_elem );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &conj_beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &dot_product );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_upsilon1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_conj_upsilon1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_psi1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_conj_psi1 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_zeta1 );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &v );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
  FLA_Part_2x1( u,    &uT, 
                      &uB,            0, FLA_TOP );
  FLA_Part_2x1( y,    &yT, 
                      &yB,            0, FLA_TOP );
  FLA_Part_2x1( z,    &zT, 
                      &zB,            0, FLA_TOP );
  FLA_Part_2x1( v,    &vT, 
                      &vB,            0, FLA_TOP );
  FLA_Part_2x1( w,    &wT, 
                      &wB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < b_alg )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************** */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
    FLA_Repart_2x1_to_3x1( uT,                &u0, 
                        /* ** */            /* ******** */
                                              &upsilon1, 
                           uB,                &u2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( yT,                &y0, 
                        /* ** */            /* **** */
                                              &psi1, 
                           yB,                &y2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( zT,                &z0, 
                        /* ** */            /* ***** */
                                              &zeta1, 
                           zB,                &z2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( vT,                &v0, 
                        /* ** */            /* *** */
                                              &nu1, 
                           vB,                &v2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( wT,                &w0, 
                        /* ** */            /* ****** */
                                              &omega1, 
                           wB,                &w2,        1, FLA_BOTTOM );

    /*------------------------------------------------------------*/
    
    if ( FLA_Obj_length( ATL ) > 0 )
    {
      FLA_Copy( upsilon1, minus_upsilon1 );
      FLA_Scal( FLA_MINUS_ONE, minus_upsilon1 );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, minus_conj_upsilon1 );

      FLA_Copy( psi1, minus_psi1 );
      FLA_Scal( FLA_MINUS_ONE, minus_psi1 );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_psi1, minus_conj_psi1 );

      FLA_Copy( zeta1, minus_zeta1 );
      FLA_Scal( FLA_MINUS_ONE, minus_zeta1 );

      // alpha11 = alpha11 - upsilon11 * conj(psi11) - zeta11 * conj(upsilon11);
      FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon1, psi1,     alpha11 );
      FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta1,    upsilon1, alpha11 );

      // a12t = a12t - upsilon11 * y21' - zeta11 * u21';
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon1, y2, a12t );
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta1,    u2, a12t );

      // a21 = a21 - conj(psi11) * u21 - conj(upsilon11) * z21;
      FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi1,     u2, a21 );
      FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon1, z2, a21 );
    }

    if ( FLA_Obj_length( A22 ) > 0 )
    {
      FLA_Part_2x1( a21,    &a21_t,
                            &a21_b,            1, FLA_TOP );

      // [ x21, tau11, a21 ] = House( a21 );
      FLA_Househ2_UT( FLA_LEFT,
                      a21_t,
                      a21_b, tau11 );

      // inv_tau11            =  1 / tau11;
      // minus_inv_tau11      = -1 / tau11;
      FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      FLA_Copy( inv_tau11, minus_inv_tau11 );
      FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );

      // Save first element of a21_t and set it to one so we can use a21 as
      // u21 in subsequent computations. We will restore a21_t later on.
      FLA_Copy( a21_t, first_elem );
      FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
    }

    if ( FLA_Obj_length( ATL ) > 0 )
    {
      // A22 = A22 - u21 * y21' - z21 * u21';
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
    }

    if ( FLA_Obj_length( A22 ) > 0 )
    {
      // v2 = A22' * x21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, v2 );

      // w2 = A22 * x21;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, w2 );

      // u21 = x21; 
      // y21 = v2;
      // z21 = w2;
      FLA_Copy( a21, u2 );
      FLA_Copy( v2, y2 );
      FLA_Copy( w2, z2 );

      // beta      = u21' * z21 / 2;
      // conj_beta = conj(beta);
      FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
      FLA_Inv_scal( FLA_TWO, beta );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );

      // y21' = ( y21' - beta / tau * u21' ) / tau;
      // y21  = ( y21 - conj(beta) / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, conj_beta );
      FLA_Axpy( conj_beta, a21, y2 );
      FLA_Scal( inv_tau11, y2 );

      // z21 = ( z21 - beta / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, beta );
      FLA_Axpy( beta, a21, z2 );
      FLA_Scal( inv_tau11, z2 );

      // a12t = a12t * ( I - u21 * u21' / tau );
      //      = a12t - ( a12t * u21 ) * u21' / tau;
      FLA_Dot( a12t, a21, dot_product );
      FLA_Scal( minus_inv_tau11, dot_product );
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );

      // A02 = A02 * ( I - u21 * u21' / tau );
      //     = A02 - ( A02 * u21 ) * u21' / tau;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );

      // t01 = U20' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );

      // Restore first element of a21.
      FLA_Copy( first_elem, a21_t );
    }

    // Update A22 if this is the last iteration; this is needed when we're
    // being called from the blocked routine so A22 is left in a valid state.
    if ( FLA_Obj_length( ATL ) + 1 == b_alg &&
         FLA_Obj_length( A22 ) > 0 )
    {
      // A22 = A22 - u21 * y21' - z21 * u21';
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u2, y2, A22 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, u2, A22 );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ************************ */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &uT,                u0, 
                                                  upsilon1, 
                            /* ** */           /* ******** */
                              &uB,                u2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &yT,                y0, 
                                                  psi1, 
                            /* ** */           /* **** */
                              &yB,                y2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &zT,                z0, 
                                                  zeta1, 
                            /* ** */           /* ***** */
                              &zB,                z2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &vT,                v0, 
                                                  nu1, 
                            /* ** */           /* *** */
                              &vB,                v2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &wT,                w0, 
                                                  omega1, 
                            /* ** */           /* ****** */
                              &wB,                w2,     FLA_TOP );
  }

  FLA_Obj_free( &inv_tau11 );
  FLA_Obj_free( &minus_inv_tau11 );
  FLA_Obj_free( &first_elem );
  FLA_Obj_free( &beta );
  FLA_Obj_free( &conj_beta );
  FLA_Obj_free( &dot_product );
  FLA_Obj_free( &minus_upsilon1 );
  FLA_Obj_free( &minus_conj_upsilon1 );
  FLA_Obj_free( &minus_psi1 );
  FLA_Obj_free( &minus_conj_psi1 );
  FLA_Obj_free( &minus_zeta1 );
  FLA_Obj_free( &u );
  FLA_Obj_free( &y );
  FLA_Obj_free( &z );
  FLA_Obj_free( &v );
  FLA_Obj_free( &w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_unb_var4 ( FLA_Obj  A,
FLA_Obj  Y,
FLA_Obj  Z,
FLA_Obj  T 
)

References FLA_Axpy(), FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dotc(), FLA_Gemv(), FLA_Gemvc(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_TWO, and FLA_ZERO.

Referenced by FLA_Hess_UT_unb_var4().

{
  FLA_Obj  ATL,   ATR,      A00,  a01,     A02, 
           ABL,   ABR,      a10t, alpha11, a12t,
                            A20,  a21,     A22;
  FLA_Obj  YTL,   YTR,      Y00,  y01,   Y02, 
           YBL,   YBR,      y10t, psi11, y12t,
                            Y20,  y21,   Y22;
  FLA_Obj  ZTL,   ZTR,      Z00,  z01,    Z02, 
           ZBL,   ZBR,      z10t, zeta11, z12t,
                            Z20,  z21,    Z22;
  FLA_Obj  TTL,   TTR,      T00,  t01,   T02, 
           TBL,   TBR,      t10t, tau11, t12t,
                            T20,  t21,   T22;
  FLA_Obj  dT,              d0,
           dB,              delta1,
                            d2;
  FLA_Obj  eT,              e0,
           eB,              epsilon1,
                            e2;
  FLA_Obj  fT,              f0,
           fB,              phi1,
                            f2;
  FLA_Obj  d, e, f;

  FLA_Obj  inv_tau11;
  FLA_Obj  minus_inv_tau11;
  FLA_Obj  first_elem;
  FLA_Obj  last_elem;
  FLA_Obj  beta;
  FLA_Obj  conj_beta;
  FLA_Obj  dot_product;

  FLA_Obj  a10t_l, a10t_r;
  FLA_Obj  a21_t,
           a21_b;
  FLA_Obj  a2;

  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg;


  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &minus_inv_tau11 );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &first_elem );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &last_elem );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &conj_beta );
  FLA_Obj_create( datatype_A, 1,   1, 0, 0, &dot_product );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &d );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );

  FLA_Obj_set_to_scalar( FLA_ZERO, Y );
  FLA_Obj_set_to_scalar( FLA_ZERO, Z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x2( Y,    &YTL, &YTR,
                      &YBL, &YBR,     0, 0, FLA_TL );
  FLA_Part_2x2( Z,    &ZTL, &ZTR,
                      &ZBL, &ZBR,     0, 0, FLA_TL );
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
  FLA_Part_2x1( d,    &dT, 
                      &dB,            0, FLA_TOP );
  FLA_Part_2x1( e,    &eT, 
                      &eB,            0, FLA_TOP );
  FLA_Part_2x1( f,    &fT, 
                      &fB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < b_alg )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( YTL, /**/ YTR,       &Y00,  /**/ &y01,   &Y02,
                        /* ************* */   /* ************************ */
                                                &y10t, /**/ &psi11, &y12t,
                           YBL, /**/ YBR,       &Y20,  /**/ &y21,   &Y22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( ZTL, /**/ ZTR,       &Z00,  /**/ &z01,    &Z02,
                        /* ************* */   /* ************************* */
                                                &z10t, /**/ &zeta11, &z12t,
                           ZBL, /**/ ZBR,       &Z20,  /**/ &z21,    &Z22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************** */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
    FLA_Repart_2x1_to_3x1( dT,                &d0, 
                        /* ** */            /* ****** */
                                              &delta1, 
                           dB,                &d2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( eT,                &e0, 
                        /* ** */            /* ******** */
                                              &epsilon1, 
                           eB,                &e2,        1, FLA_BOTTOM );
    FLA_Repart_2x1_to_3x1( fT,                &f0, 
                        /* ** */            /* **** */
                                              &phi1, 
                           fB,                &f2,        1, FLA_BOTTOM );

    /*------------------------------------------------------------*/

    // Save first element of a10_r and set it to one so we can use a10t as
    // u10t in subsequent computations. We will restore a10_r later on.
    if ( FLA_Obj_length( ATL ) > 0 )
    {
      FLA_Part_1x2( a10t,   &a10t_l, &a10t_r,     1, FLA_RIGHT );
      FLA_Copy( a10t_r, last_elem );
      FLA_Obj_set_to_scalar( FLA_ONE, a10t_r );
    }
 
    FLA_Merge_2x1( alpha11,
                   a21,      &a2 );

    // alpha11 = alpha11 - u10t * y10t' - z10t * u10t';
    // a21     = a21     - U20  * y10t' - Z20  * u10t';
    FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
    FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );

    // a12t = a12t - u10t * Y20' - z10t * U20';
    FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
    FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );

    // Restore last element of a10t.
    if ( FLA_Obj_length( ATL ) > 0 )
    {
      FLA_Copy( last_elem, a10t_r );
    }

    if ( FLA_Obj_length( A22 ) > 0 )
    {
      FLA_Part_2x1( a21,    &a21_t,
                            &a21_b,            1, FLA_TOP );

      // [ u21, tau11, a21 ] = House( a21 );
      FLA_Househ2_UT( FLA_LEFT,
                      a21_t,
                      a21_b, tau11 );
  
      // inv_tau11            =  1 / tau11;
      // minus_inv_tau11      = -1 / tau11;
      FLA_Obj_set_to_scalar( FLA_ONE, inv_tau11 );
      FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
      FLA_Copy( inv_tau11, minus_inv_tau11 );
      FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );

      // Save first element of a21_t and set it to one.
      FLA_Copy( a21_t, first_elem );
      FLA_Obj_set_to_scalar( FLA_ONE, a21_t );
  
      // y21 = A22' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y21 );
  
      // z21 = A22 * u21;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
 
      // y21 = y21 - Y20 * ( U20' * u21 ) - U20 * ( Z20' * u21 );
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
  
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
  
      // z21 = z21 - U20 * ( Y20' * u21 ) - Z20 * ( U20' * u21 );
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
  
      // beta      = u21' * z21 / 2;
      // conj_beta = conj(beta);
      FLA_Dotc( FLA_CONJUGATE, a21, z21, beta );
      FLA_Inv_scal( FLA_TWO, beta );
      FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
  
      // y21' = ( y21' - beta / tau * u21' ) / tau;
      // y21  = ( y21 - conj(beta) / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, conj_beta );
      FLA_Axpy( conj_beta, a21, y21 );
      FLA_Scal( inv_tau11, y21 );
  
      // z21 = ( z21 - beta / tau * u21 ) / tau;
      FLA_Scal( minus_inv_tau11, beta );
      FLA_Axpy( beta, a21, z21 );
      FLA_Scal( inv_tau11, z21 );
  
      // a12t = a12t * ( I - u21 * u21' / tau );
      //      = a12t - ( a12t * u21 ) * u21' / tau;
      FLA_Dot( a12t, a21, dot_product );
      FLA_Scal( minus_inv_tau11, dot_product );
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
  
      // A02 = A02 * ( I - u21 * u21' / tau );
      //     = A02 - ( A02 * u21 ) * u21' / tau;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, e0 );
      FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
  
      // t01 = U20' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );

      // Restore first element of a21.
      FLA_Copy( first_elem, a21_t );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &YTL, /**/ &YTR,       Y00,  y01,   /**/ Y02,
                                                     y10t, psi11, /**/ y12t,
                            /* ************** */  /* ********************** */
                              &YBL, /**/ &YBR,       Y20,  y21,   /**/ Y22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &ZTL, /**/ &ZTR,       Z00,  z01,    /**/ Z02,
                                                     z10t, zeta11, /**/ z12t,
                            /* ************** */  /* *********************** */
                              &ZBL, /**/ &ZBR,       Z20,  z21,    /**/ Z22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ************************ */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &dT,                d0, 
                                                  delta1, 
                            /* ** */           /* ****** */
                              &dB,                d2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &eT,                e0, 
                                                  epsilon1, 
                            /* ** */           /* ******** */
                              &eB,                e2,     FLA_TOP );
    FLA_Cont_with_3x1_to_2x1( &fT,                f0, 
                                                  phi1, 
                            /* ** */           /* **** */
                              &fB,                f2,     FLA_TOP );
  }

  FLA_Obj_free( &inv_tau11 );
  FLA_Obj_free( &minus_inv_tau11 );
  FLA_Obj_free( &first_elem );
  FLA_Obj_free( &last_elem );
  FLA_Obj_free( &beta );
  FLA_Obj_free( &conj_beta );
  FLA_Obj_free( &dot_product );
  FLA_Obj_free( &d );
  FLA_Obj_free( &e );
  FLA_Obj_free( &f );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_unb_var5 ( FLA_Obj  A,
FLA_Obj  U,
FLA_Obj  Z,
FLA_Obj  T 
)

References FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dots(), FLA_Gemv(), FLA_Househ2_UT(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trmvsx(), FLA_Trsv(), and FLA_ZERO.

Referenced by FLA_Hess_UT_unb_var5().

{
  FLA_Obj  ATL,   ATR,      A00,  a01,     A02, 
           ABL,   ABR,      a10t, alpha11, a12t,
                            A20,  a21,     A22;
  FLA_Obj  UTL,   UTR,      U00,  u01,       U02, 
           UBL,   UBR,      u10t, upsilon11, u12t,
                            U20,  u21,       U22;
  FLA_Obj  ZTL,   ZTR,      Z00,  z01,    Z02, 
           ZBL,   ZBR,      z10t, zeta11, z12t,
                            Z20,  z21,    Z22;
  FLA_Obj  TTL,   TTR,      T00,  t01,   T02, 
           TBL,   TBR,      t10t, tau11, t12t,
                            T20,  t21,   T22;
  FLA_Obj  wT,              w0,
           wB,              omega1,
                            w2;
  FLA_Obj  w;

  FLA_Obj  a21_t,
           a21_b;
  FLA_Obj  u21_t,
           u21_b;

  FLA_Datatype datatype_A;
  dim_t        m_A;
  dim_t        b_alg;


  b_alg      = FLA_Obj_length( T );

  datatype_A = FLA_Obj_datatype( A );
  m_A        = FLA_Obj_length( A );

  FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );

  FLA_Obj_set_to_scalar( FLA_ZERO, U );
  FLA_Obj_set_to_scalar( FLA_ZERO, Z );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
  FLA_Part_2x2( U,    &UTL, &UTR,
                      &UBL, &UBR,     0, 0, FLA_TL );
  FLA_Part_2x2( Z,    &ZTL, &ZTR,
                      &ZBL, &ZBR,     0, 0, FLA_TL );
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
  FLA_Part_2x1( w,    &wT, 
                      &wB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < b_alg )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( UTL, /**/ UTR,       &U00,  /**/ &u01,       &U02,
                        /* ************* */   /* **************************** */
                                                &u10t, /**/ &upsilon11, &u12t,
                           UBL, /**/ UBR,       &U20,  /**/ &u21,       &U22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( ZTL, /**/ ZTR,       &Z00,  /**/ &z01,    &Z02,
                        /* ************* */   /* ************************* */
                                                &z10t, /**/ &zeta11, &z12t,
                           ZBL, /**/ ZBR,       &Z20,  /**/ &z21,    &Z22,
                           1, 1, FLA_BR );
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************** */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
    FLA_Repart_2x1_to_3x1( wT,                &w0, 
                        /* ** */            /* ****** */
                                              &omega1, 
                           wB,                &w2,        1, FLA_BOTTOM );

    /*------------------------------------------------------------*/

    if ( FLA_Obj_length( ATL ) > 0 )
    {
      // w0 = inv( triu( T00 ) ) * u10t';
      FLA_Copyt( FLA_CONJ_TRANSPOSE, u10t, w0 );
      FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                T00, w0 );

      // a01     = a01     - Z00  * w0;
      // alpha11 = alpha11 - z10t * w0;
      // a21     = a21     - Z20  * w0;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z00, w0, FLA_ONE, a01 );
      FLA_Dots( FLA_MINUS_ONE, z10t, w0, FLA_ONE, alpha11 );
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, w0, FLA_ONE, a21 );
 
      // w0 = inv( triu( T00 ) )' * ( U00' * a01 + u10t' * alpha11 + U20' * a21 );
      FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                  FLA_ONE, U00, a01, FLA_ZERO, w0 );
      FLA_Axpyt( FLA_CONJ_TRANSPOSE, alpha11, u10t, w0 );
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, a21, FLA_ONE, w0 );
      
      FLA_Trsv( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                T00, w0 );
  
      // a01     = a01     - U00  * w0;
      // alpha11 = alpha11 - u10t * w0;
      // a21     = a21     - U20  * w0;
      FLA_Trmvsx( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
                  FLA_MINUS_ONE, U00, w0, FLA_ONE, a01 );
      FLA_Dots( FLA_MINUS_ONE, u10t, w0, FLA_ONE, alpha11 );
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, U20, w0, FLA_ONE, a21 );
    }
 
    if ( FLA_Obj_length( a21 ) > 0 )
    {
      FLA_Part_2x1( a21,    &a21_t,
                            &a21_b,            1, FLA_TOP );

      // [ u21, tau11, a21 ] = House( a21 );
      FLA_Househ2_UT( FLA_LEFT,
                      a21_t,
                      a21_b, tau11 );

      // u21 := a21;
      FLA_Copy( a21, u21 );

      // Explicitly set the first element of the Householder vector so we
      // can use it in regular computations.
      FLA_Part_2x1( u21,    &u21_t,
                            &u21_b,            1, FLA_TOP );
      FLA_Obj_set_to_scalar( FLA_ONE, u21_t );
  
      // z01    = A02  * u21;
      // zeta11 = a12t * u21;
      // z21    = A22  * u21;
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, u21, FLA_ZERO, z01 );
      FLA_Dot( a12t, u21, zeta11 );
      FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, u21, FLA_ZERO, z21 );
  
      // t01 = U20' * u21;
      FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, U20, u21, FLA_ZERO, t01 );
    }

    /*------------------------------------------------------------*/

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR,       U00,  u01,       /**/ U02,
                                                     u10t, upsilon11, /**/ u12t,
                            /* ************** */  /* ************************** */
                              &UBL, /**/ &UBR,       U20,  u21,       /**/ U22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &ZTL, /**/ &ZTR,       Z00,  z01,    /**/ Z02,
                                                     z10t, zeta11, /**/ z12t,
                            /* ************** */  /* *********************** */
                              &ZBL, /**/ &ZBR,       Z20,  z21,    /**/ Z22,
                              FLA_TL );
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ************************ */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
    FLA_Cont_with_3x1_to_2x1( &wT,                w0, 
                                                  omega1, 
                            /* ** */           /* ****** */
                              &wB,                w2,     FLA_TOP );
  }

  FLA_Obj_free( &w );

  return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_unb_var1 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_unb_var1().

Referenced by FLA_Hess_UT_internal().

{
  return FLA_Hess_UT_step_unb_var1( A, T );
}
FLA_Error FLA_Hess_UT_unb_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_unb_var2().

Referenced by FLA_Hess_UT_internal().

{
  return FLA_Hess_UT_step_unb_var2( A, T );
}
FLA_Error FLA_Hess_UT_unb_var3 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_unb_var3().

Referenced by FLA_Hess_UT_internal().

{
  return FLA_Hess_UT_step_unb_var3( A, T );
}
FLA_Error FLA_Hess_UT_unb_var4 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_unb_var4(), FLA_Obj_create_conf_to(), and FLA_Obj_free().

Referenced by FLA_Hess_UT_internal().

{
  FLA_Error r_val;
  FLA_Obj   Y, Z;

  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Y );
  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );

  r_val = FLA_Hess_UT_step_unb_var4( A, Y, Z, T );

  FLA_Obj_free( &Y );
  FLA_Obj_free( &Z );

  return r_val;
}
FLA_Error FLA_Hess_UT_unb_var5 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Hess_UT_step_unb_var5(), FLA_Obj_create_conf_to(), and FLA_Obj_free().

Referenced by FLA_Hess_UT_internal().

{
  FLA_Error r_val;
  FLA_Obj   U, Z;

  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &U );
  FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );

  r_val = FLA_Hess_UT_step_unb_var5( A, U, Z, T );

  FLA_Obj_free( &U );
  FLA_Obj_free( &Z );

  return r_val;
}