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Functions
FLA_LQ_UT_vars.h File Reference

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Functions

FLA_Error FLA_LQ_UT_unb_var1 (FLA_Obj A, FLA_Obj t)
FLA_Error FLA_LQ_UT_blk_var1 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)
FLA_Error FLA_LQ_UT_opt_var1 (FLA_Obj A, FLA_Obj t)
FLA_Error FLA_LQ_UT_ops_var1 (int m_A, int n_A, float *A, int rs_A, int cs_A, float *t, int inc_t)
FLA_Error FLA_LQ_UT_opd_var1 (int m_A, int n_A, double *A, int rs_A, int cs_A, double *t, int inc_t)
FLA_Error FLA_LQ_UT_opc_var1 (int m_A, int n_A, scomplex *A, int rs_A, int cs_A, scomplex *t, int inc_t)
FLA_Error FLA_LQ_UT_opz_var1 (int m_A, int n_A, dcomplex *A, int rs_A, int cs_A, dcomplex *t, int inc_t)
FLA_Error FLA_LQ_UT_unb_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_LQ_UT_blk_var2 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)
FLA_Error FLA_LQ_UT_opt_var2 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_LQ_UT_ops_var2 (int m_A, int n_A, float *A, int rs_A, int cs_A, float *T, int rs_T, int cs_T)
FLA_Error FLA_LQ_UT_opd_var2 (int m_A, int n_A, double *A, int rs_A, int cs_A, double *T, int rs_T, int cs_T)
FLA_Error FLA_LQ_UT_opc_var2 (int m_A, int n_A, scomplex *A, int rs_A, int cs_A, scomplex *T, int rs_T, int cs_T)
FLA_Error FLA_LQ_UT_opz_var2 (int m_A, int n_A, dcomplex *A, int rs_A, int cs_A, dcomplex *T, int rs_T, int cs_T)
FLA_Error FLA_LQ_UT_blk_var3 (FLA_Obj A, FLA_Obj T, fla_lqut_t *cntl)

Function Documentation

FLA_Error FLA_LQ_UT_blk_var1 ( FLA_Obj  A,
FLA_Obj  T,
fla_lqut_t cntl 
)

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_LQ_UT_internal().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj TL,    TR,       T0,  T1,  W12;

  FLA_Obj T1T,   T2B;

  FLA_Obj AR1,   AR2;

  dim_t   b_alg, b;

  // Query the algorithmic blocksize by inspecting the length of T.
  b_alg = FLA_Obj_length( T );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT );

  while ( FLA_Obj_min_dim( ABR ) > 0 ){

    b = min( b_alg, FLA_Obj_min_dim( ABR ) );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );

    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &W12,
                           b, FLA_RIGHT );

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

    FLA_Part_2x1( T1,   &T1T,
                        &T2B,    b, FLA_TOP );

    FLA_Merge_1x2( A11, A12,   &AR1 );

    // Perform an LQ factorization via the UT transform on AR1:
    //
    //   ( A11 A12 ) -> L11 QR1
    //
    // where:
    //  - QR1 is formed from UR1 (which is stored row-wise above the
    //    diagonal of AR1) and T11 (which is stored to the upper triangle
    //    of T11).
    //  - L11 is stored to the lower triangle of AR1.
  
    FLA_LQ_UT_internal( AR1, T1T, 
                        FLA_Cntl_sub_lqut( cntl ));


    if ( FLA_Obj_length( A21 ) > 0 )
    {
      FLA_Merge_1x2( A21, A22,   &AR2 );

      // Apply the Householder transforms associated with UR1 and T11 to 
      // AR2:
      //
      //   ( A21 A22 ) := ( A21 A22 ) Q1
      //
      // where QR1 is formed from UR1 and T11.

      FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE,
                               AR1, T1T, W12, AR2,
                               FLA_Cntl_sub_apqut( cntl ) );
    }

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );

    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ W12,
                              FLA_LEFT );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_blk_var2 ( FLA_Obj  A,
FLA_Obj  T,
fla_lqut_t cntl 
)

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trmm_external().

Referenced by FLA_LQ_UT_internal().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj TTL,   TTR,      T00, T01, T02, 
          TBL,   TBR,      T10, T11, W12,
                           T20, T21, T22;

  FLA_Obj AR1,
          AR2;

  dim_t   b;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );

  while ( FLA_Obj_min_dim( ABR ) > 0 ){

    b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );

    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00, /**/ &T01, &T02,
                        /* ************* */   /* ******************** */
                                                &T10, /**/ &T11, &W12,
                           TBL, /**/ TBR,       &T20, /**/ &T21, &T22,
                           b, b, FLA_BR );

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

    FLA_Merge_1x2( A11, A12,   &AR1 );

    // Perform an LQ factorization via the UT transform on AR1:
    //
    //   ( A11 A12 ) -> L11 QR1
    //
    // where:
    //  - QR1 is formed from UR1 (which is stored row-wise above the
    //    diagonal of AR1) and T11 (which is stored to the upper triangle
    //    of T11).
    //  - L11 is stored to the lower triangle of AR1.
  
    FLA_LQ_UT_internal( AR1, T11, 
                        FLA_Cntl_sub_lqut( cntl ) );


    if ( FLA_Obj_length( A21 ) > 0 )
    {
      FLA_Merge_1x2( A21, A22,   &AR2 );

      // Apply the Householder transforms associated with UR1 and T11 to 
      // AR2:
      //
      //   ( A21 A22 ) := ( A21 A22 ) Q1
      //
      // where QR1 is formed from UR1 and T11.

      FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE,
                               AR1, T11, W12, AR2,
                               FLA_Cntl_sub_apqut( cntl ) );
    }


    // Update T
    //
    // T01 = conj(A01) * U11^T + conj(A02) * U12^T;
    //
    // Recall: U11 = triuu( A11 );
    //         U12 = A12;

    FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, A01, T01 );
    FLA_Trmm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
                       FLA_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, A11, T01 );
    FLA_Gemm_external( FLA_CONJ_NO_TRANSPOSE, FLA_TRANSPOSE, 
                       FLA_ONE, A02, A12, FLA_ONE, T01 );

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );

    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00, T01, /**/ T02,
                                                     T10, T11, /**/ W12,
                            /* ************** */  /* ****************** */
                              &TBL, /**/ &TBR,       T20, T21, /**/ T22,
                              FLA_TL );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_blk_var3 ( FLA_Obj  A,
FLA_Obj  T,
fla_lqut_t cntl 
)

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_LQ_UT_internal(), FLA_Merge_1x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Part_2x2(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_LQ_UT_internal().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj TWTL,  TWTR,     TW00, TW01, TW02, 
          TWBL,  TWBR,     TW10,  T11,  W12,
                           TW20, TW21, TW22;

  FLA_Obj AR1,
          AR2;

  dim_t   b;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  FLA_Part_2x2( TW,   &TWTL, &TWTR,
                      &TWBL, &TWBR,     0, 0, FLA_TL );

  while ( FLA_Obj_min_dim( ABR ) > 0 ){

    b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );

    FLA_Repart_2x2_to_3x3( TWTL, /**/ TWTR,     &TW00, /**/ &TW01, &TW02,
                        /* ************* */   /* ******************** */
                                                &TW10, /**/  &T11,  &W12,
                           TWBL, /**/ TWBR,     &TW20, /**/ &TW21, &TW22,
                           b, b, FLA_BR );

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

    FLA_Merge_1x2( A11, A12,   &AR1 );

    // Perform an LQ factorization via the UT transform on AR1:
    //
    //   ( A11 A12 ) -> L11 QR1
    //
    // where:
    //  - QR1 is formed from UR1 (which is stored row-wise above the
    //    diagonal of AR1) and T11 (which is stored to the upper triangle
    //    of T11).
    //  - L11 is stored to the lower triangle of AR1.
  
    FLA_LQ_UT_internal( AR1, T11, 
                        FLA_Cntl_sub_lqut( cntl ) );


    if ( FLA_Obj_length( A21 ) > 0 )
    {
      FLA_Merge_1x2( A21, A22,   &AR2 );

      // Apply the Householder transforms associated with UR1 and T11 to 
      // AR2:
      //
      //   ( A21 A22 ) := ( A21 A22 ) Q1
      //
      // where QR1 is formed from UR1 and T11.

      FLA_Apply_Q_UT_internal( FLA_RIGHT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE,
                               AR1, T11, W12, AR2,
                               FLA_Cntl_sub_apqut( cntl ) );
    }

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );

    FLA_Cont_with_3x3_to_2x2( &TWTL, /**/ &TWTR,     TW00, TW01, /**/ TW02,
                                                     TW10,  T11, /**/  W12,
                            /* ************** */  /* ****************** */
                              &TWBL, /**/ &TWBR,     TW20, TW21, /**/ TW22,
                              FLA_TL );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opc_var1 ( int  m_A,
int  n_A,
scomplex A,
int  rs_A,
int  cs_A,
scomplex t,
int  inc_t 
)

References FLA_Apply_H2_UT_r_opc_var1(), and FLA_Househ2_UT_r_opc().

Referenced by FLA_LQ_UT_opt_var1().

{
  int min_m_n = min( m_A, n_A );
  int i;

  for ( i = 0; i < min_m_n; ++i )
  {
    scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*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* tau1     = buff_t + (i  )*inc_t;

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau1 );
    FLA_Househ2_UT_r_opc( n_ahead,
                          alpha11,
                          a12t, cs_A,
                          tau1 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_opc_var1( m_ahead,
                                n_ahead,
                                tau1,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opc_var2 ( int  m_A,
int  n_A,
scomplex A,
int  rs_A,
int  cs_A,
scomplex T,
int  rs_T,
int  cs_T 
)

References bli_ccopyv(), bli_cgemv(), FLA_Apply_H2_UT_r_opc_var1(), FLA_Househ2_UT_r_opc(), and FLA_ONE.

Referenced by FLA_LQ_UT_opt_var2().

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

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

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau11 );
    FLA_Househ2_UT_r_opc( n_ahead,
                          alpha11,
                          a12t, cs_A,
                          tau11 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_opc_var1( m_ahead,
                                n_ahead,
                                tau11,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

    // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 );
    bli_ccopyv( BLIS_CONJUGATE,
                m_behind,
                a01, rs_A,
                t01, rs_T );

    // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE,
    //                     FLA_ONE, A02, a12t, FLA_ONE, t01 );
    bli_cgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_behind,
               n_ahead,
               buff_1,
               A02, rs_A, cs_A,
               a12t, cs_A,
               buff_1,
               t01, rs_T );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opd_var1 ( int  m_A,
int  n_A,
double *  A,
int  rs_A,
int  cs_A,
double *  t,
int  inc_t 
)

References FLA_Apply_H2_UT_r_opd_var1(), and FLA_Househ2_UT_r_opd().

Referenced by FLA_LQ_UT_opt_var1().

{
  int min_m_n = min( m_A, n_A );
  int i;

  for ( i = 0; i < min_m_n; ++i )
  {
    double* alpha11 = buff_A + (i  )*cs_A + (i  )*rs_A;
    double* a21     = buff_A + (i  )*cs_A + (i+1)*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* tau1    = buff_t + (i  )*inc_t;

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau1 );
    FLA_Househ2_UT_r_opd( n_ahead,
                          alpha11,
                          a12t, cs_A,
                          tau1 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_opd_var1( m_ahead,
                                n_ahead,
                                tau1,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opd_var2 ( int  m_A,
int  n_A,
double *  A,
int  rs_A,
int  cs_A,
double *  T,
int  rs_T,
int  cs_T 
)

References bli_dcopyv(), bli_dgemv(), FLA_Apply_H2_UT_r_opd_var1(), FLA_Househ2_UT_r_opd(), and FLA_ONE.

Referenced by FLA_LQ_UT_opt_var2().

{
  double* buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  int     min_m_n = min( m_A, n_A );
  int     i;

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

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau11 );
    FLA_Househ2_UT_r_opd( n_ahead,
                        alpha11,
                        a12t, cs_A,
                        tau11 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_opd_var1( m_ahead,
                                n_ahead,
                                tau11,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

    // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 );
    bli_dcopyv( BLIS_CONJUGATE,
                m_behind,
                a01, rs_A,
                t01, rs_T );

    // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE,
    //                     FLA_ONE, A02, a12t, FLA_ONE, t01 );
    bli_dgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_behind,
               n_ahead,
               buff_1,
               A02, rs_A, cs_A,
               a12t, cs_A,
               buff_1,
               t01, rs_T );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_ops_var1 ( int  m_A,
int  n_A,
float *  A,
int  rs_A,
int  cs_A,
float *  t,
int  inc_t 
)

References FLA_Apply_H2_UT_r_ops_var1(), and FLA_Househ2_UT_r_ops().

Referenced by FLA_LQ_UT_opt_var1().

{
  int min_m_n = min( m_A, n_A );
  int i;

  for ( i = 0; i < min_m_n; ++i )
  {
    float* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    float* a21      = buff_A + (i  )*cs_A + (i+1)*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* tau1     = buff_t + (i  )*inc_t;

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau1 );
    FLA_Househ2_UT_r_ops( n_ahead,
                          alpha11,
                          a12t, cs_A,
                          tau1 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_ops_var1( m_ahead,
                                n_ahead,
                                tau1,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_ops_var2 ( int  m_A,
int  n_A,
float *  A,
int  rs_A,
int  cs_A,
float *  T,
int  rs_T,
int  cs_T 
)

References bli_scopyv(), bli_sgemv(), FLA_Apply_H2_UT_r_ops_var1(), FLA_Househ2_UT_r_ops(), and FLA_ONE.

Referenced by FLA_LQ_UT_opt_var2().

{
  float* buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  int    min_m_n = min( m_A, n_A );
  int    i;

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

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau11 );
    FLA_Househ2_UT_r_ops( n_ahead,
                          alpha11,
                          a12t, cs_A,
                          tau11 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_ops_var1( m_ahead,
                                n_ahead,
                                tau11,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

    // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 );
    bli_scopyv( BLIS_CONJUGATE,
                m_behind,
                a01, rs_A,
                t01, rs_T );

    // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE,
    //                     FLA_ONE, A02, a12t, FLA_ONE, t01 );
    bli_sgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_behind,
               n_ahead,
               buff_1,
               A02, rs_A, cs_A,
               a12t, cs_A,
               buff_1,
               t01, rs_T );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opt_var1 ( FLA_Obj  A,
FLA_Obj  t 
)

References FLA_LQ_UT_opc_var1(), FLA_LQ_UT_opd_var1(), FLA_LQ_UT_ops_var1(), FLA_LQ_UT_opz_var1(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_vector_inc(), and FLA_Obj_width().

Referenced by FLA_LQ_UT_internal().

{
  FLA_Datatype datatype;
  int          m_A, n_A;
  int          rs_A, cs_A;
  int          inc_t;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  n_A      = FLA_Obj_width( A );
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  inc_t    = FLA_Obj_vector_inc( t );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_t = FLA_FLOAT_PTR( t );

      FLA_LQ_UT_ops_var1( m_A,
                          n_A,
                          buff_A, rs_A, cs_A,
                          buff_t, inc_t );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_t = FLA_DOUBLE_PTR( t );

      FLA_LQ_UT_opd_var1( m_A,
                          n_A,
                          buff_A, rs_A, cs_A,
                          buff_t, inc_t );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_t = FLA_COMPLEX_PTR( t );

      FLA_LQ_UT_opc_var1( m_A,
                          n_A,
                          buff_A, rs_A, cs_A,
                          buff_t, inc_t );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_t = FLA_DOUBLE_COMPLEX_PTR( t );

      FLA_LQ_UT_opz_var1( m_A,
                          n_A,
                          buff_A, rs_A, cs_A,
                          buff_t, inc_t );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opt_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_LQ_UT_opc_var2(), FLA_LQ_UT_opd_var2(), FLA_LQ_UT_ops_var2(), FLA_LQ_UT_opz_var2(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), and FLA_Obj_width().

Referenced by FLA_LQ_UT_internal().

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

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  n_A      = FLA_Obj_width( A );
  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_LQ_UT_ops_var2( m_A,
                          n_A,
                          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_LQ_UT_opd_var2( m_A,
                          n_A,
                          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_LQ_UT_opc_var2( m_A,
                          n_A,
                          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_LQ_UT_opz_var2( m_A,
                          n_A,
                          buff_A, rs_A, cs_A,
                          buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opz_var1 ( int  m_A,
int  n_A,
dcomplex A,
int  rs_A,
int  cs_A,
dcomplex t,
int  inc_t 
)

References FLA_Apply_H2_UT_r_opz_var1(), and FLA_Househ2_UT_r_opz().

Referenced by FLA_LQ_UT_opt_var1().

{
  int min_m_n = min( m_A, n_A );
  int i;

  for ( i = 0; i < min_m_n; ++i )
  {
    dcomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*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* tau1     = buff_t + (i  )*inc_t;

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau1 );
    FLA_Househ2_UT_r_opz( n_ahead,
                          alpha11,
                          a12t, cs_A,
                          tau1 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_opz_var1( m_ahead,
                                n_ahead,
                                tau1,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_opz_var2 ( int  m_A,
int  n_A,
dcomplex A,
int  rs_A,
int  cs_A,
dcomplex T,
int  rs_T,
int  cs_T 
)

References bli_zcopyv(), bli_zgemv(), FLA_Apply_H2_UT_r_opz_var1(), FLA_Househ2_UT_r_opz(), and FLA_ONE.

Referenced by FLA_LQ_UT_opt_var2().

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

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

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

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

    // FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t
    //                 tau11 );
    FLA_Househ2_UT_r_opz( n_ahead,
                          alpha11,
                          a12t, cs_A,
                          tau11 );

    // FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 );
    FLA_Apply_H2_UT_r_opz_var1( m_ahead,
                                n_ahead,
                                tau11,
                                a12t, cs_A,
                                a21, rs_A,
                                A22, rs_A, cs_A );

    // FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 );
    bli_zcopyv( BLIS_CONJUGATE,
                m_behind,
                a01, rs_A,
                t01, rs_T );

    // FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE,
    //                     FLA_ONE, A02, a12t, FLA_ONE, t01 );
    bli_zgemv( BLIS_CONJ_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_behind,
               n_ahead,
               buff_1,
               A02, rs_A, cs_A,
               a12t, cs_A,
               buff_1,
               t01, rs_T );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_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_Househ2_UT(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_LQ_UT_internal().

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;

  FLA_Obj tLt,   tRt,      t0t,  tau1,  t2t;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  FLA_Part_1x2( t,    &tLt,  &tRt,      0, FLA_LEFT );

  while ( FLA_Obj_min_dim( ABR ) > 0 ){

    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( tLt,  /**/ tRt,      &t0t, /**/ &tau1, &t2t,
                           1, FLA_RIGHT );

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

    // Compute tau11 and u12t from alpha11 and a12t such that tau11 and u12t
    // determine a Householder transform H such that applying H from the
    // right to the row vector consisting of alpha11 and a12t annihilates
    // the entries in a12t (and updates alpha11).
    FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t,
                    tau1 );

    // ( a21 A22 ) = ( a21 A22 ) H
    //
    // where H is formed from tau11 and u12t.
    FLA_Apply_H2_UT( FLA_RIGHT, tau1, a12t, a21, 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_1x3_to_1x2( &tLt,  /**/ &tRt,      t0t, tau1, /**/ t2t,
                              FLA_LEFT );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LQ_UT_unb_var2 ( FLA_Obj  A,
FLA_Obj  T 
)

References FLA_Apply_H2_UT(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemvc_external(), FLA_Househ2_UT(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_LQ_UT_internal().

{
  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_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );

  while ( FLA_Obj_min_dim( ABR ) > 0 ){

    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 );

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

    // Compute tau11 and u12t from alpha11 and a12t such that tau11 and u12t
    // determine a Householder transform H such that applying H from the
    // right to the row vector consisting of alpha11 and a12t annihilates
    // the entries in a12t (and updates alpha11).
    FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t,
                    tau11 );

    // ( a21 A22 ) = ( a21 A22 ) H
    //
    // where H is formed from tau11 and u12t.
    FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 );

    // t01 = conj(a01) + conj(A02) * u12t^T;
    FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 );
    FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE, FLA_ONE, A02, a12t, FLA_ONE, 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( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ********************** */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );

  }

  return FLA_SUCCESS;
}