libflame revision_anchor
Functions
FLA_LU_piv_vars.h File Reference

(r)

Go to the source code of this file.

Functions

FLA_Error FLA_LU_piv_blk_var3 (FLA_Obj A, FLA_Obj p, fla_lu_t *cntl)
FLA_Error FLA_LU_piv_blk_var4 (FLA_Obj A, FLA_Obj p, fla_lu_t *cntl)
FLA_Error FLA_LU_piv_blk_var5 (FLA_Obj A, FLA_Obj p, fla_lu_t *cntl)
FLA_Error FLA_LU_piv_unb_var3 (FLA_Obj A, FLA_Obj p)
FLA_Error FLA_LU_piv_unb_var3b (FLA_Obj A, FLA_Obj p)
FLA_Error FLA_LU_piv_unb_var4 (FLA_Obj A, FLA_Obj p)
FLA_Error FLA_LU_piv_unb_var5 (FLA_Obj A, FLA_Obj p)
FLA_Error FLA_LU_piv_opt_var3 (FLA_Obj A, FLA_Obj p)
FLA_Error FLA_LU_piv_ops_var3 (int m_A, int n_A, float *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opd_var3 (int m_A, int n_A, double *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opc_var3 (int m_A, int n_A, scomplex *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opz_var3 (int m_A, int n_A, dcomplex *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opt_var4 (FLA_Obj A, FLA_Obj p)
FLA_Error FLA_LU_piv_ops_var4 (int m_A, int n_A, float *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opd_var4 (int m_A, int n_A, double *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opc_var4 (int m_A, int n_A, scomplex *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opz_var4 (int m_A, int n_A, dcomplex *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opt_var5 (FLA_Obj A, FLA_Obj p)
FLA_Error FLA_LU_piv_ops_var5 (int m_A, int n_A, float *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opd_var5 (int m_A, int n_A, double *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opc_var5 (int m_A, int n_A, scomplex *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)
FLA_Error FLA_LU_piv_opz_var5 (int m_A, int n_A, dcomplex *buff_A, int rs_A, int cs_A, int *buff_p, int inc_p)

Function Documentation

FLA_Error FLA_LU_piv_blk_var3 ( FLA_Obj  A,
FLA_Obj  p,
fla_lu_t cntl 
)

References FLA_Apply_pivots_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Gemm_internal(), FLA_LU_piv_internal(), FLA_Merge_2x1(), FLA_MINUS_ONE, 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_Trsm_internal().

Referenced by FLA_LU_piv_internal().

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

  FLA_Obj AL,    AR,       A0,  A1,  A2;

  FLA_Obj pT,              p0,
          pB,              p1,
                           p2;

  FLA_Obj AB0, AB1;

  dim_t b;


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

  FLA_Part_1x2( A,    &AL,  &AR,      0, FLA_LEFT );

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    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_1x2_to_1x3( AL,  /**/ AR,        &A0, /**/ &A1, &A2,
                           b, FLA_RIGHT );

    FLA_Repart_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* ** */
                                              &p1, 
                           pB,                &p2,        b, FLA_BOTTOM );

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

    // Apply previously computed pivots
    FLA_Apply_pivots_internal( FLA_LEFT, FLA_NO_TRANSPOSE, p0, A1,
                               FLA_Cntl_sub_appiv1( cntl ) );

    // A01 = trilu( A00 ) \ A10 
    FLA_Trsm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, A00, A01,
                       FLA_Cntl_sub_trsm1( cntl ) );

    // A11 = A11 - A10 * A01
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_MINUS_ONE, A10, A01, FLA_ONE, A11,
                       FLA_Cntl_sub_gemm1( cntl ) );

    // A21 = A21 - A20 * A01
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_MINUS_ONE, A20, A01, FLA_ONE, A21,
                       FLA_Cntl_sub_gemm2( cntl ) );

    // AB1 = / A11 \
    //       \ A21 /
    FLA_Merge_2x1( A11,
                   A21,      &AB1 );

    // AB1, p1 = LU_piv( AB1 )
    FLA_LU_piv_internal( AB1, p1, 
                         FLA_Cntl_sub_lu( cntl ) );

    // AB0 = / A10 \
    //       \ A20 /
    FLA_Merge_2x1( A10,
                   A20,      &AB0 );

    // Apply pivots to previous columns
    FLA_Apply_pivots_internal( FLA_LEFT, FLA_NO_TRANSPOSE, p1, AB0,
                               FLA_Cntl_sub_appiv2( 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( &AL,  /**/ &AR,        A0, A1, /**/ A2,
                              FLA_LEFT );

    FLA_Cont_with_3x1_to_2x1( &pT,                p0, 
                                                  p1, 
                            /* ** */           /* ** */
                              &pB,                p2,     FLA_TOP );

  }

  if ( FLA_Obj_width( ATR ) > 0 )
  {
    /* Apply pivots to untouched columns */
    FLA_Apply_pivots_internal( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR,
                               FLA_Cntl_sub_appiv1( cntl ) );

    /* ATR = trilu( ATL ) \ ATR */ 
    FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, ATL, ATR );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_blk_var4 ( FLA_Obj  A,
FLA_Obj  p,
fla_lu_t cntl 
)

References FLA_Apply_pivots_internal(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Gemm_internal(), FLA_LU_piv_internal(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), and FLA_Trsm_internal().

Referenced by FLA_LU_piv_internal().

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

  FLA_Obj pT,              p0,
          pB,              p1,
                           p2;

  FLA_Obj AB0, AB1, AB2;

  dim_t b;


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

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    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_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* ** */
                                              &p1, 
                           pB,                &p2,        b, FLA_BOTTOM );

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

    // A11 = A11 - A10 * A0
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_MINUS_ONE, A10, A01, FLA_ONE, A11,
                       FLA_Cntl_sub_gemm1( cntl ) );

    // A21 = A21 - A20 * A01
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_MINUS_ONE, A20, A01, FLA_ONE, A21,
                       FLA_Cntl_sub_gemm3( cntl ) );

    // AB1 = / A11 \
    //       \ A21 /
    FLA_Merge_2x1( A11,
                   A21,      &AB1 );

    // AB1, p1 = LU_piv( AB1 )
    FLA_LU_piv_internal( AB1, p1, 
                         FLA_Cntl_sub_lu( cntl ) );

    // AB0 = / A10 \
    //       \ A20 /
    FLA_Merge_2x1( A10,
                   A20,      &AB0 );

    // AB2 = / A12 \
    //       \ A22 /
    FLA_Merge_2x1( A12,
                   A22,      &AB2 );

    // Apply pivots to remaining columns
    FLA_Apply_pivots_internal( FLA_LEFT, FLA_NO_TRANSPOSE, p1, AB0,
                               FLA_Cntl_sub_appiv1( cntl ) );
    FLA_Apply_pivots_internal( FLA_LEFT, FLA_NO_TRANSPOSE, p1, AB2,
                               FLA_Cntl_sub_appiv1( cntl ) );

    // A12 = A12 - A10 * A02
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_MINUS_ONE, A10, A02, FLA_ONE, A12,
                       FLA_Cntl_sub_gemm2( cntl ) );

    // A12 = trilu( A11 ) \ A12 
    FLA_Trsm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, A11, A12,
                       FLA_Cntl_sub_trsm1( 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_3x1_to_2x1( &pT,                p0, 
                                                  p1, 
                            /* ** */           /* ** */
                              &pB,                p2,     FLA_TOP );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_blk_var5 ( FLA_Obj  A,
FLA_Obj  p,
fla_lu_t cntl 
)

References FLA_Apply_pivots_internal(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Gemm_internal(), FLA_LU_piv_internal(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), and FLA_Trsm_internal().

Referenced by FLA_LU_piv_internal().

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

  FLA_Obj pT,              p0,
          pB,              p1,
                           p2;

  FLA_Obj AB0, AB1, AB2;

  dim_t b;


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

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    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_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* ** */
                                              &p1, 
                           pB,                &p2,        b, FLA_BOTTOM );

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

    // AB1 = / A11 \
    //       \ A21 /
    FLA_Merge_2x1( A11,
                   A21,      &AB1 );

    // AB1, p1 = LU_piv( AB1 )
    FLA_LU_piv_internal( AB1, p1, 
                         FLA_Cntl_sub_lu( cntl ) );

    // AB0 = / A10 \
    //       \ A20 /
    FLA_Merge_2x1( A10,
                   A20,      &AB0 );

    // Apply computed pivots to AB0
    FLA_Apply_pivots_internal( FLA_LEFT, FLA_NO_TRANSPOSE, p1, AB0,
                               FLA_Cntl_sub_appiv1( cntl ) );

    // AB2 = / A12 \
    //       \ A22 /
    FLA_Merge_2x1( A12,
                   A22,      &AB2 );

    // Apply computed pivots to AB2
    FLA_Apply_pivots_internal( FLA_LEFT, FLA_NO_TRANSPOSE, p1, AB2,
                               FLA_Cntl_sub_appiv1( cntl ) );

    // A12 = trilu( A11 ) \ A12
    FLA_Trsm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, A11, A12,
                       FLA_Cntl_sub_trsm1( cntl ) );

    // A22 = A22 - A21 * A12
    FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
                       FLA_MINUS_ONE, A21, A12, FLA_ONE, A22,
                       FLA_Cntl_sub_gemm1( 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_3x1_to_2x1( &pT,                p0, 
                                                  p1, 
                            /* ** */           /* ** */
                              &pB,                p2,     FLA_TOP );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opc_var3 ( int  m_A,
int  n_A,
scomplex buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_camax(), bli_cdots(), bli_cgemv(), bli_cinvscalv(), bli_ctrsm(), bli_ctrsv(), FLA_Apply_pivots_ln_opc_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var3().

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    scomplex* A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    scomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    scomplex* A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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* a1        = buff_A + (i  )*cs_A + (0  )*rs_A;

    int*      p0        = buff_p;
    int*      pi1       = buff_p + i*inc_p;

    int       m_ahead   = m_A - i - 1;
    int       mn_behind = i;

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

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p0, a1 );
    FLA_Apply_pivots_ln_opc_var1( 1,
                                  a1, rs_A, cs_A,
                                  0,
                                  mn_behind - 1,
                                  p0, inc_p );

    // FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );
    bli_ctrsv( BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_cdots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_cgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_camax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_opc_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_cinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_opc_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

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

  }

  if ( m_A < n_A )
  {
    scomplex* ATL = buff_A;
    scomplex* ATR = buff_A + m_A*cs_A;

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR );
    FLA_Apply_pivots_ln_opc_var1( n_A - m_A,
                                  ATR, rs_A, cs_A,
                                  0,
                                  m_A - 1,
                                  buff_p, inc_p );

    // FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR,
    //                    FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
    //                    FLA_ONE, ATL, ATR );
    bli_ctrsm( BLIS_LEFT,
               BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               m_A,
               n_A - m_A,
               buff_1,
               ATL, rs_A, cs_A,
               ATR, rs_A, cs_A );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opc_var4 ( int  m_A,
int  n_A,
scomplex buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_camax(), bli_cdots(), bli_cgemv(), bli_cinvscalv(), FLA_Apply_pivots_ln_opc_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var4().

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    scomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    scomplex* A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_cdots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_cgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_camax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_opc_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_opc_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a12t,
    //                A22,      &AB2 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB2 );
    FLA_Apply_pivots_ln_opc_var1( n_ahead,
                                  a12t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Gemv_external( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, a10t, FLA_ONE, a12t );
    bli_cgemv( BLIS_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               mn_behind,
               n_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_cinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opc_var5 ( int  m_A,
int  n_A,
scomplex buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_camax(), bli_cger(), bli_cinvscalv(), FLA_Apply_pivots_ln_opc_var1(), and FLA_MINUS_ONE.

Referenced by FLA_LU_piv_opt_var5().

{
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    scomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_camax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Merge_1x2( ABL, ABR,      &AB );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB );
    FLA_Apply_pivots_ln_opc_var1( n_A,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_cinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Ger_external( FLA_MINUS_ONE, a21, a12t, A22 );
    bli_cger( BLIS_NO_CONJUGATE,
              BLIS_NO_CONJUGATE,
              m_ahead,
              n_ahead,
              buff_m1,
              a21, rs_A,
              a12t, cs_A,
              A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opd_var3 ( int  m_A,
int  n_A,
double *  buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_damax(), bli_ddots(), bli_dgemv(), bli_dinvscalv(), bli_dtrsm(), bli_dtrsv(), FLA_Apply_pivots_ln_opd_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var3().

{
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    double*   A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    double*   a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    double*   A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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*   a1        = buff_A + (i  )*cs_A + (0  )*rs_A;

    int*      p0        = buff_p;
    int*      pi1       = buff_p + i*inc_p;

    int       m_ahead   = m_A - i - 1;
    int       mn_behind = i;

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

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p0, a1 );
    FLA_Apply_pivots_ln_opd_var1( 1,
                                  a1, rs_A, cs_A,
                                  0,
                                  mn_behind - 1,
                                  p0, inc_p );

    // FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );
    bli_dtrsv( BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_ddots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_dgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_damax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_opd_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_dinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_opd_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

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

  }

  if ( m_A < n_A )
  {
    double*   ATL = buff_A;
    double*   ATR = buff_A + m_A*cs_A;

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR );
    FLA_Apply_pivots_ln_opd_var1( n_A - m_A,
                                  ATR, rs_A, cs_A,
                                  0,
                                  m_A - 1,
                                  buff_p, inc_p );

    // FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR,
    //                    FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
    //                    FLA_ONE, ATL, ATR );
    bli_dtrsm( BLIS_LEFT,
               BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               m_A,
               n_A - m_A,
               buff_1,
               ATL, rs_A, cs_A,
               ATR, rs_A, cs_A );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opd_var4 ( int  m_A,
int  n_A,
double *  buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_damax(), bli_ddots(), bli_dgemv(), bli_dinvscalv(), FLA_Apply_pivots_ln_opd_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var4().

{
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    double*   a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    double*   A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_ddots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_dgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_damax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_opd_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_opd_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a12t,
    //                A22,      &AB2 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB2 );
    FLA_Apply_pivots_ln_opd_var1( n_ahead,
                                  a12t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Gemv_external( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, a10t, FLA_ONE, a12t );
    bli_dgemv( BLIS_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               mn_behind,
               n_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_dinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opd_var5 ( int  m_A,
int  n_A,
double *  buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_damax(), bli_dger(), bli_dinvscalv(), FLA_Apply_pivots_ln_opd_var1(), and FLA_MINUS_ONE.

Referenced by FLA_LU_piv_opt_var5().

{
  double*   buff_m1 = FLA_DOUBLE_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    double*   a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_damax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Merge_1x2( ABL, ABR,      &AB );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB );
    FLA_Apply_pivots_ln_opd_var1( n_A,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_dinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Ger_external( FLA_MINUS_ONE, a21, a12t, A22 );
    bli_dger( BLIS_NO_CONJUGATE,
              BLIS_NO_CONJUGATE,
              m_ahead,
              n_ahead,
              buff_m1,
              a21, rs_A,
              a12t, cs_A,
              A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_ops_var3 ( int  m_A,
int  n_A,
float *  buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_samax(), bli_sdots(), bli_sgemv(), bli_sinvscalv(), bli_strsm(), bli_strsv(), FLA_Apply_pivots_ln_ops_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var3().

{
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    float*    A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    float*    a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    float*    A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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*    a1        = buff_A + (i  )*cs_A + (0  )*rs_A;

    int*      p0        = buff_p;
    int*      pi1       = buff_p + i*inc_p;

    int       m_ahead   = m_A - i - 1;
    int       mn_behind = i;

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

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p0, a1 );
    FLA_Apply_pivots_ln_ops_var1( 1,
                                  a1, rs_A, cs_A,
                                  0,
                                  mn_behind - 1,
                                  p0, inc_p );

    // FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );
    bli_strsv( BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_sdots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_sgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_samax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_ops_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_sinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_ops_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

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

  }

  if ( m_A < n_A )
  {
    float*    ATL = buff_A;
    float*    ATR = buff_A + m_A*cs_A;

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR );
    FLA_Apply_pivots_ln_ops_var1( n_A - m_A,
                                  ATR, rs_A, cs_A,
                                  0,
                                  m_A - 1,
                                  buff_p, inc_p );

    // FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR,
    //                    FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
    //                    FLA_ONE, ATL, ATR );
    bli_strsm( BLIS_LEFT,
               BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               m_A,
               n_A - m_A,
               buff_1,
               ATL, rs_A, cs_A,
               ATR, rs_A, cs_A );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_ops_var4 ( int  m_A,
int  n_A,
float *  buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_samax(), bli_sdots(), bli_sgemv(), bli_sinvscalv(), FLA_Apply_pivots_ln_ops_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var4().

{
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    float*    a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    float*    A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_sdots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_sgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_samax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_ops_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_ops_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a12t,
    //                A22,      &AB2 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB2 );
    FLA_Apply_pivots_ln_ops_var1( n_ahead,
                                  a12t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Gemv_external( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, a10t, FLA_ONE, a12t );
    bli_sgemv( BLIS_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               mn_behind,
               n_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_sinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_ops_var5 ( int  m_A,
int  n_A,
float *  buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_samax(), bli_sger(), bli_sinvscalv(), FLA_Apply_pivots_ln_ops_var1(), and FLA_MINUS_ONE.

Referenced by FLA_LU_piv_opt_var5().

{
  float*    buff_m1 = FLA_FLOAT_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    float*    a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_samax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Merge_1x2( ABL, ABR,      &AB );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB );
    FLA_Apply_pivots_ln_ops_var1( n_A,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_sinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Ger_external( FLA_MINUS_ONE, a21, a12t, A22 );
    bli_sger( BLIS_NO_CONJUGATE,
              BLIS_NO_CONJUGATE,
              m_ahead,
              n_ahead,
              buff_m1,
              a21, rs_A,
              a12t, cs_A,
              A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opt_var3 ( FLA_Obj  A,
FLA_Obj  p 
)

References FLA_LU_piv_opc_var3(), FLA_LU_piv_opd_var3(), FLA_LU_piv_ops_var3(), FLA_LU_piv_opz_var3(), 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_LU_piv_internal().

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

  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_p    = FLA_Obj_vector_inc( p );


  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      int*   buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_ops_var3( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      int*    buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opd_var3( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opc_var3( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opz_var3( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opt_var4 ( FLA_Obj  A,
FLA_Obj  p 
)

References FLA_LU_piv_opc_var4(), FLA_LU_piv_opd_var4(), FLA_LU_piv_ops_var4(), FLA_LU_piv_opz_var4(), 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_LU_piv_internal().

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

  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_p    = FLA_Obj_vector_inc( p );


  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      int*   buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_ops_var4( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      int*    buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opd_var4( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opc_var4( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opz_var4( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opt_var5 ( FLA_Obj  A,
FLA_Obj  p 
)

References FLA_LU_piv_opc_var5(), FLA_LU_piv_opd_var5(), FLA_LU_piv_ops_var5(), FLA_LU_piv_opz_var5(), 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_LU_piv_internal().

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

  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_p    = FLA_Obj_vector_inc( p );


  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      int*   buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_ops_var5( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      int*    buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opd_var5( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opc_var5( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      FLA_LU_piv_opz_var5( m_A,
                           n_A,
                           buff_A, rs_A, cs_A,
                           buff_p, inc_p );

      break;
    }
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opz_var3 ( int  m_A,
int  n_A,
dcomplex buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_zamax(), bli_zdots(), bli_zgemv(), bli_zinvscalv(), bli_ztrsm(), bli_ztrsv(), FLA_Apply_pivots_ln_opz_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var3().

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    dcomplex* A00       = buff_A + (0  )*cs_A + (0  )*rs_A;
    dcomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    dcomplex* A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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* a1        = buff_A + (i  )*cs_A + (0  )*rs_A;

    int*      p0        = buff_p;
    int*      pi1       = buff_p + i*inc_p;

    int       m_ahead   = m_A - i - 1;
    int       mn_behind = i;

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

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p0, a1 );
    FLA_Apply_pivots_ln_opz_var1( 1,
                                  a1, rs_A, cs_A,
                                  0,
                                  mn_behind - 1,
                                  p0, inc_p );

    // FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );
    bli_ztrsv( BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               mn_behind,
               A00, rs_A, cs_A,
               a01, rs_A );

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_zdots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_zgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_zamax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_opz_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_zinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_opz_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

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

  }

  if ( m_A < n_A )
  {
    dcomplex* ATL = buff_A;
    dcomplex* ATR = buff_A + m_A*cs_A;

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR );
    FLA_Apply_pivots_ln_opz_var1( n_A - m_A,
                                  ATR, rs_A, cs_A,
                                  0,
                                  m_A - 1,
                                  buff_p, inc_p );

    // FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR,
    //                    FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
    //                    FLA_ONE, ATL, ATR );
    bli_ztrsm( BLIS_LEFT,
               BLIS_LOWER_TRIANGULAR,
               BLIS_NO_TRANSPOSE,
               BLIS_UNIT_DIAG,
               m_A,
               n_A - m_A,
               buff_1,
               ATL, rs_A, cs_A,
               ATR, rs_A, cs_A );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opz_var4 ( int  m_A,
int  n_A,
dcomplex buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_zamax(), bli_zdots(), bli_zgemv(), bli_zinvscalv(), FLA_Apply_pivots_ln_opz_var1(), FLA_MINUS_ONE, and FLA_ONE.

Referenced by FLA_LU_piv_opt_var4().

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    dcomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    dcomplex* A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
    bli_zdots( BLIS_NO_CONJUGATE,
               mn_behind,
               buff_m1,
               a10t, cs_A,
               a01, rs_A,
               buff_1,
               alpha11 );

    // FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
    bli_zgemv( BLIS_NO_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               m_ahead,
               mn_behind,
               buff_m1,
               A20, rs_A, cs_A,
               a01, rs_A,
               buff_1,
               a21, rs_A );

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_zamax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
    FLA_Apply_pivots_ln_opz_var1( 1,
                                  alpha11, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a10t,
    //                A20,      &AB0 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots_ln_opz_var1( mn_behind,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Merge_2x1( a12t,
    //                A22,      &AB2 );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB2 );
    FLA_Apply_pivots_ln_opz_var1( n_ahead,
                                  a12t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Gemv_external( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, a10t, FLA_ONE, a12t );
    bli_zgemv( BLIS_TRANSPOSE,
               BLIS_NO_CONJUGATE,
               mn_behind,
               n_ahead,
               buff_m1,
               A02, rs_A, cs_A,
               a10t, cs_A,
               buff_1,
               a12t, cs_A );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_zinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_opz_var5 ( int  m_A,
int  n_A,
dcomplex buff_A,
int  rs_A,
int  cs_A,
int *  buff_p,
int  inc_p 
)

References bli_zamax(), bli_zger(), bli_zinvscalv(), FLA_Apply_pivots_ln_opz_var1(), and FLA_MINUS_ONE.

Referenced by FLA_LU_piv_opt_var5().

{
  dcomplex* buff_m1 = FLA_DOUBLE_COMPLEX_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    dcomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    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;

    int*      pi1       = buff_p + i*inc_p;

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

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

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bli_zamax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // FLA_Merge_1x2( ABL, ABR,      &AB );

    // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB );
    FLA_Apply_pivots_ln_opz_var1( n_A,
                                  a10t, rs_A, cs_A,
                                  0,
                                  0,
                                  pi1, inc_p );

    // FLA_Inv_scal_external( alpha11, a21 );
    bli_zinvscalv( BLIS_NO_CONJUGATE,
                   m_ahead,
                   alpha11,
                   a21, rs_A );

    // FLA_Ger_external( FLA_MINUS_ONE, a21, a12t, A22 );
    bli_zger( BLIS_NO_CONJUGATE,
              BLIS_NO_CONJUGATE,
              m_ahead,
              n_ahead,
              buff_m1,
              a21, rs_A,
              a12t, cs_A,
              A22, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_unb_var3 ( FLA_Obj  A,
FLA_Obj  p 
)

References FLA_Amax_external(), FLA_Apply_pivots(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Dots_external(), FLA_Gemv_external(), FLA_Inv_scal_external(), FLA_Merge_2x1(), FLA_MINUS_ONE, 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_Trsv_external().

Referenced by FLA_LU_piv_internal().

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

  FLA_Obj AL,    AR,       A0,  a1,  A2;

  FLA_Obj pT,              p0,
          pB,              pi1,
                           p2;

  FLA_Obj AB0, aB1;


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

  FLA_Part_1x2( A,    &AL,  &AR,      0, FLA_LEFT );

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    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_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* *** */
                                              &pi1, 
                           pB,                &p2,        1, FLA_BOTTOM );

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

    // Apply previously computed pivots
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p0, a1 );

    // a01 = trilu( A00 ) \ a01 
    FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );

    // alpha11 = alpha11 - a10t * a01
    FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );

    // a21 = a21 - A20 * a01
    FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );

    // aB1 = / alpha11 \
    //       \  a21    /
    FLA_Merge_2x1( alpha11,
                       a21,      &aB1 );

    // Determine pivot index
    FLA_Amax_external( aB1, pi1 );

    // Apply pivots to current column
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );

    // a21 = a21 / alpha11 
    FLA_Inv_scal_external( alpha11, a21 );

    // AB0 = / a10t \
    //       \ A20  /
    FLA_Merge_2x1( a10t,
                   A20,      &AB0 );

    // Apply pivots to previous columns
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );

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

    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_3x1_to_2x1( &pT,                p0, 
                                                  pi1, 
                            /* ** */           /* *** */
                              &pB,                p2,     FLA_TOP );

  }

  if ( FLA_Obj_width( ATR ) > 0 )
  {
    /* Apply pivots to untouched columns */
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR );

    /* ATR = trilu( ATL ) \ ATR */ 
    FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, ATL, ATR );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_unb_var3b ( FLA_Obj  A,
FLA_Obj  p 
)

References FLA_Amax_external(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Dots_external(), FLA_Gemv_external(), FLA_Inv_scal_external(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trsm_external(), and FLA_Trsv_external().

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

  FLA_Obj pT,              p0,
          pB,              pi1,
                           p2;

  FLA_Obj AB0, aB1, AB2;


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

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    FLA_Repart_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* *** */
                                              &pi1, 
                           pB,                &p2,        1, FLA_BOTTOM );

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

    // a01 = trilu( A00 ) \ a01
    FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );

    // alpha11 = alpha11 - a10t * a01
    FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );

    // a21 = a21 - A20 * a01
    FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );

    // aB1 = / alpha11 \
    //       \  a21    /
    FLA_Merge_2x1( alpha11,
                   a21,      &aB1 );

    // Determine pivot index
    FLA_Amax_external( aB1, pi1 );

    // Apply pivots to current column
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );

    // AB0 = / a10t \
    //       \ A20  /
    FLA_Merge_2x1( a10t,
                   A20,      &AB0 );

    // AB2 = / a12t \
    //       \ A22  /
    FLA_Merge_2x1( a12t,
                   A22,      &AB2 );

    // Apply pivots to remaining columns
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB2 );

    // a21 = a21 / alpha11
    FLA_Inv_scal_external( alpha11, a21 );

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );

    FLA_Cont_with_3x1_to_2x1( &pT,                p0, 
                                                  pi1, 
                            /* ** */           /* *** */
                              &pB,                p2,     FLA_TOP );

  }

  if ( FLA_Obj_width( ATR ) > 0 )
  {
    /* ATR = trilu( ATL ) \ ATR */ 
    FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR, 
                       FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
                       FLA_ONE, ATL, ATR );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_unb_var4 ( FLA_Obj  A,
FLA_Obj  p 
)

References FLA_Amax_external(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Dots_external(), FLA_Gemv_external(), FLA_Inv_scal_external(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_LU_piv_internal().

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

  FLA_Obj pT,              p0,
          pB,              pi1,
                           p2;

  FLA_Obj AB0, aB1, AB2;


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

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    FLA_Repart_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* *** */
                                              &pi1, 
                           pB,                &p2,        1, FLA_BOTTOM );

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

    // alpha11 = alpha11 - a10t * a01
    FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );

    // a21 = a21 - A20 * a01
    FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );

    // aB1 = / alpha11 \
    //       \  a21    /
    FLA_Merge_2x1( alpha11,
                   a21,      &aB1 );

    // Determine pivot index
    FLA_Amax_external( aB1, pi1 );

    // Apply pivots to current column
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );

    // AB0 = / a10t \
    //       \ A20  /
    FLA_Merge_2x1( a10t,
                   A20,      &AB0 );

    // AB2 = / a12t \
    //       \ A22  /
    FLA_Merge_2x1( a12t,
                   A22,      &AB2 );

    // Apply pivots to remaining columns
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB2 );

    // a21 = a21 / alpha11 
    FLA_Inv_scal_external( alpha11, a21 );

    // a12t = a12t - a10t * A02
    FLA_Gemv_external( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, a10t, FLA_ONE, a12t );

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );

    FLA_Cont_with_3x1_to_2x1( &pT,                p0, 
                                                  pi1, 
                            /* ** */           /* *** */
                              &pB,                p2,     FLA_TOP );

  }

  return FLA_SUCCESS;
}
FLA_Error FLA_LU_piv_unb_var5 ( FLA_Obj  A,
FLA_Obj  p 
)

References FLA_Amax_external(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Ger_external(), FLA_Inv_scal_external(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_width(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_LU_piv_internal().

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

  FLA_Obj pT,              p0,
          pB,              pi1,
                           p2;

  FLA_Obj AB0, aB1, AB2;


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

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
          FLA_Obj_width( ATL ) < FLA_Obj_width( A )){

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );

    FLA_Repart_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* *** */
                                              &pi1, 
                           pB,                &p2,        1, FLA_BOTTOM );

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

    // aB1 = / alpha11 \
    //       \  a21    /
    FLA_Merge_2x1( alpha11,
                       a21,      &aB1 );

    // Determine pivot index
    FLA_Amax_external( aB1, pi1 );

    // Apply pivots to current column
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );

    // a21 = a21 / alpha11 
    FLA_Inv_scal_external( alpha11, a21 );

    // AB0 = / a10t \
    //       \ A20  /
    FLA_Merge_2x1( a10t,
                   A20,      &AB0 );

    // Apply pivots to previous columns
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );

    // AB2 = / a12t \
    //       \ A22  /
    FLA_Merge_2x1( a12t,
                   A22,      &AB2 );

    // Apply pivots to remaining columns
    FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB2 );

    // A22 = A22 - a21 * a12t
    FLA_Ger_external( FLA_MINUS_ONE, a21, a12t, 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_3x1_to_2x1( &pT,                p0, 
                                                  pi1, 
                            /* ** */           /* *** */
                              &pB,                p2,     FLA_TOP );

  }

  return FLA_SUCCESS;
}