FLA_CAQR2_UT_vars.h File Reference

(r)

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Functions
FLA_Error	FLA_CAQR2_UT_blk_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T, fla_caqr2ut_t *cntl)
FLA_Error	FLA_CAQR2_UT_blk_var2 (FLA_Obj U, FLA_Obj D, FLA_Obj T, fla_caqr2ut_t *cntl)
FLA_Error	FLA_CAQR2_UT_unb_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T)
FLA_Error	FLA_CAQR2_UT_opt_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T)
FLA_Error	FLA_CAQR2_UT_ops_var1 (int m_UT, int m_D, float *U, int rs_U, int cs_U, float *D, int rs_D, int cs_D, float *T, int rs_T, int cs_T)
FLA_Error	FLA_CAQR2_UT_opd_var1 (int m_UT, int m_D, double *U, int rs_U, int cs_U, double *D, int rs_D, int cs_D, double *T, int rs_T, int cs_T)
FLA_Error	FLA_CAQR2_UT_opc_var1 (int m_UT, int m_D, scomplex *U, int rs_U, int cs_U, scomplex *D, int rs_D, int cs_D, scomplex *T, int rs_T, int cs_T)
FLA_Error	FLA_CAQR2_UT_opz_var1 (int m_UT, int m_D, dcomplex *U, int rs_U, int cs_U, dcomplex *D, int rs_D, int cs_D, dcomplex *T, int rs_T, int cs_T)

Function Documentation

FLA_CAQR2_UT_blk_var1()

FLA_Error FLA_CAQR2_UT_blk_var1	(	FLA_Obj	U,
		FLA_Obj	D,
		FLA_Obj	T,
		fla_caqr2ut_t *	cntl
	)

{
  FLA_Obj UTL,   UTR,      U00, U01, U02, 
          UBL,   UBR,      U10, U11, U12,
                           U20, U21, U22;
 
  FLA_Obj DTL,   DTR,      D00, D01, D02, 
          DBL,   DBR,      D10, D11, D12,
                           D20, D21, D22;
 
  FLA_Obj TL,    TR,       T0,  T1,  W12;
 
  FLA_Obj D1;
 
  FLA_Obj W12T, W12B;
 
  FLA_Obj T1T, T2B;
 
  dim_t   b_alg, b;
  dim_t   m_DT;
 
  // Query the algorithmic blocksize by inspecting the length of T.
  b_alg = FLA_Obj_length( T );
 
  // Begin partitioning diagonally through D with m - n rows above
  // the diagonal.
  m_DT = FLA_Obj_length( D ) - FLA_Obj_width( D );
 
  FLA_Part_2x2( U,    &UTL, &UTR,
                      &UBL, &UBR,     0, 0, FLA_TL );
 
  FLA_Part_2x2( D,    &DTL, &DTR,
                      &DBL, &DBR,     m_DT, 0, FLA_TL );
 
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT );
 
  while ( FLA_Obj_min_dim( UBR ) > 0 ){
 
    b = min( b_alg, FLA_Obj_min_dim( UBR ) );
 
    FLA_Repart_2x2_to_3x3( UTL, /**/ UTR,       &U00, /**/ &U01, &U02,
                        /* ************* */   /* ******************** */
                                                &U10, /**/ &U11, &U12,
                           UBL, /**/ UBR,       &U20, /**/ &U21, &U22,
                           b, b, FLA_BR );
 
    FLA_Repart_2x2_to_3x3( DTL, /**/ DTR,       &D00, /**/ &D01, &D02,
                        /* ************* */   /* ******************** */
                                                &D10, /**/ &D11, &D12,
                           DBL, /**/ DBR,       &D20, /**/ &D21, &D22,
                           b, b, FLA_BR );
 
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &W12,
                           b, FLA_RIGHT );
 
    /*------------------------------------------------------------*/
 
    // T1T = FLA_Top_part( T1, b );
 
    FLA_Part_2x1( T1,   &T1T, 
                        &T2B,    b, FLA_TOP );
 
    FLA_Merge_2x1( D01,
                   D11,   &D1 );
 
    // [ U11, ...
    //   D1, T1 ] = FLA_CAQR2_UT( U11
    //                            D1, T1T );
 
    FLA_CAQR2_UT_internal( U11,
                           D1, T1T, 
                           FLA_Cntl_sub_caqr2ut( cntl ) );
 
 
    if ( FLA_Obj_width( U12 ) > 0 )
    {
      // W12T = FLA_Top_part( W12, b );
 
      FLA_Part_2x1( W12,  &W12T, 
                          &W12B, b, FLA_TOP );
 
      // W12T = inv( triu( T1T ) )' * ( U12 + D1' * D2 );
      //      = inv( triu( T1T ) )' * ( U12 + D01' * D02 + D11' * D12 );
 
      FLA_Copy_internal( D12, W12T,
                         FLA_Cntl_sub_copy( cntl ) );
 
      FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                         FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, 
                         FLA_ONE, D11, W12T,
                         FLA_Cntl_sub_trmm1( cntl ) );
 
      FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_ONE, D01, D02, FLA_ONE, W12T,
                         FLA_Cntl_sub_gemm1( cntl ) );
 
      FLA_Axpy_internal( FLA_ONE, U12, W12T,
                         FLA_Cntl_sub_axpy1( cntl ) );
 
      FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                         FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, 
                         FLA_ONE, T1T, W12T,
                         FLA_Cntl_sub_trsm( cntl ) );
 
      // U12 = U12 - W12T;
      // D2  = D2  - D1 * W12T;
      //  => D02 = D02 - D01 * W12T;
      //     D12 = D12 - D11 * W12T;
 
      FLA_Axpy_internal( FLA_MINUS_ONE, W12T, U12,
                         FLA_Cntl_sub_axpy2( cntl ) );
 
      FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, 
                         FLA_MINUS_ONE, D01, W12T, FLA_ONE, D02,
                         FLA_Cntl_sub_gemm2( cntl ) );
 
      FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                         FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, 
                         FLA_ONE, D11, W12T,
                         FLA_Cntl_sub_trmm2( cntl ) );
 
      FLA_Axpy_internal( FLA_MINUS_ONE, W12T, D12,
                         FLA_Cntl_sub_axpy3( cntl ) );
    }
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR,       U00, U01, /**/ U02,
                                                     U10, U11, /**/ U12,
                            /* ************** */  /* ****************** */
                              &UBL, /**/ &UBR,       U20, U21, /**/ U22,
                              FLA_TL );
 
    FLA_Cont_with_3x3_to_2x2( &DTL, /**/ &DTR,       D00, D01, /**/ D02,
                                                     D10, D11, /**/ D12,
                            /* ************** */  /* ****************** */
                              &DBL, /**/ &DBR,       D20, D21, /**/ D22,
                              FLA_TL );
 
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ W12,
                              FLA_LEFT );
 
  }
 
  return FLA_SUCCESS;
}

References FLA_Axpy_internal(), FLA_CAQR2_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_internal(), FLA_Gemm_internal(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_internal(), FLA_Trsm_internal(), and i.

Referenced by FLA_CAQR2_UT_internal().

FLA_CAQR2_UT_blk_var2()

FLA_Error FLA_CAQR2_UT_blk_var2	(	FLA_Obj	U,
		FLA_Obj	D,
		FLA_Obj	T,
		fla_caqr2ut_t *	cntl
	)

{
  FLA_Obj DT,              D0,
          DB,              D1,
                           D2;
 
  FLA_Obj TT,              T0,
          TB,              T1,
                           T2;
 
  dim_t b;
 
  FLA_Part_2x1( D,    &DT, 
                      &DB,            0, FLA_TOP );
 
  FLA_Part_2x1( T,    &TT, 
                      &TB,            0, FLA_TOP );
 
  while ( FLA_Obj_length( DT ) < FLA_Obj_length( D ) ){
 
    b = FLA_Determine_blocksize( DB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) );
 
    FLA_Repart_2x1_to_3x1( DT,                &D0, 
                        /* ** */            /* ****** */
                                              &D1, 
                           DB,                &D2,        b, FLA_BOTTOM );
 
    FLA_Repart_2x1_to_3x1( TT,                &T0, 
                        /* ** */            /* ****** */
                                              &T1, 
                           TB,                &T2,        b, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
    // [ U, ...
    //   D1, T ] = FLA_CAQR2_UT( U
    //                           D1, T1 );
 
    FLA_CAQR2_UT_internal( U,
                           D1, T1, 
                           FLA_Cntl_sub_caqr2ut( cntl ) );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x1_to_2x1( &DT,                D0, 
                                                  D1, 
                            /* ** */           /* ****** */
                              &DB,                D2,     FLA_TOP );
 
    FLA_Cont_with_3x1_to_2x1( &TT,                T0, 
                                                  T1, 
                            /* ** */           /* ****** */
                              &TB,                T2,     FLA_TOP );
  }
 
  return FLA_SUCCESS;
}

References FLA_CAQR2_UT_internal(), FLA_Cont_with_3x1_to_2x1(), FLA_Determine_blocksize(), FLA_Obj_length(), FLA_Part_2x1(), FLA_Repart_2x1_to_3x1(), and i.

Referenced by FLA_CAQR2_UT_internal().

FLA_CAQR2_UT_opc_var1()

FLA_Error FLA_CAQR2_UT_opc_var1	(	int	m_UT,
		int	m_D,
		scomplex *	U,
		int	rs_U,
		int	cs_U,
		scomplex *	D,
		int	rs_D,
		int	cs_D,
		scomplex *	T,
		int	rs_T,
		int	cs_T
	)

{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  int       i, j;
  int       m_DT = m_D - mn_UT;
 
  for ( i = m_DT, j = 0; j < mn_UT; ++i, ++j )
  {
    scomplex* upsilon11 = buff_U + (j  )*cs_U + (j  )*rs_U;
    scomplex* u12t      = buff_U + (j+1)*cs_U + (j  )*rs_U;
 
    scomplex* D00       = buff_D + (0  )*cs_D + (0  )*rs_D;
    scomplex* d1        = buff_D + (j  )*cs_D + (0  )*rs_D;
    scomplex* D2        = buff_D + (j+1)*cs_D + (0  )*rs_D;
 
    scomplex* tau11     = buff_T + (j  )*cs_T + (j  )*rs_T;
    scomplex* t01       = buff_T + (j  )*cs_T + (0  )*rs_T;
 
    scomplex* d1B       = d1  + (m_DT)*rs_D;
    scomplex* D00B      = D00 + (m_DT)*rs_D;
 
    int       m_behind = i;
    int       n_behind = j;
    int       mn_ahead = mn_UT - j - 1;
 
    //------------------------------------------------------------//
 
    // FLA_Househ2_UT( FLA_LEFT,
    //                 upsilon11,
    //                 d1, tau11 );
    FLA_Househ2_UT_l_opc( m_behind + 1,
                          upsilon11,
                          d1, rs_D,
                          tau11 );
 
    // FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t,
    //                                       D2 );
    FLA_Apply_H2_UT_l_opc_var1( m_behind + 1,
                                mn_ahead,
                                tau11,
                                d1, rs_D,
                                u12t, cs_U,
                                D2, rs_D, cs_D );
 
    // FLA_Copy_external( d01B, t01 );
    // FLA_Trmv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
    //                    D00B, t01 );
    // FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D00T, d01T, FLA_ONE, t01 );
    bl1_ccopyv( BLIS1_NO_CONJUGATE,
                n_behind,
                d1B, rs_D,
                t01, rs_T );
    bl1_ctrmv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               n_behind,
               D00B, rs_D, cs_D,
               t01, rs_T );
    bl1_cgemv( BLIS1_CONJ_TRANSPOSE,
               BLIS1_NO_CONJUGATE,
               m_DT,
               n_behind,
               buff_1,
               D00, rs_D, cs_D,
               d1,  rs_D,
               buff_1,
               t01, rs_T );
 
    //------------------------------------------------------------//
 
  }
 
  return FLA_SUCCESS;
}

References bl1_ccopyv(), bl1_cgemv(), bl1_ctrmv(), BLIS1_CONJ_TRANSPOSE, BLIS1_NO_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_Apply_H2_UT_l_opc_var1(), FLA_Househ2_UT_l_opc(), FLA_ONE, and i.

Referenced by FLA_CAQR2_UT_opt_var1().

FLA_CAQR2_UT_opd_var1()

FLA_Error FLA_CAQR2_UT_opd_var1	(	int	m_UT,
		int	m_D,
		double *	U,
		int	rs_U,
		int	cs_U,
		double *	D,
		int	rs_D,
		int	cs_D,
		double *	T,
		int	rs_T,
		int	cs_T
	)

{
  double*   buff_1  = FLA_DOUBLE_PTR( FLA_ONE );
  int       i, j;
  int       m_DT = m_D - mn_UT;
 
  for ( i = m_DT, j = 0; j < mn_UT; ++i, ++j )
  {
    double*   upsilon11 = buff_U + (j  )*cs_U + (j  )*rs_U;
    double*   u12t      = buff_U + (j+1)*cs_U + (j  )*rs_U;
 
    double*   D00       = buff_D + (0  )*cs_D + (0  )*rs_D;
    double*   d1        = buff_D + (j  )*cs_D + (0  )*rs_D;
    double*   D2        = buff_D + (j+1)*cs_D + (0  )*rs_D;
 
    double*   tau11     = buff_T + (j  )*cs_T + (j  )*rs_T;
    double*   t01       = buff_T + (j  )*cs_T + (0  )*rs_T;
 
    double*   d1B       = d1  + (m_DT)*rs_D;
    double*   D00B      = D00 + (m_DT)*rs_D;
 
    int       m_behind = i;
    int       n_behind = j;
    int       mn_ahead = mn_UT - j - 1;
 
    //------------------------------------------------------------//
 
    // FLA_Househ2_UT( FLA_LEFT,
    //                 upsilon11,
    //                 d1, tau11 );
    FLA_Househ2_UT_l_opd( m_behind + 1,
                          upsilon11,
                          d1, rs_D,
                          tau11 );
 
    // FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t,
    //                                       D2 );
    FLA_Apply_H2_UT_l_opd_var1( m_behind + 1,
                                mn_ahead,
                                tau11,
                                d1, rs_D,
                                u12t, cs_U,
                                D2, rs_D, cs_D );
 
    // FLA_Copy_external( d01B, t01 );
    // FLA_Trmv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
    //                    D00B, t01 );
    // FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D00T, d01T, FLA_ONE, t01 );
    bl1_dcopyv( BLIS1_NO_CONJUGATE,
                n_behind,
                d1B, rs_D,
                t01, rs_T );
    bl1_dtrmv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               n_behind,
               D00B, rs_D, cs_D,
               t01, rs_T );
    bl1_dgemv( BLIS1_CONJ_TRANSPOSE,
               BLIS1_NO_CONJUGATE,
               m_DT,
               n_behind,
               buff_1,
               D00, rs_D, cs_D,
               d1,  rs_D,
               buff_1,
               t01, rs_T );
 
    //------------------------------------------------------------//
 
  }
 
  return FLA_SUCCESS;
}

References bl1_dcopyv(), bl1_dgemv(), bl1_dtrmv(), BLIS1_CONJ_TRANSPOSE, BLIS1_NO_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_Apply_H2_UT_l_opd_var1(), FLA_Househ2_UT_l_opd(), FLA_ONE, and i.

Referenced by FLA_CAQR2_UT_opt_var1().

FLA_CAQR2_UT_ops_var1()

FLA_Error FLA_CAQR2_UT_ops_var1	(	int	m_UT,
		int	m_D,
		float *	U,
		int	rs_U,
		int	cs_U,
		float *	D,
		int	rs_D,
		int	cs_D,
		float *	T,
		int	rs_T,
		int	cs_T
	)

{
  float*    buff_1  = FLA_FLOAT_PTR( FLA_ONE );
  int       i, j;
  int       m_DT = m_D - mn_UT;
 
  for ( i = m_DT, j = 0; j < mn_UT; ++i, ++j )
  {
    float*    upsilon11 = buff_U + (j  )*cs_U + (j  )*rs_U;
    float*    u12t      = buff_U + (j+1)*cs_U + (j  )*rs_U;
 
    float*    D00       = buff_D + (0  )*cs_D + (0  )*rs_D;
    float*    d1        = buff_D + (j  )*cs_D + (0  )*rs_D;
    float*    D2        = buff_D + (j+1)*cs_D + (0  )*rs_D;
 
    float*    tau11     = buff_T + (j  )*cs_T + (j  )*rs_T;
    float*    t01       = buff_T + (j  )*cs_T + (0  )*rs_T;
 
    float*    d1B       = d1  + (m_DT)*rs_D;
    float*    D00B      = D00 + (m_DT)*rs_D;
 
    int       m_behind = i;
    int       n_behind = j;
    int       mn_ahead = mn_UT - j - 1;
 
    //------------------------------------------------------------//
 
    // FLA_Househ2_UT( FLA_LEFT,
    //                 upsilon11,
    //                 d1, tau11 );
    FLA_Househ2_UT_l_ops( m_behind + 1,
                          upsilon11,
                          d1, rs_D,
                          tau11 );
 
    // FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t,
    //                                       D2 );
    FLA_Apply_H2_UT_l_ops_var1( m_behind + 1,
                                mn_ahead,
                                tau11,
                                d1, rs_D,
                                u12t, cs_U,
                                D2, rs_D, cs_D );
 
    // FLA_Copy_external( d01B, t01 );
    // FLA_Trmv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
    //                    D00B, t01 );
    // FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D00T, d01T, FLA_ONE, t01 );
    bl1_scopyv( BLIS1_NO_CONJUGATE,
                n_behind,
                d1B, rs_D,
                t01, rs_T );
    bl1_strmv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               n_behind,
               D00B, rs_D, cs_D,
               t01, rs_T );
    bl1_sgemv( BLIS1_CONJ_TRANSPOSE,
               BLIS1_NO_CONJUGATE,
               m_DT,
               n_behind,
               buff_1,
               D00, rs_D, cs_D,
               d1,  rs_D,
               buff_1,
               t01, rs_T );
 
    //------------------------------------------------------------//
 
  }
 
  return FLA_SUCCESS;
}

References bl1_scopyv(), bl1_sgemv(), bl1_strmv(), BLIS1_CONJ_TRANSPOSE, BLIS1_NO_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_Apply_H2_UT_l_ops_var1(), FLA_Househ2_UT_l_ops(), FLA_ONE, and i.

Referenced by FLA_CAQR2_UT_opt_var1().

FLA_CAQR2_UT_opt_var1()

FLA_Error FLA_CAQR2_UT_opt_var1	(	FLA_Obj	U,
		FLA_Obj	D,
		FLA_Obj	T
	)

{
  FLA_Datatype datatype;
  int          mn_UT, m_D;
  int          rs_U, cs_U;
  int          rs_D, cs_D;
  int          rs_T, cs_T;
 
  datatype = FLA_Obj_datatype( U );
 
  mn_UT    = FLA_Obj_width( U );
  m_D      = FLA_Obj_length( D );
 
  rs_U     = FLA_Obj_row_stride( U );
  cs_U     = FLA_Obj_col_stride( U );
  rs_D     = FLA_Obj_row_stride( D );
  cs_D     = FLA_Obj_col_stride( D );
  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  
 
  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_U = FLA_FLOAT_PTR( U );
      float* buff_D = FLA_FLOAT_PTR( D );
      float* buff_T = FLA_FLOAT_PTR( T );
 
      FLA_CAQR2_UT_ops_var1( mn_UT,
                             m_D,
                             buff_U, rs_U, cs_U,
                             buff_D, rs_D, cs_D,
                             buff_T, rs_T, cs_T );
 
      break;
    }
 
    case FLA_DOUBLE:
    {
      double* buff_U = FLA_DOUBLE_PTR( U );
      double* buff_D = FLA_DOUBLE_PTR( D );
      double* buff_T = FLA_DOUBLE_PTR( T );
 
      FLA_CAQR2_UT_opd_var1( mn_UT,
                             m_D,
                             buff_U, rs_U, cs_U,
                             buff_D, rs_D, cs_D,
                             buff_T, rs_T, cs_T );
 
      break;
    }
 
    case FLA_COMPLEX:
    {
      scomplex* buff_U = FLA_COMPLEX_PTR( U );
      scomplex* buff_D = FLA_COMPLEX_PTR( D );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );
 
      FLA_CAQR2_UT_opc_var1( mn_UT,
                             m_D,
                             buff_U, rs_U, cs_U,
                             buff_D, rs_D, cs_D,
                             buff_T, rs_T, cs_T );
 
      break;
    }
 
    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_U = FLA_DOUBLE_COMPLEX_PTR( U );
      dcomplex* buff_D = FLA_DOUBLE_COMPLEX_PTR( D );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );
 
      FLA_CAQR2_UT_opz_var1( mn_UT,
                             m_D,
                             buff_U, rs_U, cs_U,
                             buff_D, rs_D, cs_D,
                             buff_T, rs_T, cs_T );
 
      break;
    }
  }
 
  return FLA_SUCCESS;
}

References FLA_CAQR2_UT_opc_var1(), FLA_CAQR2_UT_opd_var1(), FLA_CAQR2_UT_ops_var1(), FLA_CAQR2_UT_opz_var1(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_width(), and i.

Referenced by FLA_CAQR2_UT_internal().

FLA_CAQR2_UT_opz_var1()

FLA_Error FLA_CAQR2_UT_opz_var1	(	int	m_UT,
		int	m_D,
		dcomplex *	U,
		int	rs_U,
		int	cs_U,
		dcomplex *	D,
		int	rs_D,
		int	cs_D,
		dcomplex *	T,
		int	rs_T,
		int	cs_T
	)

{
  dcomplex* buff_1  = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
  int       i, j;
  int       m_DT = m_D - mn_UT;
 
  for ( i = m_DT, j = 0; j < mn_UT; ++i, ++j )
  {
    dcomplex* upsilon11 = buff_U + (j  )*cs_U + (j  )*rs_U;
    dcomplex* u12t      = buff_U + (j+1)*cs_U + (j  )*rs_U;
 
    dcomplex* D00       = buff_D + (0  )*cs_D + (0  )*rs_D;
    dcomplex* d1        = buff_D + (j  )*cs_D + (0  )*rs_D;
    dcomplex* D2        = buff_D + (j+1)*cs_D + (0  )*rs_D;
 
    dcomplex* tau11     = buff_T + (j  )*cs_T + (j  )*rs_T;
    dcomplex* t01       = buff_T + (j  )*cs_T + (0  )*rs_T;
 
    dcomplex* d1B       = d1  + (m_DT)*rs_D;
    dcomplex* D00B      = D00 + (m_DT)*rs_D;
 
    int       m_behind = i;
    int       n_behind = j;
    int       mn_ahead = mn_UT - j - 1;
 
    //------------------------------------------------------------//
 
    // FLA_Househ2_UT( FLA_LEFT,
    //                 upsilon11,
    //                 d1, tau11 );
    FLA_Househ2_UT_l_opz( m_behind + 1,
                          upsilon11,
                          d1, rs_D,
                          tau11 );
 
    // FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t,
    //                                       D2 );
    FLA_Apply_H2_UT_l_opz_var1( m_behind + 1,
                                mn_ahead,
                                tau11,
                                d1, rs_D,
                                u12t, cs_U,
                                D2, rs_D, cs_D );
 
    // FLA_Copy_external( d01B, t01 );
    // FLA_Trmv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
    //                    D00B, t01 );
    // FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D00T, d01T, FLA_ONE, t01 );
    bl1_zcopyv( BLIS1_NO_CONJUGATE,
                n_behind,
                d1B, rs_D,
                t01, rs_T );
    bl1_ztrmv( BLIS1_UPPER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               n_behind,
               D00B, rs_D, cs_D,
               t01, rs_T );
    bl1_zgemv( BLIS1_CONJ_TRANSPOSE,
               BLIS1_NO_CONJUGATE,
               m_DT,
               n_behind,
               buff_1,
               D00, rs_D, cs_D,
               d1,  rs_D,
               buff_1,
               t01, rs_T );
 
    //------------------------------------------------------------//
 
  }
 
  return FLA_SUCCESS;
}

References bl1_zcopyv(), bl1_zgemv(), bl1_ztrmv(), BLIS1_CONJ_TRANSPOSE, BLIS1_NO_CONJUGATE, BLIS1_NONUNIT_DIAG, BLIS1_UPPER_TRIANGULAR, FLA_Apply_H2_UT_l_opz_var1(), FLA_Househ2_UT_l_opz(), FLA_ONE, and i.

Referenced by FLA_CAQR2_UT_opt_var1().

FLA_CAQR2_UT_unb_var1()

FLA_Error FLA_CAQR2_UT_unb_var1	(	FLA_Obj	U,
		FLA_Obj	D,
		FLA_Obj	T
	)

{
  FLA_Obj UTL,   UTR,      U00,  u01,       U02, 
          UBL,   UBR,      u10t, upsilon11, u12t,
                           U20,  u21,       U22;
 
  FLA_Obj DTL,   DTR,      D00,  d01,     D02, 
          DBL,   DBR,      d10t, delta11, d12t,
                           D20,  d21,     D22;
 
  FLA_Obj TTL,   TTR,      T00,  t01,   T02, 
          TBL,   TBR,      t10t, tau11, t12t,
                           T20,  t21,   T22;
 
  FLA_Obj d1, D2;
 
  FLA_Obj d01T,
          d01B;
 
  FLA_Obj D00T,
          D00B;
 
  dim_t   m_DT;
 
  // Begin partitioning diagonally through D with m - n rows above
  // the diagonal.
  m_DT = FLA_Obj_length( D ) - FLA_Obj_width( D );
 
  FLA_Part_2x2( U,    &UTL, &UTR,
                      &UBL, &UBR,     0, 0, FLA_TL );
 
  FLA_Part_2x2( D,    &DTL, &DTR,
                      &DBL, &DBR,     m_DT, 0, FLA_TL );
 
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
 
  while ( FLA_Obj_min_dim( UBR ) > 0 ){
 
    FLA_Repart_2x2_to_3x3( UTL, /**/ UTR,       &U00,  /**/ &u01,       &U02,
                        /* ************* */   /* ************************** */
                                                &u10t, /**/ &upsilon11, &u12t,
                           UBL, /**/ UBR,       &U20,  /**/ &u21,       &U22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x2_to_3x3( DTL, /**/ DTR,       &D00,  /**/ &d01,     &D02,
                        /* ************* */   /* ************************** */
                                                &d10t, /**/ &delta11, &d12t,
                           DBL, /**/ DBR,       &D20,  /**/ &d21,     &D22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************ */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
 
    /*------------------------------------------------------------*/
 
    FLA_Merge_2x1( d01,
                   delta11,  &d1 );
 
    FLA_Merge_2x1( D02,
                   d12t,     &D2 );
 
    // Compute tau11 and u2 from upsilon11 and d1 such that tau11 and u2
    // determine a Householder transform H such that applying H from the
    // left to the column vector consisting of upsilon11 and d1 annihilates
    // the entries in d1 (and updates upsilon11).
    FLA_Househ2_UT( FLA_LEFT,
                    upsilon11,
                    d1, tau11 );
 
    // / u12t \ =  H / u12t \
    // \  D2  /      \  D2  / 
    //
    // where H is formed from tau11 and d1.
    FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t,
                                          D2 );
 
    FLA_Part_2x1( d01,   &d01T,
                         &d01B,    m_DT, FLA_TOP );
 
    FLA_Part_2x1( D00,   &D00T,
                         &D00B,    m_DT, FLA_TOP );
 
    // t01 = D00' * d01;
    //     = D00T' * d01T + triu( D00B )' * d01B;
    FLA_Copy_external( d01B, t01 );
    FLA_Trmv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
                       D00B, t01 );
    FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D00T, d01T, FLA_ONE, t01 );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR,       U00,  u01,       /**/ U02,
                                                     u10t, upsilon11, /**/ u12t,
                            /* ************** */  /* ************************ */
                              &UBL, /**/ &UBR,       U20,  u21,       /**/ U22,
                              FLA_TL );
 
    FLA_Cont_with_3x3_to_2x2( &DTL, /**/ &DTR,       D00,  d01,     /**/ D02,
                                                     d10t, delta11, /**/ d12t,
                            /* ************** */  /* ************************ */
                              &DBL, /**/ &DBR,       D20,  d21,     /**/ D22,
                              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;
}

References FLA_Apply_H2_UT(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_2x1(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), FLA_Trmv_external(), and i.

Referenced by FLA_CAQR2_UT_internal().