FLA_Tridiag_UT.h File Reference

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Functions
FLA_Error	FLA_Tridiag_UT (FLA_Uplo uplo, FLA_Obj A, FLA_Obj T)
FLA_Error	FLA_Tridiag_UT_internal (FLA_Uplo uplo, FLA_Obj A, FLA_Obj T, fla_tridiagut_t *cntl)
FLA_Error	FLA_Tridiag_UT_l (FLA_Obj A, FLA_Obj T, fla_tridiagut_t *cntl)
FLA_Error	FLA_Tridiag_UT_u (FLA_Obj A, FLA_Obj T, fla_tridiagut_t *cntl)
FLA_Error	FLA_Tridiag_UT_create_T (FLA_Obj A, FLA_Obj *T)
FLA_Error	FLA_Tridiag_UT_recover_tau (FLA_Obj T, FLA_Obj t)
FLA_Error	FLA_Tridiag_UT_scale_diagonals (FLA_Uplo uplo, FLA_Obj alpha, FLA_Obj A)
FLA_Error	FLA_Tridiag_UT_extract_diagonals (FLA_Uplo uplo, FLA_Obj A, FLA_Obj d, FLA_Obj e)
FLA_Error	FLA_Tridiag_UT_extract_real_diagonals (FLA_Uplo uplo, FLA_Obj A, FLA_Obj d, FLA_Obj e)
FLA_Error	FLA_Tridiag_UT_realify (FLA_Uplo uplo, FLA_Obj A, FLA_Obj d)
FLA_Error	FLA_Tridiag_UT_l_realify_unb (FLA_Obj A, FLA_Obj d)
FLA_Error	FLA_Tridiag_UT_l_realify_opt (FLA_Obj A, FLA_Obj d)
FLA_Error	FLA_Tridiag_UT_u_realify_unb (FLA_Obj A, FLA_Obj d)
FLA_Error	FLA_Tridiag_UT_u_realify_opt (FLA_Obj A, FLA_Obj d)
FLA_Error	FLA_Tridiag_UT_realify_subdiagonal (FLA_Obj b, FLA_Obj d)
FLA_Error	FLA_Tridiag_UT_realify_subdiagonal_opt (FLA_Obj b, FLA_Obj d)
FLA_Error	FLA_Tridiag_UT_shift_U (FLA_Uplo uplo, FLA_Obj A)
FLA_Error	FLA_Tridiag_UT_shift_U_l_ops (int m_A, float *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_shift_U_u_ops (int m_A, float *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_shift_U_l_opd (int m_A, double *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_shift_U_u_opd (int m_A, double *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_shift_U_l_opc (int m_A, scomplex *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_shift_U_u_opc (int m_A, scomplex *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_shift_U_l_opz (int m_A, dcomplex *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_shift_U_u_opz (int m_A, dcomplex *buff_A, int rs_A, int cs_A)
FLA_Error	FLA_Tridiag_UT_form_Q (FLA_Uplo uplo, FLA_Obj A, FLA_Obj T, FLA_Obj Q)
FLA_Error	FLA_Tridiag_UT_form_Q_l_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W)
FLA_Error	FLA_Tridiag_UT_form_Q_u_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W)
FLA_Error	FLA_Tridiag_UT_form_Q_l_opt_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error	FLA_Tridiag_UT_form_Q_l_ops_var1 (int m_A, int n_AT, float *buff_A, int rs_A, int cs_A, float *buff_T, int rs_T, int cs_T)
FLA_Error	FLA_Tridiag_UT_form_Q_l_opd_var1 (int m_A, int n_AT, double *buff_A, int rs_A, int cs_A, double *buff_T, int rs_T, int cs_T)
FLA_Error	FLA_Tridiag_UT_form_Q_l_opc_var1 (int m_A, int n_AT, scomplex *buff_A, int rs_A, int cs_A, scomplex *buff_T, int rs_T, int cs_T)
FLA_Error	FLA_Tridiag_UT_form_Q_l_opz_var1 (int m_A, int n_AT, dcomplex *buff_A, int rs_A, int cs_A, dcomplex *buff_T, int rs_T, int cs_T)

Function Documentation

FLA_Tridiag_UT()

FLA_Error FLA_Tridiag_UT	(	FLA_Uplo	uplo,
		FLA_Obj	A,
		FLA_Obj	T
	)

{
  FLA_Error r_val;
 
  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Tridiag_UT_check( uplo, A, T );
 
  if ( FLA_Obj_row_stride( A ) == 1 &&
       FLA_Obj_is_double_precision( A ) )
    // Temporary fix not to use the fused version (numerically unstable).
    r_val = FLA_Tridiag_UT_internal( uplo, A, T, fla_tridiagut_cntl_plain );
  else
    r_val = FLA_Tridiag_UT_internal( uplo, A, T, fla_tridiagut_cntl_nofus );
 
  return r_val;
}

References FLA_Check_error_level(), FLA_Obj_is_double_precision(), FLA_Obj_row_stride(), FLA_Tridiag_UT_check(), FLA_Tridiag_UT_internal(), fla_tridiagut_cntl_nofus, fla_tridiagut_cntl_plain, and i.

Referenced by FLA_Hevd_lv_unb_var1(), and FLA_Hevd_lv_unb_var2().

FLA_Tridiag_UT_create_T()

FLA_Error FLA_Tridiag_UT_create_T	(	FLA_Obj	A,
		FLA_Obj *	T
	)

{
  FLA_Datatype datatype;
  dim_t        b_alg, k;
  dim_t        rs_T, cs_T;
 
  // Query the datatype of A.
  datatype = FLA_Obj_datatype( A );
 
  // Query the blocksize from the library.
  b_alg = FLA_Query_blocksize( datatype, FLA_DIMENSION_MIN );
 
  // Scale the blocksize by a pre-set global constant.
  b_alg = ( dim_t )( ( ( double ) b_alg ) * FLA_TRIDIAG_INNER_TO_OUTER_B_RATIO );
 
  // Query the minimum dimension of A.
  k = FLA_Obj_min_dim( A );
 
  // Adjust the blocksize with respect to the min-dim of A.
  b_alg = min( b_alg, k );
 
  // Figure out whether T should be row-major or column-major.
  if ( FLA_Obj_row_stride( A ) == 1 )
  {
    rs_T = 1;
    cs_T = b_alg;
  }
  else // if ( FLA_Obj_col_stride( A ) == 1 )
  {
    rs_T = k;
    cs_T = 1;
  }
 
  // Create a b_alg x k matrix to hold the block Householder transforms that
  // will be accumulated within the tridiagonal reduction algorithm.
  FLA_Obj_create( datatype, b_alg, k, rs_T, cs_T, T );
 
  return FLA_SUCCESS;
}

References FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_min_dim(), FLA_Obj_row_stride(), FLA_Query_blocksize(), and i.

Referenced by FLA_Hevd_lv_unb_var1(), and FLA_Hevd_lv_unb_var2().

FLA_Tridiag_UT_extract_diagonals()

FLA_Error FLA_Tridiag_UT_extract_diagonals	(	FLA_Uplo	uplo,
		FLA_Obj	A,
		FLA_Obj	d,
		FLA_Obj	e
	)

{
  FLA_Error r_val = FLA_SUCCESS;
 
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Tridiag_UT_extract_diagonals_check( uplo, A, d, e );
 
  if ( uplo == FLA_LOWER_TRIANGULAR )
    r_val = FLA_Bidiag_UT_l_extract_diagonals( A, d, e );
  else
    r_val = FLA_Bidiag_UT_u_extract_diagonals( A, d, e );
 
  return r_val;
}

References FLA_Bidiag_UT_l_extract_diagonals(), FLA_Bidiag_UT_u_extract_diagonals(), FLA_Check_error_level(), FLA_Tridiag_UT_extract_diagonals_check(), and i.

FLA_Tridiag_UT_extract_real_diagonals()

FLA_Error FLA_Tridiag_UT_extract_real_diagonals	(	FLA_Uplo	uplo,
		FLA_Obj	A,
		FLA_Obj	d,
		FLA_Obj	e
	)

{
  FLA_Error r_val = FLA_SUCCESS;
 
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Tridiag_UT_extract_real_diagonals_check( uplo, A, d, e );
 
  if ( uplo == FLA_LOWER_TRIANGULAR )
    r_val = FLA_Bidiag_UT_l_extract_real_diagonals( A, d, e );
  else
    r_val = FLA_Bidiag_UT_u_extract_real_diagonals( A, d, e );
 
  return r_val;
}

References FLA_Bidiag_UT_l_extract_real_diagonals(), FLA_Bidiag_UT_u_extract_real_diagonals(), FLA_Check_error_level(), FLA_Tridiag_UT_extract_real_diagonals_check(), and i.

Referenced by FLA_Hevd_lv_unb_var1(), and FLA_Hevd_lv_unb_var2().

FLA_Tridiag_UT_form_Q()

FLA_Error FLA_Tridiag_UT_form_Q	(	FLA_Uplo	uplo,
		FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	Q
	)

{
    FLA_Error r_val = FLA_SUCCESS;
    FLA_Obj   ATL, ATR,
              ABL, ABR;
    FLA_Obj   QTL, QTR,
              QBL, QBR;
    FLA_Obj   TL,  TR;
 
    if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
        FLA_Tridiag_UT_form_Q_check( uplo, A, T, Q );
 
    // Adjust T.
    FLA_Part_1x2( T,    &TL, &TR,     1, FLA_RIGHT );
 
    if ( FLA_Obj_is( A, Q ) == FALSE )
    {
        FLA_Part_2x2( Q,  &QTL, &QTR,
                          &QBL, &QBR,   1, 1, FLA_TL );
 
        FLA_Set( FLA_ONE,  QTL );
        FLA_Set( FLA_ZERO, QTR );
        FLA_Set( FLA_ZERO, QBL );
 
        if ( uplo == FLA_LOWER_TRIANGULAR )
        {
            FLA_Part_2x2( A,  &ATL, &ATR,
                              &ABL, &ABR,   1, 1, FLA_TR );
            FLA_QR_UT_form_Q( ABL, TL, QBR );
        }
        else // ( uplo == FLA_UPPER_TRIANGULAR )
        {
            FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
        }
    }
    else
    {
        // Shift the Householder vectors one row/column towards the diagonal.
        FLA_Tridiag_UT_shift_U( uplo, A );
 
        FLA_Part_2x2( A,  &ATL, &ATR,
                          &ABL, &ABR,   1, 1, FLA_TL );
 
        if ( uplo == FLA_LOWER_TRIANGULAR )
        {
            FLA_QR_UT_form_Q( ABR, TL, ABR );
        }
        else // ( uplo == FLA_UPPER_TRIANGULAR )
        {
            FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
        }
    }
    return r_val;
}

References FLA_Check_error_level(), FLA_Obj_is(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x2(), FLA_QR_UT_form_Q(), FLA_Set(), FLA_Tridiag_UT_form_Q_check(), FLA_Tridiag_UT_shift_U(), FLA_ZERO, and i.

Referenced by FLA_Hevd_lv_unb_var1(), and FLA_Hevd_lv_unb_var2().

FLA_Tridiag_UT_form_Q_l_blk_var1()

FLA_Error FLA_Tridiag_UT_form_Q_l_blk_var1	(	FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	W
	)

FLA_Tridiag_UT_form_Q_l_opc_var1()

FLA_Error FLA_Tridiag_UT_form_Q_l_opc_var1	(	int	m_A,
		int	n_AT,
		scomplex *	buff_A,
		int	rs_A,
		int	cs_A,
		scomplex *	buff_T,
		int	rs_T,
		int	cs_T
	)

FLA_Tridiag_UT_form_Q_l_opd_var1()

FLA_Error FLA_Tridiag_UT_form_Q_l_opd_var1	(	int	m_A,
		int	n_AT,
		double *	buff_A,
		int	rs_A,
		int	cs_A,
		double *	buff_T,
		int	rs_T,
		int	cs_T
	)

FLA_Tridiag_UT_form_Q_l_ops_var1()

FLA_Error FLA_Tridiag_UT_form_Q_l_ops_var1	(	int	m_A,
		int	n_AT,
		float *	buff_A,
		int	rs_A,
		int	cs_A,
		float *	buff_T,
		int	rs_T,
		int	cs_T
	)

FLA_Tridiag_UT_form_Q_l_opt_var1()

FLA_Error FLA_Tridiag_UT_form_Q_l_opt_var1	(	FLA_Obj	A,
		FLA_Obj	T
	)

FLA_Tridiag_UT_form_Q_l_opz_var1()

FLA_Error FLA_Tridiag_UT_form_Q_l_opz_var1	(	int	m_A,
		int	n_AT,
		dcomplex *	buff_A,
		int	rs_A,
		int	cs_A,
		dcomplex *	buff_T,
		int	rs_T,
		int	cs_T
	)

FLA_Tridiag_UT_form_Q_u_blk_var1()

FLA_Error FLA_Tridiag_UT_form_Q_u_blk_var1	(	FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	W
	)

FLA_Tridiag_UT_internal()

FLA_Error FLA_Tridiag_UT_internal	(	FLA_Uplo	uplo,
		FLA_Obj	A,
		FLA_Obj	T,
		fla_tridiagut_t *	cntl
	)

{
    FLA_Error r_val = FLA_SUCCESS;
    
    if ( FLA_Check_error_level() == FLA_FULL_ERROR_CHECKING )
        FLA_Tridiag_UT_internal_check( uplo, A, T, cntl );
 
    if ( uplo == FLA_LOWER_TRIANGULAR )
    {
          r_val = FLA_Tridiag_UT_l( A, T, cntl );
    }
    else // if ( uplo == FLA_UPPER_TRIANGULAR )
    {
          FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
    }
 
    return r_val;
}

References FLA_Check_error_level(), FLA_Tridiag_UT_internal_check(), FLA_Tridiag_UT_l(), and i.

Referenced by FLA_Tridiag_UT().

FLA_Tridiag_UT_l()

FLA_Error FLA_Tridiag_UT_l	(	FLA_Obj	A,
		FLA_Obj	T,
		fla_tridiagut_t *	cntl
	)

{
    FLA_Error r_val = FLA_SUCCESS;
    
    if      ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT1 )
    {
        r_val = FLA_Tridiag_UT_l_unb_var1( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT2 )
    {
        r_val = FLA_Tridiag_UT_l_unb_var2( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT3 )
    {
        r_val = FLA_Tridiag_UT_l_unb_var3( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT1 )
    {
        r_val = FLA_Tridiag_UT_l_opt_var1( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT2 )
    {
        r_val = FLA_Tridiag_UT_l_opt_var2( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT3 )
    {
        r_val = FLA_Tridiag_UT_l_opt_var3( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT1 )
    {
        r_val = FLA_Tridiag_UT_l_blk_var1( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT2 )
    {
        r_val = FLA_Tridiag_UT_l_blk_var2( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT3 )
    {
        r_val = FLA_Tridiag_UT_l_blk_var3( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLK_FUS_VARIANT2 )
    {
        r_val = FLA_Tridiag_UT_l_blf_var2( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLK_FUS_VARIANT3 )
    {
        r_val = FLA_Tridiag_UT_l_blf_var3( A, T );
    }
    else
    {
        FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
    }
 
    return r_val;
}

References FLA_Tridiag_UT_l_blf_var2(), FLA_Tridiag_UT_l_blf_var3(), FLA_Tridiag_UT_l_blk_var1(), FLA_Tridiag_UT_l_blk_var2(), FLA_Tridiag_UT_l_blk_var3(), FLA_Tridiag_UT_l_opt_var1(), FLA_Tridiag_UT_l_opt_var2(), FLA_Tridiag_UT_l_opt_var3(), FLA_Tridiag_UT_l_unb_var1(), FLA_Tridiag_UT_l_unb_var2(), FLA_Tridiag_UT_l_unb_var3(), and i.

Referenced by FLA_Tridiag_UT_internal().

FLA_Tridiag_UT_l_realify_opt()

FLA_Error FLA_Tridiag_UT_l_realify_opt	(	FLA_Obj	A,
		FLA_Obj	d
	)

{
  FLA_Datatype datatype;
  int          m_A;
  int          rs_A, cs_A;
  int          inc_d;
  int          i;
 
  datatype = FLA_Obj_datatype( A );
 
  m_A      = FLA_Obj_length( A );
 
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );
 
  inc_d    = FLA_Obj_vector_inc( d );
 
 
  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_d = FLA_FLOAT_PTR( d );
      float* buff_1 = FLA_FLOAT_PTR( FLA_ONE );
 
      bl1_ssetv( m_A,
                 buff_1,
                 buff_d, inc_d );
 
      break;
    }
 
    case FLA_DOUBLE:
    {
      double* buff_d = FLA_DOUBLE_PTR( d );
      double* buff_1 = FLA_DOUBLE_PTR( FLA_ONE );
 
      bl1_dsetv( m_A,
                 buff_1,
                 buff_d, inc_d );
 
      break;
    }
 
    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_d = FLA_COMPLEX_PTR( d );
      scomplex* buff_1 = FLA_COMPLEX_PTR( FLA_ONE );
 
      bl1_csetv( 1,
                 buff_1,
                 buff_d, inc_d );
 
      for ( i = 1; i < m_A; ++i )
      {
        scomplex* a10t_r   = buff_A + (i-1)*cs_A + (i  )*rs_A;
        scomplex* a21_t    = buff_A + (i  )*cs_A + (i+1)*rs_A;
        scomplex* delta1   = buff_d + (i  )*inc_d;
        scomplex  absv;
        scomplex  conj_delta1;
 
        int       m_ahead  = m_A - i - 1;
 
        // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, a10t_r, delta1 );
        // FLA_Copyt( FLA_NO_TRANSPOSE, a10t_r, absv );
        // FLA_Absolute_value( absv );
        // FLA_Inv_scal( absv, delta1 );
        bl1_ccopys( BLIS1_CONJUGATE, a10t_r, delta1 );
        bl1_cabsval2( a10t_r, &absv );
        bl1_cinvscals( &absv, delta1 );
 
        // FLA_Copyt( FLA_NO_TRANSPOSE, absv, a10t_r );
        // FLA_Scalc( FLA_CONJUGATE, delta1, a21_t );
        *a10t_r = absv;
        if ( m_ahead > 0 )
        {
          bl1_ccopyconj( delta1, &conj_delta1 );
          bl1_cscals( &conj_delta1, a21_t );
        }
      }
 
      break;
    }
 
    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_d = FLA_DOUBLE_COMPLEX_PTR( d );
      dcomplex* buff_1 = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
 
      bl1_zsetv( 1,
                 buff_1,
                 buff_d, inc_d );
 
      for ( i = 1; i < m_A; ++i )
      {
        dcomplex* a10t_r   = buff_A + (i-1)*cs_A + (i  )*rs_A;
        dcomplex* a21_t    = buff_A + (i  )*cs_A + (i+1)*rs_A;
        dcomplex* delta1   = buff_d + (i  )*inc_d;
        dcomplex  absv;
        dcomplex  conj_delta1;
 
        int       m_ahead  = m_A - i - 1;
 
        // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, a10t_r, delta1 );
        // FLA_Copyt( FLA_NO_TRANSPOSE, a10t_r, absv );
        // FLA_Absolute_value( absv );
        // FLA_Inv_scal( absv, delta1 );
        bl1_zcopys( BLIS1_CONJUGATE, a10t_r, delta1 );
        bl1_zabsval2( a10t_r, &absv );
        bl1_zinvscals( &absv, delta1 );
 
        // FLA_Copyt( FLA_NO_TRANSPOSE, absv, a10t_r );
        // FLA_Scalc( FLA_CONJUGATE, delta1, a21_t );
        *a10t_r = absv;
        if ( m_ahead > 0 )
        {
          bl1_zcopyconj( delta1, &conj_delta1 );
          bl1_zscals( &conj_delta1, a21_t );
        }
      }
 
      break;
    }
  }
 
  return FLA_SUCCESS;
}

References bl1_csetv(), bl1_dsetv(), bl1_ssetv(), bl1_zscals(), bl1_zsetv(), BLIS1_CONJUGATE, FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_vector_inc(), FLA_ONE, and i.

Referenced by FLA_Tridiag_UT_realify().

FLA_Tridiag_UT_l_realify_unb()

FLA_Error FLA_Tridiag_UT_l_realify_unb	(	FLA_Obj	A,
		FLA_Obj	d
	)

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;
 
  FLA_Obj dT,              d0,
          dB,              delta1,
                           d2;
 
  FLA_Obj a10t_l, a10t_r;
 
  FLA_Obj a21_t,
          a21_b;
 
  FLA_Obj absv;
 
 
  FLA_Obj_create( FLA_Obj_datatype( A ), 1, 1, 0, 0, &absv );
 
  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     1, 1, FLA_TL );
 
  FLA_Part_2x1( d,    &dT,
                      &dB,            1, FLA_TOP );
 
  // Set first element of vector d to one.
  FLA_Set( FLA_ONE, dT );
 
  while ( FLA_Obj_min_dim( ABR ) > 0 )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x1_to_3x1( dT,                &d0, 
                        /* ** */            /* ****** */
                                              &delta1, 
                           dB,                &d2,        1, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
    FLA_Part_1x2( a10t,   &a10t_l, &a10t_r,    1, FLA_RIGHT );
 
    FLA_Part_2x1( a21,    &a21_t,
                          &a21_b,              1, FLA_TOP );
 
    // delta1 = conj(a10t_r) / abs(a10t_r);
    FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, a10t_r, delta1 );
    FLA_Copyt( FLA_NO_TRANSPOSE, a10t_r, absv );
    FLA_Absolute_value( absv );
    FLA_Inv_scal( absv, delta1 );
 
    // a10t_r  = delta1 * a10t_r;
    //         = abs(a10t_r);
    // alpha11 = delta1 * alpha11 * conj(delta1);
    //         = alpha11;
    // a21_t   = a21_t * conj(delta1);
    FLA_Copyt( FLA_NO_TRANSPOSE, absv, a10t_r );
    FLA_Scalc( FLA_CONJUGATE, delta1, a21_t );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
 
    FLA_Cont_with_3x1_to_2x1( &dT,                d0, 
                                                  delta1, 
                            /* ** */           /* ****** */
                              &dB,                d2,     FLA_TOP );
  }
 
  FLA_Obj_free( &absv );
 
  return FLA_SUCCESS;
}

References FLA_Absolute_value(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt(), FLA_Inv_scal(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scalc(), FLA_Set(), and i.

FLA_Tridiag_UT_realify()

FLA_Error FLA_Tridiag_UT_realify	(	FLA_Uplo	uplo,
		FLA_Obj	A,
		FLA_Obj	d
	)

{
  FLA_Error r_val = FLA_SUCCESS;
 
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Tridiag_UT_realify_check( uplo, A, d );
 
  if ( FLA_Obj_is_real( A ) )
  {
    FLA_Set( FLA_ONE, d );
    return FLA_SUCCESS;
  }
 
  if ( uplo == FLA_LOWER_TRIANGULAR )
    //r_val = FLA_Tridiag_UT_l_realify_unb( A, d );
    r_val = FLA_Tridiag_UT_l_realify_opt( A, d );
  else
    //r_val = FLA_Tridiag_UT_u_realify_unb( A, d );
    r_val = FLA_Tridiag_UT_u_realify_opt( A, d );
 
  return r_val;
}

References FLA_Check_error_level(), FLA_Obj_is_real(), FLA_ONE, FLA_Set(), FLA_Tridiag_UT_l_realify_opt(), FLA_Tridiag_UT_realify_check(), FLA_Tridiag_UT_u_realify_opt(), and i.

Referenced by FLA_Hevd_lv_unb_var1(), and FLA_Hevd_lv_unb_var2().

FLA_Tridiag_UT_realify_subdiagonal()

FLA_Error FLA_Tridiag_UT_realify_subdiagonal	(	FLA_Obj	b,
		FLA_Obj	d
	)

{
  FLA_Error r_val = FLA_SUCCESS;
 
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Tridiag_UT_realify_subdiagonal_check( b, d );
 
  r_val = FLA_Tridiag_UT_realify_subdiagonal_opt( b, d );
 
  return r_val;
}

References FLA_Check_error_level(), FLA_Tridiag_UT_realify_subdiagonal_check(), FLA_Tridiag_UT_realify_subdiagonal_opt(), and i.

FLA_Tridiag_UT_realify_subdiagonal_opt()

FLA_Error FLA_Tridiag_UT_realify_subdiagonal_opt	(	FLA_Obj	b,
		FLA_Obj	d
	)

{
  FLA_Datatype datatype;
  int          m, inc_b, inc_d;
  int          i;
 
  datatype = FLA_Obj_datatype( d );
 
  m        = FLA_Obj_vector_dim( d );
  inc_d    = FLA_Obj_vector_inc( d );
 
  inc_b    = ( m > 1 ? FLA_Obj_vector_inc( b ) : 0 );
 
  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_d = FLA_FLOAT_PTR( d );
      float* buff_1 = FLA_FLOAT_PTR( FLA_ONE );
 
      bl1_ssetv( m,
                 buff_1,
                 buff_d, inc_d );
 
      break;
    }
    case FLA_DOUBLE:
    {
      double* buff_d = FLA_DOUBLE_PTR( d );
      double* buff_1 = FLA_DOUBLE_PTR( FLA_ONE );
 
      bl1_dsetv( m,
                 buff_1,
                 buff_d, inc_d );
 
      break;
    }
    case FLA_COMPLEX:
    {
      scomplex* buff_b = ( m > 1 ? FLA_COMPLEX_PTR( b ) : NULL );
      scomplex* buff_d = FLA_COMPLEX_PTR( d );
      scomplex* buff_1 = FLA_COMPLEX_PTR( FLA_ONE );
 
      bl1_csetv( 1,
                 buff_1,
                 buff_d, inc_d );
 
      for ( i = 1; i < m; ++i )
      {
        scomplex* beta1  = buff_b + (i-1)*inc_b;
        scomplex* delta1 = buff_d + (i  )*inc_d;
        scomplex  absv;
        scomplex  conj_delta1;
 
        if ( beta1->imag == 0.0F )
          *delta1 = *buff_1;
        else
        {
          bl1_ccopys( BLIS1_CONJUGATE, beta1, delta1 );
          bl1_cabsval2( beta1, &absv );
          bl1_cinvscals( &absv, delta1 );
          
          *beta1 = absv;
        }
        if ( i < ( m - 1 ) )
        {
          scomplex* beta2 = buff_b + (i  )*inc_b;
          bl1_ccopyconj( delta1, &conj_delta1 );
          bl1_cscals( &conj_delta1, beta2 );
        }
      }
      break;
    }
    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_b = ( m > 1 ? FLA_DOUBLE_COMPLEX_PTR( b ) : NULL );
      dcomplex* buff_d = FLA_DOUBLE_COMPLEX_PTR( d );
      dcomplex* buff_1 = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
 
      bl1_zsetv( 1,
                 buff_1,
                 buff_d, inc_d );
 
      for ( i = 1; i < m; ++i )
      {
        dcomplex* beta1  = buff_b + (i-1)*inc_b;
        dcomplex* delta1 = buff_d + (i  )*inc_d;
        dcomplex  absv;
        dcomplex  conj_delta1;
 
        if ( beta1->imag == 0.0 )
          *delta1 = *buff_1;
        else
        {
          bl1_zcopys( BLIS1_CONJUGATE, beta1, delta1 );
          bl1_zabsval2( beta1, &absv );
          bl1_zinvscals( &absv, delta1 );
 
          *beta1 = absv;
        }
        if ( i < ( m - 1 ) )
        {
          dcomplex* beta2 = buff_b + (i  )*inc_b;
          bl1_zcopyconj( delta1, &conj_delta1 );
          bl1_zscals( &conj_delta1, beta2 );
        }
      }
      break;
    }
  }
 
  return FLA_SUCCESS;
}

References bl1_csetv(), bl1_dsetv(), bl1_ssetv(), bl1_zscals(), bl1_zsetv(), BLIS1_CONJUGATE, FLA_Obj_datatype(), FLA_Obj_vector_dim(), FLA_Obj_vector_inc(), FLA_ONE, and i.

Referenced by FLA_Tridiag_UT_realify_subdiagonal().

FLA_Tridiag_UT_recover_tau()

FLA_Error FLA_Tridiag_UT_recover_tau	(	FLA_Obj	T,
		FLA_Obj	t
	)

{
  FLA_Obj TL,    TR,       T0,  T1,  T2;
 
  FLA_Obj tT,              t0,
          tB,              t1,
                           t2;
 
  dim_t b_alg, b;
 
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Tridiag_UT_recover_tau_check( T, t );
 
  b_alg = FLA_Obj_length( T );
 
  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT );
 
  FLA_Part_2x1( t,    &tT, 
                      &tB,            0, FLA_TOP );
 
  while ( FLA_Obj_length( tT ) < FLA_Obj_length( t ) ){
 
    b = min( FLA_Obj_length( tB ), b_alg );
 
    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &T2,
                           b, FLA_RIGHT );
 
    FLA_Repart_2x1_to_3x1( tT,                &t0, 
                        /* ** */            /* ** */
                                              &t1, 
                           tB,                &t2,        b, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
    FLA_Tridiag_UT_recover_tau_submatrix( T1, t1 );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ T2,
                              FLA_LEFT );
 
    FLA_Cont_with_3x1_to_2x1( &tT,                t0, 
                                                  t1, 
                            /* ** */           /* ** */
                              &tB,                t2,     FLA_TOP );
  }
 
  return FLA_SUCCESS;
}

References FLA_Check_error_level(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Obj_length(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Tridiag_UT_recover_tau_check(), FLA_Tridiag_UT_recover_tau_submatrix(), and i.

FLA_Tridiag_UT_scale_diagonals()

FLA_Error FLA_Tridiag_UT_scale_diagonals	(	FLA_Uplo	uplo,
		FLA_Obj	alpha,
		FLA_Obj	A
	)

{
  FLA_Error r_val = FLA_SUCCESS;
 
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Tridiag_UT_scale_diagonals_check( uplo, alpha, A );
  
  if ( uplo == FLA_LOWER_TRIANGULAR )
    r_val = FLA_Bidiag_UT_l_scale_diagonals( alpha, A );
  else
    r_val = FLA_Bidiag_UT_u_scale_diagonals( alpha, A );
 
  return r_val;
}

References FLA_Bidiag_UT_l_scale_diagonals(), FLA_Bidiag_UT_u_scale_diagonals(), FLA_Check_error_level(), FLA_Tridiag_UT_scale_diagonals_check(), and i.

FLA_Tridiag_UT_shift_U()

FLA_Error FLA_Tridiag_UT_shift_U	(	FLA_Uplo	uplo,
		FLA_Obj	A
	)

{
    FLA_Datatype datatype;
    int          m_A;
    int          rs_A, cs_A;
 
    if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
        FLA_Tridiag_UT_shift_U_check( uplo, A );
 
    datatype = FLA_Obj_datatype( A );
 
        // Play with swapping of cs rs; we do not need "u" version.
        if ( uplo == FLA_LOWER_TRIANGULAR ) 
          {
            m_A      = FLA_Obj_length( A );
            rs_A     = FLA_Obj_row_stride( A );
            cs_A     = FLA_Obj_col_stride( A );
          }
        else
          {
            m_A      = FLA_Obj_width( A );
            cs_A     = FLA_Obj_row_stride( A );
            rs_A     = FLA_Obj_col_stride( A );
          }
 
    switch ( datatype )
    {
        case FLA_FLOAT:
        {
            float*    buff_A = ( float* ) FLA_FLOAT_PTR( A );
                        FLA_Tridiag_UT_shift_U_l_ops( m_A,
                                                      buff_A, rs_A, cs_A );
            break;
        }
 
        case FLA_DOUBLE:
        {
            double*   buff_A = ( double* ) FLA_DOUBLE_PTR( A );
                        FLA_Tridiag_UT_shift_U_l_opd( m_A,
                                                      buff_A, rs_A, cs_A );
            break;
        }
 
        case FLA_COMPLEX:
        {
            scomplex* buff_A = ( scomplex* ) FLA_COMPLEX_PTR( A );
                        FLA_Tridiag_UT_shift_U_l_opc( m_A,
                                                      buff_A, rs_A, cs_A );
            break;
        }
 
        case FLA_DOUBLE_COMPLEX:
        {
            dcomplex* buff_A = ( dcomplex* ) FLA_DOUBLE_COMPLEX_PTR( A );
                        FLA_Tridiag_UT_shift_U_l_opz( m_A,
                                                      buff_A, rs_A, cs_A );
            break;
        }
    }
 
    return FLA_SUCCESS;
}

References FLA_Check_error_level(), FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_width(), FLA_Tridiag_UT_shift_U_check(), FLA_Tridiag_UT_shift_U_l_opc(), FLA_Tridiag_UT_shift_U_l_opd(), FLA_Tridiag_UT_shift_U_l_ops(), FLA_Tridiag_UT_shift_U_l_opz(), and i.

Referenced by FLA_Tridiag_UT_form_Q().

FLA_Tridiag_UT_shift_U_l_opc()

FLA_Error FLA_Tridiag_UT_shift_U_l_opc	(	int	m_A,
		scomplex *	buff_A,
		int	rs_A,
		int	cs_A
	)

{
    scomplex* a00  = buff_A;
    scomplex* a10  = buff_A + rs_A;
    scomplex  zero = bl1_c0();
    scomplex  one  = bl1_c1();
    int       j;
 
    for ( j = m_A - 1; j > 0; --j )
    {
        scomplex* alpha01  = buff_A + (j  )*cs_A + (0  )*rs_A;
        scomplex* alpha11  = buff_A + (j  )*cs_A + (j  )*rs_A;
        scomplex* a20      = buff_A + (j-1)*cs_A + (j+1)*rs_A;
        scomplex* a21      = buff_A + (j  )*cs_A + (j+1)*rs_A;
 
        int       m_ahead  = m_A - j - 1;
 
        *alpha01 = zero;
        *alpha11 = one;
        bl1_ccopyv( BLIS1_NO_CONJUGATE,
                    m_ahead,
                    a20, rs_A,
                    a21, rs_A );
    }
 
    *a00 = one;
    bl1_csetv( m_A - 1,
               &zero,
               a10, rs_A );
 
    return FLA_SUCCESS;
}

References bl1_c0(), bl1_c1(), bl1_ccopyv(), bl1_csetv(), BLIS1_NO_CONJUGATE, and i.

Referenced by FLA_Tridiag_UT_shift_U().

FLA_Tridiag_UT_shift_U_l_opd()

FLA_Error FLA_Tridiag_UT_shift_U_l_opd	(	int	m_A,
		double *	buff_A,
		int	rs_A,
		int	cs_A
	)

{
    double* a00  = buff_A;
    double* a10  = buff_A + rs_A;
    double  zero = bl1_d0();
    double  one  = bl1_d1();
    int     j;
 
    for ( j = m_A - 1; j > 0; --j )
    {
        double*   alpha01  = buff_A + (j  )*cs_A + (0  )*rs_A;
        double*   alpha11  = buff_A + (j  )*cs_A + (j  )*rs_A;
        double*   a20      = buff_A + (j-1)*cs_A + (j+1)*rs_A;
        double*   a21      = buff_A + (j  )*cs_A + (j+1)*rs_A;
 
        int       m_ahead  = m_A - j - 1;
 
        *alpha01 = zero;
        *alpha11 = one;
        bl1_dcopyv( BLIS1_NO_CONJUGATE,
                    m_ahead,
                    a20, rs_A,
                    a21, rs_A );
    }
 
    *a00 = one;
    bl1_dsetv( m_A - 1,
               &zero,
               a10, rs_A );
 
    return FLA_SUCCESS;
}

References bl1_d0(), bl1_d1(), bl1_dcopyv(), bl1_dsetv(), BLIS1_NO_CONJUGATE, and i.

Referenced by FLA_Tridiag_UT_shift_U().

FLA_Tridiag_UT_shift_U_l_ops()

FLA_Error FLA_Tridiag_UT_shift_U_l_ops	(	int	m_A,
		float *	buff_A,
		int	rs_A,
		int	cs_A
	)

{
    float*  a00  = buff_A;
    float*  a10  = buff_A + rs_A;
    float   zero = bl1_s0();
    float   one  = bl1_s1();
    int     j;
 
    for ( j = m_A - 1; j > 0; --j )
    {
        float*    alpha01  = buff_A + (j  )*cs_A + (0  )*rs_A;
        float*    alpha11  = buff_A + (j  )*cs_A + (j  )*rs_A;
        float*    a20      = buff_A + (j-1)*cs_A + (j+1)*rs_A;
        float*    a21      = buff_A + (j  )*cs_A + (j+1)*rs_A;
 
        int       m_ahead  = m_A - j - 1;
 
        *alpha01 = zero;
        *alpha11 = one;
        bl1_scopyv( BLIS1_NO_CONJUGATE,
                    m_ahead,
                    a20, rs_A,
                    a21, rs_A );
    }
 
    *a00 = one;
    bl1_ssetv( m_A - 1,
               &zero,
               a10, rs_A );
 
    return FLA_SUCCESS;
}

References bl1_s0(), bl1_s1(), bl1_scopyv(), bl1_ssetv(), BLIS1_NO_CONJUGATE, and i.

Referenced by FLA_Tridiag_UT_shift_U().

FLA_Tridiag_UT_shift_U_l_opz()

FLA_Error FLA_Tridiag_UT_shift_U_l_opz	(	int	m_A,
		dcomplex *	buff_A,
		int	rs_A,
		int	cs_A
	)

{
    dcomplex* a00  = buff_A;
    dcomplex* a10  = buff_A + rs_A;
    dcomplex  zero = bl1_z0();
    dcomplex  one  = bl1_z1();
    int       j;
 
    for ( j = m_A - 1; j > 0; --j )
    {
        dcomplex* alpha01  = buff_A + (j  )*cs_A + (0  )*rs_A;
        dcomplex* alpha11  = buff_A + (j  )*cs_A + (j  )*rs_A;
        dcomplex* a20      = buff_A + (j-1)*cs_A + (j+1)*rs_A;
        dcomplex* a21      = buff_A + (j  )*cs_A + (j+1)*rs_A;
 
        int       m_ahead  = m_A - j - 1;
 
        *alpha01 = zero;
        *alpha11 = one;
        bl1_zcopyv( BLIS1_NO_CONJUGATE,
                    m_ahead,
                    a20, rs_A,
                    a21, rs_A );
    }
 
    *a00 = one;
    bl1_zsetv( m_A - 1,
               &zero,
               a10, rs_A );
 
    return FLA_SUCCESS;
}

References bl1_z0(), bl1_z1(), bl1_zcopyv(), bl1_zsetv(), BLIS1_NO_CONJUGATE, and i.

Referenced by FLA_Tridiag_UT_shift_U().

FLA_Tridiag_UT_shift_U_u_opc()

FLA_Error FLA_Tridiag_UT_shift_U_u_opc	(	int	m_A,
		scomplex *	buff_A,
		int	rs_A,
		int	cs_A
	)

FLA_Tridiag_UT_shift_U_u_opd()

FLA_Error FLA_Tridiag_UT_shift_U_u_opd	(	int	m_A,
		double *	buff_A,
		int	rs_A,
		int	cs_A
	)

FLA_Tridiag_UT_shift_U_u_ops()

FLA_Error FLA_Tridiag_UT_shift_U_u_ops	(	int	m_A,
		float *	buff_A,
		int	rs_A,
		int	cs_A
	)

FLA_Tridiag_UT_shift_U_u_opz()

FLA_Error FLA_Tridiag_UT_shift_U_u_opz	(	int	m_A,
		dcomplex *	buff_A,
		int	rs_A,
		int	cs_A
	)

FLA_Tridiag_UT_u()

FLA_Error FLA_Tridiag_UT_u	(	FLA_Obj	A,
		FLA_Obj	T,
		fla_tridiagut_t *	cntl
	)

{
    FLA_Error r_val = FLA_SUCCESS;
    
/*
    if      ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT1 )
    {
        r_val = FLA_Tridiag_UT_u_unb_var1( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT2 )
    {
        r_val = FLA_Tridiag_UT_u_unb_var2( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT3 )
    {
        r_val = FLA_Tridiag_UT_u_unb_var3( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT1 )
    {
        r_val = FLA_Tridiag_UT_u_opt_var1( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT2 )
    {
        r_val = FLA_Tridiag_UT_u_opt_var2( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT3 )
    {
        r_val = FLA_Tridiag_UT_u_opt_var3( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT1 )
    {
        r_val = FLA_Tridiag_UT_u_blk_var1( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT2 )
    {
        r_val = FLA_Tridiag_UT_u_blk_var2( A, T );
    }
    else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT3 )
    {
        r_val = FLA_Tridiag_UT_u_blk_var3( A, T );
    }
    else
*/
    {
        FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
    }
 
    return r_val;
}

References i.

FLA_Tridiag_UT_u_realify_opt()

FLA_Error FLA_Tridiag_UT_u_realify_opt	(	FLA_Obj	A,
		FLA_Obj	d
	)

{
  FLA_Datatype datatype;
  int          m_A;
  int          rs_A, cs_A;
  int          inc_d;
  int          i;
 
  datatype = FLA_Obj_datatype( A );
 
  m_A      = FLA_Obj_length( A );
 
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );
 
  inc_d    = FLA_Obj_vector_inc( d );
 
 
  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_d = FLA_FLOAT_PTR( d );
      float* buff_1 = FLA_FLOAT_PTR( FLA_ONE );
 
      bl1_ssetv( m_A,
                 buff_1,
                 buff_d, inc_d );
 
      break;
    }
 
    case FLA_DOUBLE:
    {
      double* buff_d = FLA_DOUBLE_PTR( d );
      double* buff_1 = FLA_DOUBLE_PTR( FLA_ONE );
 
      bl1_dsetv( m_A,
                 buff_1,
                 buff_d, inc_d );
 
      break;
    }
 
    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_d = FLA_COMPLEX_PTR( d );
      scomplex* buff_1 = FLA_COMPLEX_PTR( FLA_ONE );
 
      bl1_csetv( 1,
                 buff_1,
                 buff_d, inc_d );
 
      for ( i = 1; i < m_A; ++i )
      {
        scomplex* a01_b    = buff_A + (i  )*cs_A + (i-1)*rs_A;
        scomplex* a12t_l   = buff_A + (i+1)*cs_A + (i  )*rs_A;
        scomplex* delta1   = buff_d + (i  )*inc_d;
        scomplex  absv;
        scomplex  conj_delta1;
 
        int       m_ahead  = m_A - i - 1;
 
        // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, a01_b, delta1 );
        // FLA_Copyt( FLA_NO_TRANSPOSE, a01_b, absv );
        // FLA_Absolute_value( absv );
        // FLA_Inv_scal( absv, delta1 );
        bl1_ccopys( BLIS1_CONJUGATE, a01_b, delta1 );
        bl1_cabsval2( a01_b, &absv );
        bl1_cinvscals( &absv, delta1 );
 
        // FLA_Copyt( FLA_NO_TRANSPOSE, absv, a01_b );
        // FLA_Scalc( FLA_CONJUGATE, delta1, a12t_l );
        *a01_b = absv;
        if ( m_ahead > 0 )
        {
          bl1_ccopyconj( delta1, &conj_delta1 );
          bl1_cscals( &conj_delta1, a12t_l );
        }
      }
 
      break;
    }
 
    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_d = FLA_DOUBLE_COMPLEX_PTR( d );
      dcomplex* buff_1 = FLA_DOUBLE_COMPLEX_PTR( FLA_ONE );
 
      bl1_zsetv( 1,
                 buff_1,
                 buff_d, inc_d );
 
      for ( i = 1; i < m_A; ++i )
      {
        dcomplex* a01_b    = buff_A + (i  )*cs_A + (i-1)*rs_A;
        dcomplex* a12t_l   = buff_A + (i+1)*cs_A + (i  )*rs_A;
        dcomplex* delta1   = buff_d + (i  )*inc_d;
        dcomplex  absv;
        dcomplex  conj_delta1;
 
        int       m_ahead  = m_A - i - 1;
 
        // FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, a01_b, delta1 );
        // FLA_Copyt( FLA_NO_TRANSPOSE, a01_b, absv );
        // FLA_Absolute_value( absv );
        // FLA_Inv_scal( absv, delta1 );
        bl1_zcopys( BLIS1_CONJUGATE, a01_b, delta1 );
        bl1_zabsval2( a01_b, &absv );
        bl1_zinvscals( &absv, delta1 );
 
        // FLA_Copyt( FLA_NO_TRANSPOSE, absv, a01_b );
        // FLA_Scalc( FLA_CONJUGATE, delta1, a12t_l );
        *a01_b = absv;
        if ( m_ahead > 0 )
        {
          bl1_zcopyconj( delta1, &conj_delta1 );
          bl1_zscals( &conj_delta1, a12t_l );
        }
      }
 
      break;
    }
  }
 
  return FLA_SUCCESS;
}

References bl1_csetv(), bl1_dsetv(), bl1_ssetv(), bl1_zscals(), bl1_zsetv(), BLIS1_CONJUGATE, FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_vector_inc(), FLA_ONE, and i.

Referenced by FLA_Tridiag_UT_realify().

FLA_Tridiag_UT_u_realify_unb()

FLA_Error FLA_Tridiag_UT_u_realify_unb	(	FLA_Obj	A,
		FLA_Obj	d
	)

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;
 
  FLA_Obj dT,              d0,
          dB,              delta1,
                           d2;
 
  FLA_Obj a01_t,
          a01_b;
 
  FLA_Obj a12t_l, a12t_r;
 
 
  FLA_Obj absv;
 
 
  FLA_Obj_create( FLA_Obj_datatype( A ), 1, 1, 0, 0, &absv );
 
  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     1, 1, FLA_TL );
 
  FLA_Part_2x1( d,    &dT,
                      &dB,            1, FLA_TOP );
 
  // Set first element of vector d to one.
  FLA_Set( FLA_ONE, dT );
 
  while ( FLA_Obj_min_dim( ABR ) > 0 )
  {
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x1_to_3x1( dT,                &d0, 
                        /* ** */            /* ****** */
                                              &delta1, 
                           dB,                &d2,        1, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
    FLA_Part_2x1( a01,    &a01_t,
                          &a01_b,              1, FLA_BOTTOM );
 
    FLA_Part_1x2( a12t,   &a12t_l, &a12t_r,    1, FLA_LEFT );
 
    // delta1 = conj(a01_b) / abs(a01_b);
    FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, a01_b, delta1 );
    FLA_Copyt( FLA_NO_TRANSPOSE, a01_b, absv );
    FLA_Absolute_value( absv );
    FLA_Inv_scal( absv, delta1 );
 
    // a01_b   = delta1 * a01_b;
    //         = abs(a01_b);
    // alpha11 = delta1 * alpha11 * conj(delta1);
    //         = alpha11;
    // a12t_l  = a12t_l * conj(delta1);
    FLA_Copyt( FLA_NO_TRANSPOSE, absv, a01_b );
    FLA_Scalc( FLA_CONJUGATE, delta1, a12t_l );
 
    /*------------------------------------------------------------*/
 
    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( &dT,                d0, 
                                                  delta1, 
                            /* ** */           /* ****** */
                              &dB,                d2,     FLA_TOP );
  }
 
  FLA_Obj_free( &absv );
 
  return FLA_SUCCESS;
}

References FLA_Absolute_value(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt(), FLA_Inv_scal(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scalc(), FLA_Set(), and i.