libflame  revision_anchor
Functions
FLA_QR_UT.h File Reference

(r)

Go to the source code of this file.

Functions

FLA_Error FLA_QR_UT (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_QR_UT_internal (FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl)
FLA_Error FLA_QR_UT_copy_internal (FLA_Obj A, FLA_Obj T, FLA_Obj U, fla_qrut_t *cntl)
FLA_Error FLA_QR_UT_create_T (FLA_Obj A, FLA_Obj *T)
FLA_Error FLA_QR_UT_recover_tau (FLA_Obj T, FLA_Obj tau)
FLA_Error FLA_QR_UT_solve (FLA_Obj A, FLA_Obj T, FLA_Obj B, FLA_Obj X)
FLA_Error FLASH_QR_UT (FLA_Obj A, FLA_Obj TW)
FLA_Error FLASH_QR_UT_create_hier_matrices (FLA_Obj A_flat, dim_t depth, dim_t *b_flash, FLA_Obj *A, FLA_Obj *TW)
FLA_Error FLASH_QR_UT_solve (FLA_Obj A, FLA_Obj T, FLA_Obj B, FLA_Obj X)
FLA_Error FLA_QR_UT_form_Q (FLA_Obj A, FLA_Obj T, FLA_Obj Q)
FLA_Error FLA_QR_UT_form_Q_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W)
FLA_Error FLA_QR_UT_form_Q_opt_var1 (FLA_Obj A, FLA_Obj T)
FLA_Error FLA_QR_UT_form_Q_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_QR_UT_form_Q_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_QR_UT_form_Q_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_QR_UT_form_Q_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

References FLA_Check_error_level(), FLA_QR_UT_check(), and FLA_QR_UT_internal().

{
  FLA_Error r_val;

  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_QR_UT_check( A, T );

  // Invoke FLA_QR_UT_internal() with the standard control tree.
  //r_val = FLA_QR_UT_internal( A, T, fla_qrut_cntl2 );
  r_val = FLA_QR_UT_internal( A, T, fla_qrut_cntl_leaf );

  return r_val;
}

References FLA_Check_error_level(), FLA_QR_UT_copy_internal_check(), FLA_QR_UT_copy_task(), and FLASH_Queue_get_enabled().

Referenced by FLA_QR_UT_inc_blk_var2().

{
    FLA_Error r_val = FLA_SUCCESS;
    
    if ( FLA_Check_error_level() == FLA_FULL_ERROR_CHECKING )
        FLA_QR_UT_copy_internal_check( A, T, U, cntl );

    if ( FLASH_Queue_get_enabled() )
    {
        // Enqueue task.
        ENQUEUE_FLASH_QR_UT_copy( *FLASH_OBJ_PTR_AT( A ),
                                  *FLASH_OBJ_PTR_AT( T ),
                                  *FLASH_OBJ_PTR_AT( U ),
                                  NULL );
    }
    else
    {
        // Execute task immediately.
        FLA_QR_UT_copy_task( *FLASH_OBJ_PTR_AT( A ),
                             *FLASH_OBJ_PTR_AT( T ),
                             *FLASH_OBJ_PTR_AT( U ),
                             NULL );
    }

    return r_val;
}

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

Referenced by FLA_Random_unitary_matrix(), FLA_Svd_uv_unb_var1(), and FLA_Svd_uv_unb_var2().

{
  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_QR_INNER_TO_OUTER_B_RATIO );

  // Query the minimum dimension of A.
  k = FLA_Obj_min_dim( A );

  // 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 QR factorization algorithm.
  FLA_Obj_create( datatype, b_alg, k, rs_T, cs_T, T );

  return FLA_SUCCESS;
}

References FLA_Apply_Q_UT_create_workspace(), FLA_Check_error_level(), FLA_Copyr(), FLA_Merge_2x1(), FLA_Obj_free(), FLA_Obj_is(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x2(), FLA_QR_UT_form_Q_blk_var1(), FLA_QR_UT_form_Q_check(), FLA_Set_diag(), FLA_Setr(), and FLA_ZERO.

Referenced by FLA_Bidiag_UT_form_U(), FLA_Bidiag_UT_form_V(), FLA_Random_unitary_matrix(), FLA_Svd_uv_unb_var1(), FLA_Svd_uv_unb_var2(), and FLA_Tridiag_UT_form_Q().

{
    FLA_Error r_val = FLA_SUCCESS;
    FLA_Obj   QTL, QTR,
              QBL, QBR;
    FLA_Obj   QL;
    FLA_Obj   W;
    dim_t     n_A;

    if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
        FLA_QR_UT_form_Q_check( A, T, Q );

    // Zero out the upper triangle of Q.
    FLA_Setr( FLA_UPPER_TRIANGULAR, FLA_ZERO, Q );

    // If A and Q are different objects, copy the Householder vectors
    // from A to QT, and zero out the lower triangle of QBR. If they
    // are the same object, we don't need to do the copy, and don't
    // need to zero anything out since the user should only have A and
    // Q be the same object if A is square, since Q needs to be square
    // (specifically, dim(Q) needs to equal m(A)).
    if ( FLA_Obj_is( A, Q ) == FALSE )
    {
        n_A = FLA_Obj_width( A );
        FLA_Part_2x2( Q,   &QTL, &QTR,
                           &QBL, &QBR,   n_A, n_A, FLA_TL );
        FLA_Merge_2x1( QTL,
                       QBL,  &QL );

        // Copy the Householder vectors in A to QL.
        FLA_Copyr( FLA_LOWER_TRIANGULAR, A, QL );

        // Zero out the lower triangle of QBR.
        FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, QBR );
    }

    // Set the digaonal to one.
    FLA_Set_diag( FLA_ONE, Q );

    // Create workspace for applying the block Householder transforms.
    FLA_Apply_Q_UT_create_workspace( T, Q, &W );

    // Overwrite Q, which currently contains Householder vectors in the
    // strictly lower triangle and identity in the upper triangle, with
    // the unitary matrix associated with those Householder transforms.
    r_val = FLA_QR_UT_form_Q_blk_var1( Q, T, W );
    
    // Free the temporary workspace.
    FLA_Obj_free( &W );

/*
FLA_Apply_Q_UT_create_workspace( T, Q, &W );
FLA_Set_to_identity( Q );
FLA_Apply_Q_UT( FLA_LEFT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                A, T, W, Q );
FLA_Obj_free( &W );
FLA_Obj_show( "Q", Q, "%8.1e %8.1e ", "" );
*/

    return r_val;
}

References FLA_Apply_Q_UT(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Merge_2x1(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_form_Q_opt_var1(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_QR_UT_form_Q().

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

  FLA_Obj TL,    TR,       T0,  T1,  T2;

  FLA_Obj T1T,
          T2B;

  FLA_Obj WTL,  WTR,
          WBL,  WBR;

  FLA_Obj AB1,   AB2;

  dim_t   b, b_alg;
  dim_t   m_BR, n_BR;

  b_alg = FLA_Obj_length( T );

  // If A is wider than T, then we need to position ourseves carefully
  // within the matrix for the initial partitioning.
  if ( FLA_Obj_width( A ) > FLA_Obj_width( T ) )
  {
    m_BR = FLA_Obj_length( A ) - FLA_Obj_width( T );
    n_BR = FLA_Obj_width( A ) - FLA_Obj_width( T );
  }
  else
  {
    m_BR = 0;
    n_BR = 0;
  }
//printf( "\nn(A) n(T) = %d %d\n", FLA_Obj_width( A ), FLA_Obj_width( T ) );
//printf(   "m_BR n_BR = %d %d\n", m_BR, n_BR );

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     m_BR, n_BR, FLA_BR );

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

  while ( FLA_Obj_length( ATL ) > 0 )
  {
    b = min( b_alg, FLA_Obj_min_dim( ATL ) );

    // Since T was filled from left to right, and since we need to access them
    // in reverse order, we need to handle the case where the last block is
    // smaller than the other b x b blocks.
    if ( FLA_Obj_width( TR ) == 0 && FLA_Obj_width( T ) % b_alg > 0 )
      b = FLA_Obj_width( T ) % b_alg;

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

    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, &T1, /**/ &T2,
                           b, FLA_LEFT );

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

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

    FLA_Part_2x2( W,     &WTL, &WTR,
                         &WBL, &WBR,     b, FLA_Obj_width( A12 ), FLA_TL );

    // Use an unblocked algorithm for the first (or only) block.
    if ( FLA_Obj_length( ABR ) == 0 )
    {
      FLA_QR_UT_form_Q_opt_var1( A11, T1T );
    }
    else
    {
      FLA_Merge_2x1( A11,
                     A21,   &AB1 );
      FLA_Merge_2x1( A12,
                     A22,   &AB2 );

      // Apply the block Householder transforms to A12 and A22.
      FLA_Apply_Q_UT( FLA_LEFT, FLA_NO_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                      AB1, T1T, WTL, AB2 );

      // Apply H to the current block panel consisting of A11 and A21.
      FLA_QR_UT_form_Q_opt_var1( AB1, T1T );
    }

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

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

    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, /**/ T1, T2,
                              FLA_RIGHT );
  }

  return FLA_SUCCESS;
}
FLA_Error FLA_QR_UT_form_Q_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 
)

References bli_c0(), bli_c1(), bli_cscalv(), BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_opc_var1(), scomplex::imag, and scomplex::real.

Referenced by FLA_QR_UT_form_Q_opt_var1().

{
    scomplex zero    = bli_c0();
    scomplex one     = bli_c1();
    int      min_m_n = min( m_A, n_A );
    int      i;

    for ( i = min_m_n - 1; i >= 0; --i )
    {
        //scomplex* a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
        scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
        scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
        scomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
        scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

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

        scomplex  minus_inv_tau11;

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

        FLA_Apply_H2_UT_l_opc_var1( m_ahead,
                                    n_ahead,
                                    tau11,
                                    a21,  rs_A,
                                    a12t, cs_A,
                                    A22,  rs_A, cs_A );

        minus_inv_tau11.real = -one.real / tau11->real;
        minus_inv_tau11.imag = zero.imag;

        alpha11->real = one.real + minus_inv_tau11.real;
        alpha11->imag = zero.imag;

        bli_cscalv( BLIS_NO_CONJUGATE,
                    m_ahead,
                    &minus_inv_tau11,
                    a21, rs_A );

        // Not necessary if upper triangle of A is initialized to identity.
        //bli_csetv( m_behind,
        //           &zero,
        //           a01, rs_A );
    }

    return FLA_SUCCESS;
}
FLA_Error FLA_QR_UT_form_Q_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 
)

References bli_d1(), bli_dscalv(), BLIS_NO_CONJUGATE, and FLA_Apply_H2_UT_l_opd_var1().

Referenced by FLA_QR_UT_form_Q_opt_var1().

{
    double   one     = bli_d1();
    int      min_m_n = min( m_A, n_A );
    int      i;

    for ( i = min_m_n - 1; i >= 0; --i )
    {
        //double*   a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
        double*   alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
        double*   a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
        double*   a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
        double*   A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

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

        double    minus_inv_tau11;

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

        FLA_Apply_H2_UT_l_opd_var1( m_ahead,
                                    n_ahead,
                                    tau11,
                                    a21,  rs_A,
                                    a12t, cs_A,
                                    A22,  rs_A, cs_A );

        minus_inv_tau11 = -one / *tau11;

        *alpha11 = one + minus_inv_tau11;

        bli_dscalv( BLIS_NO_CONJUGATE,
                    m_ahead,
                    &minus_inv_tau11,
                    a21, rs_A );

        // Not necessary if upper triangle of A is initialized to identity.
        //bli_dsetv( m_behind,
        //           &zero,
        //           a01, rs_A );
    }

    return FLA_SUCCESS;
}
FLA_Error FLA_QR_UT_form_Q_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 
)

References bli_d1(), bli_sscalv(), BLIS_NO_CONJUGATE, and FLA_Apply_H2_UT_l_ops_var1().

Referenced by FLA_QR_UT_form_Q_opt_var1().

{
    float    one     = bli_d1();
    int      min_m_n = min( m_A, n_A );
    int      i;

    for ( i = min_m_n - 1; i >= 0; --i )
    {
        //float*    a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
        float*    alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
        float*    a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
        float*    a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
        float*    A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

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

        float     minus_inv_tau11;

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

        FLA_Apply_H2_UT_l_ops_var1( m_ahead,
                                    n_ahead,
                                    tau11,
                                    a21,  rs_A,
                                    a12t, cs_A,
                                    A22,  rs_A, cs_A );

        minus_inv_tau11 = -one / *tau11;

        *alpha11 = one + minus_inv_tau11;

        bli_sscalv( BLIS_NO_CONJUGATE,
                    m_ahead,
                    &minus_inv_tau11,
                    a21, rs_A );

        // Not necessary if upper triangle of A is initialized to identity.
        //bli_ssetv( m_behind,
        //           &zero,
        //           a01, rs_A );
    }

    return FLA_SUCCESS;
}

References FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_width(), FLA_QR_UT_form_Q_opc_var1(), FLA_QR_UT_form_Q_opd_var1(), FLA_QR_UT_form_Q_ops_var1(), and FLA_QR_UT_form_Q_opz_var1().

Referenced by FLA_QR_UT_form_Q_blk_var1().

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

    datatype = FLA_Obj_datatype( A );

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

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

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

            FLA_QR_UT_form_Q_ops_var1( m_A,
                                       n_A,
                                       buff_A, rs_A, cs_A,
                                       buff_T, rs_T, cs_T );

            break;
        }

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

            FLA_QR_UT_form_Q_opd_var1( m_A,
                                       n_A,
                                       buff_A, rs_A, cs_A,
                                       buff_T, rs_T, cs_T );

            break;
        }

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

            FLA_QR_UT_form_Q_opc_var1( m_A,
                                       n_A,
                                       buff_A, rs_A, cs_A,
                                       buff_T, rs_T, cs_T );

            break;
        }

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

            FLA_QR_UT_form_Q_opz_var1( m_A,
                                       n_A,
                                       buff_A, rs_A, cs_A,
                                       buff_T, rs_T, cs_T );

            break;
        }
    }

    return FLA_SUCCESS;
}
FLA_Error FLA_QR_UT_form_Q_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 
)

References bli_z0(), bli_z1(), bli_zscalv(), BLIS_NO_CONJUGATE, FLA_Apply_H2_UT_l_opz_var1(), dcomplex::imag, and dcomplex::real.

Referenced by FLA_QR_UT_form_Q_opt_var1().

{
    dcomplex zero    = bli_z0();
    dcomplex one     = bli_z1();
    int      min_m_n = min( m_A, n_A );
    int      i;

    for ( i = min_m_n - 1; i >= 0; --i )
    {
        //dcomplex* a01      = buff_A + (i  )*cs_A + (0  )*rs_A;
        dcomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
        dcomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
        dcomplex* a12t     = buff_A + (i+1)*cs_A + (i  )*rs_A;
        dcomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

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

        dcomplex  minus_inv_tau11;

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

        FLA_Apply_H2_UT_l_opz_var1( m_ahead,
                                    n_ahead,
                                    tau11,
                                    a21,  rs_A,
                                    a12t, cs_A,
                                    A22,  rs_A, cs_A );

        minus_inv_tau11.real = -one.real / tau11->real;
        minus_inv_tau11.imag = zero.imag;

        alpha11->real = one.real + minus_inv_tau11.real;
        alpha11->imag = zero.imag;

        bli_zscalv( BLIS_NO_CONJUGATE,
                    m_ahead,
                    &minus_inv_tau11,
                    a21, rs_A );

        // Not necessary if upper triangle of A is initialized to identity.
        //bli_zsetv( m_behind,
        //           &zero,
        //           a01, rs_A );
    }

    return FLA_SUCCESS;
}

References FLA_Check_error_level(), FLA_QR_UT_blk_var1(), FLA_QR_UT_blk_var2(), FLA_QR_UT_blk_var3(), FLA_QR_UT_internal_check(), FLA_QR_UT_macro_task(), FLA_QR_UT_opt_var1(), FLA_QR_UT_opt_var2(), FLA_QR_UT_unb_var1(), FLA_QR_UT_unb_var2(), and FLASH_Queue_get_enabled().

Referenced by FLA_QR_UT(), FLA_QR_UT_blk_var1(), FLA_QR_UT_blk_var2(), FLA_QR_UT_blk_var3(), FLA_QR_UT_copy_task(), FLA_QR_UT_inc_blk_var1(), FLA_QR_UT_macro_task(), FLA_QR_UT_task(), and FLASH_QR_UT().

{
    FLA_Error r_val = FLA_SUCCESS;
    
    if ( FLA_Check_error_level() == FLA_FULL_ERROR_CHECKING )
        FLA_QR_UT_internal_check( A, T, cntl );

    if      ( FLA_Cntl_matrix_type( cntl ) == FLA_HIER &&
              FLA_Cntl_variant( cntl ) == FLA_SUBPROBLEM )
    {
        if ( FLASH_Queue_get_enabled( ) )
        {
            // Enqueue
            ENQUEUE_FLASH_QR_UT_macro( A, *FLASH_OBJ_PTR_AT( T ), cntl );
        }
        else
        {
            // Execute
            r_val = FLA_QR_UT_macro_task( A, *FLASH_OBJ_PTR_AT( T ), cntl );
        }
    }
    else
    {
        if      ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT1 )
        {
            r_val = FLA_QR_UT_unb_var1( A, T );
        }
        else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT1 )
        {
            r_val = FLA_QR_UT_opt_var1( A, T );
        }
        else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT1 )
        {
            r_val = FLA_QR_UT_blk_var1( A, T, cntl );
        }
        else if ( FLA_Cntl_variant( cntl ) == FLA_UNBLOCKED_VARIANT2 )
        {
            r_val = FLA_QR_UT_unb_var2( A, T );
        }
        else if ( FLA_Cntl_variant( cntl ) == FLA_UNB_OPT_VARIANT2 )
        {
            r_val = FLA_QR_UT_opt_var2( A, T );
        }
        else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT2 )
        {
            r_val = FLA_QR_UT_blk_var2( A, T, cntl );
        }
        else if ( FLA_Cntl_variant( cntl ) == FLA_BLOCKED_VARIANT3 )
        {
            r_val = FLA_QR_UT_blk_var3( A, T, cntl );
        }
        else
        {
            FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
        }
    }

    return r_val;
}

References FLA_Check_error_level(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Obj_length(), FLA_Obj_width(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_QR_UT_recover_tau_check(), FLA_QR_UT_recover_tau_submatrix(), FLA_Repart_1x2_to_1x3(), and FLA_Repart_2x1_to_3x1().

{
  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_QR_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_width( TL ) < FLA_Obj_width( T ) ){

    b = min( FLA_Obj_width( TR ), 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_QR_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_Apply_Q_UT(), FLA_Apply_Q_UT_create_workspace(), FLA_Check_error_level(), FLA_Copy_external(), FLA_Obj_create_copy_of(), FLA_Obj_free(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_QR_UT_solve_check(), and FLA_Trsm_external().

{
  FLA_Obj W, Y;
  FLA_Obj AT, AB;
  FLA_Obj YT, YB;

  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_QR_UT_solve_check( A, T, B, X );

  FLA_Apply_Q_UT_create_workspace( T, B, &W );

  FLA_Obj_create_copy_of( FLA_NO_TRANSPOSE, B, &Y );

  FLA_Apply_Q_UT( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                  A, T, W, Y );

  FLA_Part_2x1( A,   &AT,
                     &AB,    FLA_Obj_width( A ), FLA_TOP );
  FLA_Part_2x1( Y,   &YT,
                     &YB,    FLA_Obj_width( A ), FLA_TOP );

  FLA_Trsm_external( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE,
                     FLA_NONUNIT_DIAG, FLA_ONE, AT, YT );

  FLA_Copy_external( YT, X );

  FLA_Obj_free( &Y );
  FLA_Obj_free( &W );

  return FLA_SUCCESS;
}

References FLA_Abort(), FLA_Check_error_level(), FLA_Print_message(), FLA_QR_UT_check(), FLA_QR_UT_internal(), FLASH_Obj_depth(), FLASH_Obj_scalar_length_tl(), FLASH_Obj_scalar_min_dim(), FLASH_Obj_scalar_width_tl(), FLASH_Queue_begin(), and FLASH_Queue_end().

{
  FLA_Error r_val;
  dim_t     b_alg, b_flash;

  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_QR_UT_check( A, TW );

  // *** The current hierarchical QR_UT algorithm assumes that the matrix
  // has a hierarchical depth of 1. We check for that here, because we
  //  anticipate that we'll use a more general algorithm in the future, and
  // we don't want to forget to remove the constraint. ***
  if ( FLASH_Obj_depth( A ) != 1 )
  {
    FLA_Print_message( "FLASH_QR_UT() currently only supports matrices of depth 1",
                       __FILE__, __LINE__ );
    FLA_Abort();
  }

  // Inspect the length of TTL to get the blocksize used by the QR
  // factorization, which will be our inner blocksize for Apply_Q_UT.
  b_alg   = FLASH_Obj_scalar_length_tl( TW );
  b_flash = FLASH_Obj_scalar_width_tl( TW );

  // The traditional (non-incremental) QR_UT algorithm-by-blocks requires
  // that the algorithmic blocksize be equal to the storage blocksize.
  if ( b_alg != b_flash )
  {
    FLA_Print_message( "FLASH_QR_UT() requires that b_alg == b_store",
                       __FILE__, __LINE__ );
    FLA_Abort();
  }

  // The traditional (non-incremental) QR_UT algorithm-by-blocks requires
  // that min_dim(A) % b_flash == 0.
  if ( FLASH_Obj_scalar_min_dim( A ) % b_flash != 0 )
  {
    FLA_Print_message( "FLASH_QR_UT() requires that min_dim( A ) %% b_store == 0",
                       __FILE__, __LINE__ );
    FLA_Abort();
  }

  // Begin a parallel region.
  FLASH_Queue_begin();

  // Invoke FLA_QR_UT_internal() with hierarchical control tree.
  r_val = FLA_QR_UT_internal( A, TW, flash_qrut_cntl );

  // End the parallel region.
  FLASH_Queue_end();

  return r_val;
}
FLA_Error FLASH_QR_UT_create_hier_matrices ( FLA_Obj  A_flat,
dim_t  depth,
dim_t b_flash,
FLA_Obj A,
FLA_Obj TW 
)

References FLA_Abort(), FLA_Obj_datatype(), FLA_Obj_min_dim(), FLA_Print_message(), FLASH_Obj_create_ext(), and FLASH_Obj_create_hier_copy_of_flat().

{
    FLA_Datatype datatype;
    dim_t        m, n;
    dim_t        min_m_n;
    
    // *** The current QR_UT algorithm implemented assumes that
    // the matrix has a hierarchical depth of 1. We check for that here
    // because we anticipate that we'll use a more general algorithm in the
    // future, and we don't want to forget to remove the constraint. ***
    if ( depth != 1 )
    {
       FLA_Print_message( "FLASH_QR_UT() currently only supports matrices of depth 1",
                          __FILE__, __LINE__ );
       FLA_Abort();
    }

    // Create hierarchical copy of matrix A_flat.
    FLASH_Obj_create_hier_copy_of_flat( A_flat, depth, b_flash, A );

    // Query the datatype of matrix A_flat.
    datatype = FLA_Obj_datatype( A_flat );
    
    // Query the minimum dimension of A_flat.
    min_m_n = FLA_Obj_min_dim( A_flat );

    // Set the m and n dimensions of TW to be min_m_n.
    m = min_m_n;
    n = min_m_n;

    // Create hierarchical matrices T and W.
    FLASH_Obj_create_ext( datatype, m, n, 
                          depth, b_flash, b_flash, 
                          TW );
       
    return FLA_SUCCESS;
}

References FLA_Check_error_level(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_QR_UT_solve_check(), FLASH_Apply_Q_UT(), FLASH_Apply_Q_UT_create_workspace(), FLASH_Copy(), FLASH_Obj_create_copy_of(), FLASH_Obj_free(), and FLASH_Trsm().

{
  FLA_Obj W, Y;
  FLA_Obj AT, AB;
  FLA_Obj YT, YB;

  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_QR_UT_solve_check( A, TW, B, X );

  FLASH_Apply_Q_UT_create_workspace( TW, B, &W );

  FLASH_Obj_create_copy_of( FLA_NO_TRANSPOSE, B, &Y );

  FLASH_Apply_Q_UT( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                    A, TW, W, Y );

  FLA_Part_2x1( A,   &AT,
                     &AB,    FLA_Obj_width( A ), FLA_TOP );
  FLA_Part_2x1( Y,   &YT,
                     &YB,    FLA_Obj_width( A ), FLA_TOP );

  FLASH_Trsm( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
              FLA_ONE, AT, YT );

  FLASH_Copy( YT, X );

  FLASH_Obj_free( &Y );
  FLASH_Obj_free( &W );

  return FLA_SUCCESS;
}