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)

Function Documentation

FLA_Error FLA_QR_UT ( FLA_Obj  A,
FLA_Obj  T 
)

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;
}
FLA_Error FLA_QR_UT_copy_internal ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  U,
fla_qrut_t cntl 
)

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;
}
FLA_Error FLA_QR_UT_create_T ( FLA_Obj  A,
FLA_Obj T 
)

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

{
  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 );

  // 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;
}
FLA_Error FLA_QR_UT_internal ( FLA_Obj  A,
FLA_Obj  T,
fla_qrut_t cntl 
)

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;
}
FLA_Error FLA_QR_UT_recover_tau ( FLA_Obj  T,
FLA_Obj  tau 
)

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;
}
FLA_Error FLA_QR_UT_solve ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  B,
FLA_Obj  X 
)

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;
}
FLA_Error FLASH_QR_UT ( FLA_Obj  A,
FLA_Obj  TW 
)

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;
}
FLA_Error FLASH_QR_UT_solve ( FLA_Obj  A,
FLA_Obj  T,
FLA_Obj  B,
FLA_Obj  X 
)

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;
}