FLA_CAQR_UT_inc.h File Reference

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Functions
FLA_Error	FLASH_CAQR_UT_inc (dim_t p, FLA_Obj A, FLA_Obj ATW, FLA_Obj R, FLA_Obj RTW)
FLA_Error	FLASH_CAQR_UT_inc_noopt (dim_t p, FLA_Obj A, FLA_Obj ATW, FLA_Obj R, FLA_Obj RTW)
FLA_Error	FLASH_CAQR_UT_inc_create_hier_matrices (dim_t p, FLA_Obj A_flat, dim_t depth, dim_t *b_flash, dim_t b_alg, FLA_Obj *A, FLA_Obj *ATW, FLA_Obj *R, FLA_Obj *RTW)
dim_t	FLASH_CAQR_UT_inc_determine_alg_blocksize (FLA_Obj A)
FLA_Error	FLASH_CAQR_UT_inc_adjust_views (FLA_Obj A, FLA_Obj TW)
void	FLA_CAQR_UT_inc_init_structure (dim_t p, dim_t nb_part, FLA_Obj R)
dim_t	FLA_CAQR_UT_inc_compute_blocks_per_part (dim_t p, FLA_Obj A)
FLA_Error	FLA_CAQR_UT_inc_factorize_panels (dim_t nb_part, FLA_Obj A, FLA_Obj ATW)
FLA_Error	FLA_CAQR_UT_inc_copy_triangles (dim_t nb_part, FLA_Obj A, FLA_Obj R)
FLA_Error	FLA_CAQR_UT_inc_blk_var1 (FLA_Obj R, FLA_Obj TW, fla_caqrutinc_t *cntl)
FLA_Error	FLASH_CAQR_UT_inc_solve (dim_t p, FLA_Obj A, FLA_Obj ATW, FLA_Obj R, FLA_Obj RTW, FLA_Obj B, FLA_Obj X)

Function Documentation

FLA_CAQR_UT_inc_blk_var1()

FLA_Error FLA_CAQR_UT_inc_blk_var1	(	FLA_Obj	R,
		FLA_Obj	TW,
		fla_caqrutinc_t *	cntl
	)

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;
 
  FLA_Obj TTL,   WTR,      T00, W01, W02, 
          TBL,   TBR,      T10, T11, W12,
                           T20, T21, T22;
 
  dim_t b;
 
  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
 
  FLA_Part_2x2( TW,   &TTL, &WTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
 
  while ( FLA_Obj_min_dim( ABR ) > 0 ){
 
    b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) );
 
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );
 
    FLA_Repart_2x2_to_3x3( TTL, /**/ WTR,       &T00, /**/ &W01, &W02,
                        /* ************* */   /* ******************** */
                                                &T10, /**/ &T11, &W12,
                           TBL, /**/ TBR,       &T20, /**/ &T21, &T22,
                           b, b, FLA_BR );
 
    /*------------------------------------------------------------*/
 
    FLA_CAQR2_UT_internal( A11,
                           A21, T21, 
                           FLA_Cntl_sub_caqr2ut( cntl ) );
 
 
    if ( FLA_Obj_width( A12 ) > 0 )
    {
      FLA_Apply_CAQ2_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                                  A21, T21, W12, A12,
                                                 A22,
                                  FLA_Cntl_sub_apcaq2ut( cntl ) );
    }
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );
 
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &WTR,       T00, W01, /**/ W02,
                                                     T10, T11, /**/ W12,
                            /* ************** */  /* ****************** */
                              &TBL, /**/ &TBR,       T20, T21, /**/ T22,
                              FLA_TL );
 
  }
 
  return FLA_SUCCESS;
}

References FLA_Apply_CAQ2_UT_internal(), FLA_CAQR2_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and i.

Referenced by FLASH_CAQR_UT_inc_noopt().

FLA_CAQR_UT_inc_compute_blocks_per_part()

dim_t FLA_CAQR_UT_inc_compute_blocks_per_part	(	dim_t	p,
		FLA_Obj	A
	)

{
    dim_t nb_part;
    dim_t nb_left;
    dim_t num_blocks;
 
    // Query the element (not scalar) length of A.
    num_blocks = FLA_Obj_length( A );
    
    // Compute the number of blocks per partitions.
    nb_part = num_blocks / p;
    nb_left = num_blocks % p;
 
    // If there are leftover blocks, increase nb_part by one.
    if ( nb_left > 0 ) nb_part += 1;
 
    return nb_part;
}

References FLA_Obj_length(), and i.

Referenced by FLASH_Apply_CAQ_UT_inc(), FLASH_CAQR_UT_inc_create_hier_matrices(), and FLASH_CAQR_UT_inc_noopt().

FLA_CAQR_UT_inc_copy_triangles()

FLA_Error FLA_CAQR_UT_inc_copy_triangles	(	dim_t	nb_part,
		FLA_Obj	A,
		FLA_Obj	R
	)

{
  FLA_Obj AT,              A0, 
          AB,              A1,
                           A2;
 
  FLA_Obj RT,              R0, 
          RB,              R1,
                           R2;
 
  dim_t b;
 
  FLA_Part_2x1( A,    &AT, 
                      &AB,            0, FLA_TOP );
 
  FLA_Part_2x1( R,    &RT, 
                      &RB,            0, FLA_TOP );
 
  while ( FLA_Obj_length( AB ) > 0 ){
 
    b = min( nb_part, FLA_Obj_length( AB ) );
 
    FLA_Repart_2x1_to_3x1( AT,                &A0, 
                        /* ** */            /* ** */
                                              &A1, 
                           AB,                &A2,        b, FLA_BOTTOM );
 
    FLA_Repart_2x1_to_3x1( RT,                &R0, 
                        /* ** */             /* ** */
                                              &R1, 
                           RB,                &R2,        b, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
    // Copy the individual upper triangles in A into R.
    FLASH_Copyr( FLA_UPPER_TRIANGULAR, A1, R1 );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x1_to_2x1( &AT,               A0, 
                                                 A1, 
                            /* ** */          /* ** */
                              &AB,               A2,      FLA_TOP );
 
    FLA_Cont_with_3x1_to_2x1( &RT,               R0, 
                                                 R1, 
                            /* ** */           /* ** */
                              &RB,               R2,      FLA_TOP );
  }
 
  return FLA_SUCCESS;
}

References FLA_Cont_with_3x1_to_2x1(), FLA_Obj_length(), FLA_Part_2x1(), FLA_Repart_2x1_to_3x1(), FLASH_Copyr(), and i.

Referenced by FLASH_CAQR_UT_inc_noopt().

FLA_CAQR_UT_inc_factorize_panels()

FLA_Error FLA_CAQR_UT_inc_factorize_panels	(	dim_t	nb_part,
		FLA_Obj	A,
		FLA_Obj	ATW
	)

{
  FLA_Obj AT,              A0, 
          AB,              A1,
                           A2;
 
  FLA_Obj TWT,             TW0, 
          TWB,             TW1,
                           TW2;
 
  dim_t b;
 
  FLA_Part_2x1( A,    &AT, 
                      &AB,            0, FLA_TOP );
 
  FLA_Part_2x1( TW,   &TWT, 
                      &TWB,           0, FLA_TOP );
 
  while ( FLA_Obj_length( AB ) > 0 ){
 
    b = min( nb_part, FLA_Obj_length( AB ) );
 
    FLA_Repart_2x1_to_3x1( AT,                &A0, 
                        /* ** */            /* ** */
                                              &A1, 
                           AB,                &A2,        b, FLA_BOTTOM );
 
    FLA_Repart_2x1_to_3x1( TWT,               &TW0, 
                        /* ** */            /* ** */
                                              &TW1, 
                           TWB,               &TW2,       b, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
    // Perform an incremental QR factorization on A1, writing triangular
    // block Householder factors to T in TW1.
    FLASH_QR_UT_inc( A1, TW1 );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x1_to_2x1( &AT,               A0, 
                                                 A1, 
                            /* ** */          /* ** */
                              &AB,               A2,      FLA_TOP );
 
    FLA_Cont_with_3x1_to_2x1( &TWT,              TW0, 
                                                 TW1, 
                            /* ** */          /* ** */
                              &TWB,              TW2,     FLA_TOP );
  }
 
  return FLA_SUCCESS;
}

References FLA_Cont_with_3x1_to_2x1(), FLA_Obj_length(), FLA_Part_2x1(), FLA_Repart_2x1_to_3x1(), FLASH_QR_UT_inc(), and i.

Referenced by FLASH_CAQR_UT_inc_noopt().

FLA_CAQR_UT_inc_init_structure()

void FLA_CAQR_UT_inc_init_structure	(	dim_t	p,
		dim_t	nb_part,
		FLA_Obj	R
	)

{
    dim_t    m, n;
    dim_t    rs, cs;
    dim_t    i, j, ip;
    FLA_Obj* buff_R;
 
    m      = FLA_Obj_length( R );
    n      = FLA_Obj_width( R );
    rs     = FLA_Obj_row_stride( R );
    cs     = FLA_Obj_col_stride( R );
    buff_R = FLA_Obj_buffer_at_view( R );
 
    // Fill in R by row panels.
    for ( ip = 0; ip < p; ++ip )
    {
        FLA_Obj* buff_R1 = buff_R + (ip*nb_part)*rs;
 
        int  m_behind   = ip*nb_part;
        int  m_ahead    = m - m_behind;
 
        int  m_cur      = min( nb_part, m_ahead );
        int  n_cur      = n;
 
        // Iterate across columns for the current panel.
        for ( j = 0; j < n_cur; ++j )
        {
            FLA_Obj* rho = buff_R1 + j*cs;
 
            // Mark the above-diagonal blocks as full.
            for ( i = 0; i < j; ++i )
            {
                rho->base->uplo = FLA_FULL_MATRIX;
                rho += rs;
            }
 
            // Mark the diagonal block as triangular.
            rho->base->uplo = FLA_UPPER_TRIANGULAR;
            rho += rs;
            
            // Mark the below-diagonal blocks as zero.
            for ( i = j + 1; i < m_cur; ++i )
            {
                rho->base->uplo = FLA_ZERO_MATRIX;
                rho += rs;
            }
        }
    }
}

References FLA_Obj_view::base, FLA_Obj_buffer_at_view(), FLA_Obj_col_stride(), FLA_Obj_length(), FLA_Obj_row_stride(), FLA_Obj_width(), i, rho, and FLA_Obj_struct::uplo.

Referenced by FLASH_CAQR_UT_inc_create_hier_matrices().

FLASH_CAQR_UT_inc()

FLA_Error FLASH_CAQR_UT_inc	(	dim_t	p,
		FLA_Obj	A,
		FLA_Obj	ATW,
		FLA_Obj	R,
		FLA_Obj	RTW
	)

{
  FLA_Error r_val;
 
  //if ( FLASH_Queue_stack_depth() == 0 )
  //  r_val = FLASH_CAQR_UT_inc_opt1( A, ATW, R, RTW );
  //else
    r_val = FLASH_CAQR_UT_inc_noopt( p, A, ATW, R, RTW );
 
  return r_val;
}

References FLASH_CAQR_UT_inc_noopt(), and i.

FLASH_CAQR_UT_inc_adjust_views()

FLA_Error FLASH_CAQR_UT_inc_adjust_views	(	FLA_Obj	A,
		FLA_Obj	TW
	)

{
    dim_t b_flash;
    dim_t n, n_last;
 
    // We can query b_flash as the width of the top-left element of TW.
    b_flash = FLASH_Obj_scalar_width_tl( TW );
 
    // Query the element (not scalar) n dimension of A.
    n = FLA_Obj_width( A );
 
    // If the bottom-right-most block along the diagonal is a partial block,
    // adjust the view of the corresponding T block.
    n_last = FLASH_Obj_scalar_width( A ) % b_flash;
 
    if ( n_last > 0 )
    {
        FLA_Obj  TWTL, TWTR,
                 TWBL, TWBR;
        FLA_Obj  TWL,  TWR;
        FLA_Obj  TWT,  TW0,
                 TWB,  TW1,
                       TW2;
        FLA_Obj* TW1p;
 
        FLA_Part_2x2( TW,    &TWTL, &TWTR,
                             &TWBL, &TWBR,    n-1, n-1, FLA_TL );
 
        FLA_Part_2x1( TWBR,    &TWT,
                               &TWB,     0, FLA_TOP );
 
        while ( FLA_Obj_length( TWB ) > 0 )
        {
            FLA_Repart_2x1_to_3x1( TWT,                &TW0, 
                                /* *** */            /* *** */
                                                       &TW1, 
                                   TWB,                &TW2,        1, FLA_BOTTOM );
 
            // -----------------------------------------------------------
 
            TW1p = FLASH_OBJ_PTR_AT( TW1 );
 
            FLA_Part_1x2( *TW1p,   &TWL, &TWR,    n_last, FLA_LEFT );
 
            *TW1p = TWL;
            TW1p->m_inner = TW1p->m;
            TW1p->n_inner = TW1p->n;
 
            // -----------------------------------------------------------
 
            FLA_Cont_with_3x1_to_2x1( &TWT,                TW0, 
                                                           TW1, 
                                    /* *** */           /* *** */
                                      &TWB,                TW2,     FLA_TOP );
        }
    }
       
    return FLA_SUCCESS;
}

References FLA_Cont_with_3x1_to_2x1(), FLA_Obj_length(), FLA_Obj_width(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLASH_Obj_scalar_width(), FLASH_Obj_scalar_width_tl(), and i.

Referenced by FLASH_CAQR_UT_inc_create_hier_matrices().

FLASH_CAQR_UT_inc_create_hier_matrices()

FLA_Error FLASH_CAQR_UT_inc_create_hier_matrices	(	dim_t	p,
		FLA_Obj	A_flat,
		dim_t	depth,
		dim_t *	b_flash,
		dim_t	b_alg,
		FLA_Obj *	A,
		FLA_Obj *	ATW,
		FLA_Obj *	R,
		FLA_Obj *	RTW
	)

{
    FLA_Datatype datatype;
    dim_t        m, n;
    dim_t        nb_part;
    
    // *** The current CAQR_UT_inc algorithm implemented assumes that
    // the matrix has a hierarchical depth of 1.
    if ( depth != 1 )
    {
       FLA_Print_message( "FLASH_CAQR_UT_inc() 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 );
 
    // Create hierarchical copy of matrix A_flat.
    FLASH_Obj_create_conf_to( FLA_NO_TRANSPOSE, *A, R );
 
    // Query the datatype of matrix A_flat.
    datatype = FLA_Obj_datatype( A_flat );
    
    // If the user passed in zero for b_alg, then we need to set the
    // algorithmic (inner) blocksize to a reasonable default value.
    if ( b_alg == 0 )
    {
        b_alg = FLASH_CAQR_UT_inc_determine_alg_blocksize( *A );
    }
 
    // Query the element (not scalar) dimensions of the new hierarchical
    // matrix. This is done so we can create T with full blocks for the
    // bottom and right "edge cases" of A.
    m = FLA_Obj_length( *A );
    n = FLA_Obj_width( *A );
 
    // Create hierarchical matrices T and W for both A and R. T is lower
    // triangular where each block is b_alg-by-b_flash and W is strictly
    // upper triangular where each block is b_alg-by-b_flash. So we can
    // create them simultaneously as part of the same hierarchical matrix.
    FLASH_Obj_create_ext( datatype, m * b_alg, n * b_flash[0], 
                          depth, &b_alg, b_flash, 
                          ATW );
    FLASH_Obj_create_ext( datatype, m * b_alg, n * b_flash[0], 
                          depth, &b_alg, b_flash, 
                          RTW );
 
    // If the bottom-right-most block along the diagonal is a partial block,
    // adjust the view of the corresponding T block.
    FLASH_CAQR_UT_inc_adjust_views( *A, *ATW );
    FLASH_CAQR_UT_inc_adjust_views( *A, *RTW );
 
    // Compute the partition length from the number of partitions.
    nb_part = FLA_CAQR_UT_inc_compute_blocks_per_part( p, *A );
 
    // Encode block structure (upper tri, full, or zero) into blocks of R.
    FLA_CAQR_UT_inc_init_structure( p, nb_part, *R );
 
    return FLA_SUCCESS;
}

References FLA_Abort(), FLA_CAQR_UT_inc_compute_blocks_per_part(), FLA_CAQR_UT_inc_init_structure(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_width(), FLA_Print_message(), FLASH_CAQR_UT_inc_adjust_views(), FLASH_CAQR_UT_inc_determine_alg_blocksize(), FLASH_Obj_create_conf_to(), FLASH_Obj_create_ext(), FLASH_Obj_create_hier_copy_of_flat(), and i.

FLASH_CAQR_UT_inc_determine_alg_blocksize()

dim_t FLASH_CAQR_UT_inc_determine_alg_blocksize

(

FLA_Obj

A

)

{
    dim_t b_alg;
    dim_t b_flash;
 
    // Acquire the storage blocksize.
    b_flash = FLA_Obj_length( *FLASH_OBJ_PTR_AT( A ) );
 
    // Scale the storage blocksize by a pre-defined scalar to arrive at a
    // reasonable algorithmic blocksize, but make sure it's at least 1.
    b_alg = ( dim_t ) max( ( double ) b_flash * FLA_CAQR_INNER_TO_OUTER_B_RATIO, 1 );
 
    return b_alg;
}

References FLA_Obj_length(), and i.

Referenced by FLASH_CAQR_UT_inc_create_hier_matrices().

FLASH_CAQR_UT_inc_noopt()

FLA_Error FLASH_CAQR_UT_inc_noopt	(	dim_t	p,
		FLA_Obj	A,
		FLA_Obj	ATW,
		FLA_Obj	R,
		FLA_Obj	RTW
	)

{
  FLA_Error r_val = FLA_SUCCESS;
  dim_t     nb_part;
 
  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_CAQR_UT_inc_check( p, A, ATW, R, RTW );
 
  // Compute the partition length from the number of partitions.
  nb_part = FLA_CAQR_UT_inc_compute_blocks_per_part( p, A );
 
  // Begin a parallel region.
  FLASH_Queue_begin();
 
  // Perform incremental QR's on each of the p partitions.
  FLA_CAQR_UT_inc_factorize_panels( nb_part, A, ATW );
 
  // Copy the triangles of A into R.
  FLA_CAQR_UT_inc_copy_triangles( nb_part, A, R );
 
  // Perform an incremental CAQR on the resulting upper triangular R's in A.
  FLA_CAQR_UT_inc_blk_var1( R, RTW, flash_caqrutinc_cntl );
 
  // End the parallel region.
  FLASH_Queue_end();
 
  return r_val;
}

References FLA_CAQR_UT_inc_blk_var1(), FLA_CAQR_UT_inc_check(), FLA_CAQR_UT_inc_compute_blocks_per_part(), FLA_CAQR_UT_inc_copy_triangles(), FLA_CAQR_UT_inc_factorize_panels(), FLA_Check_error_level(), flash_caqrutinc_cntl, FLASH_Queue_begin(), FLASH_Queue_end(), and i.

Referenced by FLASH_CAQR_UT_inc().

FLASH_CAQR_UT_inc_solve()

FLA_Error FLASH_CAQR_UT_inc_solve	(	dim_t	p,
		FLA_Obj	A,
		FLA_Obj	ATW,
		FLA_Obj	R,
		FLA_Obj	RTW,
		FLA_Obj	B,
		FLA_Obj	X
	)

{
  FLA_Obj  W, Y;
  FLA_Obj  RT, RB;
  FLA_Obj  YT, YB;
 
  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_CAQR_UT_inc_solve_check( p, A, ATW, R, RTW, B, X );
 
  FLASH_Apply_CAQ_UT_inc_create_workspace( p, RTW, B, &W );
 
  FLASH_Obj_create_copy_of( FLA_NO_TRANSPOSE, B, &Y );
 
  // Create a temporary hierarchical view of only the top n-by-n part of R in
  // case m > n so that RT captures the upper triangle. We do the same for Y
  // to ensure conformality.
  FLASH_Part_create_2x1( R,   &RT,    
                              &RB,    FLASH_Obj_scalar_width( R ), FLA_TOP );
  FLASH_Part_create_2x1( Y,   &YT,    
                              &YB,    FLASH_Obj_scalar_width( R ), FLA_TOP );
 
  FLASH_Apply_CAQ_UT_inc( p,
                          FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                          A, ATW, R, RTW, W, Y );
 
  FLASH_Trsm( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
              FLA_ONE, RT, YT );
 
  FLASH_Copy( YT, X );
 
  // Free the temporary hierarchical views.
  FLASH_Part_free_2x1( &RT,
                       &RB );
  FLASH_Part_free_2x1( &YT,
                       &YB );
 
  FLASH_Obj_free( &Y );
  FLASH_Obj_free( &W );
 
  return FLA_SUCCESS;
}

References FLA_CAQR_UT_inc_solve_check(), FLA_Check_error_level(), FLA_ONE, FLASH_Apply_CAQ_UT_inc(), FLASH_Apply_CAQ_UT_inc_create_workspace(), FLASH_Copy(), FLASH_Obj_create_copy_of(), FLASH_Obj_free(), FLASH_Obj_scalar_width(), FLASH_Part_create_2x1(), FLASH_Part_free_2x1(), FLASH_Trsm(), and i.