FLA_QR_UT_inc.h File Reference

(r)

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Functions
FLA_Error	FLASH_QR_UT_inc (FLA_Obj A, FLA_Obj TW)
FLA_Error	FLASH_QR_UT_inc_noopt (FLA_Obj A, FLA_Obj TW)
FLA_Error	FLASH_QR_UT_inc_opt1 (FLA_Obj A, FLA_Obj TW)
FLA_Error	FLA_QR_UT_inc_blk_var1 (FLA_Obj A, FLA_Obj TW, fla_qrutinc_t *cntl)
FLA_Error	FLA_QR_UT_inc_blk_var2 (FLA_Obj A, FLA_Obj TW, FLA_Obj U, fla_qrutinc_t *cntl)
FLA_Error	FLASH_QR_UT_inc_create_hier_matrices (FLA_Obj A_flat, dim_t depth, dim_t *b_flash, dim_t b_alg, FLA_Obj *A, FLA_Obj *TW)
dim_t	FLASH_QR_UT_inc_determine_alg_blocksize (FLA_Obj A)
FLA_Error	FLASH_QR_UT_inc_solve (FLA_Obj A, FLA_Obj TW, FLA_Obj B, FLA_Obj X)

Function Documentation

FLA_QR_UT_inc_blk_var1()

FLA_Error FLA_QR_UT_inc_blk_var1	(	FLA_Obj	A,
		FLA_Obj	TW,
		fla_qrutinc_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 );
 
    /*------------------------------------------------------------*/
 
    /*
       Perform a QR factorization (via UT transform) on A11:
     
         [ A11, T11 ] = QR_UT( A11, T11 );
 
       where T11 refers to a single storage block that refers to an
       b_alg-by-b row-panel of upper triangular block Householder
       transforms. Here, b is the storage blocksize while b_alg is
       the algorithmic blocksize used by the QR factorization.
       Typically b_alg << b.
       
    */
 
    FLA_QR_UT_internal( A11, T11,
                        FLA_Cntl_sub_qrut( cntl ) );
 
 
    if ( FLA_Obj_width( A12 ) > 0 )
    {
      /*
         Apply Q^H to A12 from the left:
     
           A12 = Q^H * A12
     
         where Q is formed from A11 and T11. Note that W12 refers
         to a row-panel of blocks where each block refers to an
         b_alg-by-b row-panel of workspace.
      */
 
      FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                               A11, T11, W12, A12,
                               FLA_Cntl_sub_apqut( cntl ) );
    }
 
 
    /*
       Update QR factorization of A11 with each block of A21, storing
       block Householder transforms into corresponding blocks of T21.
     
         [ A11, ...
           A21, T21 ] = QR2_UT( A11, ...
                                A21, T21 );
    */
 
    FLA_QR2_UT_internal( A11,
                         A21, T21, 
                         FLA_Cntl_sub_qr2ut( cntl ) );
 
 
    if ( FLA_Obj_width( A12 ) > 0 )
    {
      /*
         Apply Q^H to A12 and A22 from the left:
     
             / A12 \ = Q^H * / A12 \
             \ A22 /         \ A22 / 
     
         where Q is formed from A21 and T21.
      */
 
      FLA_Apply_Q2_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                                A21, T21, W12, A12,
                                               A22,
                                FLA_Cntl_sub_apq2ut( 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_Q2_UT_internal(), FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_Part_2x2(), FLA_QR2_UT_internal(), FLA_QR_UT_internal(), FLA_Repart_2x2_to_3x3(), and i.

Referenced by FLASH_QR_UT_inc_noopt().

FLA_QR_UT_inc_blk_var2()

FLA_Error FLA_QR_UT_inc_blk_var2	(	FLA_Obj	A,
		FLA_Obj	TW,
		FLA_Obj	U,
		fla_qrutinc_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;
 
  FLA_Obj UL,    UR,       U0,  U11,  U2;
 
  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 );
 
  FLA_Part_1x2( U,    &UL,  &UR,      0, FLA_LEFT );
 
  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_Repart_1x2_to_1x3( UL,  /**/ UR,        &U0, /**/ &U11, &U2,
                           b, FLA_RIGHT );
 
    /*------------------------------------------------------------*/
 
    /*
       Use U11 to hold a copy of A11 to avoid a false
       write-after-read dependency so that FLA_QR2_UT() may proceed
       while FLA_Apply_Q_UT() executes.
    */
 
 
    /*
       Perform a QR factorization (via UT transform) on A11:
     
         [ A11, T11 ] = QR_UT( A11, T11 );
 
       where T11 refers to a single storage block that refers to an
       b_alg-by-b row-panel of upper triangular block Householder
       transforms. Here, b is the storage blocksize while b_alg is
       the algorithmic blocksize used by the QR factorization.
       Typically b_alg << b.
       
       After the factorization is complete, A11 is copied into U11.
     
    */
 
    FLA_QR_UT_copy_internal( A11, T11, U11,
                             FLA_Cntl_sub_qrut( cntl ) );
 
 
    /*
       Apply Q^H to A12 from the left:
     
         A12 = Q^H * A12
     
       where Q is formed from A11 and T11. Note that W12 refers
       to a row-panel of blocks where each block refers to an
       b_alg-by-b row-panel of workspace.
    */
 
    FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                             U11, T11, W12, A12,
                             FLA_Cntl_sub_apqut( cntl ) );
 
 
    /*
       Update QR factorization of A11 with each block of A21, storing
       block Householder transforms into corresponding blocks of T21.
     
         [ A11, ...
           A21, T21 ] = QR2_UT( A11, ...
                                A21, T21 );
    */
 
    FLA_QR2_UT_internal( A11,
                         A21, T21, 
                         FLA_Cntl_sub_qr2ut( cntl ) );
 
 
    /*
       Apply Q^H to A12 and A22 from the left:
     
           / A12 \ = Q^H * / A12 \
           \ A22 /         \ A22 / 
     
       where Q is formed from A21 and T21.
    */
 
    FLA_Apply_Q2_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                              A21, T21, W12, A12,
                                             A22,
                              FLA_Cntl_sub_apq2ut( 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 );
 
    FLA_Cont_with_1x3_to_1x2( &UL,  /**/ &UR,        U0, U11, /**/ U2,
                              FLA_LEFT );
 
  }
 
  return FLA_SUCCESS;
}

References FLA_Apply_Q2_UT_internal(), FLA_Apply_Q_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x2(), FLA_QR2_UT_internal(), FLA_QR_UT_copy_internal(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), and i.

Referenced by FLASH_QR_UT_inc_opt1().

FLASH_QR_UT_inc()

FLA_Error FLASH_QR_UT_inc	(	FLA_Obj	A,
		FLA_Obj	TW
	)

{
  FLA_Error r_val;
 
  if ( FLASH_Queue_stack_depth() == 0 )
    r_val = FLASH_QR_UT_inc_opt1( A, TW );
  else
    r_val = FLASH_QR_UT_inc_noopt( A, TW );
 
  return r_val;
}

FLASH_QR_UT_inc_create_hier_matrices()

FLA_Error FLASH_QR_UT_inc_create_hier_matrices	(	FLA_Obj	A_flat,
		dim_t	depth,
		dim_t *	b_flash,
		dim_t	b_alg,
		FLA_Obj *	A,
		FLA_Obj *	TW
	)

{
    FLA_Datatype datatype;
    dim_t        m, n;
    dim_t        n_last;
    
    // *** The current QR_UT_inc 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_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 );
 
    // 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_QR_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. 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, 
                          TW );
 
    // 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_Abort(), FLA_Cont_with_3x1_to_2x1(), FLA_Obj_datatype(), FLA_Obj_length(), FLA_Obj_width(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Print_message(), FLA_Repart_2x1_to_3x1(), FLASH_Obj_create_ext(), FLASH_Obj_create_hier_copy_of_flat(), FLASH_Obj_scalar_width(), FLASH_QR_UT_inc_determine_alg_blocksize(), and i.

FLASH_QR_UT_inc_determine_alg_blocksize()

dim_t FLASH_QR_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_QR_INNER_TO_OUTER_B_RATIO, 1 );
 
    return b_alg;
}

References FLA_Obj_length(), and i.

Referenced by FLASH_QR_UT_inc_create_hier_matrices().

FLASH_QR_UT_inc_noopt()

FLA_Error FLASH_QR_UT_inc_noopt	(	FLA_Obj	A,
		FLA_Obj	TW
	)

{
  FLA_Error r_val;
 
  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_QR_UT_inc_check( A, TW );
 
  // Begin a parallel region.
  FLASH_Queue_begin();
 
  // Invoke FLA_QR_UT_inc_blk_var1() with the standard control tree.
  r_val = FLA_QR_UT_inc_blk_var1( A, TW, flash_qrutinc_cntl );
 
  // End the parallel region.
  FLASH_Queue_end();
 
  return r_val;
}

References FLA_Check_error_level(), FLA_QR_UT_inc_blk_var1(), FLA_QR_UT_inc_check(), flash_qrutinc_cntl, FLASH_Queue_begin(), FLASH_Queue_end(), and i.

Referenced by FLASH_QR_UT_inc().

FLASH_QR_UT_inc_opt1()

FLA_Error FLASH_QR_UT_inc_opt1	(	FLA_Obj	A,
		FLA_Obj	TW
	)

{
  FLA_Error r_val;
  FLA_Obj   U;
 
  // Check parameters.
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_QR_UT_inc_check( A, TW );
 
  // Create a temporary matrix to hold copies of all of the blocks along the
  // diagonal of A.
  FLASH_Obj_create_diag_panel( A, &U );
 
  // Begin a parallel region.
  FLASH_Queue_begin();
 
  // Invoke FLA_QR_UT_inc_blk_var2() with the standard control tree.
  r_val = FLA_QR_UT_inc_blk_var2( A, TW, U, flash_qrutinc_cntl );
 
  // End the parallel region.
  FLASH_Queue_end();
 
  // Free the temporary matrix.
  FLASH_Obj_free( &U );
 
  return r_val;
}

References FLA_Check_error_level(), FLA_QR_UT_inc_blk_var2(), FLA_QR_UT_inc_check(), FLASH_Obj_create_diag_panel(), FLASH_Obj_free(), flash_qrutinc_cntl, FLASH_Queue_begin(), FLASH_Queue_end(), and i.

Referenced by FLASH_QR_UT_inc().

FLASH_QR_UT_inc_solve()

FLA_Error FLASH_QR_UT_inc_solve	(	FLA_Obj	A,
		FLA_Obj	TW,
		FLA_Obj	B,
		FLA_Obj	X
	)

{
  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_inc_solve_check( A, TW, B, X );
 
  FLASH_Apply_Q_UT_inc_create_workspace( TW, B, &W );
 
  FLASH_Obj_create_copy_of( FLA_NO_TRANSPOSE, B, &Y );
 
  FLASH_Apply_Q_UT_inc( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
                        A, TW, W, Y );
 
  // Create a temporary hierarchical view of only the top n-by-n part of A in
  // case m > n so that AT captures the upper triangular factor R. We do the
  // same for Y to ensure conformality.
  FLASH_Part_create_2x1( A,   &AT,    
                              &AB,    FLASH_Obj_scalar_width( A ), FLA_TOP );
  FLASH_Part_create_2x1( Y,   &YT,    
                              &YB,    FLASH_Obj_scalar_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 );
 
  // Free the temporary hierarchical views.
  FLASH_Part_free_2x1( &AT,
                       &AB );
  FLASH_Part_free_2x1( &YT,
                       &YB );
 
  FLASH_Obj_free( &Y );
  FLASH_Obj_free( &W );
 
  return FLA_SUCCESS;
}