version 1.3, 2010/08/06 15:28:41
|
version 1.12, 2012/08/22 09:48:18
|
Line 1
|
Line 1
|
|
*> \brief \b DLAQPS |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download DLAQPS + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqps.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqps.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqps.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, |
|
* VN2, AUXV, F, LDF ) |
|
* |
|
* .. Scalar Arguments .. |
|
* INTEGER KB, LDA, LDF, M, N, NB, OFFSET |
|
* .. |
|
* .. Array Arguments .. |
|
* INTEGER JPVT( * ) |
|
* DOUBLE PRECISION A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ), |
|
* $ VN1( * ), VN2( * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> DLAQPS computes a step of QR factorization with column pivoting |
|
*> of a real M-by-N matrix A by using Blas-3. It tries to factorize |
|
*> NB columns from A starting from the row OFFSET+1, and updates all |
|
*> of the matrix with Blas-3 xGEMM. |
|
*> |
|
*> In some cases, due to catastrophic cancellations, it cannot |
|
*> factorize NB columns. Hence, the actual number of factorized |
|
*> columns is returned in KB. |
|
*> |
|
*> Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] M |
|
*> \verbatim |
|
*> M is INTEGER |
|
*> The number of rows of the matrix A. M >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The number of columns of the matrix A. N >= 0 |
|
*> \endverbatim |
|
*> |
|
*> \param[in] OFFSET |
|
*> \verbatim |
|
*> OFFSET is INTEGER |
|
*> The number of rows of A that have been factorized in |
|
*> previous steps. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] NB |
|
*> \verbatim |
|
*> NB is INTEGER |
|
*> The number of columns to factorize. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] KB |
|
*> \verbatim |
|
*> KB is INTEGER |
|
*> The number of columns actually factorized. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] A |
|
*> \verbatim |
|
*> A is DOUBLE PRECISION array, dimension (LDA,N) |
|
*> On entry, the M-by-N matrix A. |
|
*> On exit, block A(OFFSET+1:M,1:KB) is the triangular |
|
*> factor obtained and block A(1:OFFSET,1:N) has been |
|
*> accordingly pivoted, but no factorized. |
|
*> The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has |
|
*> been updated. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDA |
|
*> \verbatim |
|
*> LDA is INTEGER |
|
*> The leading dimension of the array A. LDA >= max(1,M). |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] JPVT |
|
*> \verbatim |
|
*> JPVT is INTEGER array, dimension (N) |
|
*> JPVT(I) = K <==> Column K of the full matrix A has been |
|
*> permuted into position I in AP. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] TAU |
|
*> \verbatim |
|
*> TAU is DOUBLE PRECISION array, dimension (KB) |
|
*> The scalar factors of the elementary reflectors. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] VN1 |
|
*> \verbatim |
|
*> VN1 is DOUBLE PRECISION array, dimension (N) |
|
*> The vector with the partial column norms. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] VN2 |
|
*> \verbatim |
|
*> VN2 is DOUBLE PRECISION array, dimension (N) |
|
*> The vector with the exact column norms. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] AUXV |
|
*> \verbatim |
|
*> AUXV is DOUBLE PRECISION array, dimension (NB) |
|
*> Auxiliar vector. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] F |
|
*> \verbatim |
|
*> F is DOUBLE PRECISION array, dimension (LDF,NB) |
|
*> Matrix F**T = L*Y**T*A. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDF |
|
*> \verbatim |
|
*> LDF is INTEGER |
|
*> The leading dimension of the array F. LDF >= max(1,N). |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date November 2011 |
|
* |
|
*> \ingroup doubleOTHERauxiliary |
|
* |
|
*> \par Contributors: |
|
* ================== |
|
*> |
|
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain |
|
*> X. Sun, Computer Science Dept., Duke University, USA |
|
*> \n |
|
*> Partial column norm updating strategy modified on April 2011 |
|
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics, |
|
*> University of Zagreb, Croatia. |
|
* |
|
*> \par References: |
|
* ================ |
|
*> |
|
*> LAPACK Working Note 176 |
|
* |
|
*> \htmlonly |
|
*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a> |
|
*> \endhtmlonly |
|
* |
|
* ===================================================================== |
SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, |
SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, |
$ VN2, AUXV, F, LDF ) |
$ VN2, AUXV, F, LDF ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER KB, LDA, LDF, M, N, NB, OFFSET |
INTEGER KB, LDA, LDF, M, N, NB, OFFSET |
Line 15
|
Line 191
|
$ VN1( * ), VN2( * ) |
$ VN1( * ), VN2( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DLAQPS computes a step of QR factorization with column pivoting |
|
* of a real M-by-N matrix A by using Blas-3. It tries to factorize |
|
* NB columns from A starting from the row OFFSET+1, and updates all |
|
* of the matrix with Blas-3 xGEMM. |
|
* |
|
* In some cases, due to catastrophic cancellations, it cannot |
|
* factorize NB columns. Hence, the actual number of factorized |
|
* columns is returned in KB. |
|
* |
|
* Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* M (input) INTEGER |
|
* The number of rows of the matrix A. M >= 0. |
|
* |
|
* N (input) INTEGER |
|
* The number of columns of the matrix A. N >= 0 |
|
* |
|
* OFFSET (input) INTEGER |
|
* The number of rows of A that have been factorized in |
|
* previous steps. |
|
* |
|
* NB (input) INTEGER |
|
* The number of columns to factorize. |
|
* |
|
* KB (output) INTEGER |
|
* The number of columns actually factorized. |
|
* |
|
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
|
* On entry, the M-by-N matrix A. |
|
* On exit, block A(OFFSET+1:M,1:KB) is the triangular |
|
* factor obtained and block A(1:OFFSET,1:N) has been |
|
* accordingly pivoted, but no factorized. |
|
* The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has |
|
* been updated. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. LDA >= max(1,M). |
|
* |
|
* JPVT (input/output) INTEGER array, dimension (N) |
|
* JPVT(I) = K <==> Column K of the full matrix A has been |
|
* permuted into position I in AP. |
|
* |
|
* TAU (output) DOUBLE PRECISION array, dimension (KB) |
|
* The scalar factors of the elementary reflectors. |
|
* |
|
* VN1 (input/output) DOUBLE PRECISION array, dimension (N) |
|
* The vector with the partial column norms. |
|
* |
|
* VN2 (input/output) DOUBLE PRECISION array, dimension (N) |
|
* The vector with the exact column norms. |
|
* |
|
* AUXV (input/output) DOUBLE PRECISION array, dimension (NB) |
|
* Auxiliar vector. |
|
* |
|
* F (input/output) DOUBLE PRECISION array, dimension (LDF,NB) |
|
* Matrix F' = L*Y'*A. |
|
* |
|
* LDF (input) INTEGER |
|
* The leading dimension of the array F. LDF >= max(1,N). |
|
* |
|
* Further Details |
|
* =============== |
|
* |
|
* Based on contributions by |
|
* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain |
|
* X. Sun, Computer Science Dept., Duke University, USA |
|
* |
|
* Partial column norm updating strategy modified by |
|
* Z. Drmac and Z. Bujanovic, Dept. of Mathematics, |
|
* University of Zagreb, Croatia. |
|
* June 2006. |
|
* For more details see LAPACK Working Note 176. |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 104
|
Line 202
|
DOUBLE PRECISION AKK, TEMP, TEMP2, TOL3Z |
DOUBLE PRECISION AKK, TEMP, TEMP2, TOL3Z |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DGEMM, DGEMV, DLARFP, DSWAP |
EXTERNAL DGEMM, DGEMV, DLARFG, DSWAP |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DBLE, MAX, MIN, NINT, SQRT |
INTRINSIC ABS, DBLE, MAX, MIN, NINT, SQRT |
Line 142
|
Line 240
|
END IF |
END IF |
* |
* |
* Apply previous Householder reflectors to column K: |
* Apply previous Householder reflectors to column K: |
* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'. |
* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**T. |
* |
* |
IF( K.GT.1 ) THEN |
IF( K.GT.1 ) THEN |
CALL DGEMV( 'No transpose', M-RK+1, K-1, -ONE, A( RK, 1 ), |
CALL DGEMV( 'No transpose', M-RK+1, K-1, -ONE, A( RK, 1 ), |
Line 152
|
Line 250
|
* Generate elementary reflector H(k). |
* Generate elementary reflector H(k). |
* |
* |
IF( RK.LT.M ) THEN |
IF( RK.LT.M ) THEN |
CALL DLARFP( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) ) |
CALL DLARFG( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) ) |
ELSE |
ELSE |
CALL DLARFP( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) ) |
CALL DLARFG( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) ) |
END IF |
END IF |
* |
* |
AKK = A( RK, K ) |
AKK = A( RK, K ) |
Line 162
|
Line 260
|
* |
* |
* Compute Kth column of F: |
* Compute Kth column of F: |
* |
* |
* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K). |
* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**T*A(RK:M,K). |
* |
* |
IF( K.LT.N ) THEN |
IF( K.LT.N ) THEN |
CALL DGEMV( 'Transpose', M-RK+1, N-K, TAU( K ), |
CALL DGEMV( 'Transpose', M-RK+1, N-K, TAU( K ), |
Line 177
|
Line 275
|
20 CONTINUE |
20 CONTINUE |
* |
* |
* Incremental updating of F: |
* Incremental updating of F: |
* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)' |
* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**T |
* *A(RK:M,K). |
* *A(RK:M,K). |
* |
* |
IF( K.GT.1 ) THEN |
IF( K.GT.1 ) THEN |
Line 189
|
Line 287
|
END IF |
END IF |
* |
* |
* Update the current row of A: |
* Update the current row of A: |
* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. |
* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**T. |
* |
* |
IF( K.LT.N ) THEN |
IF( K.LT.N ) THEN |
CALL DGEMV( 'No transpose', N-K, K, -ONE, F( K+1, 1 ), LDF, |
CALL DGEMV( 'No transpose', N-K, K, -ONE, F( K+1, 1 ), LDF, |
Line 229
|
Line 327
|
* |
* |
* Apply the block reflector to the rest of the matrix: |
* Apply the block reflector to the rest of the matrix: |
* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - |
* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - |
* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'. |
* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**T. |
* |
* |
IF( KB.LT.MIN( N, M-OFFSET ) ) THEN |
IF( KB.LT.MIN( N, M-OFFSET ) ) THEN |
CALL DGEMM( 'No transpose', 'Transpose', M-RK, N-KB, KB, -ONE, |
CALL DGEMM( 'No transpose', 'Transpose', M-RK, N-KB, KB, -ONE, |