version 1.10, 2011/11/21 22:19:51
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version 1.19, 2023/08/07 08:39:29
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*> \brief \b ZLAHR2 |
*> \brief \b ZLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. |
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download ZLAHR2 + dependencies |
*> Download ZLAHR2 + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahr2.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahr2.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahr2.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahr2.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahr2.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahr2.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) |
* SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER K, LDA, LDT, LDY, N, NB |
* INTEGER K, LDA, LDT, LDY, N, NB |
* .. |
* .. |
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* COMPLEX*16 A( LDA, * ), T( LDT, NB ), TAU( NB ), |
* COMPLEX*16 A( LDA, * ), T( LDT, NB ), TAU( NB ), |
* $ Y( LDY, NB ) |
* $ Y( LDY, NB ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
|
*> \date November 2011 |
|
* |
* |
*> \ingroup complex16OTHERauxiliary |
*> \ingroup complex16OTHERauxiliary |
* |
* |
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*> modified element of the upper Hessenberg matrix H, and vi denotes an |
*> modified element of the upper Hessenberg matrix H, and vi denotes an |
*> element of the vector defining H(i). |
*> element of the vector defining H(i). |
*> |
*> |
*> This subroutine is a slight modification of LAPACK-3.0's DLAHRD |
*> This subroutine is a slight modification of LAPACK-3.0's ZLAHRD |
*> incorporating improvements proposed by Quintana-Orti and Van de |
*> incorporating improvements proposed by Quintana-Orti and Van de |
*> Gejin. Note that the entries of A(1:K,2:NB) differ from those |
*> Gejin. Note that the entries of A(1:K,2:NB) differ from those |
*> returned by the original LAPACK-3.0's DLAHRD routine. (This |
*> returned by the original LAPACK-3.0's ZLAHRD routine. (This |
*> subroutine is not backward compatible with LAPACK-3.0's DLAHRD.) |
*> subroutine is not backward compatible with LAPACK-3.0's ZLAHRD.) |
*> \endverbatim |
*> \endverbatim |
* |
* |
*> \par References: |
*> \par References: |
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* ===================================================================== |
* ===================================================================== |
SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) |
SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK auxiliary routine -- |
* -- 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 2011 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER K, LDA, LDT, LDY, N, NB |
INTEGER K, LDA, LDT, LDY, N, NB |
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* |
* |
* .. Parameters .. |
* .. Parameters .. |
COMPLEX*16 ZERO, ONE |
COMPLEX*16 ZERO, ONE |
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), |
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), |
$ ONE = ( 1.0D+0, 0.0D+0 ) ) |
$ ONE = ( 1.0D+0, 0.0D+0 ) ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
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* |
* |
* Update I-th column of A - Y * V**H |
* Update I-th column of A - Y * V**H |
* |
* |
CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) |
CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) |
CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY, |
CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY, |
$ A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 ) |
$ A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 ) |
CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) |
CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) |
* |
* |
* Apply I - V * T**H * V**H to this column (call it b) from the |
* Apply I - V * T**H * V**H to this column (call it b) from the |
* left, using the last column of T as workspace |
* left, using the last column of T as workspace |
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* w := V1**H * b1 |
* w := V1**H * b1 |
* |
* |
CALL ZCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 ) |
CALL ZCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 ) |
CALL ZTRMV( 'Lower', 'Conjugate transpose', 'UNIT', |
CALL ZTRMV( 'Lower', 'Conjugate transpose', 'UNIT', |
$ I-1, A( K+1, 1 ), |
$ I-1, A( K+1, 1 ), |
$ LDA, T( 1, NB ), 1 ) |
$ LDA, T( 1, NB ), 1 ) |
* |
* |
* w := w + V2**H * b2 |
* w := w + V2**H * b2 |
* |
* |
CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, |
CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, |
$ ONE, A( K+I, 1 ), |
$ ONE, A( K+I, 1 ), |
$ LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 ) |
$ LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 ) |
* |
* |
* w := T**H * w |
* w := T**H * w |
* |
* |
CALL ZTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT', |
CALL ZTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT', |
$ I-1, T, LDT, |
$ I-1, T, LDT, |
$ T( 1, NB ), 1 ) |
$ T( 1, NB ), 1 ) |
* |
* |
* b2 := b2 - V2*w |
* b2 := b2 - V2*w |
* |
* |
CALL ZGEMV( 'NO TRANSPOSE', N-K-I+1, I-1, -ONE, |
CALL ZGEMV( 'NO TRANSPOSE', N-K-I+1, I-1, -ONE, |
$ A( K+I, 1 ), |
$ A( K+I, 1 ), |
$ LDA, T( 1, NB ), 1, ONE, A( K+I, I ), 1 ) |
$ LDA, T( 1, NB ), 1, ONE, A( K+I, I ), 1 ) |
* |
* |
* b1 := b1 - V1*w |
* b1 := b1 - V1*w |
* |
* |
CALL ZTRMV( 'Lower', 'NO TRANSPOSE', |
CALL ZTRMV( 'Lower', 'NO TRANSPOSE', |
$ 'UNIT', I-1, |
$ 'UNIT', I-1, |
$ A( K+1, 1 ), LDA, T( 1, NB ), 1 ) |
$ A( K+1, 1 ), LDA, T( 1, NB ), 1 ) |
CALL ZAXPY( I-1, -ONE, T( 1, NB ), 1, A( K+1, I ), 1 ) |
CALL ZAXPY( I-1, -ONE, T( 1, NB ), 1, A( K+1, I ), 1 ) |
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* |
* |
* Compute Y(K+1:N,I) |
* Compute Y(K+1:N,I) |
* |
* |
CALL ZGEMV( 'NO TRANSPOSE', N-K, N-K-I+1, |
CALL ZGEMV( 'NO TRANSPOSE', N-K, N-K-I+1, |
$ ONE, A( K+1, I+1 ), |
$ ONE, A( K+1, I+1 ), |
$ LDA, A( K+I, I ), 1, ZERO, Y( K+1, I ), 1 ) |
$ LDA, A( K+I, I ), 1, ZERO, Y( K+1, I ), 1 ) |
CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, |
CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, |
$ ONE, A( K+I, 1 ), LDA, |
$ ONE, A( K+I, 1 ), LDA, |
$ A( K+I, I ), 1, ZERO, T( 1, I ), 1 ) |
$ A( K+I, I ), 1, ZERO, T( 1, I ), 1 ) |
CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, |
CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, |
$ Y( K+1, 1 ), LDY, |
$ Y( K+1, 1 ), LDY, |
$ T( 1, I ), 1, ONE, Y( K+1, I ), 1 ) |
$ T( 1, I ), 1, ONE, Y( K+1, I ), 1 ) |
CALL ZSCAL( N-K, TAU( I ), Y( K+1, I ), 1 ) |
CALL ZSCAL( N-K, TAU( I ), Y( K+1, I ), 1 ) |
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* Compute T(1:I,I) |
* Compute T(1:I,I) |
* |
* |
CALL ZSCAL( I-1, -TAU( I ), T( 1, I ), 1 ) |
CALL ZSCAL( I-1, -TAU( I ), T( 1, I ), 1 ) |
CALL ZTRMV( 'Upper', 'No Transpose', 'NON-UNIT', |
CALL ZTRMV( 'Upper', 'No Transpose', 'NON-UNIT', |
$ I-1, T, LDT, |
$ I-1, T, LDT, |
$ T( 1, I ), 1 ) |
$ T( 1, I ), 1 ) |
T( I, I ) = TAU( I ) |
T( I, I ) = TAU( I ) |
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* Compute Y(1:K,1:NB) |
* Compute Y(1:K,1:NB) |
* |
* |
CALL ZLACPY( 'ALL', K, NB, A( 1, 2 ), LDA, Y, LDY ) |
CALL ZLACPY( 'ALL', K, NB, A( 1, 2 ), LDA, Y, LDY ) |
CALL ZTRMM( 'RIGHT', 'Lower', 'NO TRANSPOSE', |
CALL ZTRMM( 'RIGHT', 'Lower', 'NO TRANSPOSE', |
$ 'UNIT', K, NB, |
$ 'UNIT', K, NB, |
$ ONE, A( K+1, 1 ), LDA, Y, LDY ) |
$ ONE, A( K+1, 1 ), LDA, Y, LDY ) |
IF( N.GT.K+NB ) |
IF( N.GT.K+NB ) |
$ CALL ZGEMM( 'NO TRANSPOSE', 'NO TRANSPOSE', K, |
$ CALL ZGEMM( 'NO TRANSPOSE', 'NO TRANSPOSE', K, |
$ NB, N-K-NB, ONE, |
$ NB, N-K-NB, ONE, |
$ A( 1, 2+NB ), LDA, A( K+1+NB, 1 ), LDA, ONE, Y, |
$ A( 1, 2+NB ), LDA, A( K+1+NB, 1 ), LDA, ONE, Y, |
$ LDY ) |
$ LDY ) |
CALL ZTRMM( 'RIGHT', 'Upper', 'NO TRANSPOSE', |
CALL ZTRMM( 'RIGHT', 'Upper', 'NO TRANSPOSE', |
$ 'NON-UNIT', K, NB, |
$ 'NON-UNIT', K, NB, |
$ ONE, T, LDT, Y, LDY ) |
$ ONE, T, LDT, Y, LDY ) |
* |
* |