version 1.2, 2010/04/21 13:45:41
|
version 1.18, 2018/05/29 07:18:41
|
Line 1
|
Line 1
|
|
*> \brief \b ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download ZUNM2L + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunm2l.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunm2l.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunm2l.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
|
* WORK, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* CHARACTER SIDE, TRANS |
|
* INTEGER INFO, K, LDA, LDC, M, N |
|
* .. |
|
* .. Array Arguments .. |
|
* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> ZUNM2L overwrites the general complex m-by-n matrix C with |
|
*> |
|
*> Q * C if SIDE = 'L' and TRANS = 'N', or |
|
*> |
|
*> Q**H* C if SIDE = 'L' and TRANS = 'C', or |
|
*> |
|
*> C * Q if SIDE = 'R' and TRANS = 'N', or |
|
*> |
|
*> C * Q**H if SIDE = 'R' and TRANS = 'C', |
|
*> |
|
*> where Q is a complex unitary matrix defined as the product of k |
|
*> elementary reflectors |
|
*> |
|
*> Q = H(k) . . . H(2) H(1) |
|
*> |
|
*> as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n |
|
*> if SIDE = 'R'. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] SIDE |
|
*> \verbatim |
|
*> SIDE is CHARACTER*1 |
|
*> = 'L': apply Q or Q**H from the Left |
|
*> = 'R': apply Q or Q**H from the Right |
|
*> \endverbatim |
|
*> |
|
*> \param[in] TRANS |
|
*> \verbatim |
|
*> TRANS is CHARACTER*1 |
|
*> = 'N': apply Q (No transpose) |
|
*> = 'C': apply Q**H (Conjugate transpose) |
|
*> \endverbatim |
|
*> |
|
*> \param[in] M |
|
*> \verbatim |
|
*> M is INTEGER |
|
*> The number of rows of the matrix C. M >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The number of columns of the matrix C. N >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] K |
|
*> \verbatim |
|
*> K is INTEGER |
|
*> The number of elementary reflectors whose product defines |
|
*> the matrix Q. |
|
*> If SIDE = 'L', M >= K >= 0; |
|
*> if SIDE = 'R', N >= K >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] A |
|
*> \verbatim |
|
*> A is COMPLEX*16 array, dimension (LDA,K) |
|
*> The i-th column must contain the vector which defines the |
|
*> elementary reflector H(i), for i = 1,2,...,k, as returned by |
|
*> ZGEQLF in the last k columns of its array argument A. |
|
*> A is modified by the routine but restored on exit. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDA |
|
*> \verbatim |
|
*> LDA is INTEGER |
|
*> The leading dimension of the array A. |
|
*> If SIDE = 'L', LDA >= max(1,M); |
|
*> if SIDE = 'R', LDA >= max(1,N). |
|
*> \endverbatim |
|
*> |
|
*> \param[in] TAU |
|
*> \verbatim |
|
*> TAU is COMPLEX*16 array, dimension (K) |
|
*> TAU(i) must contain the scalar factor of the elementary |
|
*> reflector H(i), as returned by ZGEQLF. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] C |
|
*> \verbatim |
|
*> C is COMPLEX*16 array, dimension (LDC,N) |
|
*> On entry, the m-by-n matrix C. |
|
*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDC |
|
*> \verbatim |
|
*> LDC is INTEGER |
|
*> The leading dimension of the array C. LDC >= max(1,M). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] WORK |
|
*> \verbatim |
|
*> WORK is COMPLEX*16 array, dimension |
|
*> (N) if SIDE = 'L', |
|
*> (M) if SIDE = 'R' |
|
*> \endverbatim |
|
*> |
|
*> \param[out] INFO |
|
*> \verbatim |
|
*> INFO is INTEGER |
|
*> = 0: successful exit |
|
*> < 0: if INFO = -i, the i-th argument had an illegal value |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date December 2016 |
|
* |
|
*> \ingroup complex16OTHERcomputational |
|
* |
|
* ===================================================================== |
SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
$ WORK, INFO ) |
$ WORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER SIDE, TRANS |
CHARACTER SIDE, TRANS |
Line 14
|
Line 172
|
COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZUNM2L overwrites the general complex m-by-n matrix C with |
|
* |
|
* Q * C if SIDE = 'L' and TRANS = 'N', or |
|
* |
|
* Q'* C if SIDE = 'L' and TRANS = 'C', or |
|
* |
|
* C * Q if SIDE = 'R' and TRANS = 'N', or |
|
* |
|
* C * Q' if SIDE = 'R' and TRANS = 'C', |
|
* |
|
* where Q is a complex unitary matrix defined as the product of k |
|
* elementary reflectors |
|
* |
|
* Q = H(k) . . . H(2) H(1) |
|
* |
|
* as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n |
|
* if SIDE = 'R'. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* SIDE (input) CHARACTER*1 |
|
* = 'L': apply Q or Q' from the Left |
|
* = 'R': apply Q or Q' from the Right |
|
* |
|
* TRANS (input) CHARACTER*1 |
|
* = 'N': apply Q (No transpose) |
|
* = 'C': apply Q' (Conjugate transpose) |
|
* |
|
* M (input) INTEGER |
|
* The number of rows of the matrix C. M >= 0. |
|
* |
|
* N (input) INTEGER |
|
* The number of columns of the matrix C. N >= 0. |
|
* |
|
* K (input) INTEGER |
|
* The number of elementary reflectors whose product defines |
|
* the matrix Q. |
|
* If SIDE = 'L', M >= K >= 0; |
|
* if SIDE = 'R', N >= K >= 0. |
|
* |
|
* A (input) COMPLEX*16 array, dimension (LDA,K) |
|
* The i-th column must contain the vector which defines the |
|
* elementary reflector H(i), for i = 1,2,...,k, as returned by |
|
* ZGEQLF in the last k columns of its array argument A. |
|
* A is modified by the routine but restored on exit. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. |
|
* If SIDE = 'L', LDA >= max(1,M); |
|
* if SIDE = 'R', LDA >= max(1,N). |
|
* |
|
* TAU (input) COMPLEX*16 array, dimension (K) |
|
* TAU(i) must contain the scalar factor of the elementary |
|
* reflector H(i), as returned by ZGEQLF. |
|
* |
|
* C (input/output) COMPLEX*16 array, dimension (LDC,N) |
|
* On entry, the m-by-n matrix C. |
|
* On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q. |
|
* |
|
* LDC (input) INTEGER |
|
* The leading dimension of the array C. LDC >= max(1,M). |
|
* |
|
* WORK (workspace) COMPLEX*16 array, dimension |
|
* (N) if SIDE = 'L', |
|
* (M) if SIDE = 'R' |
|
* |
|
* INFO (output) INTEGER |
|
* = 0: successful exit |
|
* < 0: if INFO = -i, the i-th argument had an illegal value |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 168
|
Line 252
|
DO 10 I = I1, I2, I3 |
DO 10 I = I1, I2, I3 |
IF( LEFT ) THEN |
IF( LEFT ) THEN |
* |
* |
* H(i) or H(i)' is applied to C(1:m-k+i,1:n) |
* H(i) or H(i)**H is applied to C(1:m-k+i,1:n) |
* |
* |
MI = M - K + I |
MI = M - K + I |
ELSE |
ELSE |
* |
* |
* H(i) or H(i)' is applied to C(1:m,1:n-k+i) |
* H(i) or H(i)**H is applied to C(1:m,1:n-k+i) |
* |
* |
NI = N - K + I |
NI = N - K + I |
END IF |
END IF |
* |
* |
* Apply H(i) or H(i)' |
* Apply H(i) or H(i)**H |
* |
* |
IF( NOTRAN ) THEN |
IF( NOTRAN ) THEN |
TAUI = TAU( I ) |
TAUI = TAU( I ) |