version 1.3, 2010/08/06 15:28:52
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version 1.13, 2012/12/14 12:30:28
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*> \brief \b ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm. |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZGEQR2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqr2.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqr2.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqr2.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDA, M, N |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZGEQR2 computes a QR factorization of a complex m by n matrix A: |
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*> A = Q * R. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix A. M >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of columns of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension (LDA,N) |
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*> On entry, the m by n matrix A. |
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*> On exit, the elements on and above the diagonal of the array |
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*> contain the min(m,n) by n upper trapezoidal matrix R (R is |
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*> upper triangular if m >= n); the elements below the diagonal, |
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*> with the array TAU, represent the unitary matrix Q as a |
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*> product of elementary reflectors (see Further Details). |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[out] TAU |
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*> \verbatim |
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*> TAU is COMPLEX*16 array, dimension (min(M,N)) |
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*> The scalar factors of the elementary reflectors (see Further |
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*> Details). |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension (N) |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date September 2012 |
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* |
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*> \ingroup complex16GEcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> The matrix Q is represented as a product of elementary reflectors |
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*> |
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*> Q = H(1) H(2) . . . H(k), where k = min(m,n). |
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*> |
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*> Each H(i) has the form |
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*> |
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*> H(i) = I - tau * v * v**H |
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*> |
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*> where tau is a complex scalar, and v is a complex vector with |
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*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), |
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*> and tau in TAU(i). |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO ) |
SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- 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 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, M, N |
INTEGER INFO, LDA, M, N |
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COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZGEQR2 computes a QR factorization of a complex m by n matrix A: |
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* A = Q * R. |
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* |
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* Arguments |
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* ========= |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= 0. |
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* |
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* A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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* On entry, the m by n matrix A. |
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* On exit, the elements on and above the diagonal of the array |
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* contain the min(m,n) by n upper trapezoidal matrix R (R is |
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* upper triangular if m >= n); the elements below the diagonal, |
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* with the array TAU, represent the unitary matrix Q as a |
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* product of elementary reflectors (see Further Details). |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,M). |
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* |
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* TAU (output) COMPLEX*16 array, dimension (min(M,N)) |
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* The scalar factors of the elementary reflectors (see Further |
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* Details). |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension (N) |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* |
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* Further Details |
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* =============== |
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* |
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* The matrix Q is represented as a product of elementary reflectors |
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* |
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* Q = H(1) H(2) . . . H(k), where k = min(m,n). |
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* |
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* Each H(i) has the form |
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* |
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* H(i) = I - tau * v * v' |
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* |
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* where tau is a complex scalar, and v is a complex vector with |
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* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), |
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* and tau in TAU(i). |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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COMPLEX*16 ALPHA |
COMPLEX*16 ALPHA |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL XERBLA, ZLARF, ZLARFP |
EXTERNAL XERBLA, ZLARF, ZLARFG |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC DCONJG, MAX, MIN |
INTRINSIC DCONJG, MAX, MIN |
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* |
* |
* Generate elementary reflector H(i) to annihilate A(i+1:m,i) |
* Generate elementary reflector H(i) to annihilate A(i+1:m,i) |
* |
* |
CALL ZLARFP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, |
CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, |
$ TAU( I ) ) |
$ TAU( I ) ) |
IF( I.LT.N ) THEN |
IF( I.LT.N ) THEN |
* |
* |
* Apply H(i)' to A(i:m,i+1:n) from the left |
* Apply H(i)**H to A(i:m,i+1:n) from the left |
* |
* |
ALPHA = A( I, I ) |
ALPHA = A( I, I ) |
A( I, I ) = ONE |
A( I, I ) = ONE |