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version 1.17, 2017/06/17 10:53:49
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*> \brief \b DGERQ2 computes the RQ 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 DGERQ2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgerq2.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/dgerq2.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/dgerq2.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 DGERQ2( 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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* DOUBLE PRECISION 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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*> DGERQ2 computes an RQ factorization of a real m by n matrix A: |
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*> A = R * Q. |
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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 DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, the m by n matrix A. |
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*> On exit, if m <= n, the upper triangle of the subarray |
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*> A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; |
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*> if m >= n, the elements on and above the (m-n)-th subdiagonal |
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*> contain the m by n upper trapezoidal matrix R; the remaining |
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*> elements, with the array TAU, represent the orthogonal matrix |
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*> Q as a product of elementary reflectors (see Further |
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*> 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (M) |
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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 December 2016 |
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* |
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*> \ingroup doubleGEcomputational |
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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**T |
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*> |
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*> where tau is a real scalar, and v is a real vector with |
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*> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in |
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*> A(m-k+i,1:n-k+i-1), and tau in TAU(i). |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO ) |
SUBROUTINE DGERQ2( M, N, A, LDA, TAU, 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 .. |
INTEGER INFO, LDA, M, N |
INTEGER INFO, LDA, M, N |
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGERQ2 computes an RQ factorization of a real m by n matrix A: |
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* A = R * Q. |
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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) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the m by n matrix A. |
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* On exit, if m <= n, the upper triangle of the subarray |
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* A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; |
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* if m >= n, the elements on and above the (m-n)-th subdiagonal |
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* contain the m by n upper trapezoidal matrix R; the remaining |
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* elements, with the array TAU, represent the orthogonal matrix |
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* Q as a product of elementary reflectors (see Further |
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* 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (M) |
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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 real scalar, and v is a real vector with |
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* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in |
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* A(m-k+i,1:n-k+i-1), and tau in TAU(i). |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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DOUBLE PRECISION AII |
DOUBLE PRECISION AII |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DLARF, DLARFP, XERBLA |
EXTERNAL DLARF, DLARFG, XERBLA |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC MAX, MIN |
INTRINSIC MAX, MIN |
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* Generate elementary reflector H(i) to annihilate |
* Generate elementary reflector H(i) to annihilate |
* A(m-k+i,1:n-k+i-1) |
* A(m-k+i,1:n-k+i-1) |
* |
* |
CALL DLARFP( N-K+I, A( M-K+I, N-K+I ), A( M-K+I, 1 ), LDA, |
CALL DLARFG( N-K+I, A( M-K+I, N-K+I ), A( M-K+I, 1 ), LDA, |
$ TAU( I ) ) |
$ TAU( I ) ) |
* |
* |
* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right |
* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right |