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version 1.18, 2023/08/07 08:38:49
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* |
* |
* =========== 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 DGEQR2P + dependencies |
*> Download DGEQR2P + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2p.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2p.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2p.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2p.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2p.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2p.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO ) |
* SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER INFO, LDA, M, N |
* INTEGER INFO, LDA, M, N |
* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
*> |
*> |
*> \verbatim |
*> \verbatim |
*> |
*> |
*> DGEQR2 computes a QR factorization of a real m by n matrix A: |
*> DGEQR2P computes a QR factorization of a real m-by-n matrix A: |
*> A = Q * R. |
*> |
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*> A = Q * ( R ), |
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*> ( 0 ) |
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*> |
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*> where: |
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*> |
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*> Q is a m-by-m orthogonal matrix; |
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*> R is an upper-triangular n-by-n matrix with nonnegative diagonal |
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*> entries; |
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*> 0 is a (m-n)-by-n zero matrix, if m > n. |
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*> |
*> \endverbatim |
*> \endverbatim |
* |
* |
* Arguments: |
* Arguments: |
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*> On entry, the m by n matrix A. |
*> On entry, the m by n matrix A. |
*> On exit, the elements on and above the diagonal of the array |
*> On exit, the elements on and above the diagonal of the array |
*> contain the min(m,n) by n upper trapezoidal matrix R (R is |
*> contain the min(m,n) by n upper trapezoidal matrix R (R is |
*> upper triangular if m >= n); the elements below the diagonal, |
*> upper triangular if m >= n). The diagonal entries of R are |
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*> nonnegative; the elements below the diagonal, |
*> with the array TAU, represent the orthogonal matrix Q as a |
*> with the array TAU, represent the orthogonal matrix Q as a |
*> product of elementary reflectors (see Further Details). |
*> product of elementary reflectors (see Further Details). |
*> \endverbatim |
*> \endverbatim |
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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. |
* |
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*> \date September 2012 |
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* |
* |
*> \ingroup doubleGEcomputational |
*> \ingroup doubleGEcomputational |
* |
* |
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*> where tau is a real scalar, and v is a real vector with |
*> where tau is a real scalar, and v is a real vector with |
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), |
*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), |
*> and tau in TAU(i). |
*> and tau in TAU(i). |
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*> |
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*> See Lapack Working Note 203 for details |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
* ===================================================================== |
* ===================================================================== |
SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO ) |
SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- LAPACK computational 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..-- |
* September 2012 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, M, N |
INTEGER INFO, LDA, M, N |