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version 1.12, 2012/08/22 09:48:20
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*> \brief \b DLASD0 |
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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 DLASD0 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd0.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/dlasd0.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/dlasd0.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 DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, |
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* WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IWORK( * ) |
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* DOUBLE PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), |
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* $ 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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*> Using a divide and conquer approach, DLASD0 computes the singular |
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*> value decomposition (SVD) of a real upper bidiagonal N-by-M |
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*> matrix B with diagonal D and offdiagonal E, where M = N + SQRE. |
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*> The algorithm computes orthogonal matrices U and VT such that |
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*> B = U * S * VT. The singular values S are overwritten on D. |
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*> |
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*> A related subroutine, DLASDA, computes only the singular values, |
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*> and optionally, the singular vectors in compact form. |
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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] N |
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*> \verbatim |
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*> N is INTEGER |
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*> On entry, the row dimension of the upper bidiagonal matrix. |
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*> This is also the dimension of the main diagonal array D. |
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*> \endverbatim |
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*> |
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*> \param[in] SQRE |
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*> \verbatim |
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*> SQRE is INTEGER |
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*> Specifies the column dimension of the bidiagonal matrix. |
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*> = 0: The bidiagonal matrix has column dimension M = N; |
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*> = 1: The bidiagonal matrix has column dimension M = N+1; |
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*> \endverbatim |
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*> |
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*> \param[in,out] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> On entry D contains the main diagonal of the bidiagonal |
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*> matrix. |
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*> On exit D, if INFO = 0, contains its singular values. |
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*> \endverbatim |
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*> |
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*> \param[in] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (M-1) |
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*> Contains the subdiagonal entries of the bidiagonal matrix. |
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*> On exit, E has been destroyed. |
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*> \endverbatim |
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*> |
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*> \param[out] U |
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*> \verbatim |
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*> U is DOUBLE PRECISION array, dimension at least (LDQ, N) |
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*> On exit, U contains the left singular vectors. |
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*> \endverbatim |
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*> |
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*> \param[in] LDU |
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*> \verbatim |
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*> LDU is INTEGER |
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*> On entry, leading dimension of U. |
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*> \endverbatim |
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*> |
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*> \param[out] VT |
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*> \verbatim |
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*> VT is DOUBLE PRECISION array, dimension at least (LDVT, M) |
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*> On exit, VT**T contains the right singular vectors. |
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*> \endverbatim |
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*> |
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*> \param[in] LDVT |
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*> \verbatim |
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*> LDVT is INTEGER |
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*> On entry, leading dimension of VT. |
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*> \endverbatim |
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*> |
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*> \param[in] SMLSIZ |
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*> \verbatim |
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*> SMLSIZ is INTEGER |
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*> On entry, maximum size of the subproblems at the |
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*> bottom of the computation tree. |
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*> \endverbatim |
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*> |
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*> \param[out] IWORK |
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*> \verbatim |
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*> IWORK is INTEGER work array. |
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*> Dimension must be at least (8 * N) |
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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 work array. |
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*> Dimension must be at least (3 * M**2 + 2 * 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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*> > 0: if INFO = 1, a singular value did not converge |
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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 November 2011 |
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* |
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*> \ingroup auxOTHERauxiliary |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Ming Gu and Huan Ren, Computer Science Division, University of |
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*> California at Berkeley, USA |
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*> |
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* ===================================================================== |
SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, |
SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, |
$ WORK, INFO ) |
$ WORK, INFO ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- 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 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE |
INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE |
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$ WORK( * ) |
$ WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
|
* |
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* Using a divide and conquer approach, DLASD0 computes the singular |
|
* value decomposition (SVD) of a real upper bidiagonal N-by-M |
|
* matrix B with diagonal D and offdiagonal E, where M = N + SQRE. |
|
* The algorithm computes orthogonal matrices U and VT such that |
|
* B = U * S * VT. The singular values S are overwritten on D. |
|
* |
|
* A related subroutine, DLASDA, computes only the singular values, |
|
* and optionally, the singular vectors in compact form. |
|
* |
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* Arguments |
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* ========= |
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* |
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* N (input) INTEGER |
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* On entry, the row dimension of the upper bidiagonal matrix. |
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* This is also the dimension of the main diagonal array D. |
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* |
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* SQRE (input) INTEGER |
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* Specifies the column dimension of the bidiagonal matrix. |
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* = 0: The bidiagonal matrix has column dimension M = N; |
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* = 1: The bidiagonal matrix has column dimension M = N+1; |
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* |
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* D (input/output) DOUBLE PRECISION array, dimension (N) |
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* On entry D contains the main diagonal of the bidiagonal |
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* matrix. |
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* On exit D, if INFO = 0, contains its singular values. |
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* |
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* E (input) DOUBLE PRECISION array, dimension (M-1) |
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* Contains the subdiagonal entries of the bidiagonal matrix. |
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* On exit, E has been destroyed. |
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* |
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* U (output) DOUBLE PRECISION array, dimension at least (LDQ, N) |
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* On exit, U contains the left singular vectors. |
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* |
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* LDU (input) INTEGER |
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* On entry, leading dimension of U. |
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* |
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* VT (output) DOUBLE PRECISION array, dimension at least (LDVT, M) |
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* On exit, VT' contains the right singular vectors. |
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* |
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* LDVT (input) INTEGER |
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* On entry, leading dimension of VT. |
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* |
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* SMLSIZ (input) INTEGER |
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* On entry, maximum size of the subproblems at the |
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* bottom of the computation tree. |
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* |
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* IWORK (workspace) INTEGER work array. |
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* Dimension must be at least (8 * N) |
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* |
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* WORK (workspace) DOUBLE PRECISION work array. |
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* Dimension must be at least (3 * M**2 + 2 * 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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* > 0: if INFO = 1, an singular value did not converge |
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* |
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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* Ming Gu and Huan Ren, Computer Science Division, University of |
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* California at Berkeley, USA |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |