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Diffstat (limited to 'SRC/dgesvd.f')
-rw-r--r-- | SRC/dgesvd.f | 327 |
1 files changed, 206 insertions, 121 deletions
diff --git a/SRC/dgesvd.f b/SRC/dgesvd.f index 9a1c8489..e7a005c6 100644 --- a/SRC/dgesvd.f +++ b/SRC/dgesvd.f @@ -1,10 +1,214 @@ +*> \brief <b> DGESVD computes the singular value decomposition (SVD) for GE matrices</b> +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, +* WORK, LWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBU, JOBVT +* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), +* $ VT( LDVT, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> DGESVD computes the singular value decomposition (SVD) of a real +*> M-by-N matrix A, optionally computing the left and/or right singular +*> vectors. The SVD is written +*> +*> A = U * SIGMA * transpose(V) +*> +*> where SIGMA is an M-by-N matrix which is zero except for its +*> min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and +*> V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA +*> are the singular values of A; they are real and non-negative, and +*> are returned in descending order. The first min(m,n) columns of +*> U and V are the left and right singular vectors of A. +*> +*> Note that the routine returns V**T, not V. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] JOBU +*> \verbatim +*> JOBU is CHARACTER*1 +*> Specifies options for computing all or part of the matrix U: +*> = 'A': all M columns of U are returned in array U: +*> = 'S': the first min(m,n) columns of U (the left singular +*> vectors) are returned in the array U; +*> = 'O': the first min(m,n) columns of U (the left singular +*> vectors) are overwritten on the array A; +*> = 'N': no columns of U (no left singular vectors) are +*> computed. +*> \endverbatim +*> +*> \param[in] JOBVT +*> \verbatim +*> JOBVT is CHARACTER*1 +*> Specifies options for computing all or part of the matrix +*> V**T: +*> = 'A': all N rows of V**T are returned in the array VT; +*> = 'S': the first min(m,n) rows of V**T (the right singular +*> vectors) are returned in the array VT; +*> = 'O': the first min(m,n) rows of V**T (the right singular +*> vectors) are overwritten on the array A; +*> = 'N': no rows of V**T (no right singular vectors) are +*> computed. +*> \endverbatim +*> \verbatim +*> JOBVT and JOBU cannot both be 'O'. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the input matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the input matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the M-by-N matrix A. +*> On exit, +*> if JOBU = 'O', A is overwritten with the first min(m,n) +*> columns of U (the left singular vectors, +*> stored columnwise); +*> if JOBVT = 'O', A is overwritten with the first min(m,n) +*> rows of V**T (the right singular vectors, +*> stored rowwise); +*> if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A +*> are destroyed. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension (min(M,N)) +*> The singular values of A, sorted so that S(i) >= S(i+1). +*> \endverbatim +*> +*> \param[out] U +*> \verbatim +*> U is DOUBLE PRECISION array, dimension (LDU,UCOL) +*> (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. +*> If JOBU = 'A', U contains the M-by-M orthogonal matrix U; +*> if JOBU = 'S', U contains the first min(m,n) columns of U +*> (the left singular vectors, stored columnwise); +*> if JOBU = 'N' or 'O', U is not referenced. +*> \endverbatim +*> +*> \param[in] LDU +*> \verbatim +*> LDU is INTEGER +*> The leading dimension of the array U. LDU >= 1; if +*> JOBU = 'S' or 'A', LDU >= M. +*> \endverbatim +*> +*> \param[out] VT +*> \verbatim +*> VT is DOUBLE PRECISION array, dimension (LDVT,N) +*> If JOBVT = 'A', VT contains the N-by-N orthogonal matrix +*> V**T; +*> if JOBVT = 'S', VT contains the first min(m,n) rows of +*> V**T (the right singular vectors, stored rowwise); +*> if JOBVT = 'N' or 'O', VT is not referenced. +*> \endverbatim +*> +*> \param[in] LDVT +*> \verbatim +*> LDVT is INTEGER +*> The leading dimension of the array VT. LDVT >= 1; if +*> JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK; +*> if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged +*> superdiagonal elements of an upper bidiagonal matrix B +*> whose diagonal is in S (not necessarily sorted). B +*> satisfies A = U * B * VT, so it has the same singular values +*> as A, and singular vectors related by U and VT. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. +*> LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): +*> - PATH 1 (M much larger than N, JOBU='N') +*> - PATH 1t (N much larger than M, JOBVT='N') +*> LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths +*> For good performance, LWORK should generally be larger. +*> \endverbatim +*> \verbatim +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit. +*> < 0: if INFO = -i, the i-th argument had an illegal value. +*> > 0: if DBDSQR did not converge, INFO specifies how many +*> superdiagonals of an intermediate bidiagonal form B +*> did not converge to zero. See the description of WORK +*> above for details. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleGEsing +* +* ===================================================================== SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, $ WORK, LWORK, INFO ) * -* -- LAPACK driver routine (version 3.3.1) -- +* -- LAPACK sing routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. CHARACTER JOBU, JOBVT @@ -15,125 +219,6 @@ $ VT( LDVT, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DGESVD computes the singular value decomposition (SVD) of a real -* M-by-N matrix A, optionally computing the left and/or right singular -* vectors. The SVD is written -* -* A = U * SIGMA * transpose(V) -* -* where SIGMA is an M-by-N matrix which is zero except for its -* min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and -* V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA -* are the singular values of A; they are real and non-negative, and -* are returned in descending order. The first min(m,n) columns of -* U and V are the left and right singular vectors of A. -* -* Note that the routine returns V**T, not V. -* -* Arguments -* ========= -* -* JOBU (input) CHARACTER*1 -* Specifies options for computing all or part of the matrix U: -* = 'A': all M columns of U are returned in array U: -* = 'S': the first min(m,n) columns of U (the left singular -* vectors) are returned in the array U; -* = 'O': the first min(m,n) columns of U (the left singular -* vectors) are overwritten on the array A; -* = 'N': no columns of U (no left singular vectors) are -* computed. -* -* JOBVT (input) CHARACTER*1 -* Specifies options for computing all or part of the matrix -* V**T: -* = 'A': all N rows of V**T are returned in the array VT; -* = 'S': the first min(m,n) rows of V**T (the right singular -* vectors) are returned in the array VT; -* = 'O': the first min(m,n) rows of V**T (the right singular -* vectors) are overwritten on the array A; -* = 'N': no rows of V**T (no right singular vectors) are -* computed. -* -* JOBVT and JOBU cannot both be 'O'. -* -* M (input) INTEGER -* The number of rows of the input matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the input matrix A. N >= 0. -* -* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) -* On entry, the M-by-N matrix A. -* On exit, -* if JOBU = 'O', A is overwritten with the first min(m,n) -* columns of U (the left singular vectors, -* stored columnwise); -* if JOBVT = 'O', A is overwritten with the first min(m,n) -* rows of V**T (the right singular vectors, -* stored rowwise); -* if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A -* are destroyed. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* S (output) DOUBLE PRECISION array, dimension (min(M,N)) -* The singular values of A, sorted so that S(i) >= S(i+1). -* -* U (output) DOUBLE PRECISION array, dimension (LDU,UCOL) -* (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. -* If JOBU = 'A', U contains the M-by-M orthogonal matrix U; -* if JOBU = 'S', U contains the first min(m,n) columns of U -* (the left singular vectors, stored columnwise); -* if JOBU = 'N' or 'O', U is not referenced. -* -* LDU (input) INTEGER -* The leading dimension of the array U. LDU >= 1; if -* JOBU = 'S' or 'A', LDU >= M. -* -* VT (output) DOUBLE PRECISION array, dimension (LDVT,N) -* If JOBVT = 'A', VT contains the N-by-N orthogonal matrix -* V**T; -* if JOBVT = 'S', VT contains the first min(m,n) rows of -* V**T (the right singular vectors, stored rowwise); -* if JOBVT = 'N' or 'O', VT is not referenced. -* -* LDVT (input) INTEGER -* The leading dimension of the array VT. LDVT >= 1; if -* JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). -* -* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK; -* if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged -* superdiagonal elements of an upper bidiagonal matrix B -* whose diagonal is in S (not necessarily sorted). B -* satisfies A = U * B * VT, so it has the same singular values -* as A, and singular vectors related by U and VT. -* -* LWORK (input) INTEGER -* The dimension of the array WORK. -* LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): -* - PATH 1 (M much larger than N, JOBU='N') -* - PATH 1t (N much larger than M, JOBVT='N') -* LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths -* For good performance, LWORK should generally be larger. -* -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the optimal size of the WORK array, returns -* this value as the first entry of the WORK array, and no error -* message related to LWORK is issued by XERBLA. -* -* INFO (output) INTEGER -* = 0: successful exit. -* < 0: if INFO = -i, the i-th argument had an illegal value. -* > 0: if DBDSQR did not converge, INFO specifies how many -* superdiagonals of an intermediate bidiagonal form B -* did not converge to zero. See the description of WORK -* above for details. -* * ===================================================================== * * .. Parameters .. |