dgesdd
dgesdd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors
SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
* LWORK, IWORK, INFO)
CHARACTER * 1 JOBZ
INTEGER M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION A(LDA,*), S(*), U(LDU,*), VT(LDVT,*), WORK(*)
SUBROUTINE DGESDD_64( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
* LWORK, IWORK, INFO)
CHARACTER * 1 JOBZ
INTEGER*8 M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION A(LDA,*), S(*), U(LDU,*), VT(LDVT,*), WORK(*)
SUBROUTINE GESDD( JOBZ, [M], [N], A, [LDA], S, U, [LDU], VT, [LDVT],
* [WORK], [LWORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ
INTEGER :: M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: S, WORK
REAL(8), DIMENSION(:,:) :: A, U, VT
SUBROUTINE GESDD_64( JOBZ, [M], [N], A, [LDA], S, U, [LDU], VT,
* [LDVT], [WORK], [LWORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ
INTEGER(8) :: M, N, LDA, LDU, LDVT, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: S, WORK
REAL(8), DIMENSION(:,:) :: A, U, VT
#include <sunperf.h>
void dgesdd(char jobz, int m, int n, double *a, int lda, double *s, double *u, int ldu, double *vt, int ldvt, int *info);
void dgesdd_64(char jobz, long m, long n, double *a, long lda, double *s, double *u, long ldu, double *vt, long ldvt, long *info);
dgesdd computes the singular value decomposition (SVD) of a real
M-by-N matrix A, optionally computing the left and right singular
vectors. If singular vectors are desired, it uses a
divide-and-conquer algorithm.
The SVD is written
= 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 VT = V**T, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
-
* JOBZ (input)
-
Specifies options for computing all or part of the matrix U:
-
* M (input)
-
The number of rows of the input matrix A. M >= 0.
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* N (input)
-
The number of columns of the input matrix A. N >= 0.
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* A (input/output)
-
On entry, the M-by-N matrix A.
On exit,
if JOBZ = 'O', A is overwritten with the first N columns
of U (the left singular vectors, stored
columnwise) if M >= N;
A is overwritten with the first M rows
of V**T (the right singular vectors, stored
rowwise) otherwise.
if JOBZ .ne. 'O', the contents of A are destroyed.
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* LDA (input)
-
The leading dimension of the array A. LDA >= max(1,M).
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* S (output)
-
The singular values of A, sorted so that S(i) >= S(i+1).
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* U (output)
-
UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
UCOL = min(M,N) if JOBZ = 'S'.
If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
orthogonal matrix U;
if JOBZ = 'S', U contains the first min(M,N) columns of U
(the left singular vectors, stored columnwise);
if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
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* LDU (input)
-
The leading dimension of the array U. LDU >= 1; if
JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
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* VT (output)
-
If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
N-by-N orthogonal matrix V**T;
if JOBZ = 'S', VT contains the first min(M,N) rows of
V**T (the right singular vectors, stored rowwise);
if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
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* LDVT (input)
-
The leading dimension of the array VT. LDVT >= 1; if
JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
if JOBZ = 'S', LDVT >= min(M,N).
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* WORK (workspace)
-
On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
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* LWORK (input)
-
The dimension of the array WORK. LWORK >= 1.
If JOBZ = 'N',
LWORK >= 3*min(M,N) + max(max(M,N),6*min(M,N)).
If JOBZ = 'O',
LWORK >= 3*min(M,N)*min(M,N) + max(max(M,N),5*min(M,N)*
min(M,N)+4*min(M,N)).
If JOBZ = 'S' or 'A'
LWORK >= 3*min(M,N)*min(M,N) + max(max(M,N),4*min(M,N)*
min(M,N)+4*min(M,N)).
For good performance, LWORK should generally be larger.
If LWORK < 0 but other input arguments are legal, WORK(1)
returns optimal LWORK.
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* IWORK (workspace)
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dimension(8*MIN(M,N))
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* INFO (output)
-