Contents
sgesdd - compute the singular value decomposition (SVD) of a
real M-by-N matrix A, optionally computing the left and
right singular vectors
SUBROUTINE SGESDD(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(*)
REAL A(LDA,*), S(*), U(LDU,*), VT(LDVT,*), WORK(*)
SUBROUTINE SGESDD_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(*)
REAL A(LDA,*), S(*), U(LDU,*), VT(LDVT,*), WORK(*)
F95 INTERFACE
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, DIMENSION(:) :: S, WORK
REAL, 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, DIMENSION(:) :: S, WORK
REAL, DIMENSION(:,:) :: A, U, VT
C INTERFACE
#include <sunperf.h>
void sgesdd(char jobz, int m, int n, float *a, int lda,
float *s, float *u, int ldu, float *vt, int ldvt,
int *info);
void sgesdd_64(char jobz, long m, long n, float *a, long
lda, float *s, float *u, long ldu, float *vt, long
ldvt, long *info);
sgesdd 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:
= 'A': all M columns of U and all N rows of V**T
are returned in the arrays U and VT; = 'S': the
first min(M,N) columns of U and the first min(M,N)
rows of V**T are returned in the arrays U and VT;
= 'O': If M >= N, the first N columns of U are
overwritten on the array A and all rows of V**T
are returned in the array VT; otherwise, all
columns of U are returned in the array U and the
first M rows of V**T are overwritten in the array
VT; = 'N': no columns of U or rows of V**T are
computed.
M (input) The number of rows of the input matrix A. M >= 0.
N (input) The number of columns of the input matrix A. N >=
0.
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 row-
wise) otherwise. if JOBZ .ne. 'O', the contents
of A are destroyed.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
S (output)
The singular values of A, sorted so that S(i) >=
S(i+1).
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.
LDU (input)
The leading dimension of the array U. LDU >= 1;
if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU
>= M.
VT (output)
If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT con-
tains 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.
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).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK;
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.
IWORK (workspace)
dimension(8*MIN(M,N))
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
> 0: SBDSDC did not converge, updating process
failed.
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, Univer-
sity of
California at Berkeley, USA