Contents
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(*)
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(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
C INTERFACE
#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:
= '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 on the array
A; = '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
LWORK = -1, then a workspace query is assumed. In
this case, 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 mes-
sage related to LWORK is issued. The minimum
workspace size requirement is as follows:
If M is much larger than N such that M >= (N *
11/6):
If JOBZ = 'N', LWORK >= 7*N + N
If JOBZ = 'O', LWORK >= 3*N*N + 4*N + 2*N*N +
3*N
If JOBZ = 'S', LWORK >= 3*N*N + 4*N + N*N + 3*N
If JOBZ = 'A', LWORK >= 3*N*N + 4*N + N*N + 3*N
If M is at least N but not much larger (N <= M <
(N * 11/6)):
If JOBZ = 'N', LWORK >= 3*N + MAX(M, (7*N))
If JOBZ = 'O', LWORK >= 3*N + MAX(M, N*N +
(3*N*N + 4*N))
If JOBZ = 'S', LWORK >= 3*N + MAX(M, (3*N*N +
4*N))
If JOBZ = 'A', LWORK >= 3*N + MAX( M, (3*N*N +
4*N)) If N is much larger than M such that N >= (M
* 11/6):
If JOBZ = 'N', LWORK >= 7*M + M
If JOBZ = 'O', LWORK >= 3*M*M + 4*M + 2*M*M +
3*M
If JOBZ = 'S', LWORK >= 3*M*M + 4*M + M*M + 3*M
If JOBZ = 'A', LWORK >= 3*M*M + 4*M + M*M + 3*M
If N is at least M but not much larger (M <= N <
(M * 11/6):
If JOBZ = 'N', LWORK >= 3*M + MAX(N, 7*M)
If JOBZ = 'O', LWORK >= 3*M + MAX(N, M*M +
(3*M*M + 4*M))
If JOBZ = 'S', LWORK >= 3*M + MAX(N, (3*M*M +
4*M))
If JOBZ = 'A', LWORK >= 3*M + MAX(N, (3*M*M +
4*M))
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