sbdsdc(3P) Sun Performance Library sbdsdc(3P)NAMEsbdsdc - compute the singular value decomposition (SVD) of a real N-by-
N (upper or lower) bidiagonal matrix B
SYNOPSIS
SUBROUTINE SBDSDC(UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
WORK, IWORK, INFO)
CHARACTER * 1 UPLO, COMPQ
INTEGER N, LDU, LDVT, INFO
INTEGER IQ(*), IWORK(*)
REAL D(*), E(*), U(LDU,*), VT(LDVT,*), Q(*), WORK(*)
SUBROUTINE SBDSDC_64(UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
WORK, IWORK, INFO)
CHARACTER * 1 UPLO, COMPQ
INTEGER*8 N, LDU, LDVT, INFO
INTEGER*8 IQ(*), IWORK(*)
REAL D(*), E(*), U(LDU,*), VT(LDVT,*), Q(*), WORK(*)
F95 INTERFACE
SUBROUTINE BDSDC(UPLO, COMPQ, [N], D, E, U, [LDU], VT, [LDVT], Q, IQ,
[WORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: UPLO, COMPQ
INTEGER :: N, LDU, LDVT, INFO
INTEGER, DIMENSION(:) :: IQ, IWORK
REAL, DIMENSION(:) :: D, E, Q, WORK
REAL, DIMENSION(:,:) :: U, VT
SUBROUTINE BDSDC_64(UPLO, COMPQ, [N], D, E, U, [LDU], VT, [LDVT], Q,
IQ, [WORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: UPLO, COMPQ
INTEGER(8) :: N, LDU, LDVT, INFO
INTEGER(8), DIMENSION(:) :: IQ, IWORK
REAL, DIMENSION(:) :: D, E, Q, WORK
REAL, DIMENSION(:,:) :: U, VT
C INTERFACE
#include <sunperf.h>
void sbdsdc(char uplo, char compq, int n, float *d, float *e, float *u,
int ldu, float *vt, int ldvt, float *q, int *iq, int *info);
void sbdsdc_64(char uplo, char compq, long n, float *d, float *e, float
*u, long ldu, float *vt, long ldvt, float *q, long *iq, long
*info);
PURPOSEsbdsdc computes the singular value decomposition (SVD) of a real N-by-N
(upper or lower) bidiagonal matrix B: B = U * S * VT, using a divide
and conquer method, where S is a diagonal matrix with non-negative
diagonal elements (the singular values of B), and U and VT are orthogo‐
nal matrices of left and right singular vectors, respectively. SBDSDC
can be used to compute all singular values, and optionally, singular
vectors or singular vectors in compact form.
This code 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. See SLASD3 for details.
The code currently call SLASDQ if singular values only are desired.
However, it can be slightly modified to compute singular values using
the divide and conquer method.
ARGUMENTS
UPLO (input)
= 'U': B is upper bidiagonal.
= 'L': B is lower bidiagonal.
COMPQ (input)
Specifies whether singular vectors are to be computed as fol‐
lows:
= 'N': Compute singular values only;
= 'P': Compute singular values and compute singular vectors
in compact form; = 'I': Compute singular values and singular
vectors.
N (input) The order of the matrix B. N >= 0.
D (input/output)
On entry, the n diagonal elements of the bidiagonal matrix B.
On exit, if INFO=0, the singular values of B.
E (input/output)
On entry, the elements of E contain the offdiagonal elements
of the bidiagonal matrix whose SVD is desired. On exit, E
has been destroyed.
U (output)
If COMPQ = 'I', then: On exit, if INFO = 0, U contains the
left singular vectors of the bidiagonal matrix. For other
values of COMPQ, U is not referenced.
LDU (input)
The leading dimension of the array U. LDU >= 1. If singular
vectors are desired, then LDU >= max( 1, N ).
VT (output)
If COMPQ = 'I', then: On exit, if INFO = 0, VT' contains the
right singular vectors of the bidiagonal matrix. For other
values of COMPQ, VT is not referenced.
LDVT (input)
The leading dimension of the array VT. LDVT >= 1. If singu‐
lar vectors are desired, then LDVT >= max( 1, N ).
Q (output)
If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain
the left and right singular vectors in a compact form,
requiring O(N log N) space instead of 2*N**2. In particular,
Q contains all the REAL data in LDQ >= N*(11 + 2*SMLSIZ +
8*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is
returned by ILAENV and is equal to the maximum size of the
subproblems at the bottom of the computation tree (usually
about 25). For other values of COMPQ, Q is not referenced.
IQ (output)
If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain
the left and right singular vectors in a compact form,
requiring O(N log N) space instead of 2*N**2. In particular,
IQ contains all INTEGER data in LDIQ >= N*(3 +
3*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is
returned by ILAENV and is equal to the maximum size of the
subproblems at the bottom of the computation tree (usually
about 25). For other values of COMPQ, IQ is not referenced.
WORK (workspace)
If COMPQ = 'N' then LWORK >= (4 * N). If COMPQ = 'P' then
LWORK >= (8 * N + (SMLSIZ+1) * (SMLSIZ+1) - 2). If COMPQ =
'I' then LWORK >= (3 * N**2 + 4 * N).
IWORK (workspace)
dimension(8*N)
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute an singular value. The
update process of divide and conquer failed.
FURTHER DETAILS
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
6 Mar 2009 sbdsdc(3P)
