Contents
sbdsdc - compute the singular value decomposition (SVD) of a
real N-by-N (upper or lower) bidiagonal matrix B
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);
sbdsdc 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 diago-
nal matrix with non-negative diagonal elements (the singular
values of B), and U and VT are orthogonal 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.
UPLO (input)
= 'U': B is upper bidiagonal.
= 'L': B is lower bidiagonal.
COMPQ (input)
Specifies whether singular vectors are to be com-
puted as follows:
= 'N': Compute singular values only;
= 'P': Compute singular values and compute singu-
lar 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 bidiago-
nal matrix B. On exit, if INFO=0, the singular
values of B.
E (input/output)
On entry, the elements of E contain the offdiago-
nal 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 bidiago-
nal 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 bidiag-
onal matrix. For other values of COMPQ, VT is not
referenced.
LDVT (input)
The leading dimension of the array VT. LDVT >= 1.
If singular vectors are desired, then LDVT >= max(
1, N ).
Q (input) 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 >= (2 * N). If COMPQ =
'P' then LWORK >= (6 * N). 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 ille-
gal value.
> 0: The algorithm failed to compute an singular
value. The update process of divide and conquer
failed.
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, Univer-
sity of
California at Berkeley, USA