DBDSDC(3S)DBDSDC(3S)NAMEDBDSDC - compute the singular value decomposition (SVD) of a real N-by-N
(upper or lower) bidiagonal matrix B
SYNOPSIS
SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK,
IWORK, INFO )
CHARACTER COMPQ, UPLO
INTEGER INFO, LDU, LDVT, N
INTEGER IQ( * ), IWORK( * )
DOUBLE PRECISION D( * ), E( * ), Q( * ), U( LDU, * ), VT(
LDVT, * ), WORK( * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSEDBDSDC 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 orthogonal matrices
of left and right singular vectors, respectively. DBDSDC 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 DLASD3 for details.
The code currently call DLASDQ if singular values only are desired.
However, it can be slightly modified to compute singular values using the
divide and conquer method.
Page 1
DBDSDC(3S)DBDSDC(3S)ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': B is upper bidiagonal.
= 'L': B is lower bidiagonal.
COMPQ (input) CHARACTER*1
Specifies whether singular vectors are to be computed as follows:
= '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) INTEGER
The order of the matrix B. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the bidiagonal matrix B. On
exit, if INFO=0, the singular values of B.
E (input/output) DOUBLE PRECISION array, dimension (N)
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) DOUBLE PRECISION array, dimension (LDU,N)
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) INTEGER
The leading dimension of the array U. LDU >= 1. If singular
vectors are desired, then LDU >= max( 1, N ).
VT (output) DOUBLE PRECISION array, dimension (LDVT,N)
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) INTEGER
The leading dimension of the array VT. LDVT >= 1. If singular
vectors are desired, then LDVT >= max( 1, N ).
Q (output) DOUBLE PRECISION array, dimension (LDQ)
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 DOUBLE PRECISION 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.
Page 2
DBDSDC(3S)DBDSDC(3S)
IQ (output) INTEGER array, dimension (LDIQ)
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) DOUBLE PRECISION array, dimension (LWORK)
If COMPQ = 'N' then LWORK >= (4 * N). If COMPQ = 'P' then LWORK
>= (6 * N). If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).
IWORK (workspace) INTEGER array, dimension (8*N)
INFO (output) INTEGER
= 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
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
Page 3