DBDSDC(1) LAPACK routine (version 3.2) DBDSDC(1)NAME
DBDSDC - computes 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( * )
PURPOSE
DBDSDC 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. 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 calls DLASDQ if singular values only are
desired. However, it can be slightly modified to compute singular val‐
ues using the divide and conquer method.
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 fol‐
lows:
= 'N': Compute singular values only;
= 'P': Compute singular values and compute singular vectors in
compact form; = 'I': Compute singular values and singular vec‐
tors.
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-1)
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 val‐
ues 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, requir‐
ing O(N log N) space instead of 2*N**2. In particular, Q con‐
tains 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 sub‐
problems at the bottom of the computation tree (usually about
25). For other values of COMPQ, Q is not referenced.
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, requir‐
ing O(N log N) space instead of 2*N**2. In particular, IQ con‐
tains all INTEGER data in LDIQ >= N*(3 + 3*INT(LOG_2(N/(SML‐
SIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV
and is equal to the maximum size of the subproblems at the bot‐
tom of the computation tree (usually about 25). For other val‐
ues of COMPQ, IQ is not referenced.
WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,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
LAPACK routine (version 3.2) November 2008 DBDSDC(1)
