
SBDSDC(l) ) SBDSDC(l)
NAME
SBDSDC  compute the singular value decomposition (SVD) of a real NbyN (upper or lower)
bidiagonal matrix B
SYNOPSIS
SUBROUTINE SBDSDC( 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( * )
REAL D( * ), E( * ), Q( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
SBDSDC computes the singular value decomposition (SVD) of a real NbyN (upper or lower)
bidiagonal matrix B: B = U * S * VT, using a divide and conquer method, where S is a diag
onal matrix with nonnegative 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 XMP, Cray YMP, Cray C90, or Cray2. It could con
ceivably 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) 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) REAL 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) REAL 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) REAL 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) REAL array, dimension (LDVT,N)
If COMPQ = 'I', then: On exit, if INFO = 0, VT' contains the right singular vec
tors 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) REAL 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 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 computa
tion 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, 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/(SML
SIZ+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) REAL 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 ith 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 version 3.0 15 June 2000 SBDSDC(l) 
