DBDSDC (3)  Linux Manuals
NAME
dbdsdc.f 
SYNOPSIS
Functions/Subroutines
subroutine dbdsdc (UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO)
DBDSDC
Function/Subroutine Documentation
subroutine dbdsdc (characterUPLO, characterCOMPQ, integerN, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension( ldvt, * )VT, integerLDVT, double precision, dimension( * )Q, integer, dimension( * )IQ, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
DBDSDC
Purpose:

DBDSDC 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 diagonal matrix with nonnegative 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 XMP, Cray YMP, Cray C90, or Cray2. 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 values using the divide and conquer method.
Parameters:

UPLO
UPLO is CHARACTER*1 = 'U': B is upper bidiagonal. = 'L': B is lower bidiagonal.
COMPQCOMPQ is 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.
NN is INTEGER The order of the matrix B. N >= 0.
DD is 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.
EE is DOUBLE PRECISION array, dimension (N1) On entry, the elements of E contain the offdiagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E has been destroyed.
UU is 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.
LDULDU is INTEGER The leading dimension of the array U. LDU >= 1. If singular vectors are desired, then LDU >= max( 1, N ).
VTVT is DOUBLE PRECISION array, dimension (LDVT,N) If COMPQ = 'I', then: On exit, if INFO = 0, VT**T contains the right singular vectors of the bidiagonal matrix. For other values of COMPQ, VT is not referenced.
LDVTLDVT is INTEGER The leading dimension of the array VT. LDVT >= 1. If singular vectors are desired, then LDVT >= max( 1, N ).
QQ is 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.
IQIQ is 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.
WORKWORK is 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).
IWORKIWORK is INTEGER array, dimension (8*N)
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: The algorithm failed to compute a singular value. The update process of divide and conquer failed.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Contributors:
 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
Definition at line 205 of file dbdsdc.f.
Author
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