slasd1.f (3)  Linux Manuals
NAME
slasd1.f 
SYNOPSIS
Functions/Subroutines
subroutine slasd1 (NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT, IDXQ, IWORK, WORK, INFO)
SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.
Function/Subroutine Documentation
subroutine slasd1 (integerNL, integerNR, integerSQRE, real, dimension( * )D, realALPHA, realBETA, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, integer, dimension( * )IDXQ, integer, dimension( * )IWORK, real, dimension( * )WORK, integerINFO)
SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.
Purpose:

SLASD1 computes the SVD of an upper bidiagonal NbyM matrix B, where N = NL + NR + 1 and M = N + SQRE. SLASD1 is called from SLASD0. A related subroutine SLASD7 handles the case in which the singular values (and the singular vectors in factored form) are desired. SLASD1 computes the SVD as follows: ( D1(in) 0 0 0 ) B = U(in) * ( Z1**T a Z2**T b ) * VT(in) ( 0 0 D2(in) 0 ) = U(out) * ( D(out) 0) * VT(out) where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros elsewhere; and the entry b is empty if SQRE = 0. The left singular vectors of the original matrix are stored in U, and the transpose of the right singular vectors are stored in VT, and the singular values are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple singular values or when there are zeros in the Z vector. For each such occurence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine SLASD2. The second stage consists of calculating the updated singular values. This is done by finding the square roots of the roots of the secular equation via the routine SLASD4 (as called by SLASD3). This routine also calculates the singular vectors of the current problem. The final stage consists of computing the updated singular vectors directly using the updated singular values. The singular vectors for the current problem are multiplied with the singular vectors from the overall problem.
Parameters:

NL
NL is INTEGER The row dimension of the upper block. NL >= 1.
NRNR is INTEGER The row dimension of the lower block. NR >= 1.
SQRESQRE is INTEGER = 0: the lower block is an NRbyNR square matrix. = 1: the lower block is an NRby(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE.
DD is REAL array, dimension (NL+NR+1). N = NL+NR+1 On entry D(1:NL,1:NL) contains the singular values of the upper block; and D(NL+2:N) contains the singular values of the lower block. On exit D(1:N) contains the singular values of the modified matrix.
ALPHAALPHA is REAL Contains the diagonal element associated with the added row.
BETABETA is REAL Contains the offdiagonal element associated with the added row.
UU is REAL array, dimension (LDU,N) On entry U(1:NL, 1:NL) contains the left singular vectors of the upper block; U(NL+2:N, NL+2:N) contains the left singular vectors of the lower block. On exit U contains the left singular vectors of the bidiagonal matrix.
LDULDU is INTEGER The leading dimension of the array U. LDU >= max( 1, N ).
VTVT is REAL array, dimension (LDVT,M) where M = N + SQRE. On entry VT(1:NL+1, 1:NL+1)**T contains the right singular vectors of the upper block; VT(NL+2:M, NL+2:M)**T contains the right singular vectors of the lower block. On exit VT**T contains the right singular vectors of the bidiagonal matrix.
LDVTLDVT is INTEGER The leading dimension of the array VT. LDVT >= max( 1, M ).
IDXQIDXQ is INTEGER array, dimension (N) This contains the permutation which will reintegrate the subproblem just solved back into sorted order, i.e. D( IDXQ( I = 1, N ) ) will be in ascending order.
IWORKIWORK is INTEGER array, dimension (4*N)
WORKWORK is REAL array, dimension (3*M**2+2*M)
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: if INFO = 1, a singular value did not converge
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Contributors:
 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
Definition at line 204 of file slasd1.f.
Author
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