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CentOS 7.0 - man page for dlasd1 (centos section 3)

dlasd1.f(3)							      LAPACK							       dlasd1.f(3)

NAME
dlasd1.f -
SYNOPSIS
Functions/Subroutines subroutine dlasd1 (NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT, IDXQ, IWORK, WORK, INFO) DLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc. Function/Subroutine Documentation subroutine dlasd1 (integerNL, integerNR, integerSQRE, double precision, dimension( * )D, double precisionALPHA, double precisionBETA, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension( ldvt, * )VT, integerLDVT, integer, dimension( * )IDXQ, integer, dimension( * )IWORK, double precision, dimension( * )WORK, integerINFO) DLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc. Purpose: DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B, where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0. A related subroutine DLASD7 handles the case in which the singular values (and the singular vectors in factored form) are desired. DLASD1 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 DLASD2. 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 DLASD4 (as called by DLASD3). 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. NR NR is INTEGER The row dimension of the lower block. NR >= 1. SQRE SQRE is INTEGER = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE. D D is DOUBLE PRECISION array, dimension (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. ALPHA ALPHA is DOUBLE PRECISION Contains the diagonal element associated with the added row. BETA BETA is DOUBLE PRECISION Contains the off-diagonal element associated with the added row. U U is DOUBLE PRECISION 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. LDU LDU is INTEGER The leading dimension of the array U. LDU >= max( 1, N ). VT VT is DOUBLE PRECISION 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. LDVT LDVT is INTEGER The leading dimension of the array VT. LDVT >= max( 1, M ). IDXQ IDXQ 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. IWORK IWORK is INTEGER array, dimension( 4 * N ) WORK WORK is DOUBLE PRECISION array, dimension( 3*M**2 + 2*M ) INFO INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th 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 dlasd1.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 dlasd1.f(3)