SLASD2 (3)  Linux Man Pages
NAME
slasd2.f 
SYNOPSIS
Functions/Subroutines
subroutine slasd2 (NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO)
SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
Function/Subroutine Documentation
subroutine slasd2 (integerNL, integerNR, integerSQRE, integerK, real, dimension( * )D, real, dimension( * )Z, realALPHA, realBETA, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )DSIGMA, real, dimension( ldu2, * )U2, integerLDU2, real, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXP, integer, dimension( * )IDX, integer, dimension( * )IDXC, integer, dimension( * )IDXQ, integer, dimension( * )COLTYP, integerINFO)
SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
Purpose:

SLASD2 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more singular values are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one. SLASD2 is called from SLASD1.
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 N = NL + NR + 1 rows and M = N + SQRE >= N columns.
KK is INTEGER Contains the dimension of the nondeflated matrix, This is the order of the related secular equation. 1 <= K <=N.
DD is REAL array, dimension (N) On entry D contains the singular values of the two submatrices to be combined. On exit D contains the trailing (NK) updated singular values (those which were deflated) sorted into increasing order.
ZZ is REAL array, dimension (N) On exit Z contains the updating row vector in the secular equation.
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 contains the left singular vectors of two submatrices in the two square blocks with corners at (1,1), (NL, NL), and (NL+2, NL+2), (N,N). On exit U contains the trailing (NK) updated left singular vectors (those which were deflated) in its last NK columns.
LDULDU is INTEGER The leading dimension of the array U. LDU >= N.
VTVT is REAL array, dimension (LDVT,M) On entry VT**T contains the right singular vectors of two submatrices in the two square blocks with corners at (1,1), (NL+1, NL+1), and (NL+2, NL+2), (M,M). On exit VT**T contains the trailing (NK) updated right singular vectors (those which were deflated) in its last NK columns. In case SQRE =1, the last row of VT spans the right null space.
LDVTLDVT is INTEGER The leading dimension of the array VT. LDVT >= M.
DSIGMADSIGMA is REAL array, dimension (N) Contains a copy of the diagonal elements (K1 singular values and one zero) in the secular equation.
U2U2 is REAL array, dimension (LDU2,N) Contains a copy of the first K1 left singular vectors which will be used by SLASD3 in a matrix multiply (SGEMM) to solve for the new left singular vectors. U2 is arranged into four blocks. The first block contains a column with 1 at NL+1 and zero everywhere else; the second block contains nonzero entries only at and above NL; the third contains nonzero entries only below NL+1; and the fourth is dense.
LDU2LDU2 is INTEGER The leading dimension of the array U2. LDU2 >= N.
VT2VT2 is REAL array, dimension (LDVT2,N) VT2**T contains a copy of the first K right singular vectors which will be used by SLASD3 in a matrix multiply (SGEMM) to solve for the new right singular vectors. VT2 is arranged into three blocks. The first block contains a row that corresponds to the special 0 diagonal element in SIGMA; the second block contains nonzeros only at and before NL +1; the third block contains nonzeros only at and after NL +2.
LDVT2LDVT2 is INTEGER The leading dimension of the array VT2. LDVT2 >= M.
IDXPIDXP is INTEGER array, dimension (N) This will contain the permutation used to place deflated values of D at the end of the array. On output IDXP(2:K) points to the nondeflated Dvalues and IDXP(K+1:N) points to the deflated singular values.
IDXIDX is INTEGER array, dimension (N) This will contain the permutation used to sort the contents of D into ascending order.
IDXCIDXC is INTEGER array, dimension (N) This will contain the permutation used to arrange the columns of the deflated U matrix into three groups: the first group contains nonzero entries only at and above NL, the second contains nonzero entries only below NL+2, and the third is dense.
IDXQIDXQ is INTEGER array, dimension (N) This contains the permutation which separately sorts the two subproblems in D into ascending order. Note that entries in the first hlaf of this permutation must first be moved one position backward; and entries in the second half must first have NL+1 added to their values.
COLTYPCOLTYP is INTEGER array, dimension (N) As workspace, this will contain a label which will indicate which of the following types a column in the U2 matrix or a row in the VT2 matrix is: 1 : nonzero in the upper half only 2 : nonzero in the lower half only 3 : dense 4 : deflated On exit, it is an array of dimension 4, with COLTYP(I) being the dimension of the Ith type columns.
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value.
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 268 of file slasd2.f.
Author
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