slasd7 (3)  Linux Man Pages
NAME
slasd7.f 
SYNOPSIS
Functions/Subroutines
subroutine slasd7 (ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, C, S, INFO)
SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.
Function/Subroutine Documentation
subroutine slasd7 (integerICOMPQ, integerNL, integerNR, integerSQRE, integerK, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )ZW, real, dimension( * )VF, real, dimension( * )VFW, real, dimension( * )VL, real, dimension( * )VLW, realALPHA, realBETA, real, dimension( * )DSIGMA, integer, dimension( * )IDX, integer, dimension( * )IDXP, integer, dimension( * )IDXQ, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, real, dimension( ldgnum, * )GIVNUM, integerLDGNUM, realC, realS, integerINFO)
SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.
Purpose:

SLASD7 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. SLASD7 is called from SLASD6.
Parameters:

ICOMPQ
ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in compact form, as follows: = 0: Compute singular values only. = 1: Compute singular vectors of upper bidiagonal matrix in compact form.
NLNL 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 ( M ) On exit Z contains the updating row vector in the secular equation.
ZWZW is REAL array, dimension ( M ) Workspace for Z.
VFVF is REAL array, dimension ( M ) On entry, VF(1:NL+1) contains the first components of all right singular vectors of the upper block; and VF(NL+2:M) contains the first components of all right singular vectors of the lower block. On exit, VF contains the first components of all right singular vectors of the bidiagonal matrix.
VFWVFW is REAL array, dimension ( M ) Workspace for VF.
VLVL is REAL array, dimension ( M ) On entry, VL(1:NL+1) contains the last components of all right singular vectors of the upper block; and VL(NL+2:M) contains the last components of all right singular vectors of the lower block. On exit, VL contains the last components of all right singular vectors of the bidiagonal matrix.
VLWVLW is REAL array, dimension ( M ) Workspace for VL.
ALPHAALPHA is REAL Contains the diagonal element associated with the added row.
BETABETA is REAL Contains the offdiagonal element associated with the added row.
DSIGMADSIGMA is REAL array, dimension ( N ) Contains a copy of the diagonal elements (K1 singular values and one zero) in the secular equation.
IDXIDX is INTEGER array, dimension ( N ) This will contain the permutation used to sort the contents of D into ascending order.
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.
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 half 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.
PERMPERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) to be applied to each singular block. Not referenced if ICOMPQ = 0.
GIVPTRGIVPTR is INTEGER The number of Givens rotations which took place in this subproblem. Not referenced if ICOMPQ = 0.
GIVCOLGIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of columns to take place in a Givens rotation. Not referenced if ICOMPQ = 0.
LDGCOLLDGCOL is INTEGER The leading dimension of GIVCOL, must be at least N.
GIVNUMGIVNUM is REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value to be used in the corresponding Givens rotation. Not referenced if ICOMPQ = 0.
LDGNUMLDGNUM is INTEGER The leading dimension of GIVNUM, must be at least N.
CC is REAL C contains garbage if SQRE =0 and the Cvalue of a Givens rotation related to the right null space if SQRE = 1.
SS is REAL S contains garbage if SQRE =0 and the Svalue of a Givens rotation related to the right null space if SQRE = 1.
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 278 of file slasd7.f.
Author
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