slasd7(3)

NAME

SLASD7 - merge the two sets of singular values together

into a single sorted set

SYNOPSIS

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 )
    INTEGER          GIVPTR,   ICOMPQ,  INFO,  K,  LDGCOL,
LDGNUM, NL, NR, SQRE
    REAL           ALPHA, BETA, C, S
    INTEGER        GIVCOL( LDGCOL, * ), IDX( * ), IDXP(  *
), IDXQ( * ), PERM( * )
    REAL            D( * ), DSIGMA( * ), GIVNUM( LDGNUM, *
), VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), ZW( * )

PURPOSE

SLASD7 merges the two sets of singular values together in

to 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.

ARGUMENTS

ICOMPQ (input) INTEGER

Specifies whether singular vectors are to be com

puted in compact form, as follows:
= 0: Compute singular values only.
= 1: Compute singular vectors of upper bidiagonal

matrix in compact form.

NL (input) INTEGER

The row dimension of the upper block. NL >= 1.

NR (input) INTEGER

The row dimension of the lower block. NR >= 1.

SQRE (input) 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 N = NL + NR + 1 rows and

M = N + SQRE >= N columns.

K (output) INTEGER

Contains the dimension of the non-deflated matrix,

this is the order of the related secular equation. 1 <= K <=N.

D (input/output) REAL array, dimension ( N )

On entry D contains the singular values of the two

submatrices to be combined. On exit D contains the trailing (N-K)

updated singular values (those which were deflated) sorted into

increasing order.

Z (output) REAL array, dimension ( M )

On exit Z contains the updating row vector in the

secular equation.

ZW (workspace) REAL array, dimension ( M )

Workspace for Z.

VF (input/output) 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 compo

nents of all right singular vectors of the bidiagonal matrix.

VFW (workspace) REAL array, dimension ( M )

Workspace for VF.

VL (input/output) 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 compo

nents of all right singular vectors of the bidiagonal matrix.

VLW (workspace) REAL array, dimension ( M )

Workspace for VL.

ALPHA (input) REAL

Contains the diagonal element associated with the

added row.

BETA (input) REAL

Contains the off-diagonal element associated with

the added row.

DSIGMA (output) REAL array, dimension ( N ) Con

tains a copy of the diagonal elements (K-1 singular values and

one zero) in the secular equation.

IDX (workspace) INTEGER array, dimension ( N )

This will contain the permutation used to sort the

contents of D into ascending order.

IDXP (workspace) INTEGER array, dimension ( N )

This will contain the permutation used to place de

flated values of D at the end of the array. On output IDXP(2:K)
points to the nondeflated D-values and IDXP(K+1:N)

points to the deflated singular values.

IDXQ (input) INTEGER array, dimension ( N )

This contains the permutation which separately

sorts the two sub-problems 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.

PERM (output) INTEGER array, dimension ( N )

The permutations (from deflation and sorting) to be

applied to each singular block. Not referenced if ICOMPQ = 0.

GIVPTR (output) INTEGER The number of Givens rota

tions which took place in this subproblem. Not referenced if

ICOMPQ = 0.

GIVCOL (output) 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.

LDGCOL (input) INTEGER The leading dimension of

GIVCOL, must be at least N.

GIVNUM (output) REAL array, dimension ( LDGNUM, 2 )

Each number indicates the C or S value to be used in the corre

sponding Givens rotation. Not referenced if ICOMPQ = 0.

LDGNUM (input) INTEGER The leading dimension of

GIVNUM, must be at least N.

C (output) REAL

C contains garbage if SQRE =0 and the C-value of a

Givens rotation related to the right null space if SQRE = 1.

S (output) REAL

S contains garbage if SQRE =0 and the S-value of a

Givens rotation related to the right null space if SQRE = 1.

INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille

gal value.

FURTHER DETAILS

Based on contributions by

Ming Gu and Huan Ren, Computer Science Division, Uni

versity of
California at Berkeley, USA

LAPACK version 3.0 15 June 2000

SLASD7(3)