# dlasd7.f - Man Page

SRC/dlasd7.f

## Synopsis

### Functions/Subroutines

subroutine **dlasd7** (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)**DLASD7** 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 dlasd7 (integer icompq, integer nl, integer nr, integer sqre, integer k, double precision, dimension( * ) d, double precision, dimension( * ) z, double precision, dimension( * ) zw, double precision, dimension( * ) vf, double precision, dimension( * ) vfw, double precision, dimension( * ) vl, double precision, dimension( * ) vlw, double precision alpha, double precision beta, double precision, dimension( * ) dsigma, integer, dimension( * ) idx, integer, dimension( * ) idxp, integer, dimension( * ) idxq, integer, dimension( * ) perm, integer givptr, integer, dimension( ldgcol, * ) givcol, integer ldgcol, double precision, dimension( ldgnum, * ) givnum, integer ldgnum, double precision c, double precision s, integer info)

**DLASD7** 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:**

DLASD7 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. DLASD7 is called from DLASD6.

**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.

*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 N = NL + NR + 1 rows and M = N + SQRE >= N columns.

*K*K is INTEGER Contains the dimension of the non-deflated matrix, this is the order of the related secular equation. 1 <= K <=N.

*D*D is DOUBLE PRECISION 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*Z is DOUBLE PRECISION array, dimension ( M ) On exit Z contains the updating row vector in the secular equation.

*ZW*ZW is DOUBLE PRECISION array, dimension ( M ) Workspace for Z.

*VF*VF is DOUBLE PRECISION 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.

*VFW*VFW is DOUBLE PRECISION array, dimension ( M ) Workspace for VF.

*VL*VL is DOUBLE PRECISION 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.

*VLW*VLW is DOUBLE PRECISION array, dimension ( M ) Workspace for VL.

*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.

*DSIGMA*DSIGMA is DOUBLE PRECISION array, dimension ( N ) Contains a copy of the diagonal elements (K-1 singular values and one zero) in the secular equation.

*IDX*IDX is INTEGER array, dimension ( N ) This will contain the permutation used to sort the contents of D into ascending order.

*IDXP*IDXP 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 D-values and IDXP(K+1:N) points to the deflated singular values.

*IDXQ*IDXQ is 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*PERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) to be applied to each singular block. Not referenced if ICOMPQ = 0.

*GIVPTR*GIVPTR is INTEGER The number of Givens rotations which took place in this subproblem. Not referenced if ICOMPQ = 0.

*GIVCOL*GIVCOL 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.

*LDGCOL*LDGCOL is INTEGER The leading dimension of GIVCOL, must be at least N.

*GIVNUM*GIVNUM is DOUBLE PRECISION 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.

*LDGNUM*LDGNUM is INTEGER The leading dimension of GIVNUM, must be at least N.

*C*C is DOUBLE PRECISION C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1.

*S*S is DOUBLE PRECISION S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1.

*INFO*INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line **276** of file **dlasd7.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlasd7(3) is an alias of dlasd7.f(3).