---
name: "dlasd7"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlasd7/3lapack"
---

# dlasd7(3lapack)

merges the two sets of singular values together into a single sorted set

## NAME

DLASD7 - merges the two sets of singular values together into a single sorted set

## SYNOPSIS

- 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 )

- INTEGER

  GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, NR, SQRE

- DOUBLE

  PRECISION ALPHA, BETA, C, S

- INTEGER

  GIVCOL( LDGCOL, \* ), IDX( \* ), IDXP( \* ), IDXQ( \* ), PERM( \* )

- DOUBLE

  PRECISION D( \* ), DSIGMA( \* ), GIVNUM( LDGNUM, \* ), VF( \* ), VFW( \* ), VL( \* ), VLW( \* ), Z( \* ), ZW( \* )

## 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.\

## ARGUMENTS

- ICOMPQ (input) 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 (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) 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 (output) DOUBLE PRECISION array, dimension ( M )

  On exit Z contains the updating row vector in the secular equation.

- ZW (workspace) DOUBLE PRECISION array, dimension ( M )

  Workspace for Z.

- VF (input/output) 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 (workspace) DOUBLE PRECISION array, dimension ( M )

  Workspace for VF.

- VL (input/output) 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 (workspace) DOUBLE PRECISION array, dimension ( M )

  Workspace for VL.

- ALPHA (input) DOUBLE PRECISION

  Contains the diagonal element associated with the added row.

- BETA (input) DOUBLE PRECISION

  Contains the off-diagonal element associated with the added row. DSIGMA (output) DOUBLE PRECISION array, dimension ( N ) Contains 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 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 (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 rotations 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) 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 (input) INTEGER The leading dimension of GIVNUM, must be at least N.

- C (output) 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 (output) 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 (output) INTEGER

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

## FURTHER DETAILS

Based on contributions by\
\
    Ming Gu and Huan Ren, Computer Science Division, University of\
    California at Berkeley, USA\