---
name: "slasd2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slasd2/3lapack"
---

# slasd2(3lapack)

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

## NAME

SLASD2 - merges the two sets of singular values together into a single sorted set

## SYNOPSIS

- 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 )

- INTEGER

  INFO, K, LDU, LDU2, LDVT, LDVT2, NL, NR, SQRE

- REAL

  ALPHA, BETA

- INTEGER

  COLTYP( \* ), IDX( \* ), IDXC( \* ), IDXP( \* ), IDXQ( \* )

- REAL

  D( \* ), DSIGMA( \* ), U( LDU, \* ), U2( LDU2, \* ), VT( LDVT, \* ), VT2( LDVT2, \* ), Z( \* )

## 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.\

## ARGUMENTS

- 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 (N)

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

- 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.

- U (input/output) 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 (N-K) updated left singular vectors (those which were deflated) in its last N-K columns.

- LDU (input) INTEGER

  The leading dimension of the array U.  LDU \>= N.

- VT (input/output) REAL array, dimension (LDVT,M)

  On entry VT' 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' contains the trailing (N-K) updated right singular vectors (those which were deflated) in its last N-K columns. In case SQRE =1, the last row of VT spans the right null space.

- LDVT (input) INTEGER

  The leading dimension of the array VT.  LDVT \>= M. DSIGMA (output) REAL array, dimension (N) Contains a copy of the diagonal elements (K-1 singular values and one zero) in the secular equation.

- U2 (output) REAL array, dimension (LDU2,N)

  Contains a copy of the first K-1 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 non-zero entries only at and above NL; the third contains non-zero entries only below NL+1; and the fourth is dense.

- LDU2 (input) INTEGER

  The leading dimension of the array U2.  LDU2 \>= N.

- VT2 (output) REAL array, dimension (LDVT2,N)

  VT2' 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 non-zeros only at and before NL +1; the third block contains non-zeros only at and after  NL +2.

- LDVT2 (input) INTEGER

  The leading dimension of the array VT2.  LDVT2 \>= M.

- 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.

- IDX (workspace) INTEGER array, dimension (N)

  This will contain the permutation used to sort the contents of D into ascending order.

- IDXC (output) 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 non-zero entries only at and above NL, the second contains non-zero entries only below NL+2, and the third is dense.

- IDXQ (input/output) 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 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. COLTYP (workspace/output) 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 : non-zero in the upper half only\
   2 : non-zero 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 I-th type columns.

- 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\