---
name: "clals0"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/clals0/3lapack"
---

# clals0(3lapack)

applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach

## NAME

CLALS0 - applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach

## SYNOPSIS

- SUBROUTINE CLALS0(

  ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO )

- INTEGER

  GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, LDGNUM, NL, NR, NRHS, SQRE

- REAL

  C, S

- INTEGER

  GIVCOL( LDGCOL, \* ), PERM( \* )

- REAL

  DIFL( \* ), DIFR( LDGNUM, \* ), GIVNUM( LDGNUM, \* ), POLES( LDGNUM, \* ), RWORK( \* ), Z( \* )

- COMPLEX

  B( LDB, \* ), BX( LDBX, \* )

## PURPOSE

CLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach. For the left singular vector matrix, three types of orthogonal matrices are involved:\
 (1L) Givens rotations: the number of such rotations is GIVPTR; the\
      pairs of columns/rows they were applied to are stored in GIVCOL;\
      and the C- and S-values of these rotations are stored in GIVNUM. (2L) Permutation. The (NL+1)-st row of B is to be moved to the first\
      row, and for J=2:N, PERM(J)-th row of B is to be moved to the\
      J-th row.\
 (3L) The left singular vector matrix of the remaining matrix. For the right singular vector matrix, four types of orthogonal matrices are involved:\
 (1R) The right singular vector matrix of the remaining matrix. (2R) If SQRE = 1, one extra Givens rotation to generate the right\
      null space.\
 (3R) The inverse transformation of (2L).\
 (4R) The inverse transformation of (1L).\

## ARGUMENTS

ICOMPQ (input) INTEGER Specifies whether singular vectors are to be computed in factored form:\
 \= 0: Left singular vector matrix.\
 \= 1: Right singular vector matrix.

- 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 row dimension N = NL + NR + 1, and column dimension M = N + SQRE.

- NRHS (input) INTEGER

  The number of columns of B and BX. NRHS must be at least 1.

- B (input/output) COMPLEX array, dimension ( LDB, NRHS )

  On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N.

- LDB (input) INTEGER

  The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).

- BX (workspace) COMPLEX array, dimension ( LDBX, NRHS )

  - LDBX (input) INTEGER

  The leading dimension of BX.

- PERM (input) INTEGER array, dimension ( N )

  The permutations (from deflation and sorting) applied to the two blocks. GIVPTR (input) INTEGER The number of Givens rotations which took place in this subproblem. GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation. LDGCOL (input) INTEGER The leading dimension of GIVCOL, must be at least N. GIVNUM (input) REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value used in the corresponding Givens rotation. LDGNUM (input) INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.

- POLES (input) REAL array, dimension ( LDGNUM, 2 )

  On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation.

- DIFL (input) REAL array, dimension ( K ).

  On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value.

- DIFR (input) REAL array, dimension ( LDGNUM, 2 ).

  On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector.

- Z (input) REAL array, dimension ( K )

  Contain the components of the deflation-adjusted updating row vector.

- K (input) INTEGER

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

- C (input) 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 (input) REAL

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

- RWORK (workspace) REAL array, dimension

  ( K\*(1+NRHS) + 2\*NRHS )

- 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 Ren-Cang Li, Computer Science Division, University of\
      California at Berkeley, USA\
\
    Osni Marques, LBNL/NERSC, USA\