# zlals0.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **zlals0** (ICOMPQ, NL, NR, SQRE, **NRHS**, B, **LDB**, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO)**ZLALS0** applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

## Function/Subroutine Documentation

### subroutine zlals0 (integer ICOMPQ, integer NL, integer NR, integer SQRE, integer NRHS, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldbx, * ) BX, integer LDBX, integer, dimension( * ) PERM, integer GIVPTR, integer, dimension( ldgcol, * ) GIVCOL, integer LDGCOL, double precision, dimension( ldgnum, * ) GIVNUM, integer LDGNUM, double precision, dimension( ldgnum, * ) POLES, double precision, dimension( * ) DIFL, double precision, dimension( ldgnum, * ) DIFR, double precision, dimension( * ) Z, integer K, double precision C, double precision S, double precision, dimension( * ) RWORK, integer INFO)

**ZLALS0** applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

**Purpose:**

ZLALS0 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).

**Parameters:***ICOMPQ*ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix.

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

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

*B*B is COMPLEX*16 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*LDB is INTEGER The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).

*BX*BX is COMPLEX*16 array, dimension ( LDBX, NRHS )

*LDBX*LDBX is INTEGER The leading dimension of BX.

*PERM*PERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) applied to the two blocks.

*GIVPTR*GIVPTR is INTEGER The number of Givens rotations which took place in this subproblem.

*GIVCOL*GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.

*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 used in the corresponding Givens rotation.

*LDGNUM*LDGNUM is INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.

*POLES*POLES is DOUBLE PRECISION 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*DIFL is DOUBLE PRECISION 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*DIFR is DOUBLE PRECISION 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*Z is DOUBLE PRECISION array, dimension ( K ) Contain the components of the deflation-adjusted updating row vector.

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

*RWORK*RWORK is DOUBLE PRECISION array, dimension ( K*(1+NRHS) + 2*NRHS )

*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.

**Date:**December 2016

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

Osni Marques, LBNL/NERSC, USA

Definition at line 272 of file zlals0.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlals0(3) is an alias of zlals0.f(3).