
clals0.f(3) LAPACK clals0.f(3)
NAME
clals0.f 
SYNOPSIS
Functions/Subroutines
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)
CLALS0 applies back multiplying factors in solving the least squares problem using
divide and conquer SVD approach. Used by sgelsd.
Function/Subroutine Documentation
subroutine clals0 (integerICOMPQ, integerNL, integerNR, integerSQRE, integerNRHS, complex,
dimension( ldb, * )B, integerLDB, complex, dimension( ldbx, * )BX, integerLDBX, integer,
dimension( * )PERM, integerGIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL,
real, dimension( ldgnum, * )GIVNUM, integerLDGNUM, real, dimension( ldgnum, * )POLES,
real, dimension( * )DIFL, real, dimension( ldgnum, * )DIFR, real, dimension( * )Z,
integerK, realC, realS, real, dimension( * )RWORK, integerINFO)
CLALS0 applies back multiplying factors in solving the least squares problem using divide
and conquer SVD approach. Used by sgelsd.
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 divideandconquer 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 Svalues 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
Jth 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 NRbyNR square matrix.
= 1: the lower block is an NRby(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 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 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 REAL 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 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
DIFL is REAL array, dimension ( K ).
On entry, DIFL(I) is the distance between Ith updated
(undeflated) singular value and the Ith (undeflated) old
singular value.
DIFR
DIFR is REAL array, dimension ( LDGNUM, 2 ).
On entry, DIFR(I, 1) contains the distances between Ith
updated (undeflated) singular value and the I+1th
(undeflated) old singular value. And DIFR(I, 2) is the
normalizing factor for the Ith right singular vector.
Z
Z is REAL array, dimension ( K )
Contain the components of the deflationadjusted updating row
vector.
K
K is INTEGER
Contains the dimension of the nondeflated matrix,
This is the order of the related secular equation. 1 <= K <=N.
C
C is REAL
C contains garbage if SQRE =0 and the Cvalue of a Givens
rotation related to the right null space if SQRE = 1.
S
S is REAL
S contains garbage if SQRE =0 and the Svalue of a Givens
rotation related to the right null space if SQRE = 1.
RWORK
RWORK is REAL array, dimension
( K*(1+NRHS) + 2*NRHS )
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
Ming Gu and RenCang Li, Computer Science Division, University of California at
Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Definition at line 269 of file clals0.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 clals0.f(3) 
