clals0.f (3)  Linux Manuals
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.
NLNL is INTEGER The row dimension of the upper block. NL >= 1.
NRNR is INTEGER The row dimension of the lower block. NR >= 1.
SQRESQRE 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.
NRHSNRHS is INTEGER The number of columns of B and BX. NRHS must be at least 1.
BB 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.
LDBLDB is INTEGER The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).
BXBX is COMPLEX array, dimension ( LDBX, NRHS )
LDBXLDBX is INTEGER The leading dimension of BX.
PERMPERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) applied to the two blocks.
GIVPTRGIVPTR is INTEGER The number of Givens rotations which took place in this subproblem.
GIVCOLGIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.
LDGCOLLDGCOL is INTEGER The leading dimension of GIVCOL, must be at least N.
GIVNUMGIVNUM is REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value used in the corresponding Givens rotation.
LDGNUMLDGNUM is INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.
POLESPOLES 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.
DIFLDIFL 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.
DIFRDIFR 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.
ZZ is REAL array, dimension ( K ) Contain the components of the deflationadjusted updating row vector.
KK is INTEGER Contains the dimension of the nondeflated matrix, This is the order of the related secular equation. 1 <= K <=N.
CC is REAL C contains garbage if SQRE =0 and the Cvalue of a Givens rotation related to the right null space if SQRE = 1.
SS is REAL S contains garbage if SQRE =0 and the Svalue of a Givens rotation related to the right null space if SQRE = 1.
RWORKRWORK is REAL array, dimension ( K*(1+NRHS) + 2*NRHS )
INFOINFO 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
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