CLALSA (3)  Linux Manuals
NAME
clalsa.f 
SYNOPSIS
Functions/Subroutines
subroutine clalsa (ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO)
CLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
Function/Subroutine Documentation
subroutine clalsa (integerICOMPQ, integerSMLSIZ, integerN, integerNRHS, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldbx, * )BX, integerLDBX, real, dimension( ldu, * )U, integerLDU, real, dimension( ldu, * )VT, integer, dimension( * )K, real, dimension( ldu, * )DIFL, real, dimension( ldu, * )DIFR, real, dimension( ldu, * )Z, real, dimension( ldu, * )POLES, integer, dimension( * )GIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, integer, dimension( ldgcol, * )PERM, real, dimension( ldu, * )GIVNUM, real, dimension( * )C, real, dimension( * )S, real, dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)
CLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
Purpose:

CLALSA is an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.). If ICOMPQ = 0, CLALSA applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ = 1, CLALSA applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in compact form by CLALSA.
Parameters:

ICOMPQ
ICOMPQ is INTEGER Specifies whether the left or the right singular vector matrix is involved. = 0: Left singular vector matrix = 1: Right singular vector matrix
SMLSIZSMLSIZ is INTEGER The maximum size of the subproblems at the bottom of the computation tree.
NN is INTEGER The row and column dimensions of the upper bidiagonal matrix.
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 in the calling subprogram. LDB must be at least max(1,MAX( M, N ) ).
BXBX is COMPLEX array, dimension ( LDBX, NRHS ) On exit, the result of applying the left or right singular vector matrix to B.
LDBXLDBX is INTEGER The leading dimension of BX.
UU is REAL array, dimension ( LDU, SMLSIZ ). On entry, U contains the left singular vector matrices of all subproblems at the bottom level.
LDULDU is INTEGER, LDU = > N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.
VTVT is REAL array, dimension ( LDU, SMLSIZ+1 ). On entry, VT**H contains the right singular vector matrices of all subproblems at the bottom level.
KK is INTEGER array, dimension ( N ).
DIFLDIFL is REAL array, dimension ( LDU, NLVL ). where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
DIFRDIFR is REAL array, dimension ( LDU, 2 * NLVL ). On entry, DIFL(*, I) and DIFR(*, 2 * I 1) record distances between singular values on the Ith level and singular values on the (I 1)th level, and DIFR(*, 2 * I) record the normalizing factors of the right singular vectors matrices of subproblems on Ith level.
ZZ is REAL array, dimension ( LDU, NLVL ). On entry, Z(1, I) contains the components of the deflation adjusted updating row vector for subproblems on the Ith level.
POLESPOLES is REAL array, dimension ( LDU, 2 * NLVL ). On entry, POLES(*, 2 * I 1: 2 * I) contains the new and old singular values involved in the secular equations on the Ith level.
GIVPTRGIVPTR is INTEGER array, dimension ( N ). On entry, GIVPTR( I ) records the number of Givens rotations performed on the Ith problem on the computation tree.
GIVCOLGIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). On entry, for each I, GIVCOL(*, 2 * I  1: 2 * I) records the locations of Givens rotations performed on the Ith level on the computation tree.
LDGCOLLDGCOL is INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM.
PERMPERM is INTEGER array, dimension ( LDGCOL, NLVL ). On entry, PERM(*, I) records permutations done on the Ith level of the computation tree.
GIVNUMGIVNUM is REAL array, dimension ( LDU, 2 * NLVL ). On entry, GIVNUM(*, 2 *I 1 : 2 * I) records the C and S values of Givens rotations performed on the Ith level on the computation tree.
CC is REAL array, dimension ( N ). On entry, if the Ith subproblem is not square, C( I ) contains the Cvalue of a Givens rotation related to the right null space of the Ith subproblem.
SS is REAL array, dimension ( N ). On entry, if the Ith subproblem is not square, S( I ) contains the Svalue of a Givens rotation related to the right null space of the Ith subproblem.
RWORKRWORK is REAL array, dimension at least MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).
IWORKIWORK is INTEGER array. The dimension must be at least 3 * N
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 266 of file clalsa.f.
Author
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