clalsa (l)  Linux Man Pages
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.)
NAME
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.)SYNOPSIS
 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 )
 INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SMLSIZ
 INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), K( * ), PERM( LDGCOL, * )
 REAL C( * ), DIFL( LDU, * ), DIFR( LDU, * ), GIVNUM( LDU, * ), POLES( LDU, * ), RWORK( * ), S( * ), U( LDU, * ), VT( LDU, * ), Z( LDU, * )
 COMPLEX B( LDB, * ), BX( LDBX, * )
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.ARGUMENTS
ICOMPQ (input) INTEGER Specifies whether the left or the right singular vector matrix is involved. = 0: Left singular vector matrix= 1: Right singular vector matrix SMLSIZ (input) INTEGER The maximum size of the subproblems at the bottom of the computation tree.
 N (input) INTEGER
 The row and column dimensions of the upper bidiagonal matrix.
 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 in the calling subprogram. LDB must be at least max(1,MAX( M, N ) ).
 BX (output) COMPLEX array, dimension ( LDBX, NRHS )
 On exit, the result of applying the left or right singular vector matrix to B.
 LDBX (input) INTEGER
 The leading dimension of BX.
 U (input) REAL array, dimension ( LDU, SMLSIZ ).
 On entry, U contains the left singular vector matrices of all subproblems at the bottom level.
 LDU (input) INTEGER, LDU = > N.
 The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.
 VT (input) REAL array, dimension ( LDU, SMLSIZ+1 ).
 On entry, VTaq contains the right singular vector matrices of all subproblems at the bottom level.
 K (input) INTEGER array, dimension ( N ).
 DIFL (input) REAL array, dimension ( LDU, NLVL ).
 where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
 DIFR (input) 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.
 Z (input) 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.
 POLES (input) 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. GIVPTR (input) INTEGER array, dimension ( N ). On entry, GIVPTR( I ) records the number of Givens rotations performed on the Ith problem on the computation tree. GIVCOL (input) 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. LDGCOL (input) INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM.
 PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).
 On entry, PERM(*, I) records permutations done on the Ith level of the computation tree. GIVNUM (input) 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.
 C (input) 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.
 S (input) 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.
 RWORK (workspace) REAL array, dimension at least
 max ( N, (SMLSZ+1)*NRHS*3 ).
 IWORK (workspace) INTEGER array.
 The dimension must be at least 3 * N
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
Based on contributions byMing Gu and RenCang Li, Computer Science Division, University of
Osni Marques, LBNL/NERSC, USA