clalsa-f(3)

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

SMLSIZ

 SMLSIZ is INTEGER
 The maximum size of the subproblems at the bottom of the
 computation tree.

 N is INTEGER
 The row and column dimensions of the upper bidiagonal matrix.

NRHS

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

 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 in the calling subprogram.
 LDB must be at least max(1,MAX( M, N ) ).

 BX is COMPLEX array, dimension ( LDBX, NRHS )
 On exit, the result of applying the left or right singular
 vector matrix to B.

LDBX

 LDBX is INTEGER
 The leading dimension of BX.

 U is REAL array, dimension ( LDU, SMLSIZ ).
 On entry, U contains the left singular vector matrices of all
 subproblems at the bottom level.

LDU

 LDU is INTEGER, LDU = > N.
 The leading dimension of arrays U, VT, DIFL, DIFR,
 POLES, GIVNUM, and Z.

 VT is REAL array, dimension ( LDU, SMLSIZ+1 ).
 On entry, VT**H contains the right singular vector matrices of
 all subproblems at the bottom level.

 K is INTEGER array, dimension ( N ).

DIFL

 DIFL is REAL array, dimension ( LDU, NLVL ).
 where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.

DIFR

 DIFR is REAL array, dimension ( LDU, 2 * NLVL ).
 On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record
 distances between singular values on the I-th 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 I-th level.

 Z 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 I-th
 level.

POLES

 POLES 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 I-th
 level.

GIVPTR

 GIVPTR is INTEGER array, dimension ( N ).
 On entry, GIVPTR( I ) records the number of Givens
 rotations performed on the I-th problem on the computation
 tree.

GIVCOL

 GIVCOL 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 I-th level on
 the computation tree.

LDGCOL

 LDGCOL is INTEGER, LDGCOL = > N.
 The leading dimension of arrays GIVCOL and PERM.

PERM

 PERM is INTEGER array, dimension ( LDGCOL, NLVL ).
 On entry, PERM(*, I) records permutations done on the I-th
 level of the computation tree.

GIVNUM

 GIVNUM 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 I-th level on the
 computation tree.

 C is REAL array, dimension ( N ).
 On entry, if the I-th subproblem is not square,
 C( I ) contains the C-value of a Givens rotation related to
 the right null space of the I-th subproblem.

 S is REAL array, dimension ( N ).
 On entry, if the I-th subproblem is not square,
 S( I ) contains the S-value of a Givens rotation related to
 the right null space of the I-th subproblem.

RWORK

 RWORK is REAL array, dimension at least
 MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).

IWORK

 IWORK is INTEGER array.
 The dimension must be at least 3 * N

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:

September 2012

Contributors:

Ming Gu and Ren-Cang 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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