clalsa.f (3) Linux Manual Page

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

 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

 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

 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

 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

 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

 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

 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

 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

 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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