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CentOS 7.0 - man page for clalsa (centos section 3)

clalsa.f(3)				      LAPACK				      clalsa.f(3)

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

	   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
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      clalsa.f(3)


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