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slals0.f(3)				      LAPACK				      slals0.f(3)

NAME
       slals0.f -

SYNOPSIS
   Functions/Subroutines
       subroutine slals0 (ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL,
	   LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO)
	   SLALS0 applies back multiplying factors in solving the least squares problem using
	   divide and conquer SVD approach. Used by sgelsd.

Function/Subroutine Documentation
   subroutine slals0 (integerICOMPQ, integerNL, integerNR, integerSQRE, integerNRHS, real,
       dimension( ldb, * )B, integerLDB, real, dimension( ldbx, * )BX, integerLDBX, integer,
       dimension( * )PERM, integerGIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL,
       real, dimension( ldgnum, * )GIVNUM, integerLDGNUM, real, dimension( ldgnum, * )POLES,
       real, dimension( * )DIFL, real, dimension( ldgnum, * )DIFR, real, dimension( * )Z,
       integerK, realC, realS, real, dimension( * )WORK, integerINFO)
       SLALS0 applies back multiplying factors in solving the least squares problem using divide
       and conquer SVD approach. Used by sgelsd.

       Purpose:

	    SLALS0 applies back the multiplying factors of either the left or the
	    right singular vector matrix of a diagonal matrix appended by a row
	    to the right hand side matrix B in solving the least squares problem
	    using the divide-and-conquer SVD approach.

	    For the left singular vector matrix, three types of orthogonal
	    matrices are involved:

	    (1L) Givens rotations: the number of such rotations is GIVPTR; the
		 pairs of columns/rows they were applied to are stored in GIVCOL;
		 and the C- and S-values of these rotations are stored in GIVNUM.

	    (2L) Permutation. The (NL+1)-st row of B is to be moved to the first
		 row, and for J=2:N, PERM(J)-th row of B is to be moved to the
		 J-th row.

	    (3L) The left singular vector matrix of the remaining matrix.

	    For the right singular vector matrix, four types of orthogonal
	    matrices are involved:

	    (1R) The right singular vector matrix of the remaining matrix.

	    (2R) If SQRE = 1, one extra Givens rotation to generate the right
		 null space.

	    (3R) The inverse transformation of (2L).

	    (4R) The inverse transformation of (1L).

       Parameters:
	   ICOMPQ

		     ICOMPQ is INTEGER
		    Specifies whether singular vectors are to be computed in
		    factored form:
		    = 0: Left singular vector matrix.
		    = 1: Right singular vector matrix.

	   NL

		     NL is INTEGER
		    The row dimension of the upper block. NL >= 1.

	   NR

		     NR is INTEGER
		    The row dimension of the lower block. NR >= 1.

	   SQRE

		     SQRE is INTEGER
		    = 0: the lower block is an NR-by-NR square matrix.
		    = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

		    The bidiagonal matrix has row dimension N = NL + NR + 1,
		    and column dimension M = N + SQRE.

	   NRHS

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

	   B

		     B is REAL 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. LDB must be at least
		    max(1,MAX( M, N ) ).

	   BX

		     BX is REAL array, dimension ( LDBX, NRHS )

	   LDBX

		     LDBX is INTEGER
		    The leading dimension of BX.

	   PERM

		     PERM is INTEGER array, dimension ( N )
		    The permutations (from deflation and sorting) applied
		    to the two blocks.

	   GIVPTR

		     GIVPTR is INTEGER
		    The number of Givens rotations which took place in this
		    subproblem.

	   GIVCOL

		     GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
		    Each pair of numbers indicates a pair of rows/columns
		    involved in a Givens rotation.

	   LDGCOL

		     LDGCOL is INTEGER
		    The leading dimension of GIVCOL, must be at least N.

	   GIVNUM

		     GIVNUM is REAL array, dimension ( LDGNUM, 2 )
		    Each number indicates the C or S value used in the
		    corresponding Givens rotation.

	   LDGNUM

		     LDGNUM is INTEGER
		    The leading dimension of arrays DIFR, POLES and
		    GIVNUM, must be at least K.

	   POLES

		     POLES is REAL array, dimension ( LDGNUM, 2 )
		    On entry, POLES(1:K, 1) contains the new singular
		    values obtained from solving the secular equation, and
		    POLES(1:K, 2) is an array containing the poles in the secular
		    equation.

	   DIFL

		     DIFL is REAL array, dimension ( K ).
		    On entry, DIFL(I) is the distance between I-th updated
		    (undeflated) singular value and the I-th (undeflated) old
		    singular value.

	   DIFR

		     DIFR is REAL array, dimension ( LDGNUM, 2 ).
		    On entry, DIFR(I, 1) contains the distances between I-th
		    updated (undeflated) singular value and the I+1-th
		    (undeflated) old singular value. And DIFR(I, 2) is the
		    normalizing factor for the I-th right singular vector.

	   Z

		     Z is REAL array, dimension ( K )
		    Contain the components of the deflation-adjusted updating row
		    vector.

	   K

		     K is INTEGER
		    Contains the dimension of the non-deflated matrix,
		    This is the order of the related secular equation. 1 <= K <=N.

	   C

		     C is REAL
		    C contains garbage if SQRE =0 and the C-value of a Givens
		    rotation related to the right null space if SQRE = 1.

	   S

		     S is REAL
		    S contains garbage if SQRE =0 and the S-value of a Givens
		    rotation related to the right null space if SQRE = 1.

	   WORK

		     WORK is REAL array, dimension ( K )

	   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 267 of file slals0.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      slals0.f(3)
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