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

Function/Subroutine Documentation

subroutine SLALS0	(	INTEGER	ICOMPQ,
		INTEGER	NL,
		INTEGER	NR,
		INTEGER	SQRE,
		INTEGER	NRHS,
		REAL, dimension( ldb, * )	B,
		INTEGER	LDB,
		REAL, dimension( ldbx, * )	BX,
		INTEGER	LDBX,
		INTEGER, dimension( * )	PERM,
		INTEGER	GIVPTR,
		INTEGER, dimension( ldgcol, * )	GIVCOL,
		INTEGER	LDGCOL,
		REAL, dimension( ldgnum, * )	GIVNUM,
		INTEGER	LDGNUM,
		REAL, dimension( ldgnum, * )	POLES,
		REAL, dimension( * )	DIFL,
		REAL, dimension( ldgnum, * )	DIFR,
		REAL, dimension( * )	Z,
		INTEGER	K,
		REAL	C,
		REAL	S,
		REAL, dimension( * )	WORK,
		INTEGER	INFO
	)

SLALS0

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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:

[in]	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.
[in]	NL	NL is INTEGER The row dimension of the upper block. NL >= 1.
[in]	NR	NR is INTEGER The row dimension of the lower block. NR >= 1.
[in]	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.
[in]	NRHS	NRHS is INTEGER The number of columns of B and BX. NRHS must be at least 1.
[in,out]	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.
[in]	LDB	LDB is INTEGER The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).
[out]	BX	BX is REAL array, dimension ( LDBX, NRHS )
[in]	LDBX	LDBX is INTEGER The leading dimension of BX.
[in]	PERM	PERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) applied to the two blocks.
[in]	GIVPTR	GIVPTR is INTEGER The number of Givens rotations which took place in this subproblem.
[in]	GIVCOL	GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.
[in]	LDGCOL	LDGCOL is INTEGER The leading dimension of GIVCOL, must be at least N.
[in]	GIVNUM	GIVNUM is REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value used in the corresponding Givens rotation.
[in]	LDGNUM	LDGNUM is INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.
[in]	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.
[in]	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.
[in]	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.
[in]	Z	Z is REAL array, dimension ( K ) Contain the components of the deflation-adjusted updating row vector.
[in]	K	K is INTEGER Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N.
[in]	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.
[in]	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.
[out]	WORK	WORK is REAL array, dimension ( K )
[out]	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:: November 2011

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.

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Functions/Subroutines

Function/Subroutine Documentation