Functions/Subroutines
subroutine	clals0 (ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO)
	CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

Function/Subroutine Documentation

subroutine clals0	(	integer	ICOMPQ,
		integer	NL,
		integer	NR,
		integer	SQRE,
		integer	NRHS,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, 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( * )	RWORK,
		integer	INFO
	)

CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

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Purpose:

 CLALS0 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 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.
[in]	LDB	LDB is INTEGER The leading dimension of B. LDB must be at least max(1,MAX( M, N ) ).
[out]	BX	BX is COMPLEX 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]	RWORK	RWORK is REAL array, dimension ( K(1+NRHS) + 2NRHS )
[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:: 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 269 of file clals0.f.

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Functions/Subroutines

Function/Subroutine Documentation