slasd7()

subroutine slasd7	(	integer	icompq,
		integer	nl,
		integer	nr,
		integer	sqre,
		integer	k,
		real, dimension( * )	d,
		real, dimension( * )	z,
		real, dimension( * )	zw,
		real, dimension( * )	vf,
		real, dimension( * )	vfw,
		real, dimension( * )	vl,
		real, dimension( * )	vlw,
		real	alpha,
		real	beta,
		real, dimension( * )	dsigma,
		integer, dimension( * )	idx,
		integer, dimension( * )	idxp,
		integer, dimension( * )	idxq,
		integer, dimension( * )	perm,
		integer	givptr,
		integer, dimension( ldgcol, * )	givcol,
		integer	ldgcol,
		real, dimension( ldgnum, * )	givnum,
		integer	ldgnum,
		real	c,
		real	s,
		integer	info )

SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.

Download SLASD7 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> SLASD7 merges the two sets of singular values together into a single
!> sorted set. Then it tries to deflate the size of the problem. There
!> are two ways in which deflation can occur:  when two or more singular
!> values are close together or if there is a tiny entry in the Z
!> vector. For each such occurrence the order of the related
!> secular equation problem is reduced by one.
!>
!> SLASD7 is called from SLASD6.
!> 

Parameters

[in]	ICOMPQ	!> ICOMPQ is INTEGER !> Specifies whether singular vectors are to be computed !> in compact form, as follows: !> = 0: Compute singular values only. !> = 1: Compute singular vectors of upper !> bidiagonal matrix in compact form. !>
[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 !> N = NL + NR + 1 rows and !> M = N + SQRE >= N columns. !>
[out]	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,out]	D	!> D is REAL array, dimension ( N ) !> On entry D contains the singular values of the two submatrices !> to be combined. On exit D contains the trailing (N-K) updated !> singular values (those which were deflated) sorted into !> increasing order. !>
[out]	Z	!> Z is REAL array, dimension ( M ) !> On exit Z contains the updating row vector in the secular !> equation. !>
[out]	ZW	!> ZW is REAL array, dimension ( M ) !> Workspace for Z. !>
[in,out]	VF	!> VF is REAL array, dimension ( M ) !> On entry, VF(1:NL+1) contains the first components of all !> right singular vectors of the upper block; and VF(NL+2:M) !> contains the first components of all right singular vectors !> of the lower block. On exit, VF contains the first components !> of all right singular vectors of the bidiagonal matrix. !>
[out]	VFW	!> VFW is REAL array, dimension ( M ) !> Workspace for VF. !>
[in,out]	VL	!> VL is REAL array, dimension ( M ) !> On entry, VL(1:NL+1) contains the last components of all !> right singular vectors of the upper block; and VL(NL+2:M) !> contains the last components of all right singular vectors !> of the lower block. On exit, VL contains the last components !> of all right singular vectors of the bidiagonal matrix. !>
[out]	VLW	!> VLW is REAL array, dimension ( M ) !> Workspace for VL. !>
[in]	ALPHA	!> ALPHA is REAL !> Contains the diagonal element associated with the added row. !>
[in]	BETA	!> BETA is REAL !> Contains the off-diagonal element associated with the added !> row. !>
[out]	DSIGMA	!> DSIGMA is REAL array, dimension ( N ) !> Contains a copy of the diagonal elements (K-1 singular values !> and one zero) in the secular equation. !>
[out]	IDX	!> IDX is INTEGER array, dimension ( N ) !> This will contain the permutation used to sort the contents of !> D into ascending order. !>
[out]	IDXP	!> IDXP is INTEGER array, dimension ( N ) !> This will contain the permutation used to place deflated !> values of D at the end of the array. On output IDXP(2:K) !> points to the nondeflated D-values and IDXP(K+1:N) !> points to the deflated singular values. !>
[in]	IDXQ	!> IDXQ is INTEGER array, dimension ( N ) !> This contains the permutation which separately sorts the two !> sub-problems in D into ascending order. Note that entries in !> the first half of this permutation must first be moved one !> position backward; and entries in the second half !> must first have NL+1 added to their values. !>
[out]	PERM	!> PERM is INTEGER array, dimension ( N ) !> The permutations (from deflation and sorting) to be applied !> to each singular block. Not referenced if ICOMPQ = 0. !>
[out]	GIVPTR	!> GIVPTR is INTEGER !> The number of Givens rotations which took place in this !> subproblem. Not referenced if ICOMPQ = 0. !>
[out]	GIVCOL	!> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) !> Each pair of numbers indicates a pair of columns to take place !> in a Givens rotation. Not referenced if ICOMPQ = 0. !>
[in]	LDGCOL	!> LDGCOL is INTEGER !> The leading dimension of GIVCOL, must be at least N. !>
[out]	GIVNUM	!> GIVNUM is REAL array, dimension ( LDGNUM, 2 ) !> Each number indicates the C or S value to be used in the !> corresponding Givens rotation. Not referenced if ICOMPQ = 0. !>
[in]	LDGNUM	!> LDGNUM is INTEGER !> The leading dimension of GIVNUM, must be at least N. !>
[out]	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. !>
[out]	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]	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.

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA