slasdq()

subroutine slasdq	(	character	uplo,
		integer	sqre,
		integer	n,
		integer	ncvt,
		integer	nru,
		integer	ncc,
		real, dimension( * )	d,
		real, dimension( * )	e,
		real, dimension( ldvt, * )	vt,
		integer	ldvt,
		real, dimension( ldu, * )	u,
		integer	ldu,
		real, dimension( ldc, * )	c,
		integer	ldc,
		real, dimension( * )	work,
		integer	info )

SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

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Purpose:

!>
!> SLASDQ computes the singular value decomposition (SVD) of a real
!> (upper or lower) bidiagonal matrix with diagonal D and offdiagonal
!> E, accumulating the transformations if desired. Letting B denote
!> the input bidiagonal matrix, the algorithm computes orthogonal
!> matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose
!> of P). The singular values S are overwritten on D.
!>
!> The input matrix U  is changed to U  * Q  if desired.
!> The input matrix VT is changed to P**T * VT if desired.
!> The input matrix C  is changed to Q**T * C  if desired.
!>
!> See  by J. Demmel and W. Kahan,
!> LAPACK Working Note #3, for a detailed description of the algorithm.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the input bidiagonal matrix !> is upper or lower bidiagonal, and whether it is square are !> not. !> UPLO = 'U' or 'u' B is upper bidiagonal. !> UPLO = 'L' or 'l' B is lower bidiagonal. !>
[in]	SQRE	!> SQRE is INTEGER !> = 0: then the input matrix is N-by-N. !> = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and !> (N+1)-by-N if UPLU = 'L'. !> !> The bidiagonal matrix has !> N = NL + NR + 1 rows and !> M = N + SQRE >= N columns. !>
[in]	N	!> N is INTEGER !> On entry, N specifies the number of rows and columns !> in the matrix. N must be at least 0. !>
[in]	NCVT	!> NCVT is INTEGER !> On entry, NCVT specifies the number of columns of !> the matrix VT. NCVT must be at least 0. !>
[in]	NRU	!> NRU is INTEGER !> On entry, NRU specifies the number of rows of !> the matrix U. NRU must be at least 0. !>
[in]	NCC	!> NCC is INTEGER !> On entry, NCC specifies the number of columns of !> the matrix C. NCC must be at least 0. !>
[in,out]	D	!> D is REAL array, dimension (N) !> On entry, D contains the diagonal entries of the !> bidiagonal matrix whose SVD is desired. On normal exit, !> D contains the singular values in ascending order. !>
[in,out]	E	!> E is REAL array. !> dimension is (N-1) if SQRE = 0 and N if SQRE = 1. !> On entry, the entries of E contain the offdiagonal entries !> of the bidiagonal matrix whose SVD is desired. On normal !> exit, E will contain 0. If the algorithm does not converge, !> D and E will contain the diagonal and superdiagonal entries !> of a bidiagonal matrix orthogonally equivalent to the one !> given as input. !>
[in,out]	VT	!> VT is REAL array, dimension (LDVT, NCVT) !> On entry, contains a matrix which on exit has been !> premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 !> and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). !>
[in]	LDVT	!> LDVT is INTEGER !> On entry, LDVT specifies the leading dimension of VT as !> declared in the calling (sub) program. LDVT must be at !> least 1. If NCVT is nonzero LDVT must also be at least N. !>
[in,out]	U	!> U is REAL array, dimension (LDU, N) !> On entry, contains a matrix which on exit has been !> postmultiplied by Q, dimension NRU-by-N if SQRE = 0 !> and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). !>
[in]	LDU	!> LDU is INTEGER !> On entry, LDU specifies the leading dimension of U as !> declared in the calling (sub) program. LDU must be at !> least max( 1, NRU ) . !>
[in,out]	C	!> C is REAL array, dimension (LDC, NCC) !> On entry, contains an N-by-NCC matrix which on exit !> has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 !> and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). !>
[in]	LDC	!> LDC is INTEGER !> On entry, LDC specifies the leading dimension of C as !> declared in the calling (sub) program. LDC must be at !> least 1. If NCC is nonzero, LDC must also be at least N. !>
[out]	WORK	!> WORK is REAL array, dimension (4*N) !> Workspace. Only referenced if one of NCVT, NRU, or NCC is !> nonzero, and if N is at least 2. !>
[out]	INFO	!> INFO is INTEGER !> On exit, a value of 0 indicates a successful exit. !> If INFO < 0, argument number -INFO is illegal. !> If INFO > 0, the algorithm did not converge, and INFO !> specifies how many superdiagonals did not converge. !>

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