zlalsd()

subroutine zlalsd	(	character	uplo,
		integer	smlsiz,
		integer	n,
		integer	nrhs,
		double precision, dimension( * )	d,
		double precision, dimension( * )	e,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		double precision	rcond,
		integer	rank,
		complex*16, dimension( * )	work,
		double precision, dimension( * )	rwork,
		integer, dimension( * )	iwork,
		integer	info )

ZLALSD uses the singular value decomposition of A to solve the least squares problem.

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Purpose:

!>
!> ZLALSD uses the singular value decomposition of A to solve the least
!> squares problem of finding X to minimize the Euclidean norm of each
!> column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
!> are N-by-NRHS. The solution X overwrites B.
!>
!> The singular values of A smaller than RCOND times the largest
!> singular value are treated as zero in solving the least squares
!> problem; in this case a minimum norm solution is returned.
!> The actual singular values are returned in D in ascending order.
!>
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': D and E define an upper bidiagonal matrix. !> = 'L': D and E define a lower bidiagonal matrix. !>
[in]	SMLSIZ	!> SMLSIZ is INTEGER !> The maximum size of the subproblems at the bottom of the !> computation tree. !>
[in]	N	!> N is INTEGER !> The dimension of the bidiagonal matrix. N >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of columns of B. NRHS must be at least 1. !>
[in,out]	D	!> D is DOUBLE PRECISION array, dimension (N) !> On entry D contains the main diagonal of the bidiagonal !> matrix. On exit, if INFO = 0, D contains its singular values. !>
[in,out]	E	!> E is DOUBLE PRECISION array, dimension (N-1) !> Contains the super-diagonal entries of the bidiagonal matrix. !> On exit, E has been destroyed. !>
[in,out]	B	!> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On input, B contains the right hand sides of the least !> squares problem. On output, B contains the solution X. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of B in the calling subprogram. !> LDB must be at least max(1,N). !>
[in]	RCOND	!> RCOND is DOUBLE PRECISION !> The singular values of A less than or equal to RCOND times !> the largest singular value are treated as zero in solving !> the least squares problem. If RCOND is negative, !> machine precision is used instead. !> For example, if diag(S)*X=B were the least squares problem, !> where diag(S) is a diagonal matrix of singular values, the !> solution would be X(i) = B(i) / S(i) if S(i) is greater than !> RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to !> RCOND*max(S). !>
[out]	RANK	!> RANK is INTEGER !> The number of singular values of A greater than RCOND times !> the largest singular value. !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (N * NRHS) !>
[out]	RWORK	!> RWORK is DOUBLE PRECISION array, dimension at least !> (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS + !> MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ), !> where !> NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) !>
[out]	IWORK	!> IWORK is INTEGER array, dimension at least !> (3*N*NLVL + 11*N). !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: The algorithm failed to compute a singular value while !> working on the submatrix lying in rows and columns !> INFO/(N+1) through MOD(INFO,N+1). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA