# dlalsd.f - Man Page

SRC/dlalsd.f

## Synopsis

### Functions/Subroutines

subroutine dlalsd (uplo, smlsiz, n, nrhs, d, e, b, ldb, rcond, rank, work, iwork, info)
DLALSD uses the singular value decomposition of A to solve the least squares problem.

## Function/Subroutine Documentation

### subroutine dlalsd (character uplo, integer smlsiz, integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, double precision rcond, integer rank, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

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

Purpose:

DLALSD 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

UPLO

UPLO is CHARACTER*1
= 'U': D and E define an upper bidiagonal matrix.
= 'L': D and E define a  lower bidiagonal matrix.

SMLSIZ

SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.

N

N is INTEGER
The dimension of the  bidiagonal matrix.  N >= 0.

NRHS

NRHS is INTEGER
The number of columns of B. NRHS must be at least 1.

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.

E

E is DOUBLE PRECISION array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On input, B contains the right hand sides of the least
squares problem. On output, B contains the solution X.

LDB

LDB is INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,N).

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,
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).

RANK

RANK is INTEGER
The number of singular values of A greater than RCOND times
the largest singular value.

WORK

WORK is DOUBLE PRECISION array, dimension at least
(9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2),
where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1).

IWORK

IWORK is INTEGER array, dimension at least
(3*N*NLVL + 11*N)

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

NAG Ltd.

Contributors:

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

Definition at line 171 of file dlalsd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlalsd(3) is an alias of dlalsd.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK