zlalsd.f - Man Page

SRC/zlalsd.f

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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.

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

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 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.```

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 COMPLEX*16 array, dimension (N * NRHS)`

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 )```

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 179 of file zlalsd.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

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