# clalsd.f man page

clalsd.f

## Synopsis

### Functions/Subroutines

subroutine clalsd (UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO)
CLALSD uses the singular value decomposition of A to solve the least squares problem.

## Function/Subroutine Documentation

### subroutine clalsd (character UPLO, integer SMLSIZ, integer N, integer NRHS, real, dimension( * ) D, real, dimension( * ) E, complex, dimension( ldb, * ) B, integer LDB, real RCOND, integer RANK, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer INFO)

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

Purpose:

``` CLALSD 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.

This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.```
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 REAL 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 REAL array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.```

B

```          B is COMPLEX 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 REAL
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 array, dimension (N * NRHS).`

RWORK

```          RWORK is REAL 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 (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.

Date:

December 2016

Contributors:

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

Definition at line 188 of file clalsd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK