# clalsd.f man page

clalsd.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine clalsd (characterUPLO, integerSMLSIZ, integerN, integerNRHS, real, dimension( * )D, real, dimension( * )E, complex, dimension( ldb, * )B, integerLDB, realRCOND, integerRANK, complex, dimension( * )WORK, real, dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)

**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,
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).
```

*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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**Contributors:**

Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Osni Marques, LBNL/NERSC, USA

Definition at line 186 of file clalsd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

clalsd(3) is an alias of clalsd.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK