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 zlalsd.f(3) LAPACK zlalsd.f(3)

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 (characterUPLO, integerSMLSIZ, integerN, integerNRHS, double precision, dimension( * )D, double precision, dimension( * )E, complex*16, dimension( ldb, * )B, integerLDB, double precisionRCOND, integerRANK, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)

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.

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 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 at least
(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.
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 188 of file zlalsd.f.

# Author

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