clalsd.f(3) LAPACK clalsd.f(3)
NAME
clalsd.f -
SYNOPSIS
Functions/Subroutines
subroutine clalsd (UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO)
CLALSD
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
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:
November 2011
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
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Version 3.4.1 Sun May 26 2013 clalsd.f(3)