clalsd - use the singular value decomposition of A to solve the least squares problem
SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO ) CHARACTER*1 UPLO INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ REAL RCOND INTEGER IWORK(*) REAL D(*),E(*), RWORK(*) COMPLEX B(LDB,*), WORK(*) SUBROUTINE CLALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO ) CHARACTER*1 UPLO INTEGER*8 INFO, LDB, N, NRHS, RANK, SMLSIZ REAL RCOND INTEGER*8 IWORK(*) REAL D(*),E(*), RWORK(*) COMPLEX B(LDB,*), WORK(*) F95 INTERFACE SUBROUTINE LALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO ) INTEGER :: SMLSIZ, N, NRHS, LDB, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: D, E, RWORK COMPLEX, DIMENSION(:,:) :: B COMPLEX, DIMENSION(:) :: WORK REAL :: RCOND SUBROUTINE LALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO ) INTEGER(8) :: SMLSIZ, N, NRHS, LDB, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: D, E, RWORK COMPLEX, DIMENSION(:,:) :: B COMPLEX, DIMENSION(:) :: WORK REAL :: RCOND C INTERFACE #include <sunperf.h> void clalsd (char uplo, int smlsiz, int n, int nrhs, float *d, float *e, floatcomplex *b, int ldb, float rcond, int *rank, int *info); void clalsd_64 (char uplo, long smlsiz, long n, long nrhs, float *d, float *e, floatcomplex *b, long ldb, float rcond, long *rank, long *info);
Oracle Solaris Studio Performance Library clalsd(3P)
NAME
clalsd - use the singular value decomposition of A to solve the least
squares problem
SYNOPSIS
SUBROUTINE CLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, RWORK, IWORK, INFO )
CHARACTER*1 UPLO
INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ
REAL RCOND
INTEGER IWORK(*)
REAL D(*),E(*), RWORK(*)
COMPLEX B(LDB,*), WORK(*)
SUBROUTINE CLALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, RWORK, IWORK, INFO )
CHARACTER*1 UPLO
INTEGER*8 INFO, LDB, N, NRHS, RANK, SMLSIZ
REAL RCOND
INTEGER*8 IWORK(*)
REAL D(*),E(*), RWORK(*)
COMPLEX B(LDB,*), WORK(*)
F95 INTERFACE
SUBROUTINE LALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, RWORK, IWORK, INFO )
INTEGER :: SMLSIZ, N, NRHS, LDB, RANK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: D, E, RWORK
COMPLEX, DIMENSION(:,:) :: B
COMPLEX, DIMENSION(:) :: WORK
REAL :: RCOND
SUBROUTINE LALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, RWORK, IWORK, INFO )
INTEGER(8) :: SMLSIZ, N, NRHS, LDB, RANK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: D, E, RWORK
COMPLEX, DIMENSION(:,:) :: B
COMPLEX, DIMENSION(:) :: WORK
REAL :: RCOND
C INTERFACE
#include <sunperf.h>
void clalsd (char uplo, int smlsiz, int n, int nrhs, float *d, float
*e, floatcomplex *b, int ldb, float rcond, int *rank, int
*info);
void clalsd_64 (char uplo, long smlsiz, long n, long nrhs, float *d,
float *e, floatcomplex *b, long ldb, float rcond, long *rank,
long *info);
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.
ARGUMENTS
UPLO (input)
UPLO is CHARACTER*1
= 'U': D and E define an upper bidiagonal matrix.
= 'L': D and E define a lower bidiagonal matrix.
SMLSIZ (input)
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N (input)
N is INTEGER
The dimension of the bidiagonal matrix. N >= 0.
NRHS (input)
NRHS is INTEGER
The number of columns of B. NRHS must be at least 1.
D (input/output)
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 (input/output)
E is REAL array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
B (input/output)
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 (input)
LDB is INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,N).
RCOND (input)
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 (output)
RANK is INTEGER
The number of singular values of A greater than RCOND times
the largest singular value.
WORK (output)
WORK is COMPLEX array, dimension (N * NRHS).
RWORK (output)
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 (output)
IWORK is INTEGER array, dimension (3*N*NLVL + 11*N).
INFO (output)
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).
7 Nov 2015 clalsd(3P)