dlalsd - use the singular value decomposition of A to solve the least squares problem
SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, IWORK, INFO ) CHARACTER*1 UPLO INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ DOUBLE PRECISION RCOND INTEGER IWORK(*) DOUBLE PRECISION B(LDB,*), D(*), E(*), WORK(*) SUBROUTINE DLALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, IWORK, INFO ) CHARACTER*1 UPLO INTEGER*8 INFO, LDB, N, NRHS, RANK, SMLSIZ DOUBLE PRECISION RCOND INTEGER*8 IWORK(*) DOUBLE PRECISION B(LDB,*), D(*), E(*), WORK(*) F95 INTERFACE SUBROUTINE LALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, IWORK, INFO ) INTEGER :: SMLSIZ, N, NRHS, LDB, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:,:) :: B REAL(8), DIMENSION(:) :: D, E, WORK REAL(8) :: RCOND SUBROUTINE LALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, IWORK, INFO ) INTEGER(8) :: SMLSIZ, N, NRHS, LDB, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:,:) :: B REAL(8), DIMENSION(:) :: D, E, WORK REAL(8) :: RCOND C INTERFACE #include <sunperf.h> void dlalsd (char uplo, int smlsiz, int n, int nrhs, double *d, double *e, double *b, int ldb, double rcond, int *rank, int *info); void dlalsd_64 (char uplo, long smlsiz, long n, long nrhs, double *d, double *e, double *b, long ldb, double rcond, long *rank, long *info);
Oracle Solaris Studio Performance Library dlalsd(3P)
NAME
dlalsd - use the singular value decomposition of A to solve the least
squares problem
SYNOPSIS
SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, IWORK, INFO )
CHARACTER*1 UPLO
INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ
DOUBLE PRECISION RCOND
INTEGER IWORK(*)
DOUBLE PRECISION B(LDB,*), D(*), E(*), WORK(*)
SUBROUTINE DLALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, IWORK, INFO )
CHARACTER*1 UPLO
INTEGER*8 INFO, LDB, N, NRHS, RANK, SMLSIZ
DOUBLE PRECISION RCOND
INTEGER*8 IWORK(*)
DOUBLE PRECISION B(LDB,*), D(*), E(*), WORK(*)
F95 INTERFACE
SUBROUTINE LALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, IWORK, INFO )
INTEGER :: SMLSIZ, N, NRHS, LDB, RANK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:,:) :: B
REAL(8), DIMENSION(:) :: D, E, WORK
REAL(8) :: RCOND
SUBROUTINE LALSD_64( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK,
WORK, IWORK, INFO )
INTEGER(8) :: SMLSIZ, N, NRHS, LDB, RANK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:,:) :: B
REAL(8), DIMENSION(:) :: D, E, WORK
REAL(8) :: RCOND
C INTERFACE
#include <sunperf.h>
void dlalsd (char uplo, int smlsiz, int n, int nrhs, double *d, double
*e, double *b, int ldb, double rcond, int *rank, int *info);
void dlalsd_64 (char uplo, long smlsiz, long n, long nrhs, double *d,
double *e, double *b, long ldb, double rcond, long *rank,
long *info);
PURPOSE
dlalsd 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 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 (input/output)
E is DOUBLE PRECISION array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
B (input/output)
B is DOUBLE PRECISION 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 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,
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 DOUBLE PRECISION array, dimension at least
(9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2),
where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1).
IWORK (output)
IWORK is INTEGER array, dimension at least
(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 dlalsd(3P)