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Updated: June 2017
 
 

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);

Description

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)