dlasq1 (3p)

Name

dlasq1 - compute the singular values of a real square bidiagonal matrix. Used by sbdsqr

Synopsis

SUBROUTINE DLASQ1( N, D, E, WORK, INFO )


INTEGER INFO, N

DOUBLE PRECISION D(*), E(*), WORK(*)


SUBROUTINE DLASQ1_64( N, D, E, WORK, INFO )


INTEGER*8 INFO, N

DOUBLE PRECISION D(*), E(*), WORK(*)


F95 INTERFACE
SUBROUTINE LASQ1( N, D, E, WORK, INFO )


INTEGER :: N, INFO

REAL(8), DIMENSION(:) :: D, E, WORK


SUBROUTINE LASQ1_64( N, D, E, WORK, INFO )


INTEGER(8) :: N, INFO

REAL(8), DIMENSION(:) :: D, E, WORK


C INTERFACE
#include <sunperf.h>

void dlasq1 (int n, double *d, double *e, int *info);


void dlasq1_64 (long n, double *d, double *e, long *info);

Description

Oracle Solaris Studio Performance Library                           dlasq1(3P)



NAME
       dlasq1  -  compute  the  singular  values  of  a real square bidiagonal
       matrix. Used by sbdsqr


SYNOPSIS
       SUBROUTINE DLASQ1( N, D, E, WORK, INFO )


       INTEGER INFO, N

       DOUBLE PRECISION D(*), E(*), WORK(*)


       SUBROUTINE DLASQ1_64( N, D, E, WORK, INFO )


       INTEGER*8 INFO, N

       DOUBLE PRECISION D(*), E(*), WORK(*)


   F95 INTERFACE
       SUBROUTINE LASQ1( N, D, E, WORK, INFO )


       INTEGER :: N, INFO

       REAL(8), DIMENSION(:) :: D, E, WORK


       SUBROUTINE LASQ1_64( N, D, E, WORK, INFO )


       INTEGER(8) :: N, INFO

       REAL(8), DIMENSION(:) :: D, E, WORK


   C INTERFACE
       #include <sunperf.h>

       void dlasq1 (int n, double *d, double *e, int *info);


       void dlasq1_64 (long n, double *d, double *e, long *info);


PURPOSE
       dlasq1 computes the singular values of a real N-by-N bidiagonal  matrix
       with diagonal D and off-diagonal E. The singular values are computed to
       high relative accuracy, in the absence  of  denormalization,  underflow
       and overflow. The algorithm was first presented in

       "Accurate  singular  values  and  differential  qd algorithms" by K. V.
       Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2,  pp.  191-230,
       1994,

       and  the  present  implementation is described in "An implementation of
       the dqds Algorithm (Positive Case)", LAPACK Working Note.


ARGUMENTS
       N (input)
                 N is INTEGER
                 The number of rows and columns in the matrix. N >= 0.


       D (input/output)
                 D is DOUBLE PRECISION array, dimension (N)
                 On entry, D contains the diagonal elements of the
                 bidiagonal matrix whose SVD is desired. On normal exit,
                 D contains the singular values in decreasing order.


       E (input/output)
                 E is DOUBLE PRECISION array, dimension (N)
                 On entry, elements E(1:N-1) contain the off-diagonal elements
                 of the bidiagonal matrix whose SVD is desired.
                 On exit, E is overwritten.


       WORK (output)
                 WORK is DOUBLE PRECISION array, dimension (4*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
                 = 1, a split was marked by a positive value in E
                 = 2, current block of Z not diagonalized after 100*N
                 iterations (in inner while loop)  On exit D and E
                 represent a matrix with the same singular values
                 which the calling subroutine could use to finish the
                 computation, or even feed back into DLASQ1
                 = 3, termination criterion of outer while loop not met
                 (program created more than N unreduced blocks)




                                  7 Nov 2015                        dlasq1(3P)