spteqr (3p)

Name

spteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor

Synopsis

SUBROUTINE SPTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

CHARACTER*1 COMPZ
INTEGER N, LDZ, INFO
REAL D(*), E(*), Z(LDZ,*), WORK(*)

SUBROUTINE SPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

CHARACTER*1 COMPZ
INTEGER*8 N, LDZ, INFO
REAL D(*), E(*), Z(LDZ,*), WORK(*)




F95 INTERFACE
SUBROUTINE PTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

CHARACTER(LEN=1) :: COMPZ
INTEGER :: N, LDZ, INFO
REAL, DIMENSION(:) :: D, E, WORK
REAL, DIMENSION(:,:) :: Z

SUBROUTINE PTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

CHARACTER(LEN=1) :: COMPZ
INTEGER(8) :: N, LDZ, INFO
REAL, DIMENSION(:) :: D, E, WORK
REAL, DIMENSION(:,:) :: Z




C INTERFACE
#include <sunperf.h>

void spteqr(char compz, int n, float *d, float *e, float *z,  int  ldz,
int *info);

void  spteqr_64(char  compz, long n, float *d, float *e, float *z, long
ldz, long *info);

Description

Oracle Solaris Studio Performance Library                           spteqr(3P)



NAME
       spteqr  -  compute  all  eigenvalues and, optionally, eigenvectors of a
       symmetric positive definite tridiagonal matrix by first  factoring  the
       matrix  using  SPTTRF,  and then calling SBDSQR to compute the singular
       values of the bidiagonal factor


SYNOPSIS
       SUBROUTINE SPTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

       CHARACTER*1 COMPZ
       INTEGER N, LDZ, INFO
       REAL D(*), E(*), Z(LDZ,*), WORK(*)

       SUBROUTINE SPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

       CHARACTER*1 COMPZ
       INTEGER*8 N, LDZ, INFO
       REAL D(*), E(*), Z(LDZ,*), WORK(*)




   F95 INTERFACE
       SUBROUTINE PTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

       CHARACTER(LEN=1) :: COMPZ
       INTEGER :: N, LDZ, INFO
       REAL, DIMENSION(:) :: D, E, WORK
       REAL, DIMENSION(:,:) :: Z

       SUBROUTINE PTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

       CHARACTER(LEN=1) :: COMPZ
       INTEGER(8) :: N, LDZ, INFO
       REAL, DIMENSION(:) :: D, E, WORK
       REAL, DIMENSION(:,:) :: Z




   C INTERFACE
       #include <sunperf.h>

       void spteqr(char compz, int n, float *d, float *e, float *z,  int  ldz,
                 int *info);

       void  spteqr_64(char  compz, long n, float *d, float *e, float *z, long
                 ldz, long *info);



PURPOSE
       spteqr computes all eigenvalues and, optionally, eigenvectors of a sym-
       metric  positive  definite  tridiagonal  matrix  by first factoring the
       matrix using SPTTRF, and then calling SBDSQR to  compute  the  singular
       values of the bidiagonal factor.

       This routine computes the eigenvalues of the positive definite tridiag-
       onal matrix to high relative accuracy.  This means that if  the  eigen-
       values  range over many orders of magnitude in size, then the small ei-
       genvalues and corresponding eigenvectors will be  computed  more  accu-
       rately than, for example, with the standard QR method.

       The  eigenvectors  of a full or band symmetric positive definite matrix
       can also be found if SSYTRD, SSPTRD, or SSBTRD has been used to  reduce
       this  matrix  to  tridiagonal form. (The reduction to tridiagonal form,
       however, may preclude the possibility of obtaining high relative  accu-
       racy  in  the small eigenvalues of the original matrix, if these eigen-
       values range over many orders of magnitude.)


ARGUMENTS
       COMPZ (input)
                 = 'N':  Compute eigenvalues only.
                 = 'V':  Compute eigenvectors  of  original  symmetric  matrix
                 also.   Array Z contains the orthogonal matrix used to reduce
                 the original matrix to tridiagonal  form.   =  'I':   Compute
                 eigenvectors of tridiagonal matrix also.


       N (input) The order of the matrix.  N >= 0.


       D (input/output)
                 On  entry, the n diagonal elements of the tridiagonal matrix.
                 On normal exit, D contains  the  eigenvalues,  in  descending
                 order.


       E (input/output)
                 On  entry,  the (n-1) subdiagonal elements of the tridiagonal
                 matrix.  On exit, E has been destroyed.


       Z (input) On entry, if COMPZ = 'V', the orthogonal matrix used  in  the
                 reduction  to tridiagonal form.  On exit, if COMPZ = 'V', the
                 orthonormal eigenvectors of the original symmetric matrix; if
                 COMPZ  = 'I', the orthonormal eigenvectors of the tridiagonal
                 matrix.  If INFO > 0 on exit,  Z  contains  the  eigenvectors
                 associated  with  only  the  stored eigenvalues.  If  COMPZ =
                 'N', then Z is not referenced.


       LDZ (input)
                 The leading dimension of the array Z.  LDZ >= 1, and if COMPZ
                 = 'V' or 'I', LDZ >= max(1,N).


       WORK (workspace)
                 dimension(4*N)

       INFO (output)
                 = 0:  successful exit.
                 < 0:  if INFO = -i, the i-th argument had an illegal value.
                 > 0:  if INFO = i, and i is: <= N  the Cholesky factorization
                 of the matrix could not be performed because the i-th princi-
                 pal minor was not positive definite.  > N   the SVD algorithm
                 failed to converge; if INFO = N+i, i off-diagonal elements of
                 the bidiagonal factor did not converge to zero.




                                  7 Nov 2015                        spteqr(3P)