cpteqr (3p)

Name

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

Synopsis

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

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

SUBROUTINE CPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

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




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

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

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

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




C INTERFACE
#include <sunperf.h>

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

void cpteqr_64(char compz, long n, float *d, float *e, complex *z, long
ldz, long *info);

Description

Oracle Solaris Studio Performance Library                           cpteqr(3P)



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


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

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

       SUBROUTINE CPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO)

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




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

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

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

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




   C INTERFACE
       #include <sunperf.h>

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

       void cpteqr_64(char compz, long n, float *d, float *e, complex *z, long
                 ldz, long *info);



PURPOSE
       cpteqr computes all eigenvalues and, optionally, eigenvectors of a sym-
       metric  positive  definite  tridiagonal  matrix  by first factoring the
       matrix using SPTTRF and then calling CBDSQR  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 positive definite Hermitian matrix
       can also be found if CHETRD, CHPTRD, or CHBTRD 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  Hermitian  matrix
                 also.  Array Z contains the unitary matrix used to reduce the
                 original matrix to tridiagonal form.  = 'I':  Compute  eigen-
                 vectors 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  unitary  matrix  used  in  the
                 reduction  to tridiagonal form.  On exit, if COMPZ = 'V', the
                 orthonormal eigenvectors of the original Hermitian 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                        cpteqr(3P)