cpteqr

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 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.

This routine computes the eigenvalues of the positive definite tridiagonal matrix to high relative accuracy. This means that if the eigenvalues range over many orders of magnitude in size, then the small eigenvalues and corresponding eigenvectors will be computed more accurately 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 accuracy in the small eigenvalues of the original matrix, if these eigenvalues range over many orders of magnitude.)

ARGUMENTS

* COMPZ (input)
* 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)