• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

zhpev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage

SYNOPSIS

  SUBROUTINE ZHPEV( JOBZ, UPLO, N, A, W, Z, LDZ, WORK, WORK2, INFO)
  CHARACTER * 1 JOBZ, UPLO
  DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*)
  INTEGER N, LDZ, INFO
  DOUBLE PRECISION W(*), WORK2(*)

  SUBROUTINE ZHPEV_64( JOBZ, UPLO, N, A, W, Z, LDZ, WORK, WORK2, INFO)
  CHARACTER * 1 JOBZ, UPLO
  DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, LDZ, INFO
  DOUBLE PRECISION W(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE HPEV( JOBZ, UPLO, [N], A, W, Z, [LDZ], [WORK], [WORK2], 
 *       [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX(8), DIMENSION(:) :: A, WORK
  COMPLEX(8), DIMENSION(:,:) :: Z
  INTEGER :: N, LDZ, INFO
  REAL(8), DIMENSION(:) :: W, WORK2

  SUBROUTINE HPEV_64( JOBZ, UPLO, [N], A, W, Z, [LDZ], [WORK], [WORK2], 
 *       [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX(8), DIMENSION(:) :: A, WORK
  COMPLEX(8), DIMENSION(:,:) :: Z
  INTEGER(8) :: N, LDZ, INFO
  REAL(8), DIMENSION(:) :: W, WORK2

C INTERFACE

#include <sunperf.h>

void zhpev(char jobz, char uplo, int n, doublecomplex *a, double *w, doublecomplex *z, int ldz, int *info);

void zhpev_64(char jobz, char uplo, long n, doublecomplex *a, double *w, doublecomplex *z, long ldz, long *info);

PURPOSE

zhpev computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.

ARGUMENTS

• JOBZ (input)
  

   = 'N':  Compute eigenvalues only;

   = 'V':  Compute eigenvalues and eigenvectors.

• UPLO (input)
  

   = 'U':  Upper triangle of A is stored;

   = 'L':  Lower triangle of A is stored.

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

• A (input/output)
  On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1 < =i < =j; if UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for j < =i < =n.

  On exit, A is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A.

• W (output)
  If INFO = 0, the eigenvalues in ascending order.

• Z (output)
  If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced.

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

• WORK (workspace)
  dimension(MAX(1,2*N-1))

• WORK2 (workspace)
  dimension(max(1,3*N-2))

• INFO (output)
  

   = 0:  successful exit.

   < 0:  if INFO  = -i, the i-th argument had an illegal value.

   > 0:  if INFO  = i, the algorithm failed to converge; i
  off-diagonal elements of an intermediate tridiagonal
  form did not converge to zero.