NAME

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

SYNOPSIS

  SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, 
 *      LRWORK, IWORK, LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  DOUBLE COMPLEX AP(*), Z(LDZ,*), WORK(*)
  INTEGER N, LDZ, LWORK, LRWORK, LIWORK, INFO
  INTEGER IWORK(*)
  DOUBLE PRECISION W(*), RWORK(*)

  SUBROUTINE ZHPEVD_64( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, 
 *      RWORK, LRWORK, IWORK, LIWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  DOUBLE COMPLEX AP(*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, LDZ, LWORK, LRWORK, LIWORK, INFO
  INTEGER*8 IWORK(*)
  DOUBLE PRECISION W(*), RWORK(*)

F95 INTERFACE

  SUBROUTINE HPEVD( JOBZ, UPLO, [N], AP, W, Z, [LDZ], WORK, [LWORK], 
 *       RWORK, [LRWORK], [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX(8), DIMENSION(:) :: AP, WORK
  COMPLEX(8), DIMENSION(:,:) :: Z
  INTEGER :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
  INTEGER, DIMENSION(:) :: IWORK
  REAL(8), DIMENSION(:) :: W, RWORK

  SUBROUTINE HPEVD_64( JOBZ, UPLO, [N], AP, W, Z, [LDZ], WORK, [LWORK], 
 *       RWORK, [LRWORK], [IWORK], [LIWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX(8), DIMENSION(:) :: AP, WORK
  COMPLEX(8), DIMENSION(:,:) :: Z
  INTEGER(8) :: N, LDZ, LWORK, LRWORK, LIWORK, INFO
  INTEGER(8), DIMENSION(:) :: IWORK
  REAL(8), DIMENSION(:) :: W, RWORK

C INTERFACE

#include <sunperf.h>

void zhpevd(char jobz, char uplo, int n, doublecomplex *ap, double *w, doublecomplex *z, int ldz, doublecomplex *work, int lwork, double *rwork, int lrwork, int *info);

void zhpevd_64(char jobz, char uplo, long n, doublecomplex *ap, double *w, doublecomplex *z, long ldz, doublecomplex *work, long lwork, double *rwork, long lrwork, long *info);

PURPOSE

zhpevd computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

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.
AP (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 AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1 < =i < =j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j < =i < =n.
On exit, AP 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 (output)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of array WORK. If N < = 1, LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least N. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
RWORK (output)
dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input)
The dimension of array RWORK. If N < = 1, LRWORK must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK is issued by XERBLA.
IWORK (workspace)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
The dimension of array IWORK. If JOBZ = 'N' or N < = 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.

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.