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

NAME

zhbev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

SYNOPSIS

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

  SUBROUTINE ZHBEV_64( JOBZ, UPLO, N, NDIAG, A, LDA, W, Z, LDZ, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 JOBZ, UPLO
  DOUBLE COMPLEX A(LDA,*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, NDIAG, LDA, LDZ, INFO
  DOUBLE PRECISION W(*), WORK2(*)

F95 INTERFACE

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

  SUBROUTINE HBEV_64( JOBZ, UPLO, [N], NDIAG, A, [LDA], W, Z, [LDZ], 
 *       [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, Z
  INTEGER(8) :: N, NDIAG, LDA, LDZ, INFO
  REAL(8), DIMENSION(:) :: W, WORK2

C INTERFACE

#include <sunperf.h>

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

void zhbev_64(char jobz, char uplo, long n, long ndiag, doublecomplex *a, long lda, double *w, doublecomplex *z, long ldz, long *info);

PURPOSE

zhbev computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.

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.

• NDIAG (input)
  The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. NDIAG > = 0.

• A (input/output)
  On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first NDIAG+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd) < =i < =j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for j < =i < =min(n,j+kd).

  On exit, A is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows NDIAG and NDIAG+1 of A, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of A.

• LDA (input)
  The leading dimension of the array A. LDA > = NDIAG + 1.

• 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(N)

• 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.