Contents


NAME

     chbev - compute all the eigenvalues and, optionally,  eigen-
     vectors of a complex Hermitian band matrix A

SYNOPSIS

     SUBROUTINE CHBEV(JOBZ, UPLO, N, KD, A, LDA, W, Z, LDZ, WORK,
           WORK2, INFO)

     CHARACTER * 1 JOBZ, UPLO
     COMPLEX A(LDA,*), Z(LDZ,*), WORK(*)
     INTEGER N, KD, LDA, LDZ, INFO
     REAL W(*), WORK2(*)

     SUBROUTINE CHBEV_64(JOBZ, UPLO, N, KD, A, LDA, W, Z, LDZ, WORK,
           WORK2, INFO)

     CHARACTER * 1 JOBZ, UPLO
     COMPLEX A(LDA,*), Z(LDZ,*), WORK(*)
     INTEGER*8 N, KD, LDA, LDZ, INFO
     REAL W(*), WORK2(*)

  F95 INTERFACE
     SUBROUTINE HBEV(JOBZ, UPLO, [N], KD, A, [LDA], W, Z, [LDZ], [WORK],
            [WORK2], [INFO])

     CHARACTER(LEN=1) :: JOBZ, UPLO
     COMPLEX, DIMENSION(:) :: WORK
     COMPLEX, DIMENSION(:,:) :: A, Z
     INTEGER :: N, KD, LDA, LDZ, INFO
     REAL, DIMENSION(:) :: W, WORK2

     SUBROUTINE HBEV_64(JOBZ, UPLO, [N], KD, A, [LDA], W, Z, [LDZ],
            [WORK], [WORK2], [INFO])

     CHARACTER(LEN=1) :: JOBZ, UPLO
     COMPLEX, DIMENSION(:) :: WORK
     COMPLEX, DIMENSION(:,:) :: A, Z
     INTEGER(8) :: N, KD, LDA, LDZ, INFO
     REAL, DIMENSION(:) :: W, WORK2

  C INTERFACE
     #include <sunperf.h>

     void chbev(char jobz, char uplo, int n, int kd, complex  *a,
               int  lda,  float  *w,  complex  *z,  int  ldz, int
               *info);
     void chbev_64(char jobz, char uplo, long n, long kd, complex
               *a, long lda, float *w, complex *z, long ldz, long
               *info);

PURPOSE

     chbev computes all the eigenvalues and,  optionally,  eigen-
     vectors 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.

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

     A (input/output)
               On entry, the upper or lower triangle of the  Her-
               mitian  band  matrix  A,  stored in the first KD+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 dur-
               ing  the reduction to tridiagonal form.  If UPLO =
               'U', the first superdiagonal and the  diagonal  of
               the  tridiagonal  matrix T are returned in rows KD
               and KD+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 >= KD +
               1.
     W (output)
               If INFO = 0, the eigenvalues in ascending order.

     Z (input) 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  associ-
               ated  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 ille-
               gal value.
               > 0:  if INFO = i, the algorithm  failed  to  con-
               verge;  i off-diagonal elements of an intermediate
               tridiagonal form did not converge to zero.