Contents


NAME

     chpevd - compute all the eigenvalues and, optionally, eigen-
     vectors of a complex Hermitian matrix A in packed storage

SYNOPSIS

     SUBROUTINE CHPEVD(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
           LRWORK, IWORK, LIWORK, INFO)

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

     SUBROUTINE CHPEVD_64(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
           RWORK, LRWORK, IWORK, LIWORK, INFO)

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

  C INTERFACE
     #include <sunperf.h>
     void chpevd(char jobz, char uplo, int n, complex *ap,  float
               *w, complex *z, int ldz, int *info);

     void chpevd_64(char jobz, char uplo, long  n,  complex  *ap,
               float *w, complex *z, long ldz, long *info);

PURPOSE

     chpevd computes all the eigenvalues and, optionally,  eigen-
     vectors  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) COMPLEX array, dimension (N*(N+1)/2)
               On entry, the upper or lower triangle of the  Her-
               mitian  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) REAL array, dimension (N)
               If INFO = 0, the eigenvalues in ascending order.

     Z (input) COMPLEX array, dimension (LDZ, N)
               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) COMPLEX array, dimension (LWORK)
               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 (workspace)
               REAL array, 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/output) INTEGER array, dimension (LIWORK)
               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 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.