NAME

CHPEVD - compute all the eigenvalues and, optionally, eigenvectors 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 JOBZ, UPLO

INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N

INTEGER IWORK( ∗ )

REAL RWORK( ∗ ), W( ∗ )

COMPLEX AP( ∗ ), WORK( ∗ ), Z( LDZ, ∗ )

PURPOSE

CHPEVD 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) CHARACTER∗1
= ’N’:  Compute eigenvalues only;
= ’V’:  Compute eigenvalues and eigenvectors.

UPLO    (input) CHARACTER∗1
= ’U’:  Upper triangle of A is stored;
= ’L’:  Lower triangle of A is stored.

N       (input) INTEGER
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 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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z       (output) 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 associated with W(i). If JOBZ = ’N’, then Z is not referenced.

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

WORK    (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
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.

RWORK   (workspace/output) REAL array,
dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the optimal LRWORK.

LRWORK  (input) INTEGER
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 + 4∗N + 2∗N∗lg N + 3∗N∗∗2 , where lg( N ) = smallest integer k such that 2∗∗k >= N.

IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

LIWORK  (input) INTEGER
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 2 + 5∗N.

INFO    (output) INTEGER
= 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.

  —  LAPACK version 2.0  —  08 October 1994