Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix in packed storage.
FORTRAN 77:
call chpev(jobz, uplo, n, ap, w, z, ldz, work, rwork, info)
call zhpev(jobz, uplo, n, ap, w, z, ldz, work, rwork, info)
FORTRAN 95:
call hpev(ap, w [,uplo] [,z] [,info])
C:
lapack_int LAPACKE_chpev( int matrix_order, char jobz, char uplo, lapack_int n, lapack_complex_float* ap, float* w, lapack_complex_float* z, lapack_int ldz );
lapack_int LAPACKE_zhpev( int matrix_order, char jobz, char uplo, lapack_int n, lapack_complex_double* ap, double* w, lapack_complex_double* z, lapack_int ldz );
The routine computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage.
The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
CHARACTER*1. Must be 'N' or 'V'.
If job = 'N', then only eigenvalues are computed.
If job = 'V', then eigenvalues and eigenvectors are computed.
CHARACTER*1. Must be 'U' or 'L'.
If uplo = 'U', ap stores the packed upper triangular part of A.
If uplo = 'L', ap stores the packed lower triangular part of A.
INTEGER. The order of the matrix A (n ≥ 0).
COMPLEX for chpev
DOUBLE COMPLEX for zhpev.
Arrays:
ap(*) contains the packed upper or lower triangle of Hermitian matrix A, as specified by uplo.
The dimension of ap must be at least max(1, n*(n+1)/2).
(*) is a workspace array, DIMENSION at least max(1, 2n-1).
INTEGER. The leading dimension of the output array z.
Constraints:
if jobz = 'N', then ldz ≥ 1;
if jobz = 'V', then ldz ≥ max(1, n) .
REAL for chpev
DOUBLE PRECISION for zhpev.
Workspace array, DIMENSION at least max(1, 3n-2).
REAL for chpev
DOUBLE PRECISION for zhpev.
Array, DIMENSION at least max(1, n).
If info = 0, w contains the eigenvalues of the matrix A in ascending order.
COMPLEX for chpev
DOUBLE COMPLEX for zhpev.
Array z(ldz,*).
The second dimension of z must be at least max(1, 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.
On exit, this array is overwritten by the values generated during the reduction to tridiagonal form. The elements of the diagonal and the off-diagonal of the tridiagonal matrix overwrite the corresponding elements of A.
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
If info = i, then the algorithm failed to converge; i indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see Fortran 95 Interface Conventions.
Specific details for the routine hpev interface are the following:
Holds the array A of size (n*(n+1)/2).
Holds the vector with the number of elements n.
Holds the matrix Z of size (n, n).
Must be 'U' or 'L'. The default value is 'U'.
Restored based on the presence of the argument z as follows:
jobz = 'V', if z is present,
jobz = 'N', if z is omitted.