NAME

chpgv - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x

SYNOPSIS

SUBROUTINE CHPGV(
ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK, INFO )

CHARACTER JOBZ, UPLO

INTEGER INFO, ITYPE, LDZ, N

REAL RWORK( ∗ ), W( ∗ )

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

PURPOSE

CHPGV computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x,  A∗Bx=(lambda)∗x,  or B∗A∗x=(lambda)∗x.  Here A and B are assumed to be Hermitian, stored in packed format, and B is also positive definite. 
 

ARGUMENTS

ITYPE   (input) INTEGER
Specifies the problem type to be solved:
= 1:  A∗x = (lambda)∗B∗x
= 2:  A∗B∗x = (lambda)∗x
= 3:  B∗A∗x = (lambda)∗x

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

UPLO    (input) CHARACTER∗1
= ’U’:  Upper triangles of A and B are stored;
= ’L’:  Lower triangles of A and B are stored.

N       (input) INTEGER
The order of the matrices A and B.  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, the contents of AP are destroyed.

BP      (input/output) COMPLEX array, dimension (N∗(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix B, packed columnwise in a linear array.  The j-th column of B is stored in the array BP as follows: if UPLO = ’U’, BP(i + (j-1)∗j/2) = B(i,j) for 1<=i<=j; if UPLO = ’L’, BP(i + (j-1)∗(2∗n-j)/2) = B(i,j) for j<=i<=n.
 
On exit, the triangular factor U or L from the Cholesky factorization B = U∗∗H∗U or B = L∗L∗∗H, in the same storage format as B.

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 matrix Z of eigenvectors.  The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z∗∗H∗B∗Z = I; if ITYPE = 3, Z∗∗H∗inv(B)∗Z = 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) COMPLEX array, dimension (max(1, 2∗N-1))

RWORK   (workspace) REAL array, dimension (max(1, 3∗N-2))

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  CPPTRF or CHPEV returned an error code:
<= N:  if INFO = i, CHPEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not convergeto zero; > N:   if INFO = N + i, for 1 <= i <= n, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

SunSoft, Inc.  —  Last change: 27 Jun 1995