.TH ZHPGV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) " .SH NAME ZHPGV - 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 .SH SYNOPSIS .TP 18 SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK, INFO ) .TP 18 .ti +4 CHARACTER JOBZ, UPLO .TP 18 .ti +4 INTEGER INFO, ITYPE, LDZ, N .TP 18 .ti +4 DOUBLE PRECISION RWORK( * ), W( * ) .TP 18 .ti +4 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) .SH PURPOSE ZHPGV 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. .br .SH ARGUMENTS .TP 8 ITYPE (input) INTEGER Specifies the problem type to be solved: .br = 1: A*x = (lambda)*B*x .br = 2: A*B*x = (lambda)*x .br = 3: B*A*x = (lambda)*x .TP 8 JOBZ (input) CHARACTER*1 .br = \(aqN\(aq: Compute eigenvalues only; .br = \(aqV\(aq: Compute eigenvalues and eigenvectors. .TP 8 UPLO (input) CHARACTER*1 .br = \(aqU\(aq: Upper triangles of A and B are stored; .br = \(aqL\(aq: Lower triangles of A and B are stored. .TP 8 N (input) INTEGER The order of the matrices A and B. N >= 0. .TP 8 AP (input/output) COMPLEX*16 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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed. .TP 8 BP (input/output) COMPLEX*16 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 = \(aqU\(aq, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, 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. .TP 8 W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. .TP 8 Z (output) COMPLEX*16 array, dimension (LDZ, N) If JOBZ = \(aqV\(aq, 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 = \(aqN\(aq, then Z is not referenced. .TP 8 LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = \(aqV\(aq, LDZ >= max(1,N). .TP 8 WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1)) .TP 8 RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: ZPPTRF or ZHPEV returned an error code: .br <= N: if INFO = i, ZHPEV 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.