chpgv-f(3)

chpgv.f –

Synopsis

Functions/Subroutines

subroutine chpgv (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK, INFO)
CHPGST

Function/Subroutine Documentation

subroutine chpgv (integerITYPE, characterJOBZ, characterUPLO, integerN, complex, dimension( * )AP, complex, dimension( * )BP, real, dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CHPGST

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.

Parameters:

ITYPE

 ITYPE is 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

 JOBZ is CHARACTER*1
 = 'N': Compute eigenvalues only;
 = 'V': Compute eigenvalues and eigenvectors.

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangles of A and B are stored;
 = 'L': Lower triangles of A and B are stored.

 N is INTEGER
 The order of the matrices A and B. N >= 0.

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

 Z is 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

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

WORK

 WORK is COMPLEX array, dimension (max(1, 2*N-1))

RWORK

 RWORK is REAL array, dimension (max(1, 3*N-2))

INFO

 INFO is 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 165 of file chpgv.f.

Author

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