chpgvd-f(3)

chpgvd.f –

Synopsis

Functions/Subroutines

subroutine chpgvd (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHPGST

Function/Subroutine Documentation

subroutine chpgvd (integerITYPE, characterJOBZ, characterUPLO, integerN, complex, dimension( * )AP, complex, dimension( * )BP, real, dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

CHPGST

Purpose:

 CHPGVD 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.
 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.

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,LWORK))
 On exit, if INFO = 0, WORK(1) returns the required LWORK.

LWORK

 LWORK is INTEGER
 The dimension of array WORK.
 If N <= 1, LWORK >= 1.
 If JOBZ = 'N' and N > 1, LWORK >= N.
 If JOBZ = 'V' and N > 1, LWORK >= 2*N.
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates the required sizes of the WORK, RWORK and
 IWORK arrays, returns these values as the first entries of
 the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

 RWORK is REAL array, dimension (MAX(1,LRWORK))
 On exit, if INFO = 0, RWORK(1) returns the required LRWORK.

LRWORK

 LRWORK is INTEGER
 The dimension of array RWORK.
 If N <= 1, LRWORK >= 1.
 If JOBZ = 'N' and N > 1, LRWORK >= N.
 If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
 If LRWORK = -1, then a workspace query is assumed; the
 routine only calculates the required sizes of the WORK, RWORK
 and IWORK arrays, returns these values as the first entries
 of the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

 IWORK is INTEGER array, dimension (MAX(1,LIWORK))
 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

LIWORK

 LIWORK is INTEGER
 The dimension of array IWORK.
 If JOBZ = 'N' or N <= 1, LIWORK >= 1.
 If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
 If LIWORK = -1, then a workspace query is assumed; the
 routine only calculates the required sizes of the WORK, RWORK
 and IWORK arrays, returns these values as the first entries
 of the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value
 > 0: CPPTRF or CHPEVD returned an error code:
 <= N: if INFO = i, CHPEVD 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

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 231 of file chpgvd.f.

Author

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