SRC/zhegvd.f(3) Library Functions Manual SRC/zhegvd.f(3) NAME SRC/zhegvd.f SYNOPSIS Functions/Subroutines subroutine zhegvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, lrwork, iwork, liwork, info) ZHEGVD Function/Subroutine Documentation subroutine zhegvd (integer itype, character jobz, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info) ZHEGVD Purpose: !> !> ZHEGVD 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 and B is also positive definite. !> If eigenvectors are desired, it uses a divide and conquer algorithm. !> !> 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 !> N is INTEGER !> The order of the matrices A and B. N >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA, N) !> On entry, the Hermitian matrix A. If UPLO = 'U', the !> leading N-by-N upper triangular part of A contains the !> upper triangular part of the matrix A. If UPLO = 'L', !> the leading N-by-N lower triangular part of A contains !> the lower triangular part of the matrix A. !> !> On exit, if JOBZ = 'V', then if INFO = 0, A 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 on exit the upper triangle (if UPLO='U') !> or the lower triangle (if UPLO='L') of A, including the !> diagonal, is destroyed. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> B !> B is COMPLEX*16 array, dimension (LDB, N) !> On entry, the Hermitian matrix B. If UPLO = 'U', the !> leading N-by-N upper triangular part of B contains the !> upper triangular part of the matrix B. If UPLO = 'L', !> the leading N-by-N lower triangular part of B contains !> the lower triangular part of the matrix B. !> !> On exit, if INFO <= N, the part of B containing the matrix is !> overwritten by the triangular factor U or L from the Cholesky !> factorization B = U**H*U or B = L*L**H. !> LDB !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> W !> W is DOUBLE PRECISION array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> WORK !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of the array WORK. !> If N <= 1, LWORK >= 1. !> If JOBZ = 'N' and N > 1, LWORK >= N + 1. !> If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal 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 DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) !> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. !> LRWORK !> LRWORK is INTEGER !> The dimension of the 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 optimal 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 optimal LIWORK. !> LIWORK !> LIWORK is INTEGER !> The dimension of the array IWORK. !> If N <= 1, LIWORK >= 1. !> If JOBZ = 'N' and 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 optimal 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: ZPOTRF or ZHEEVD returned an error code: !> <= N: if INFO = i and JOBZ = 'N', then the algorithm !> failed to converge; i off-diagonal elements of an !> intermediate tridiagonal form did not converge to !> zero; !> if INFO = i and JOBZ = 'V', then the algorithm !> failed to compute an eigenvalue while working on !> the submatrix lying in rows and columns INFO/(N+1) !> through mod(INFO,N+1); !> > N: if INFO = N + i, for 1 <= i <= N, then the leading !> principal minor of order i of B is not positive. !> 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. Further Details: !> !> Modified so that no backsubstitution is performed if ZHEEVD fails to !> converge (NEIG in old code could be greater than N causing out of !> bounds reference to A - reported by Ralf Meyer). Also corrected the !> description of INFO and the test on ITYPE. Sven, 16 Feb 05. !> Contributors: Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA Definition at line 241 of file zhegvd.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/zhegvd.f(3)