Linux & Unix Commands - Search Man Pages

CHEGVD(l)) CHEGVD(l)NAMECHEGVD - compute all the eigenvalues, and optionally, the eigenvectors of a complex gener- alized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*xSYNOPSISSUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) CHARACTER JOBZ, UPLO INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N INTEGER IWORK( * ) REAL RWORK( * ), W( * ) COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )PURPOSECHEGVD computes all the eigenvalues, and optionally, the eigenvectors of a complex gener- alized 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 defi- nite. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arith- metic. 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.ARGUMENTSITYPE (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. A (input/output) COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper trian- gular 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 (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) COMPLEX array, dimension (LDB, N) On entry, the Hermitian matrix B. If UPLO = 'U', the leading N-by-N upper trian- gular 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 (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK (workspace/output) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) 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 =, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. RWORK (workspace/output) REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. LRWORK (input) 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 size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK is issued by XERBLA. IWORK (workspace/output) INTEGER array, dimension (LIWORK) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. LIWORK (input) 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. INFO (output) INTEGER = 0: successful exit < 0: if INFO =-1, the i-th argument had an illegal value > 0: CPOTRF or CHEEVD returned an error code: <= N: if INFO = i, CHEEVD failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to 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.-iFURTHER DETAILSBased on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USALAPACK version 3.015 June 2000 CHEGVD(l)

All times are GMT -4. The time now is 09:31 AM.