zhegvd(3P) Sun Performance Library zhegvd(3P)NAMEzhegvd - compute 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
SYNOPSIS
SUBROUTINE ZHEGVD(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE ZHEGVD_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HEGVD(ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W, [WORK],
[LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER :: ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
SUBROUTINE HEGVD_64(ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W,
[WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER(8) :: ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void zhegvd(int itype, char jobz, char uplo, int n, doublecomplex *a,
int lda, doublecomplex *b, int ldb, double *w, int *info);
void zhegvd_64(long itype, char jobz, char uplo, long n, doublecomplex
*a, long lda, doublecomplex *b, long ldb, double *w, long
*info);
PURPOSEzhegvd 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 eigen‐
vectors 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 dig‐
its, but we know of none.
ARGUMENTS
ITYPE (input)
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)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) The order of the matrices A and B. N >= 0.
A (input/output)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper triangu‐
lar 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)
The leading dimension of the array A. LDA >= max(1,N).
B (input/output)
On entry, the Hermitian matrix B. If UPLO = 'U', the leading
N-by-N upper triangular part of B contains the upper triangu‐
lar 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)
The leading dimension of the array B. LDB >= max(1,N).
W (output)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
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 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)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input)
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 rou‐
tine 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)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
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)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i, ZHEEVD 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.
FURTHER DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
6 Mar 2009 zhegvd(3P)
