NAME

zhegv - 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 ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 
 *      LDWORK, WORK2, INFO)
  CHARACTER * 1 JOBZ, UPLO
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
  INTEGER ITYPE, N, LDA, LDB, LDWORK, INFO
  DOUBLE PRECISION W(*), WORK2(*)

  SUBROUTINE ZHEGV_64( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 
 *      LDWORK, WORK2, INFO)
  CHARACTER * 1 JOBZ, UPLO
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
  INTEGER*8 ITYPE, N, LDA, LDB, LDWORK, INFO
  DOUBLE PRECISION W(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE HEGV( ITYPE, JOBZ, UPLO, N, A, [LDA], B, [LDB], W, [WORK], 
 *       [LDWORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER :: ITYPE, N, LDA, LDB, LDWORK, INFO
  REAL(8), DIMENSION(:) :: W, WORK2

  SUBROUTINE HEGV_64( ITYPE, JOBZ, UPLO, N, A, [LDA], B, [LDB], W, 
 *       [WORK], [LDWORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER(8) :: ITYPE, N, LDA, LDB, LDWORK, INFO
  REAL(8), DIMENSION(:) :: W, WORK2

C INTERFACE

#include <sunperf.h>

void zhegv(int itype, char jobz, char uplo, int n, doublecomplex *a, int lda, doublecomplex *b, int ldb, double *w, int *info);

void zhegv_64(long itype, char jobz, char uplo, long n, doublecomplex *a, long lda, doublecomplex *b, long ldb, double *w, long *info);

PURPOSE

zhegv 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.

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 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)
The leading dimension of the array A. LDA > = max(1,N).
B (input/output)
On entry, the Hermitian positive definite 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 (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 LDWORK.
LDWORK (input)
The length of the array WORK. LDWORK > = max(1,2*N-1). For optimal efficiency, LDWORK > = (NB+1)*N, where NB is the blocksize for CHETRD returned by ILAENV.
If LDWORK = -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 LDWORK is issued by XERBLA.
WORK2 (workspace)
dimension(max(1,3*N-2))

INFO (output)

 = 0:  successful exit

 < 0:  if INFO  = -i, the i-th argument had an illegal value

 > 0:  CPOTRF or CHEEV returned an error code:

 < = N:  if INFO  = i, CHEEV 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.