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
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);
Oracle Solaris Studio Performance Library zhegv(3P)
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 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 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 ZHETRD returned by ILAENV.
If LDWORK = -1, then a workspace query is assumed; the rou-
tine 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 ZHEEV returned an error code:
<= N: if INFO = i, ZHEEV 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.
7 Nov 2015 zhegv(3P)