Contents
zhpgv - 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 ZHPGV(ITYPE, JOBZ, UPLO, N, A, B, W, Z, LDZ, WORK, WORK2,
INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX A(*), B(*), Z(LDZ,*), WORK(*)
INTEGER ITYPE, N, LDZ, INFO
DOUBLE PRECISION W(*), WORK2(*)
SUBROUTINE ZHPGV_64(ITYPE, JOBZ, UPLO, N, A, B, W, Z, LDZ, WORK,
WORK2, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX A(*), B(*), Z(LDZ,*), WORK(*)
INTEGER*8 ITYPE, N, LDZ, INFO
DOUBLE PRECISION W(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HPGV(ITYPE, JOBZ, UPLO, [N], A, B, W, Z, [LDZ], [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: A, B, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER :: ITYPE, N, LDZ, INFO
REAL(8), DIMENSION(:) :: W, WORK2
SUBROUTINE HPGV_64(ITYPE, JOBZ, UPLO, [N], A, B, W, Z, [LDZ], [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: A, B, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER(8) :: ITYPE, N, LDZ, INFO
REAL(8), DIMENSION(:) :: W, WORK2
C INTERFACE
#include <sunperf.h>
void zhpgv(int itype, char jobz, char uplo, int n, doub-
lecomplex *a, doublecomplex *b, double *w,
doublecomplex *z, int ldz, int *info);
void zhpgv_64(long itype, char jobz, char uplo, long n,
doublecomplex *a, doublecomplex *b, double *w,
doublecomplex *z, long ldz, long *info);
zhpgv 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, stored in packed format, and B is
also positive definite.
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) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Her-
mitian matrix A, packed columnwise in a linear
array. The j-th column of A is stored in the
array A as follows: if UPLO = 'U', A(i + (j-
1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i +
(j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of A are destroyed.
B (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Her-
mitian matrix B, packed columnwise in a linear
array. The j-th column of B is stored in the
array B as follows: if UPLO = 'U', B(i + (j-
1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', B(i +
(j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
On exit, the triangular factor U or L from the
Cholesky factorization B = U**H*U or B = L*L**H,
in the same storage format as B.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (input) COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1,
and if JOBZ = 'V', LDZ >= max(1,N).
WORK (workspace)
COMPLEX*16 array, dimension(MAX(1,2*N-1))
WORK2 (workspace)
DOUBLE PRECISION array, dimension(MAX(1,3*N-2))
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: CPPTRF or CHPEV returned an error code:
<= N: if INFO = i, CHPEV failed to converge; i
off-diagonal elements of an intermediate tridiago-
nal form did not convergeto zero; > N: if INFO =
N + i, for 1 <= i <= n, then the leading minor of
order i of B is not positive definite. The fac-
torization of B could not be completed and no
eigenvalues or eigenvectors were computed.