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, doublecomplex *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);
Oracle Solaris Studio Performance Library zhpgv(3P)
NAME
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
SYNOPSIS
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, doublecomplex *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);
PURPOSE
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.
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) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian 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 Hermitian 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 fac-
torization B = U**H*U or B = L*L**H, in the same storage for-
mat as B.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) 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 illegal value
> 0: CPPTRF or ZHPEV returned an error code:
<= N: if INFO = i, ZHPEV failed to converge; i off-diagonal
elements of an intermediate tridiagonal form did not con-
vergeto 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 eigen-
values or eigenvectors were computed.
7 Nov 2015 zhpgv(3P)