chpgv(3P) Sun Performance Library chpgv(3P)NAMEchpgv - 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 CHPGV(ITYPE, JOBZ, UPLO, N, A, B, W, Z, LDZ, WORK, WORK2,
INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(*), B(*), Z(LDZ,*), WORK(*)
INTEGER ITYPE, N, LDZ, INFO
REAL W(*), WORK2(*)
SUBROUTINE CHPGV_64(ITYPE, JOBZ, UPLO, N, A, B, W, Z, LDZ, WORK,
WORK2, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(*), B(*), Z(LDZ,*), WORK(*)
INTEGER*8 ITYPE, N, LDZ, INFO
REAL W(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HPGV(ITYPE, JOBZ, UPLO, [N], A, B, W, Z, [LDZ], [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: A, B, WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER :: ITYPE, N, LDZ, INFO
REAL, DIMENSION(:) :: W, WORK2
SUBROUTINE HPGV_64(ITYPE, JOBZ, UPLO, [N], A, B, W, Z, [LDZ], [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: A, B, WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER(8) :: ITYPE, N, LDZ, INFO
REAL, DIMENSION(:) :: W, WORK2
C INTERFACE
#include <sunperf.h>
void chpgv(int itype, char jobz, char uplo, int n, complex *a, complex
*b, float *w, complex *z, int ldz, int *info);
void chpgv_64(long itype, char jobz, char uplo, long n, complex *a,
complex *b, float *w, complex *z, long ldz, long *info);
PURPOSEchpgv 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 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 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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) COMPLEX 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 array, dimension(MAX(1,2*N-1))
WORK2 (workspace)
REAL 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 CHPEV returned an error code:
<= N: if INFO = i, CHPEV 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.
6 Mar 2009 chpgv(3P)
