Contents
zhpgvd - 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 ZHPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*)
INTEGER ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE ZHPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
DOUBLE COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*)
INTEGER*8 ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HPGVD(ITYPE, JOBZ, UPLO, [N], AP, BP, W, Z, [LDZ], [WORK],
[LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: AP, BP, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
SUBROUTINE HPGVD_64(ITYPE, JOBZ, UPLO, [N], AP, BP, W, Z, [LDZ],
[WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX(8), DIMENSION(:) :: AP, BP, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER(8) :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void zhpgvd(int itype, char jobz, char uplo, int n, doub-
lecomplex *ap, doublecomplex *bp, double *w, doub-
lecomplex *z, int ldz, int *info);
void zhpgvd_64(long itype, char jobz, char uplo, long n,
doublecomplex *ap, doublecomplex *bp, double *w,
doublecomplex *z, long ldz, long *info);
zhpgvd 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.
If eigenvectors are desired, it uses a divide and conquer
algorithm.
The divide and conquer algorithm makes very mild assumptions
about floating point arithmetic. It will work on machines
with a guard digit in add/subtract, or on those binary
machines without guard digits which subtract like the Cray
X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably
fail on hexadecimal or decimal machines without guard
digits, but we know of none.
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.
AP (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 AP as follows: if UPLO = 'U', AP(i + (j-
1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i
+ (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
BP (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 BP as follows: if UPLO = 'U', BP(i + (j-
1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(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 (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
The dimension of array WORK. If N <= 1,
LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= N.
If JOBZ = 'V' and N > 1, LWORK >= 2*N.
If LWORK = -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 LWORK is issued by XERBLA.
RWORK (workspace) DOUBLE PRECISION array, dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal
LRWORK.
LRWORK (input)
The dimension of array RWORK. If N <= 1,
LRWORK >= 1. If JOBZ = 'N' and N > 1, LRWORK >=
N. If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N +
2*N**2.
If LRWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the RWORK array, returns this value as the first
entry of the RWORK array, and no error message
related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal
LIWORK.
LIWORK (input)
The dimension of array IWORK. If JOBZ = 'N' or N
<= 1, LIWORK >= 1. If JOBZ = 'V' and N > 1,
LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the IWORK array, returns this value as the first
entry of the IWORK array, and no error message
related to LIWORK is issued by XERBLA.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: CPPTRF or ZHPEVD returned an error code:
<= N: if INFO = i, ZHPEVD 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.
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA