EPIHF
This function computes the performance index for a complex Hermitian eigensystem.
Function Return Value
EPIHF — Performance index. (Output)
Required Arguments
NEVAL — Number of eigenvalue/eigenvector pairs on which the performance index computation is based. (Input)
A — Complex Hermitian matrix of order N. (Input)
EVAL — Vector of length NEVAL containing eigenvalues of A. (Input)
EVEC — Complex N by NEVAL array containing eigenvectors of A. (Input)
The eigenvector corresponding to the eigenvalue EVAL(J) must be in the J-th column of EVEC.
The eigenvector corresponding to the eigenvalue EVAL(J) must be in the J-th column of EVEC.
Optional Arguments
N — Order of the matrix A. (Input)
Default: N = SIZE (A,2).
Default: N = SIZE (A,2).
LDA — Leading dimension of A exactly as specified in the dimension statement in the calling program. (Input)
Default: LDA = SIZE (A,1).
Default: LDA = SIZE (A,1).
LDEVEC — Leading dimension of EVEC exactly as specified in the dimension statement in the calling program. (Input)
Default: LDEVEC = SIZE (EVEC,1).
Default: LDEVEC = SIZE (EVEC,1).
FORTRAN 90 Interface
Generic: EPIHF (NEVAL, A, EVAL, EVEC [,…])
Specific: The specific interface names are S_EPIHF and D_EPIHF.
FORTRAN 77 Interface
Single: EPIHF (N, NEVAL, A, LDA, EVAL, EVEC, LDEVEC)
Double: The double precision function name is DEPIHF.
Description
Let M = NEVAL, λ = EVAL, xj = EVEC(*, J), the j-th column of EVEC. Also, let ɛ be the machine precision, given by AMACH(4), see the Reference chapter of this manual. The performance index, 
, is defined to be
, is defined to be The norms used are a modified form of the 1-norm. The norm of the complex vector v is
While the exact value of 
is highly machine dependent, the performance of EVCSF is considered excellent if 
< 1, good if 1 ≤ 
≤ 100, and poor if 
> 100. The performance index was first developed by the EISPACK project at Argonne National Laboratory; see Smith et al. (1976, pages 124 ‑ 125).
is highly machine dependent, the performance of EVCSF is considered excellent if < 1, good if 1 ≤ ≤ 100, and poor if > 100. The performance index was first developed by the EISPACK project at Argonne National Laboratory; see Smith et al. (1976, pages 124 ‑ 125).Comments
1. Workspace may be explicitly provided, if desired, by use of E2IHF/DE2IHF. The reference is:
E2IHF(N, NEVAL, A, LDA, EVAL, EVEC, LDEVEC, WK)
The additional argument is
WK — Complex work array of length N.
2. Informational errors
Type | Code | Description |
|---|---|---|
3 | 1 | Performance index is greater than 100. |
3 | 2 | An eigenvector is zero. |
3 | 3 | The matrix is zero. |
Example
For an example of EPIHF, see IMSL routine EVCHF.
