EPICG

This function computes the performance index for a complex eigensystem.

Function Return Value

EPICG — Performance index. (Output)

Required Arguments

NEVAL — Number of eigenvalue/eigenvector pairs on which the performance index computation is based. (Input)

A — Complex matrix of order N. (Input)

EVAL — Complex vector of length N containing the eigenvalues of A. (Input)

EVEC — Complex matrix of order N containing the eigenvectors of A. (Input)
The J-th eigenvalue/eigenvector pair should be in EVAL(J) and in the J-th column of EVEC.

Optional Arguments

N — Order of the matrix A. (Input)
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).

LDEVEC — Leading dimension of EVEC exactly as specified in the dimension statement in the calling program. (Input)
Default: LDEVEC = SIZE (EVEC,1).

FORTRAN 90 Interface

Generic: EPICG (NEVAL, A, EVAL, EVEC [,…])

Specific: The specific interface names are S_EPICG and D_EPICG.

FORTRAN 77 Interface

Single: EPICG (N, NEVAL, A, LDA, EVAL, EVEC, LDEVEC)

Double: The double precision function name is DEPICG.

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). The performance index, , 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 EVCCG 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 E2ICG/DE2ICG. The reference is:

E2ICG (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 EPICG, see IMSL routine EVCCG.