EPISF

This function computes the performance index for a real symmetric eigensystem.

Function Return Value

EPISF — Performance index. (Output)

Required Arguments

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

A — Symmetric matrix of order N. (Input)

EVAL — Vector of length NEVAL containing eigenvalues of A. (Input)

EVEC — 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: EPISF (NEVAL, A, EVAL, EVEC [,…])

Specific: The specific interface names are S_EPISF and D_EPISF.

FORTRAN 77 Interface

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

Double: The double precision function name is DEPISF.

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

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).

Comments

1. Workspace may be explicitly provided, if desired, by use of E2ISF/DE2ISF. The reference is:

E2ISF (N, NEVAL, A, LDA, EVAL, EVEC, LDEVEC, WORK)

The additional argument is:

WORK — Work array of length N.

E2ISF — Performance Index.

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 EPISF, see routine EVCSF.