EPISB

This function computes the performance index for a real symmetric eigensystem in band symmetric storage mode.

Required Arguments

EPISB — Performance index. (Output)

Required Arguments

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

A — Band symmetric matrix of order N. (Input)

NCODA — Number of codiagonals in A. (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.

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: EPISB (NEVAL, A, NCODA, EVAL, EVEC, …)

Specific: The specific interface names are S_EPISB and D_EPISB.

FORTRAN 77 Interface

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

Double: The double precision function name is DEPISB.

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 the 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 E2ISB/DE2ISB. The reference is:

E2ISB (N, NEVAL, A, LDA, NCODA, EVAL, EVEC, LDEVEC, WK)

The additional argument is:

WK — 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 EPISB, see IMSL routine EVCSB.