GPISP

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

Function Return Value

GPISP — Performance index. (Output)

Required Arguments

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

A — Symmetric matrix of order N. (Input)

B — Symmetric matrix of order N. (Input)

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

EVEC — N by NEVAL array containing the eigenvectors. (Input)

Optional Arguments

N — Order of the matrices A and B. (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).

LDB — Leading dimension of B exactly as specified in the dimension statement in the calling program. (Input)
Default: LDB = SIZE (B,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: GPISP (NEVAL, A, B, EVAL, EVEC [,…])

Specific: The specific interface names are S_GPISP and D_GPISP.

FORTRAN 77 Interface

Single: GPISP (N, NEVAL, A, LDA, B, LDB, EVAL, EVEC, LDEVEC)

Double: The double precision name is DGPISP.

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 GVCSP 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 Garbow et al. (1977, pages 77-79).

Comments

1. Workspace may be explicitly provided, if desired, by use of G2ISP/DG2ISP. The reference is:

G2ISP (N, NEVAL, A, LDA, B, LDB, EVAL, EVEC, LDEVEC, WORK)

The additional argument is:

WORK — Work array of length 2 * 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 A is zero.
3	4	The matrix B is zero.

3. The J-th eigenvalue should be ALPHA(J)/BETAV(J), its eigenvector should be in the J-th column of EVEC.

Example

For an example of GPISP, see routine GVCSP.