f12jfc is a setup function in a suite of functions consisting of f12jac, f12jbc, f12jfc, f12jkc, f12jsc, f12jtc, f12juc and f12jvc. It is used to find some of the eigenvalues, and the corresponding eigenvectors, of a standard, generalized or polynomial eigenvalue problem. The initialization function f12jac must have been called prior to calling f12jfc. In addition calls to f12jbc can be made to supply individual optional parameters to f12jfc.

The suite of functions is suitable for the solution of large sparse eigenproblems where only a few eigenvalues from a selected range of the spectrum are required.

2 Specification

#include <nag.h>

void	f12jfc (void handle, Complex emid, double r, NagError fail)

The function may be called by the names: f12jfc or nag_sparseig_feast_gen_contour.

3 Description

The suite of functions is designed to calculate some of the eigenvalues,

λ

, and the corresponding eigenvectors,

x

, of a standard eigenvalue problem

A x = λ x

, a generalized eigenvalue problem

A x = λ B x

, or a polynomial eigenvalue problem

\sum_{i} λ^{i} A_{i} x = 0

, where the coefficient matrices are large and sparse. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense problems.

f12jfc is used to specify a circle or ellipse in the complex plane within which eigenvalues will be sought. By default, a circle centred at

emid

with a radius of

r

is created. Optionally, f12jbc can be called prior to calling f12jfc, using the optional parameters

Ellipse Contour Ratio

and

Ellipse Rotation Angle

to change the eccentricity of the ellipse and the inclination angle of its axis. f12jfc uses these details to define nodes and weights for the elliptical contour, to be used by the solvers f12jkc, f12jsc, f12jtc, f12juc or f12jvc.

For details of the other options available and how to set them see Section 11.1 in f12jbc.

4 References

Polizzi E (2009) Density-Matrix-Based Algorithms for Solving Eigenvalue Problems Phys. Rev. B. 79 115112

5 Arguments

1: $handle$ – void * Input: On entry: the handle to the internal data structure used by the NAG FEAST suite. It needs to be initialized by f12jac. It must not be changed between calls to the NAG FEAST suite.
2: $emid$ – Complex Input: On entry: the centre of the ellipse.
3: $r$ – double Input: On entry: the radius of the horizontal axis of the ellipse (that is, the axis that would be horizontal if the rotation angle of the ellipse was set to zero).

Constraint: $r > 0.0$ .
4: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_HANDLE: The supplied handle does not define a valid handle to the data structure used by the NAG FEAST suite. It has not been properly initialized or it has been corrupted.
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_INVALID_OPTION: An invalid number of integration points was specified. For Gauss integration, the values permitted are $2$ – $40$ (even values only), $48$ , $64$ , $80$ , $96$ , $112$ .

The option $Integration Type$ was set to $Zol$ . For non-Hermitian eigenvalue problems the allowed values are $Gauss$ or $Trap$ .
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL: On entry, $r = ⟨ value ⟩$ .
Constraint: $r > 0.0$ .