f12jff is a setup routine in a suite of routines consisting of f12jaf, f12jbf, f12jff, f12jkf, f12jsf, f12jtf, f12juf and f12jvf. It is used to find some of the eigenvalues, and the corresponding eigenvectors, of a standard, generalized or polynomial eigenvalue problem. The initialization routine f12jaf must have been called prior to calling f12jff. In addition calls to f12jbf can be made to supply individual optional parameters to f12jff.

The suite of routines 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

Fortran Interface

Subroutine f12jff (

handle, emid, r, ifail)

Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	r
Complex (Kind=nag_wp), Intent (In)	::	emid
Type (c_ptr), Intent (In)	::	handle

C Header Interface

#include <nag.h>

void	f12jff_ (void *handle, const Complex emid, const double r, Integer ifail)

The routine may be called by the names f12jff or nagf_sparseig_feast_gen_contour.

3 Description

The suite of routines 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.

f12jff 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, f12jbf can be called prior to calling f12jff, 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. f12jff uses these details to define nodes and weights for the elliptical contour, to be used by the solvers f12jkf, f12jsf, f12jtf, f12juf or f12jvf.

For details of the other options available and how to set them see Section 11.1 in f12jbf.

4 References

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

5 Arguments

1: $handle$ – Type (c_ptr) Input: On entry: the handle to the internal data structure used by the NAG FEAST suite. It needs to be initialized by f12jaf. It must not be changed between calls to the NAG FEAST suite.
2: $emid$ – Complex (Kind=nag_wp) Input: On entry: the centre of the ellipse.
3: $r$ – Real (Kind=nag_wp) 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: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: 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.

$ifail = 2$: An invalid number of integration points was specified. For Gauss integration, the values permitted are $2$ – $40$ (even values only), $48$ , $64$ , $80$ , $96$ , $112$ .

$ifail = 3$: The option Integration Type was set to $Zol$ . For non-Hermitian eigenvalue problems the allowed values are $Gauss$ or $Trap$ .

$ifail = 4$: On entry, $r = ⟨ value ⟩$ .
Constraint: $r > 0.0$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.