naginterfaces.library.sparseig.feast_​custom_​contour

naginterfaces.library.sparseig.feast_custom_contour(handle, nedge, tedge, zedge)[source]

feast_custom_contour is a setup function in a suite of functions consisting of feast_init(), feast_option(), feast_custom_contour, feast_real_gen_solve(), feast_complex_symm_solve(), feast_complex_gen_solve(), feast_poly_symm_solve() and feast_poly_gen_solve(). It is used to find some of the eigenvalues, and the corresponding eigenvectors, of a standard, generalized or polynomial eigenvalue problem. The initialization function feast_init() must have been called prior to calling feast_custom_contour. In addition calls to feast_option() can be made to supply individual options to feast_custom_contour.

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.

For full information please refer to the NAG Library document for f12jg

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f12/f12jgf.html

Parameters
handleHandle

The handle to the internal data structure used by the NAG FEAST suite. It needs to be initialized by feast_init(). It must not be changed between calls to the NAG FEAST suite.

nedgeint, array-like, shape

specifies how many integration nodes and weights feast_custom_contour should use for the th piece of the contour.

tedgeint, array-like, shape

specifies what shape the th piece of the contour should be.

The th piece of the contour is straight.

The th piece of the contour is a (convex) half-ellipse, with , where is the primary radius from the endpoints of the piece, and is the radius perpendicular to this. Thus, if , then the th piece of the contour is a semicircle.

zedgecomplex, array-like, shape

specifies the endpoints of the contour piece.

The th piece has endpoints at and , for .

The last piece has endpoints at and .

Note: the contour should be described in a clockwise direction..

Raises
NagValueError
(errno )

has not been initialized properly or is corrupted.

(errno )

On entry, .

Constraint: .

(errno )

On entry, one or more elements of were less than or equal to zero.

(errno )

On entry, one or more elements of were negative.

Notes

The suite of functions is designed to calculate some of the eigenvalues, , and the corresponding eigenvectors, , of a standard eigenvalue problem , a generalized eigenvalue problem , or a polynomial eigenvalue problem , where the coefficient matrices are large and sparse. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense problems.

feast_custom_contour is used to specify a closed contour in the complex plane within which eigenvalues will be sought. The contour can be made up of a combination of line segments and half ellipses. feast_custom_contour uses this information to create a polygonal representation of the contour and to then define the integration nodes and weights to be used by the solvers feast_real_gen_solve(), feast_complex_symm_solve(), feast_complex_gen_solve(), feast_poly_symm_solve() or feast_poly_gen_solve().

The arrays , and are used to define the geometry of your contour. Each array is of size , where is the number of pieces that make up the contour. The entries in specify the endpoints in the complex plane of each piece of the contour. The entries in specify whether each piece of the contour is a line segment or a half ellipse. Finally, entries in specify the number of integration points to use for each piece of the contour. See the individual argument descriptions in Parameters for further details.

Prior to calling feast_custom_contour, the option setting function feast_option() can be called to specify various options for the solution of the eigenproblem. For details of the options available and how to set them see Other Parameters for feast_option.

References

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