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This file is part of Logtalk https://logtalk.org/ SPDX-FileCopyrightText: 1998-2023 Paulo Moura <pmoura@logtalk.org> SPDX-License-Identifier: Apache-2.0

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

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To load this example and for sample queries, please see the SCRIPT.txt file.

This folder contains a multi-threading implementation of Recursive Gaussian Quadrature Methods for Numerical Integration for functions of one-variable.

Adaptive quadrature methods are efficient techniques for numerical integration as they compensate for functional variation along the integral domain, effectively in regions with large function variations a larger sampling of point are used.

There are two parametric objects, quadrec/1 and quadsplit/1, both implementing the same integration predicate:

integrate(Function, Left, Right, NP, Epsilon, Integral)

Find the integral of a function of one variable in the interval [Left, Right] given a maximum approximation error. NP represents the method to be used, one of (0,1,2,3).

For NP = 0 an adaptive trapezoidal rule is used. FOR NP=1,2,3,4 an adaptive Gaussian quadrature of 1, 2, 3, or points is used.

For quadrec/1, the method used for the multi-threading is simply to divide the initial area amongst the number of threads available (a power of 2) and then in each interval the recursive method is applied. The threaded/1 predicate is used.

For quadsplit/1, the method used is again division (split) of the original area amongst the number of threads specified. This method has no restriction on the number of threads and uses a span/collect idea for proving thread goals and the predicates threaded_once/1 and threaded_exit/1.