Table of Contents Klasy i dziedziczenie Klasy kwadratur Przykład użycia Klasy i dziedziczenie newtocotes.py calculate_integral_quadratue_step1.py Klasy kwadratur <sxh python> #! /usr/bin/env python # -*- coding: utf-8 -*- # vim:fenc=utf-8 # # Copyright © 2017 putanowr <putanowr@foo> # # Distributed under terms of the MIT license. “”“ Newton-Cotes numerical integration formulas ”“” class NewtonCotes: def __init__(self, degree): self.degree = degree def nodes(self, a, b): n = self.degree+1 dx = (b-a)/n return [a+i*dx for i in range(n)] def weights(self, a, b): return ((b-a)*x for x in self.ref_weights) class TrapezoidQuadrature(NewtonCotes): ref_weights = (0.5, 0.5) def __init__(self): super().__init__(1) class SimpsonQuadrature(NewtonCotes): ref_weights = (x/6.0 for x in (1, 4, 1)) def __init__(self): super().__init__(2) if name == 'main': qr = TrapezoidQuadrature() a = -3; b = 5; if abs(sum(qr.weights(a,b)) - (b-a)) < 1.e-8: print("Tesing weights: OK") else: print("Testing weights: FAILED") print("TrapezoidQuadrature degree: ", qr.degree) qr = SimpsonQuadrature() if abs(sum(qr.weights(a,b)) - (b-a)) < 1.e-8: print("Tesing weights: OK") else: print("Testing weights: FAILED") print("SimpsonQuadrature degree: ", qr.degree) </sxh> Przykład użycia <sxh python> #! /usr/bin/env python # -*- coding: utf-8 -*- # vim:fenc=utf-8 # # Copyright © 2017 putanowr <putanowr@foo> # # Distributed under terms of the MIT license. “”“ Calculate integral of scalar function in 1D ”“” import sys import os import itertools import newtoncotes class Integrand: """Represents integrand as 1D scalar function """ def __init__(self, expression): self.expression = expression def evaluate(self, x): return eval(self.expression) def __call__(self, x): return self.evaluate(x) class Mesh: """Represents on dimensional mesh """ def __init__(self): self.nodes = list() def load(self, filename): """Read from file a list of nodes""" with open(filename, 'r') as f: for l in f: self.nodes.append(tuple(float(x) for x in l.split())) def nelem(self): return len(self.nodes)-1 class MeshIntegrator: """Calculate integral over a domain discretised by a mesh """ def integrate(self, mesh, integrand): """Integrate function fun using numerical integration on given mesh """ quadrature = newtoncotes.TrapezoidQuadrature(); integral = 0.0 for i in range(mesh.nelem()): integral += self.integrate_element(i, mesh, integrand, quadrature) return integral def make_mesh_fun(self, mesh, fun): xcoord = [ node[0] for node in mesh.nodes ] discrete_fun = [ fun(x) for x in xcoord ] return discrete_fun def integrate_element(self, i, mesh, integrand, quadrature): x1 = mesh.nodes[i][0] x2 = mesh.nodes[i+1][0] qr = quadrature integral = 0.0 for (x, w) in itertools.zip_longest(qr.nodes(x1, x2), qr.weights(x1,x2)): integral += w * integrand(x); return integral def parse_command_line(argv): """Parse command line""" argc = len(sys.argv) if len(sys.argv) < 2: print("Mesh file name must be given") sys.exit(22) meshfile = sys.argv[1] if len(sys.argv) > 2: fun = sys.argv[2] else: print("Using default function f(x) = x^2") fun = "x**2" return [meshfile, fun] def main(): [meshfile, fun] = parse_command_line(sys.argv) mesh = Mesh() mesh.load(meshfile) integrand = Integrand(fun) integrator = MeshIntegrator() integral = integrator.integrate(mesh, integrand) print("Integral of %s is %g" %(fun, integral)) if name == 'main': main() </sxh> pl/teaching/subjects/oop/labs/lab6.txt Last modified: 2017/10/02 15:37(external edit)