Kod źródłowy: integrand_with_call.py
<sxh python> # -*- coding: utf-8 -*- # vim:fenc=utf-8 # # Copyright © 2017 putanowr <putanowr@foo> # # Distributed under terms of the MIT license.
“”“ Define integrand as scalar function in R. ”“”
class Integrand:
def __init__(self, expression): self.expression = expression
def evaluate(self, x): return eval(self.expression)
def __call__(self, x): return self.evaluate(x)
if name == 'main':
f = Integrand("x**2") z = f(4) print("Integrand value %f" % z,)
</sxh>
Obliczanie całki z funkcji jednej zmiennej metodą trapezów na siatce nierównomiernej
Kod źródłowy: calculate_integral.py
<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
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 """ mesh_fun = self.make_mesh_fun(mesh, integrand) integral = 0.0 for i in range(mesh.nelem()): integral += self.integrate_element(i, mesh, mesh_fun) 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, mesh_fun):
x1 = mesh.nodes[i][0] x2 = mesh.nodes[i+1][0] f1 = mesh_fun[i] f2 = mesh_fun[i+1] h = x2 - x1 integral = h * (f1+f2) / 2.0 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>
Version with quadrature defined as a class.
<sxh python> import sys import os import itertools
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 TrapezoidQuadrature:
ref_nodes = (-1,1) ref_weights = (0.5, 0.5) def nodes(self, a, b): return (a,b) def weights(self, a, b): return ((b-a)*x for x in self.ref_weights)
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 = 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>