#!/usr/bin/env python
"""Simple trapezoid-rule integrator."""
import numpy as N
def trapz(x, y):
"""Simple trapezoid integrator for sequence-based innput.
Inputs:
- x,y: arrays of the same length.
Output:
- The result of applying the trapezoid rule to the input, assuming that
y[i] = f(x[i]) for some function f to be integrated.
Minimally modified from matplotlib.mlab."""
# Sanity checks
if len(x)!=len(y):
raise ValueError('x and y must have the same length')
if len(x)<2:
raise ValueError('x and y must have > 1 element')
# Efficient application of trapezoid rule via numpy
return 0.5*((x[1:]-x[:-1])*(y[1:]+y[:-1])).sum()
def trapzf(f,a,b,npts=100):
"""Simple trapezoid-based integrator.
Inputs:
- f: function to be integrated.
- a,b: limits of integration.
Optional inputs:
- npts(100): the number of equally spaced points to sample f at, between
a and b.
Output:
- The value of the trapezoid-rule approximation to the integral."""
# Generate an equally spaced grid to sample the function at
x = N.linspace(a,b,npts)
# For an equispaced grid, the x spacing can just be read off from the first
# two points and factored out of the summation.
dx = x[1]-x[0]
# Sample the input function at all values of x
y = N.array(map(f,x))
# Compute the trapezoid rule sum for the final result
return 0.5*dx*(y[1:]+y[:-1]).sum()
if __name__ == '__main__':
# Simple tests for trapezoid integrator, when this module is called as a
# script from the command line. From ipython, run it via:
#
# run -e trapezoid
#
# so that ipython ignores the SystemExit exception automatically raised by
# the unittest module at the end.
import unittest
import numpy.testing as ntest
def square(x): return x**2
class trapzTestCase(unittest.TestCase):
def test_err(self):
self.assertRaises(ValueError,trapz,range(2),range(3))
def test_call(self):
x = N.linspace(0,1,100)
y = N.array(map(square,x))
ntest.assert_almost_equal(trapz(x,y),1./3,4)
class trapzfTestCase(unittest.TestCase):
def test_square(self):
ntest.assert_almost_equal(trapzf(square,0,1),1./3,4)
def test_square2(self):
ntest.assert_almost_equal(trapzf(square,0,3,350),9.0,4)
unittest.main()
