#!/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."""
raise NotImplementedError
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."""
# you will need to apply the function f to easch element of the
# vector x. What are several ways to do this? Can you profile
# them to see what differences in timings result for long vectors
# x?
raise NotImplementedError
if __name__ == '__main__':
# Simple tests for trapezoid integrator, when this module is called as a
# script from the command line.
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()
