def test_interval():
"""Tests known special cases of the interval.
In this particular case, interval 0 to 1 with step size .2 for f(x) = 2x"""
def f(x):
value = 2 * x
return value
actual = [f(0), f(.2), f(.4), f(.6), f(.8), f(1)]
trial = gaussian.interval(f, 0, 1, .2)
print("Testing f(0):", actual[0], " ?= ", trial[0])
nose.tools.assert_almost_equal(actual[0], trial[0], 4)
print("Testing f(.2):", actual[1], " ?= ", trial[1])
nose.tools.assert_almost_equal(actual[1], trial[1], 4)
print("Testing f(.4):", actual[2], " ?= ", trial[2])
nose.tools.assert_almost_equal(actual[2], trial[2], 4)
print("Testing f(.6):", actual[3], " ?= ", trial[3])
nose.tools.assert_almost_equal(actual[3], trial[3], 4)
print("Testing interval f(.8):", actual[4], " ?= ", trial[4])
nose.tools.assert_almost_equal(actual[4], trial[4], 4)
print("Testing interval f(1.0):", actual[5], " ?= ", trial[5])
nose.tools.assert_almost_equal(actual[5], trial[5], 4)
len_actual = len(actual)
len_trial = len(trial)
print("Testing length of intervals:", len_actual, " ?= ", len_trial)
nose.tools.assert_almost_equal(len_actual, len_trial)
def test_gauss_norm():
"""Tests how accurately interval and integrate functions work on g when dx is samll.
- integrate(interval(g,0,4,.05),.05)
"""
actual = 0.49996821729336 #using online trapazoidal rule calcuator
trial = gaussian.integrate(gaussian.interval(gaussian.g, 0, 4, .05), .05)
print("Testing integrate(interval(g,0,4,.05),.05): ", actual, " ?= ",
trial)
nose.tools.assert_almost_equal(actual, trial, 4)
def test_interval():
"""Tests interval() with the following trials:
- interval(x**2,0,10,1) ?= [0,1,4,9,16,25,36,49,64,81,100]
"""
def f(x):
return x**2
actual = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
trial = gaussian.interval(f, 0, 10, 1)
print("Testing interval(x**2,0,10,1): ", actual, " ?= ", trial)
nose.tools.assert_almost_equal(actual, trial, 4)
def test_gauss_norm():
"""Checks for correct integral of gaussian function when dx is small
Test: interval from -5 to 5 with dx = .000001"""
actual = .999999
# This value was calculated with an online definite integral solver.
trial = gaussian.integrate(gaussian.interval(gaussian.g, -5, 5, .000001),
.000001)
print(
"This tests the interval from -5 to 5 with small step size of .000001: ",
actual, "?=", trial)
nose.tools.assert_almost_equal(actual, trial, 3)
def test_integrate():
"""Checks the integration for correctness
Test: integrate f(x) = 2x from 0 to 2 with spacing of steps at .000001 (dx=.000001)"""
actual = 4
def f(x):
value = 2 * x
return value
# This value was calculated with an online definite integral solver.
i = gaussian.interval(f, 0, 2, .000001)
trial = gaussian.integrate(i, .000001)
print(
"This tests the integration of 2x from 0 to 2 with step size of .000001: ",
actual, "?=", trial)
nose.tools.assert_almost_equal(actual, trial, 3)