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""" test_function.py
Tests the PieceWiseConst and PieceWiseLinear functions
Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
from __future__ import print_function
import numpy as np
from copy import copy
import pytest
from numpy.testing import assert_allclose, assert_almost_equal, \
assert_array_equal, assert_array_almost_equal
import pyspike as spk
def test_pwc():
# some random data
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f = spk.PieceWiseConstFunc(x, y)
# function values
assert_allclose(f(0.0), 1.0)
assert_allclose(f(0.5), 1.0)
assert_allclose(f(1.0), 0.25)
assert_allclose(f(2.0), 0.5)
assert_allclose(f(2.25), 1.5)
assert_allclose(f(2.5), 2.25/2)
assert_allclose(f(3.5), 0.75)
assert_allclose(f(4.0), 0.75)
assert_array_equal(f([0.0, 0.5, 1.0, 2.0, 2.25, 2.5, 3.5, 4.0]),
[1.0, 1.0, 0.25, 0.5, 1.5, 2.25/2, 0.75, 0.75])
xp, yp = f.get_plottable_data()
xp_expected = [0.0, 1.0, 1.0, 2.0, 2.0, 2.5, 2.5, 4.0]
yp_expected = [1.0, 1.0, -0.5, -0.5, 1.5, 1.5, 0.75, 0.75]
assert_array_almost_equal(xp, xp_expected, decimal=16)
assert_array_almost_equal(yp, yp_expected, decimal=16)
assert_almost_equal(f.avrg(), (1.0-0.5+0.5*1.5+1.5*0.75)/4.0, decimal=16)
# interval averaging
a = f.avrg([0.5, 3.5])
assert_almost_equal(a, (0.5-0.5+0.5*1.5+1.0*0.75)/3.0, decimal=16)
a = f.avrg([1.5, 3.5])
assert_almost_equal(a, (-0.5*0.5+0.5*1.5+1.0*0.75)/2.0, decimal=16)
a = f.avrg([1.0, 2.0])
assert_almost_equal(a, (1.0*-0.5)/1.0, decimal=16)
a = f.avrg([1.0, 3.5])
assert_almost_equal(a, (-0.5*1.0+0.5*1.5+1.0*0.75)/2.5, decimal=16)
a = f.avrg([1.0, 4.0])
assert_almost_equal(a, (-0.5*1.0+0.5*1.5+1.5*0.75)/3.0, decimal=16)
a = f.avrg([0.0, 2.2])
assert_almost_equal(a, (1.0*1.0-0.5*1.0+0.2*1.5)/2.2, decimal=15)
# averaging over multiple intervals
a = f.avrg([(0.5, 1.5), (1.5, 3.5)])
assert_almost_equal(a, (0.5-0.5+0.5*1.5+1.0*0.75)/3.0, decimal=16)
# averaging over multiple intervals
a = f.avrg([(0.5, 1.5), (2.2, 3.5)])
assert_almost_equal(a, (0.5*1.0-0.5*0.5+0.3*1.5+1.0*0.75)/2.3, decimal=15)
def test_pwc_add():
# some random data
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f = spk.PieceWiseConstFunc(x, y)
f1 = copy(f)
x = [0.0, 0.75, 2.0, 2.5, 2.7, 4.0]
y = [0.5, 1.0, -0.25, 0.0, 1.5]
f2 = spk.PieceWiseConstFunc(x, y)
f1.add(f2)
x_expected = [0.0, 0.75, 1.0, 2.0, 2.5, 2.7, 4.0]
y_expected = [1.5, 2.0, 0.5, 1.25, 0.75, 2.25]
assert_array_almost_equal(f1.x, x_expected, decimal=16)
assert_array_almost_equal(f1.y, y_expected, decimal=16)
f2.add(f)
assert_array_almost_equal(f2.x, x_expected, decimal=16)
assert_array_almost_equal(f2.y, y_expected, decimal=16)
f1.add(f2)
# same x, but y doubled
assert_array_almost_equal(f1.x, f2.x, decimal=16)
assert_array_almost_equal(f1.y, 2*f2.y, decimal=16)
def test_pwc_mul():
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f = spk.PieceWiseConstFunc(x, y)
f.mul_scalar(1.5)
assert_array_almost_equal(f.x, x, decimal=16)
assert_array_almost_equal(f.y, 1.5*np.array(y), decimal=16)
f.mul_scalar(1.0/5.0)
assert_array_almost_equal(f.y, 1.5/5.0*np.array(y), decimal=16)
def test_pwc_avrg():
# some random data
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f1 = spk.PieceWiseConstFunc(x, y)
x = [0.0, 0.75, 2.0, 2.5, 2.7, 4.0]
y = [0.5, 1.0, -0.25, 0.0, 1.5]
f2 = spk.PieceWiseConstFunc(x, y)
f1.add(f2)
f1.mul_scalar(0.5)
x_expected = [0.0, 0.75, 1.0, 2.0, 2.5, 2.7, 4.0]
y_expected = [0.75, 1.0, 0.25, 0.625, 0.375, 1.125]
assert_array_almost_equal(f1.x, x_expected, decimal=16)
assert_array_almost_equal(f1.y, y_expected, decimal=16)
def test_pwc_integral():
# some random data
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f1 = spk.PieceWiseConstFunc(x, y)
# test full interval
full = 1.0*1.0 + 1.0*-0.5 + 0.5*1.5 + 1.5*0.75;
assert_allclose(f1.integral(), full)
assert_allclose(f1.integral((np.min(x),np.max(x))), full)
# test part interval, spanning an edge
assert_allclose(f1.integral((0.5,1.5)), 0.5*1.0 + 0.5*-0.5)
# test part interval, just over two edges
assert_almost_equal(f1.integral((1.0-1e-16,2+1e-16)), 1.0*-0.5, decimal=14)
# test part interval, between two edges
assert_allclose(f1.integral((1.0,2.0)), 1.0*-0.5)
assert_allclose(f1.integral((1.2,1.7)), (1.7-1.2)*-0.5)
# test part interval, start to before and after edge
assert_allclose(f1.integral((0.0,0.7)), 0.7*1.0)
assert_allclose(f1.integral((0.0,1.1)), 1.0*1.0+0.1*-0.5)
# test part interval, before and after edge till end
assert_allclose(f1.integral((2.6,4.0)), (4.0-2.6)*0.75)
assert_allclose(f1.integral((2.4,4.0)), (2.5-2.4)*1.5+(4-2.5)*0.75)
def test_pwc_integral_bad_bounds_inv():
with pytest.raises(ValueError):
# some random data
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f1 = spk.PieceWiseConstFunc(x, y)
f1.integral((3,2))
def test_pwc_integral_bad_bounds_oob_1():
with pytest.raises(ValueError):
# some random data
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f1 = spk.PieceWiseConstFunc(x, y)
f1.integral((1,6))
def test_pwc_integral_bad_bounds_oob_2():
with pytest.raises(ValueError):
# some random data
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [1.0, -0.5, 1.5, 0.75]
f1 = spk.PieceWiseConstFunc(x, y)
f1.integral((-1,3))
def test_pwl():
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y1 = [1.0, -0.5, 1.5, 0.75]
y2 = [1.5, -0.4, 1.5, 0.25]
f = spk.PieceWiseLinFunc(x, y1, y2)
# function values
assert_allclose(f(0.0), 1.0)
assert_allclose(f(0.5), 1.25)
assert_allclose(f(1.0), 0.5)
assert_allclose(f(2.0), 1.1/2)
assert_allclose(f(2.25), 1.5)
assert_allclose(f(2.5), 2.25/2)
assert_allclose(f(3.5), 0.75-0.5*1.0/1.5)
assert_allclose(f(4.0), 0.25)
assert_array_equal(f([0.0, 0.5, 1.0, 2.0, 2.25, 2.5, 3.5, 4.0]),
[1.0, 1.25, 0.5, 0.55, 1.5, 2.25/2, 0.75-0.5/1.5, 0.25])
xp, yp = f.get_plottable_data()
xp_expected = [0.0, 1.0, 1.0, 2.0, 2.0, 2.5, 2.5, 4.0]
yp_expected = [1.0, 1.5, -0.5, -0.4, 1.5, 1.5, 0.75, 0.25]
assert_array_almost_equal(xp, xp_expected, decimal=16)
assert_array_almost_equal(yp, yp_expected, decimal=16)
avrg_expected = (1.25 - 0.45 + 0.75 + 1.5*0.5) / 4.0
assert_almost_equal(f.avrg(), avrg_expected, decimal=16)
# interval averaging
a = f.avrg([0.5, 2.5])
assert_almost_equal(a, (1.375*0.5 - 0.45 + 0.75)/2.0, decimal=16)
a = f.avrg([1.5, 3.5])
assert_almost_equal(a, (-0.425*0.5 + 0.75 + (0.75+0.75-0.5/1.5)/2) / 2.0,
decimal=16)
a = f.avrg((1.0, 3.5))
assert_almost_equal(a, (-0.45 + 0.75 + (0.75+0.75-0.5/1.5)/2) / 2.5,
decimal=16)
a = f.avrg([1.0, 4.0])
assert_almost_equal(a, (-0.45 + 0.75 + 1.5*0.5) / 3.0, decimal=16)
# interval between support points
a = f.avrg([1.1, 1.5])
assert_almost_equal(a, (-0.5+0.1*0.1 - 0.45) * 0.5, decimal=14)
# starting at a support point
a = f.avrg([1.0, 1.5])
assert_almost_equal(a, (-0.5 - 0.45) * 0.5, decimal=14)
# start and end at support point
a = f.avrg([1.0, 2.0])
assert_almost_equal(a, (-0.5 - 0.4) * 0.5, decimal=14)
# averaging over multiple intervals
a = f.avrg([(0.5, 1.5), (1.5, 2.5)])
assert_almost_equal(a, (1.375*0.5 - 0.45 + 0.75)/2.0, decimal=16)
def test_pwl_add():
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y1 = [1.0, -0.5, 1.5, 0.75]
y2 = [1.5, -0.4, 1.5, 0.25]
f = spk.PieceWiseLinFunc(x, y1, y2)
f1 = copy(f)
x = [0.0, 0.75, 2.0, 2.5, 2.7, 4.0]
y1 = [0.5, 1.0, -0.25, 0.0, 1.5]
y2 = [0.8, 0.2, -1.0, 0.0, 2.0]
f2 = spk.PieceWiseLinFunc(x, y1, y2)
f1.add(f2)
x_expected = [0.0, 0.75, 1.0, 2.0, 2.5, 2.7, 4.0]
y1_expected = [1.5, 1.0+1.0+0.5*0.75, -0.5+1.0-0.8*0.25/1.25, 1.5-0.25,
0.75, 1.5+0.75-0.5*0.2/1.5]
y2_expected = [0.8+1.0+0.5*0.75, 1.5+1.0-0.8*0.25/1.25, -0.4+0.2, 1.5-1.0,
0.75-0.5*0.2/1.5, 2.25]
assert_array_almost_equal(f1.x, x_expected, decimal=16)
assert_array_almost_equal(f1.y1, y1_expected, decimal=16)
assert_array_almost_equal(f1.y2, y2_expected, decimal=16)
f2.add(f)
assert_array_almost_equal(f2.x, x_expected, decimal=16)
assert_array_almost_equal(f2.y1, y1_expected, decimal=16)
assert_array_almost_equal(f2.y2, y2_expected, decimal=16)
f1.add(f2)
# same x, but y doubled
assert_array_almost_equal(f1.x, f2.x, decimal=16)
assert_array_almost_equal(f1.y1, 2*f2.y1, decimal=16)
assert_array_almost_equal(f1.y2, 2*f2.y2, decimal=16)
def test_pwl_mul():
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y1 = [1.0, -0.5, 1.5, 0.75]
y2 = [1.5, -0.4, 1.5, 0.25]
f = spk.PieceWiseLinFunc(x, y1, y2)
f.mul_scalar(1.5)
assert_array_almost_equal(f.x, x, decimal=16)
assert_array_almost_equal(f.y1, 1.5*np.array(y1), decimal=16)
assert_array_almost_equal(f.y2, 1.5*np.array(y2), decimal=16)
f.mul_scalar(1.0/5.0)
assert_array_almost_equal(f.y1, 1.5/5.0*np.array(y1), decimal=16)
assert_array_almost_equal(f.y2, 1.5/5.0*np.array(y2), decimal=16)
def test_pwl_avrg():
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y1 = [1.0, -0.5, 1.5, 0.75]
y2 = [1.5, -0.4, 1.5, 0.25]
f1 = spk.PieceWiseLinFunc(x, y1, y2)
x = [0.0, 0.75, 2.0, 2.5, 2.7, 4.0]
y1 = [0.5, 1.0, -0.25, 0.0, 1.5]
y2 = [0.8, 0.2, -1.0, 0.0, 2.0]
f2 = spk.PieceWiseLinFunc(x, y1, y2)
x_expected = [0.0, 0.75, 1.0, 2.0, 2.5, 2.7, 4.0]
y1_expected = np.array([1.5, 1.0+1.0+0.5*0.75, -0.5+1.0-0.8*0.25/1.25,
1.5-0.25, 0.75, 1.5+0.75-0.5*0.2/1.5]) / 2
y2_expected = np.array([0.8+1.0+0.5*0.75, 1.5+1.0-0.8*0.25/1.25, -0.4+0.2,
1.5-1.0, 0.75-0.5*0.2/1.5, 2.25]) / 2
f1.add(f2)
f1.mul_scalar(0.5)
assert_array_almost_equal(f1.x, x_expected, decimal=16)
assert_array_almost_equal(f1.y1, y1_expected, decimal=16)
assert_array_almost_equal(f1.y2, y2_expected, decimal=16)
def test_df():
# testing discrete function
x = [0.0, 1.0, 2.0, 2.5, 4.0]
y = [0.0, 1.0, 1.0, 0.0, 1.0]
mp = [1.0, 2.0, 1.0, 2.0, 1.0]
f = spk.DiscreteFunc(x, y, mp)
xp, yp = f.get_plottable_data()
xp_expected = [0.0, 1.0, 2.0, 2.5, 4.0]
yp_expected = [0.0, 0.5, 1.0, 0.0, 1.0]
assert_array_almost_equal(xp, xp_expected, decimal=16)
assert_array_almost_equal(yp, yp_expected, decimal=16)
assert_almost_equal(f.avrg(), 2.0/5.0, decimal=16)
# interval averaging
a = f.avrg([0.5, 2.4])
assert_almost_equal(a, 2.0/3.0, decimal=16)
a = f.avrg([1.5, 3.5])
assert_almost_equal(a, 1.0/3.0, decimal=16)
a = f.avrg((0.9, 3.5))
assert_almost_equal(a, 2.0/5.0, decimal=16)
a = f.avrg([1.1, 4.0])
assert_almost_equal(a, 1.0/3.0, decimal=16)
# averaging over multiple intervals
a = f.avrg([(0.5, 1.5), (1.5, 2.6)])
assert_almost_equal(a, 2.0/5.0, decimal=16)
if __name__ == "__main__":
test_pwc()
test_pwc_add()
test_pwc_mul()
test_pwc_avrg()
test_pwl()
test_pwl_add()
test_pwl_mul()
test_pwl_avrg()
test_df()
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