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Diffstat (limited to 'test/test_function.py')
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diff --git a/test/test_function.py b/test/test_function.py new file mode 100644 index 0000000..6c04839 --- /dev/null +++ b/test/test_function.py @@ -0,0 +1,344 @@ +""" 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 +from nose.tools import raises +from numpy.testing import assert_equal, 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_equal(f(0.0), 1.0) + assert_equal(f(0.5), 1.0) + assert_equal(f(1.0), 0.25) + assert_equal(f(2.0), 0.5) + assert_equal(f(2.25), 1.5) + assert_equal(f(2.5), 2.25/2) + assert_equal(f(3.5), 0.75) + assert_equal(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_equal(f1.integral(), full) + assert_equal(f1.integral((np.min(x),np.max(x))), full) + # test part interval, spanning an edge + assert_equal(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_equal(f1.integral((1.0,2.0)), 1.0*-0.5) + assert_equal(f1.integral((1.2,1.7)), (1.7-1.2)*-0.5) + # test part interval, start to before and after edge + assert_equal(f1.integral((0.0,0.7)), 0.7*1.0) + assert_equal(f1.integral((0.0,1.1)), 1.0*1.0+0.1*-0.5) + # test part interval, before and after edge till end + assert_equal(f1.integral((2.6,4.0)), (4.0-2.6)*0.75) + assert_equal(f1.integral((2.4,4.0)), (2.5-2.4)*1.5+(4-2.5)*0.75) + +@raises(ValueError) +def test_pwc_integral_bad_bounds_inv(): + # 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)) + +@raises(ValueError) +def test_pwc_integral_bad_bounds_oob_1(): + # 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)) + +@raises(ValueError) +def test_pwc_integral_bad_bounds_oob_2(): + # 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_equal(f(0.0), 1.0) + assert_equal(f(0.5), 1.25) + assert_equal(f(1.0), 0.5) + assert_equal(f(2.0), 1.1/2) + assert_equal(f(2.25), 1.5) + assert_equal(f(2.5), 2.25/2) + assert_equal(f(3.5), 0.75-0.5*1.0/1.5) + assert_equal(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() |