diff options
Diffstat (limited to 'test')
-rwxr-xr-x | test/PySpike_testdata.txt | 43 | ||||
-rw-r--r-- | test/SPIKE_Sync_Test.txt | 100 | ||||
-rw-r--r-- | test/numeric/regression_random_results_cSPIKY.mat | bin | 0 -> 149104 bytes | |||
-rw-r--r-- | test/numeric/regression_random_spikes.mat | bin | 0 -> 16241579 bytes | |||
-rw-r--r-- | test/numeric/test_regression_random_spikes.py | 138 | ||||
-rw-r--r-- | test/test_directionality.py | 97 | ||||
-rw-r--r-- | test/test_distance.py | 477 | ||||
-rw-r--r-- | test/test_empty.py | 163 | ||||
-rw-r--r-- | test/test_function.py | 344 | ||||
-rw-r--r-- | test/test_generic_interfaces.py | 105 | ||||
-rw-r--r-- | test/test_regression/test_regression_15.py | 81 | ||||
-rw-r--r-- | test/test_save_load.py | 42 | ||||
-rw-r--r-- | test/test_spikes.py | 101 | ||||
-rw-r--r-- | test/test_sync_filter.py | 95 | ||||
-rw-r--r-- | test/time_series.txt | 80 | ||||
-rw-r--r-- | test/time_series_spike_trains.txt | 80 |
16 files changed, 1946 insertions, 0 deletions
diff --git a/test/PySpike_testdata.txt b/test/PySpike_testdata.txt new file mode 100755 index 0000000..c8bea67 --- /dev/null +++ b/test/PySpike_testdata.txt @@ -0,0 +1,43 @@ +64.886 305.81 696 937.77 1059.7 1322.2 1576.1 1808.1 2121.5 2381.1 2728.6 2966.9 3223.7 3473.7 3644.3 3936.3 +65.553 307.49 696.63 948.66 1070.4 1312.2 1712.7 1934.3 2117.6 2356.9 2727.3 2980.6 3226.9 3475.7 3726.4 3944 +# test comment +69.064 319.1 688.32 947.85 1071.8 1300.8 1697.2 1930.6 2139.4 2354.2 2723.7 2963.6 3221.3 3470.1 +59.955 313.83 692.23 955.95 1070.4 1319.6 1681.9 1963.5 2151.4 2373.8 2729.4 2971.2 3220.2 3475.5 3632.3 3788.9 +# empty line + +59.977 306.84 686.09 935.08 1059.9 1325.9 1543.4 1821.9 2150.2 2390.4 2724.5 2969.6 3222.5 3471.5 3576 3913.9 +66.415 313.41 688.83 931.43 1051.8 1304.6 1555.6 1820.2 2150.5 2383.1 2723.4 2947.7 3196.6 3443.5 3575 3804.9 +66.449 311.02 689.26 947.12 1058.9 1286.6 1708.2 1957.3 2124.8 2375.7 2709.4 2977.6 3191.1 3449.6 3590.4 3831.2 +63.764 318.45 697.48 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b/test/numeric/test_regression_random_spikes.py @@ -0,0 +1,138 @@ +""" regression benchmark + +Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License +""" +from __future__ import print_function + +import numpy as np +from scipy.io import loadmat +import pyspike as spk + +from numpy.testing import assert_almost_equal + +spk.disable_backend_warning = True + + +def test_regression_random(): + + spike_file = "test/numeric/regression_random_spikes.mat" + spikes_name = "spikes" + result_name = "Distances" + result_file = "test/numeric/regression_random_results_cSPIKY.mat" + + spike_train_sets = loadmat(spike_file)[spikes_name][0] + results_cSPIKY = loadmat(result_file)[result_name] + + for i, spike_train_data in enumerate(spike_train_sets): + spike_trains = [] + for spikes in spike_train_data[0]: + spike_trains.append(spk.SpikeTrain(spikes.flatten(), 100.0)) + + isi = spk.isi_distance_multi(spike_trains) + isi_prof = spk.isi_profile_multi(spike_trains).avrg() + + spike = spk.spike_distance_multi(spike_trains) + spike_prof = spk.spike_profile_multi(spike_trains).avrg() + + spike_sync = spk.spike_sync_multi(spike_trains) + spike_sync_prof = spk.spike_sync_profile_multi(spike_trains).avrg() + + assert_almost_equal(isi, results_cSPIKY[i][0], decimal=14, + err_msg="Index: %d, ISI" % i) + assert_almost_equal(isi_prof, results_cSPIKY[i][0], decimal=14, + err_msg="Index: %d, ISI" % i) + + assert_almost_equal(spike, results_cSPIKY[i][1], decimal=14, + err_msg="Index: %d, SPIKE" % i) + assert_almost_equal(spike_prof, results_cSPIKY[i][1], decimal=14, + err_msg="Index: %d, SPIKE" % i) + + assert_almost_equal(spike_sync, spike_sync_prof, decimal=14, + err_msg="Index: %d, SPIKE-Sync" % i) + + +def check_regression_dataset(spike_file="benchmark.mat", + spikes_name="spikes", + result_file="results_cSPIKY.mat", + result_name="Distances"): + """ Debuging function """ + np.set_printoptions(precision=15) + + spike_train_sets = loadmat(spike_file)[spikes_name][0] + + results_cSPIKY = loadmat(result_file)[result_name] + + err_max = 0.0 + err_max_ind = -1 + err_count = 0 + + for i, spike_train_data in enumerate(spike_train_sets): + spike_trains = [] + for spikes in spike_train_data[0]: + spike_trains.append(spk.SpikeTrain(spikes.flatten(), 100.0)) + + isi = spk.isi_distance_multi(spike_trains) + spike = spk.spike_distance_multi(spike_trains) + # spike_sync = spk.spike_sync_multi(spike_trains) + + if abs(isi - results_cSPIKY[i][0]) > 1E-14: + print("Error in ISI:", i, isi, results_cSPIKY[i][0]) + print("Spike trains:") + for st in spike_trains: + print(st.spikes) + + err = abs(spike - results_cSPIKY[i][1]) + if err > 1E-14: + err_count += 1 + if err > err_max: + err_max = err + err_max_ind = i + + print("Total Errors:", err_count) + + if err_max_ind > -1: + print("Max SPIKE distance error:", err_max, "at index:", err_max_ind) + spike_train_data = spike_train_sets[err_max_ind] + for spikes in spike_train_data[0]: + print(spikes.flatten()) + + +def check_single_spike_train_set(index): + """ Debuging function """ + np.set_printoptions(precision=15) + spike_file = "regression_random_spikes.mat" + spikes_name = "spikes" + result_name = "Distances" + result_file = "regression_random_results_cSPIKY.mat" + + spike_train_sets = loadmat(spike_file)[spikes_name][0] + + results_cSPIKY = loadmat(result_file)[result_name] + + spike_train_data = spike_train_sets[index] + + spike_trains = [] + N = 0 + for spikes in spike_train_data[0]: + N += len(spikes.flatten()) + print("Spikes:", len(spikes.flatten())) + spikes_array = spikes.flatten() + if len(spikes_array > 0) and (spikes_array[-1] > 100.0): + spikes_array[-1] = 100.0 + spike_trains.append(spk.SpikeTrain(spikes_array, 100.0)) + print(spike_trains[-1].spikes) + + print(N) + + print(spk.spike_sync_multi(spike_trains)) + + print(spk.spike_sync_profile_multi(spike_trains).integral()) + + +if __name__ == "__main__": + + # test_regression_random() + # check_regression_dataset() + check_single_spike_train_set(4) diff --git a/test/test_directionality.py b/test/test_directionality.py new file mode 100644 index 0000000..c2e9bfe --- /dev/null +++ b/test/test_directionality.py @@ -0,0 +1,97 @@ +""" test_directionality.py + +Tests the directionality functions + +Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License + +""" + +import numpy as np +from numpy.testing import assert_equal, assert_almost_equal, \ + assert_array_equal + +import pyspike as spk +from pyspike import SpikeTrain, DiscreteFunc + + +def test_spike_directionality(): + st1 = SpikeTrain([100, 200, 300], [0, 1000]) + st2 = SpikeTrain([105, 205, 300], [0, 1000]) + assert_almost_equal(spk.spike_directionality(st1, st2), 2.0/3.0) + assert_almost_equal(spk.spike_directionality(st1, st2, normalize=False), + 2.0) + + # exchange order of spike trains should give exact negative profile + assert_almost_equal(spk.spike_directionality(st2, st1), -2.0/3.0) + assert_almost_equal(spk.spike_directionality(st2, st1, normalize=False), + -2.0) + + st3 = SpikeTrain([105, 195, 500], [0, 1000]) + assert_almost_equal(spk.spike_directionality(st1, st3), 0.0) + assert_almost_equal(spk.spike_directionality(st1, st3, normalize=False), + 0.0) + assert_almost_equal(spk.spike_directionality(st3, st1), 0.0) + + D = spk.spike_directionality_matrix([st1, st2, st3], normalize=False) + D_expected = np.array([[0, 2.0, 0.0], [-2.0, 0.0, -1.0], [0.0, 1.0, 0.0]]) + assert_array_equal(D, D_expected) + + dir_profs = spk.spike_directionality_values([st1, st2, st3]) + assert_array_equal(dir_profs[0], [1.0, 0.0, 0.0]) + assert_array_equal(dir_profs[1], [-0.5, -1.0, 0.0]) + + +def test_spike_train_order(): + st1 = SpikeTrain([100, 200, 300], [0, 1000]) + st2 = SpikeTrain([105, 205, 300], [0, 1000]) + st3 = SpikeTrain([105, 195, 500], [0, 1000]) + + expected_x12 = np.array([0, 100, 105, 200, 205, 300, 1000]) + expected_y12 = np.array([1, 1, 1, 1, 1, 0, 0]) + expected_mp12 = np.array([1, 1, 1, 1, 1, 2, 2]) + + f = spk.spike_train_order_profile(st1, st2) + + assert f.almost_equal(DiscreteFunc(expected_x12, expected_y12, + expected_mp12)) + assert_almost_equal(f.avrg(), 2.0/3.0) + assert_almost_equal(f.avrg(normalize=False), 4.0) + assert_almost_equal(spk.spike_train_order(st1, st2), 2.0/3.0) + assert_almost_equal(spk.spike_train_order(st1, st2, normalize=False), 4.0) + + expected_x23 = np.array([0, 105, 195, 205, 300, 500, 1000]) + expected_y23 = np.array([0, 0, -1, -1, 0, 0, 0]) + expected_mp23 = np.array([2, 2, 1, 1, 1, 1, 1]) + + f = spk.spike_train_order_profile(st2, st3) + + assert_array_equal(f.x, expected_x23) + assert_array_equal(f.y, expected_y23) + assert_array_equal(f.mp, expected_mp23) + assert f.almost_equal(DiscreteFunc(expected_x23, expected_y23, + expected_mp23)) + assert_almost_equal(f.avrg(), -1.0/3.0) + assert_almost_equal(f.avrg(normalize=False), -2.0) + assert_almost_equal(spk.spike_train_order(st2, st3), -1.0/3.0) + assert_almost_equal(spk.spike_train_order(st2, st3, normalize=False), -2.0) + + f = spk.spike_train_order_profile_multi([st1, st2, st3]) + + expected_x = np.array([0, 100, 105, 195, 200, 205, 300, 500, 1000]) + expected_y = np.array([2, 2, 2, -2, 0, 0, 0, 0, 0]) + expected_mp = np.array([2, 2, 4, 2, 2, 2, 4, 2, 2]) + + assert_array_equal(f.x, expected_x) + assert_array_equal(f.y, expected_y) + assert_array_equal(f.mp, expected_mp) + + # Averaging the profile should be the same as computing the synfire indicator directly. + assert_almost_equal(f.avrg(), spk.spike_train_order([st1, st2, st3])) + + # We can also compute the synfire indicator from the Directionality Matrix: + D_matrix = spk.spike_directionality_matrix([st1, st2, st3], normalize=False) + num_spikes = np.sum(len(st) for st in [st1, st2, st3]) + syn_fire = np.sum(np.triu(D_matrix)) / num_spikes + assert_almost_equal(f.avrg(), syn_fire) diff --git a/test/test_distance.py b/test/test_distance.py new file mode 100644 index 0000000..fe09f34 --- /dev/null +++ b/test/test_distance.py @@ -0,0 +1,477 @@ +""" test_distance.py + +Tests the isi- and spike-distance computation + +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 numpy.testing import assert_equal, assert_almost_equal, \ + assert_array_almost_equal + +import pyspike as spk +from pyspike import SpikeTrain + +import os +TEST_PATH = os.path.dirname(os.path.realpath(__file__)) + + +def test_isi(): + # generate two spike trains: + t1 = SpikeTrain([0.2, 0.4, 0.6, 0.7], 1.0) + t2 = SpikeTrain([0.3, 0.45, 0.8, 0.9, 0.95], 1.0) + + # pen&paper calculation of the isi distance + expected_times = [0.0, 0.2, 0.3, 0.4, 0.45, 0.6, 0.7, 0.8, 0.9, 0.95, 1.0] + expected_isi = [0.1/0.3, 0.1/0.3, 0.05/0.2, 0.05/0.2, 0.15/0.35, + 0.25/0.35, 0.05/0.35, 0.2/0.3, 0.25/0.3, 0.25/0.3] + expected_times = np.array(expected_times) + expected_isi = np.array(expected_isi) + + expected_isi_val = sum((expected_times[1:] - expected_times[:-1]) * + expected_isi)/(expected_times[-1]-expected_times[0]) + + f = spk.isi_profile(t1, t2) + + # print("ISI: ", f.y) + print("ISI value:", expected_isi_val) + + assert_equal(f.x, expected_times) + assert_array_almost_equal(f.y, expected_isi, decimal=15) + assert_equal(f.avrg(), expected_isi_val) + assert_equal(spk.isi_distance(t1, t2), expected_isi_val) + + # check with some equal spike times + t1 = SpikeTrain([0.2, 0.4, 0.6], [0.0, 1.0]) + t2 = SpikeTrain([0.1, 0.4, 0.5, 0.6], [0.0, 1.0]) + + expected_times = [0.0, 0.1, 0.2, 0.4, 0.5, 0.6, 1.0] + expected_isi = [0.1/0.3, 0.1/0.3, 0.1/0.3, 0.1/0.2, 0.1/0.2, 0.0/0.5] + expected_times = np.array(expected_times) + expected_isi = np.array(expected_isi) + + expected_isi_val = sum((expected_times[1:] - expected_times[:-1]) * + expected_isi)/(expected_times[-1]-expected_times[0]) + + f = spk.isi_profile(t1, t2) + + assert_equal(f.x, expected_times) + assert_array_almost_equal(f.y, expected_isi, decimal=15) + assert_equal(f.avrg(), expected_isi_val) + assert_equal(spk.isi_distance(t1, t2), expected_isi_val) + + +def test_spike(): + # generate two spike trains: + t1 = SpikeTrain([0.0, 2.0, 5.0, 8.0], 10.0) + t2 = SpikeTrain([0.0, 1.0, 5.0, 9.0], 10.0) + + expected_times = np.array([0.0, 1.0, 2.0, 5.0, 8.0, 9.0, 10.0]) + + f = spk.spike_profile(t1, t2) + + assert_equal(f.x, expected_times) + + # from SPIKY: + y_all = np.array([0.000000000000000000, 0.555555555555555580, + 0.222222222222222210, 0.305555555555555580, + 0.255102040816326536, 0.000000000000000000, + 0.000000000000000000, 0.255102040816326536, + 0.255102040816326536, 0.285714285714285698, + 0.285714285714285698, 0.285714285714285698]) + + #assert_array_almost_equal(f.y1, y_all[::2]) + assert_array_almost_equal(f.y2, y_all[1::2]) + + assert_almost_equal(f.avrg(), 0.186309523809523814, decimal=15) + assert_equal(spk.spike_distance(t1, t2), f.avrg()) + + t1 = SpikeTrain([0.2, 0.4, 0.6, 0.7], 1.0) + t2 = SpikeTrain([0.3, 0.45, 0.8, 0.9, 0.95], 1.0) + + # pen&paper calculation of the spike distance + expected_times = [0.0, 0.2, 0.3, 0.4, 0.45, 0.6, 0.7, 0.8, 0.9, 0.95, 1.0] + s1 = np.array([0.1, 0.1, (0.1*0.1+0.05*0.1)/0.2, 0.05, (0.05*0.15 * 2)/0.2, + 0.15, 0.1, (0.1*0.1+0.1*0.2)/0.3, (0.1*0.2+0.1*0.1)/0.3, + (0.1*0.05+0.1*0.25)/0.3, 0.1]) + s2 = np.array([0.1, (0.1*0.2+0.1*0.1)/0.3, 0.1, (0.1*0.05 * 2)/.15, 0.05, + (0.05*0.2+0.1*0.15)/0.35, (0.05*0.1+0.1*0.25)/0.35, + 0.1, 0.1, 0.05, 0.05]) + isi1 = np.array([0.2, 0.2, 0.2, 0.2, 0.2, 0.1, 0.3, 0.3, 0.3, 0.3]) + isi2 = np.array([0.3, 0.3, 0.15, 0.15, 0.35, 0.35, 0.35, 0.1, 0.05, 0.05]) + expected_y1 = (s1[:-1]*isi2+s2[:-1]*isi1) / (0.5*(isi1+isi2)**2) + expected_y2 = (s1[1:]*isi2+s2[1:]*isi1) / (0.5*(isi1+isi2)**2) + + expected_times = np.array(expected_times) + expected_y1 = np.array(expected_y1) + expected_y2 = np.array(expected_y2) + expected_spike_val = sum((expected_times[1:] - expected_times[:-1]) * + (expected_y1+expected_y2)/2) + expected_spike_val /= (expected_times[-1]-expected_times[0]) + + print("SPIKE value:", expected_spike_val) + + f = spk.spike_profile(t1, t2) + + assert_equal(f.x, expected_times) + assert_array_almost_equal(f.y1, expected_y1, decimal=15) + assert_array_almost_equal(f.y2, expected_y2, decimal=15) + assert_almost_equal(f.avrg(), expected_spike_val, decimal=15) + assert_almost_equal(spk.spike_distance(t1, t2), expected_spike_val, + decimal=15) + + # check with some equal spike times + t1 = SpikeTrain([0.2, 0.4, 0.6], [0.0, 1.0]) + t2 = SpikeTrain([0.1, 0.4, 0.5, 0.6], [0.0, 1.0]) + + expected_times = [0.0, 0.1, 0.2, 0.4, 0.5, 0.6, 1.0] + # due to the edge correction in the beginning, s1 and s2 are different + # for left and right values + s1_r = np.array([0.1, (0.1*0.1+0.1*0.1)/0.2, 0.1, 0.0, 0.0, 0.0, 0.0]) + s1_l = np.array([0.1, (0.1*0.1+0.1*0.1)/0.2, 0.1, 0.0, 0.0, 0.0, 0.0]) + # s2_r = np.array([0.1*0.1/0.3, 0.1*0.3/0.3, 0.1*0.2/0.3, + # 0.0, 0.1, 0.0, 0.0]) + # s2_l = np.array([0.1*0.1/0.3, 0.1*0.1/0.3, 0.1*0.2/0.3, 0.0, + # 0.1, 0.0, 0.0]) + # eero's edge correction: + s2_r = np.array([0.1, 0.1*0.3/0.3, 0.1*0.2/0.3, + 0.0, 0.1, 0.0, 0.0]) + s2_l = np.array([0.1, 0.1*0.3/0.3, 0.1*0.2/0.3, 0.0, + 0.1, 0.0, 0.0]) + isi1 = np.array([0.2, 0.2, 0.2, 0.2, 0.2, 0.4]) + isi2 = np.array([0.3, 0.3, 0.3, 0.1, 0.1, 0.4]) + expected_y1 = (s1_r[:-1]*isi2+s2_r[:-1]*isi1) / (0.5*(isi1+isi2)**2) + expected_y2 = (s1_l[1:]*isi2+s2_l[1:]*isi1) / (0.5*(isi1+isi2)**2) + + expected_times = np.array(expected_times) + expected_y1 = np.array(expected_y1) + expected_y2 = np.array(expected_y2) + expected_spike_val = sum((expected_times[1:] - expected_times[:-1]) * + (expected_y1+expected_y2)/2) + expected_spike_val /= (expected_times[-1]-expected_times[0]) + + f = spk.spike_profile(t1, t2) + + assert_equal(f.x, expected_times) + assert_array_almost_equal(f.y1, expected_y1, decimal=14) + assert_array_almost_equal(f.y2, expected_y2, decimal=14) + assert_almost_equal(f.avrg(), expected_spike_val, decimal=16) + assert_almost_equal(spk.spike_distance(t1, t2), expected_spike_val, + decimal=16) + + +def test_spike_sync(): + spikes1 = SpikeTrain([1.0, 2.0, 3.0], 4.0) + spikes2 = SpikeTrain([2.1], 4.0) + + expected_x = np.array([0.0, 1.0, 2.0, 2.1, 3.0, 4.0]) + expected_y = np.array([0.0, 0.0, 1.0, 1.0, 0.0, 0.0]) + + f = spk.spike_sync_profile(spikes1, spikes2) + + assert_array_almost_equal(f.x, expected_x, decimal=16) + assert_array_almost_equal(f.y, expected_y, decimal=16) + + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.5, decimal=16) + + # test with some small max_tau, spike_sync should be 0 + assert_almost_equal(spk.spike_sync(spikes1, spikes2, max_tau=0.05), + 0.0, decimal=16) + + spikes2 = SpikeTrain([3.1], 4.0) + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.5, decimal=16) + + spikes2 = SpikeTrain([1.1], 4.0) + + expected_x = np.array([0.0, 1.0, 1.1, 2.0, 3.0, 4.0]) + expected_y = np.array([1.0, 1.0, 1.0, 0.0, 0.0, 0.0]) + + f = spk.spike_sync_profile(spikes1, spikes2) + + assert_array_almost_equal(f.x, expected_x, decimal=16) + assert_array_almost_equal(f.y, expected_y, decimal=16) + + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.5, decimal=16) + + spikes2 = SpikeTrain([0.9], 4.0) + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.5, decimal=16) + + spikes2 = SpikeTrain([3.0], 4.0) + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.5, decimal=16) + + spikes2 = SpikeTrain([1.0], 4.0) + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.5, decimal=16) + + spikes2 = SpikeTrain([1.5, 3.0], 4.0) + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.4, decimal=16) + + spikes1 = SpikeTrain([1.0, 2.0, 4.0], 4.0) + spikes2 = SpikeTrain([3.8], 4.0) + spikes3 = SpikeTrain([3.9, ], 4.0) + + expected_x = np.array([0.0, 1.0, 2.0, 3.8, 4.0, 4.0]) + expected_y = np.array([0.0, 0.0, 0.0, 1.0, 1.0, 1.0]) + + f = spk.spike_sync_profile(spikes1, spikes2) + + assert_array_almost_equal(f.x, expected_x, decimal=16) + assert_array_almost_equal(f.y, expected_y, decimal=16) + + f2 = spk.spike_sync_profile(spikes2, spikes3) + + i1 = f.integral() + i2 = f2.integral() + f.add(f2) + i12 = f.integral() + + assert_equal(i1[0]+i2[0], i12[0]) + assert_equal(i1[1]+i2[1], i12[1]) + + +def check_multi_profile(profile_func, profile_func_multi, dist_func_multi): + # generate spike trains: + t1 = SpikeTrain([0.2, 0.4, 0.6, 0.7], 1.0) + t2 = SpikeTrain([0.3, 0.45, 0.8, 0.9, 0.95], 1.0) + t3 = SpikeTrain([0.2, 0.4, 0.6], 1.0) + t4 = SpikeTrain([0.1, 0.4, 0.5, 0.6], 1.0) + spike_trains = [t1, t2, t3, t4] + + f12 = profile_func(t1, t2) + f13 = profile_func(t1, t3) + f14 = profile_func(t1, t4) + f23 = profile_func(t2, t3) + f24 = profile_func(t2, t4) + f34 = profile_func(t3, t4) + + f_multi = profile_func_multi(spike_trains, [0, 1]) + assert f_multi.almost_equal(f12, decimal=14) + d = dist_func_multi(spike_trains, [0, 1]) + assert_equal(f_multi.avrg(), d) + + f_multi1 = profile_func_multi(spike_trains, [1, 2, 3]) + f_multi2 = profile_func_multi(spike_trains[1:]) + assert f_multi1.almost_equal(f_multi2, decimal=14) + d = dist_func_multi(spike_trains, [1, 2, 3]) + assert_almost_equal(f_multi1.avrg(), d, decimal=14) + + f = copy(f12) + f.add(f13) + f.add(f23) + f.mul_scalar(1.0/3) + f_multi = profile_func_multi(spike_trains, [0, 1, 2]) + assert f_multi.almost_equal(f, decimal=14) + d = dist_func_multi(spike_trains, [0, 1, 2]) + assert_almost_equal(f_multi.avrg(), d, decimal=14) + + f.mul_scalar(3) # revert above normalization + f.add(f14) + f.add(f24) + f.add(f34) + f.mul_scalar(1.0/6) + f_multi = profile_func_multi(spike_trains) + assert f_multi.almost_equal(f, decimal=14) + + +def test_multi_isi(): + check_multi_profile(spk.isi_profile, spk.isi_profile_multi, + spk.isi_distance_multi) + + +def test_multi_spike(): + check_multi_profile(spk.spike_profile, spk.spike_profile_multi, + spk.spike_distance_multi) + + +def test_multi_spike_sync(): + # some basic multivariate check + spikes1 = SpikeTrain([100, 300, 400, 405, 410, 500, 700, 800, + 805, 810, 815, 900], 1000) + spikes2 = SpikeTrain([100, 200, 205, 210, 295, 350, 400, 510, + 600, 605, 700, 910], 1000) + spikes3 = SpikeTrain([100, 180, 198, 295, 412, 420, 510, 640, + 695, 795, 820, 920], 1000) + assert_almost_equal(spk.spike_sync(spikes1, spikes2), + 0.5, decimal=15) + assert_almost_equal(spk.spike_sync(spikes1, spikes3), + 0.5, decimal=15) + assert_almost_equal(spk.spike_sync(spikes2, spikes3), + 0.5, decimal=15) + + f = spk.spike_sync_profile_multi([spikes1, spikes2, spikes3]) + # hands on definition of the average multivariate spike synchronization + # expected = (f1.integral() + f2.integral() + f3.integral()) / \ + # (np.sum(f1.mp[1:-1])+np.sum(f2.mp[1:-1])+np.sum(f3.mp[1:-1])) + expected = 0.5 + assert_almost_equal(f.avrg(), expected, decimal=15) + assert_almost_equal(spk.spike_sync_multi([spikes1, spikes2, spikes3]), + expected, decimal=15) + + # multivariate regression test + spike_trains = spk.load_spike_trains_from_txt( + os.path.join(TEST_PATH, "SPIKE_Sync_Test.txt"), edges=[0, 4000]) + # extract all spike times + spike_times = np.array([]) + for st in spike_trains: + spike_times = np.append(spike_times, st.spikes) + spike_times = np.unique(np.sort(spike_times)) + + f = spk.spike_sync_profile_multi(spike_trains) + + assert_equal(spike_times, f.x[1:-1]) + assert_equal(len(f.x), len(f.y)) + + assert_equal(np.sum(f.y[1:-1]), 39932) + assert_equal(np.sum(f.mp[1:-1]), 85554) + + # example with 2 empty spike trains + sts = [] + sts.append(SpikeTrain([1, 9], [0, 10])) + sts.append(SpikeTrain([1, 3], [0, 10])) + sts.append(SpikeTrain([], [0, 10])) + sts.append(SpikeTrain([], [0, 10])) + + assert_almost_equal(spk.spike_sync_multi(sts), 1.0/6.0, decimal=15) + assert_almost_equal(spk.spike_sync_profile_multi(sts).avrg(), 1.0/6.0, + decimal=15) + + +def check_dist_matrix(dist_func, dist_matrix_func): + # generate spike trains: + t1 = SpikeTrain([0.2, 0.4, 0.6, 0.7], 1.0) + t2 = SpikeTrain([0.3, 0.45, 0.8, 0.9, 0.95], 1.0) + t3 = SpikeTrain([0.2, 0.4, 0.6], 1.0) + t4 = SpikeTrain([0.1, 0.4, 0.5, 0.6], 1.0) + spike_trains = [t1, t2, t3, t4] + + f12 = dist_func(t1, t2) + f13 = dist_func(t1, t3) + f14 = dist_func(t1, t4) + f23 = dist_func(t2, t3) + f24 = dist_func(t2, t4) + f34 = dist_func(t3, t4) + + f_matrix = dist_matrix_func(spike_trains) + # check zero diagonal + for i in range(4): + assert_equal(0.0, f_matrix[i, i]) + for i in range(4): + for j in range(i+1, 4): + assert_equal(f_matrix[i, j], f_matrix[j, i]) + assert_equal(f12, f_matrix[1, 0]) + assert_equal(f13, f_matrix[2, 0]) + assert_equal(f14, f_matrix[3, 0]) + assert_equal(f23, f_matrix[2, 1]) + assert_equal(f24, f_matrix[3, 1]) + assert_equal(f34, f_matrix[3, 2]) + + +def test_isi_matrix(): + check_dist_matrix(spk.isi_distance, spk.isi_distance_matrix) + + +def test_spike_matrix(): + check_dist_matrix(spk.spike_distance, spk.spike_distance_matrix) + + +def test_spike_sync_matrix(): + check_dist_matrix(spk.spike_sync, spk.spike_sync_matrix) + + +def test_regression_spiky(): + # standard example + st1 = SpikeTrain(np.arange(100, 1201, 100), 1300) + st2 = SpikeTrain(np.arange(100, 1201, 110), 1300) + + isi_dist = spk.isi_distance(st1, st2) + assert_almost_equal(isi_dist, 9.0909090909090939e-02, decimal=15) + isi_profile = spk.isi_profile(st1, st2) + assert_equal(isi_profile.y, 0.1/1.1 * np.ones_like(isi_profile.y)) + + spike_dist = spk.spike_distance(st1, st2) + assert_equal(spike_dist, 0.211058782487353908) + + spike_sync = spk.spike_sync(st1, st2) + assert_equal(spike_sync, 8.6956521739130432e-01) + + # multivariate check + + spike_trains = spk.load_spike_trains_from_txt( + os.path.join(TEST_PATH, "PySpike_testdata.txt"), (0.0, 4000.0)) + isi_dist = spk.isi_distance_multi(spike_trains) + # get the full precision from SPIKY + assert_almost_equal(isi_dist, 0.17051816816999129656, decimal=15) + + spike_profile = spk.spike_profile_multi(spike_trains) + assert_equal(len(spike_profile.y1)+len(spike_profile.y2), 1252) + + spike_dist = spk.spike_distance_multi(spike_trains) + # get the full precision from SPIKY + assert_almost_equal(spike_dist, 0.25188056475463755, decimal=15) + + spike_sync = spk.spike_sync_multi(spike_trains) + # get the full precision from SPIKY + assert_equal(spike_sync, 0.7183531505298066) + + # Eero's edge correction example + st1 = SpikeTrain([0.5, 1.5, 2.5], 6.0) + st2 = SpikeTrain([3.5, 4.5, 5.5], 6.0) + + f = spk.spike_profile(st1, st2) + + expected_times = np.array([0.0, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.0]) + y_all = np.array([0.271604938271605, 0.271604938271605, 0.271604938271605, + 0.617283950617284, 0.617283950617284, 0.444444444444444, + 0.285714285714286, 0.285714285714286, 0.444444444444444, + 0.617283950617284, 0.617283950617284, 0.271604938271605, + 0.271604938271605, 0.271604938271605]) + expected_y1 = y_all[::2] + expected_y2 = y_all[1::2] + + assert_equal(f.x, expected_times) + assert_array_almost_equal(f.y1, expected_y1, decimal=14) + assert_array_almost_equal(f.y2, expected_y2, decimal=14) + + +def test_multi_variate_subsets(): + spike_trains = spk.load_spike_trains_from_txt( + os.path.join(TEST_PATH, "PySpike_testdata.txt"), (0.0, 4000.0)) + sub_set = [1, 3, 5, 7] + spike_trains_sub_set = [spike_trains[i] for i in sub_set] + + v1 = spk.isi_distance_multi(spike_trains_sub_set) + v2 = spk.isi_distance_multi(spike_trains, sub_set) + assert_equal(v1, v2) + + v1 = spk.spike_distance_multi(spike_trains_sub_set) + v2 = spk.spike_distance_multi(spike_trains, sub_set) + assert_equal(v1, v2) + + v1 = spk.spike_sync_multi(spike_trains_sub_set) + v2 = spk.spike_sync_multi(spike_trains, sub_set) + assert_equal(v1, v2) + + +if __name__ == "__main__": + test_isi() + test_spike() + test_spike_sync() + test_multi_isi() + test_multi_spike() + test_multi_spike_sync() + test_isi_matrix() + test_spike_matrix() + test_spike_sync_matrix() + test_regression_spiky() + test_multi_variate_subsets() diff --git a/test/test_empty.py b/test/test_empty.py new file mode 100644 index 0000000..4d0a5cf --- /dev/null +++ b/test/test_empty.py @@ -0,0 +1,163 @@ +""" test_empty.py + +Tests the distance measure for empty spike trains + +Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License + +""" + +from __future__ import print_function +import numpy as np +from numpy.testing import assert_equal, assert_almost_equal, \ + assert_array_equal, assert_array_almost_equal + +import pyspike as spk +from pyspike import SpikeTrain + + +def test_get_non_empty(): + st = SpikeTrain([], edges=(0.0, 1.0)) + spikes = st.get_spikes_non_empty() + assert_array_equal(spikes, [0.0, 1.0]) + + st = SpikeTrain([0.5, ], edges=(0.0, 1.0)) + spikes = st.get_spikes_non_empty() + # assert_array_equal(spikes, [0.0, 0.5, 1.0]) + # spike trains with one spike don't get edge spikes anymore + assert_array_equal(spikes, [0.5, ]) + + +def test_isi_empty(): + st1 = SpikeTrain([], edges=(0.0, 1.0)) + st2 = SpikeTrain([], edges=(0.0, 1.0)) + d = spk.isi_distance(st1, st2) + assert_equal(d, 0.0) + prof = spk.isi_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_equal(prof.x, [0.0, 1.0]) + assert_array_equal(prof.y, [0.0, ]) + + st1 = SpikeTrain([], edges=(0.0, 1.0)) + st2 = SpikeTrain([0.4, ], edges=(0.0, 1.0)) + d = spk.isi_distance(st1, st2) + assert_equal(d, 0.6*0.4+0.4*0.6) + prof = spk.isi_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_equal(prof.x, [0.0, 0.4, 1.0]) + assert_array_equal(prof.y, [0.6, 0.4]) + + st1 = SpikeTrain([0.6, ], edges=(0.0, 1.0)) + st2 = SpikeTrain([0.4, ], edges=(0.0, 1.0)) + d = spk.isi_distance(st1, st2) + assert_almost_equal(d, 0.2/0.6*0.4 + 0.0 + 0.2/0.6*0.4, decimal=15) + prof = spk.isi_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_almost_equal(prof.x, [0.0, 0.4, 0.6, 1.0], decimal=15) + assert_array_almost_equal(prof.y, [0.2/0.6, 0.0, 0.2/0.6], decimal=15) + + +def test_spike_empty(): + st1 = SpikeTrain([], edges=(0.0, 1.0)) + st2 = SpikeTrain([], edges=(0.0, 1.0)) + d = spk.spike_distance(st1, st2) + assert_equal(d, 0.0) + prof = spk.spike_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_equal(prof.x, [0.0, 1.0]) + assert_array_equal(prof.y1, [0.0, ]) + assert_array_equal(prof.y2, [0.0, ]) + + st1 = SpikeTrain([], edges=(0.0, 1.0)) + st2 = SpikeTrain([0.4, ], edges=(0.0, 1.0)) + d = spk.spike_distance(st1, st2) + d_expect = 2*0.4*0.4*1.0/(0.4+1.0)**2 + 2*0.6*0.4*1.0/(0.6+1.0)**2 + assert_almost_equal(d, d_expect, decimal=15) + prof = spk.spike_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_equal(prof.x, [0.0, 0.4, 1.0]) + assert_array_almost_equal(prof.y1, [2*0.4*1.0/(0.4+1.0)**2, + 2*0.4*1.0/(0.6+1.0)**2], + decimal=15) + assert_array_almost_equal(prof.y2, [2*0.4*1.0/(0.4+1.0)**2, + 2*0.4*1.0/(0.6+1.0)**2], + decimal=15) + + st1 = SpikeTrain([0.6, ], edges=(0.0, 1.0)) + st2 = SpikeTrain([0.4, ], edges=(0.0, 1.0)) + d = spk.spike_distance(st1, st2) + s1 = np.array([0.2, 0.2, 0.2, 0.2]) + s2 = np.array([0.2, 0.2, 0.2, 0.2]) + isi1 = np.array([0.6, 0.6, 0.4]) + isi2 = np.array([0.4, 0.6, 0.6]) + expected_y1 = (s1[:-1]*isi2+s2[:-1]*isi1) / (0.5*(isi1+isi2)**2) + expected_y2 = (s1[1:]*isi2+s2[1:]*isi1) / (0.5*(isi1+isi2)**2) + expected_times = np.array([0.0, 0.4, 0.6, 1.0]) + expected_spike_val = sum((expected_times[1:] - expected_times[:-1]) * + (expected_y1+expected_y2)/2) + expected_spike_val /= (expected_times[-1]-expected_times[0]) + + assert_almost_equal(d, expected_spike_val, decimal=15) + prof = spk.spike_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_almost_equal(prof.x, [0.0, 0.4, 0.6, 1.0], decimal=15) + assert_array_almost_equal(prof.y1, expected_y1, decimal=15) + assert_array_almost_equal(prof.y2, expected_y2, decimal=15) + + +def test_spike_sync_empty(): + st1 = SpikeTrain([], edges=(0.0, 1.0)) + st2 = SpikeTrain([], edges=(0.0, 1.0)) + d = spk.spike_sync(st1, st2) + assert_equal(d, 1.0) + prof = spk.spike_sync_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_equal(prof.x, [0.0, 1.0]) + assert_array_equal(prof.y, [1.0, 1.0]) + + st1 = SpikeTrain([], edges=(0.0, 1.0)) + st2 = SpikeTrain([0.4, ], edges=(0.0, 1.0)) + d = spk.spike_sync(st1, st2) + assert_equal(d, 0.0) + prof = spk.spike_sync_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_equal(prof.x, [0.0, 0.4, 1.0]) + assert_array_equal(prof.y, [0.0, 0.0, 0.0]) + + st1 = SpikeTrain([0.6, ], edges=(0.0, 1.0)) + st2 = SpikeTrain([0.4, ], edges=(0.0, 1.0)) + d = spk.spike_sync(st1, st2) + assert_almost_equal(d, 1.0, decimal=15) + prof = spk.spike_sync_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_almost_equal(prof.x, [0.0, 0.4, 0.6, 1.0], decimal=15) + assert_array_almost_equal(prof.y, [1.0, 1.0, 1.0, 1.0], decimal=15) + + st1 = SpikeTrain([0.2, ], edges=(0.0, 1.0)) + st2 = SpikeTrain([0.8, ], edges=(0.0, 1.0)) + d = spk.spike_sync(st1, st2) + assert_almost_equal(d, 0.0, decimal=15) + prof = spk.spike_sync_profile(st1, st2) + assert_equal(d, prof.avrg()) + assert_array_almost_equal(prof.x, [0.0, 0.2, 0.8, 1.0], decimal=15) + assert_array_almost_equal(prof.y, [0.0, 0.0, 0.0, 0.0], decimal=15) + + # test with empty intervals + st1 = SpikeTrain([2.0, 5.0], [0, 10.0]) + st2 = SpikeTrain([2.1, 7.0], [0, 10.0]) + st3 = SpikeTrain([5.1, 6.0], [0, 10.0]) + res = spk.spike_sync_profile(st1, st2).avrg(interval=[3.0, 4.0]) + assert_equal(res, 1.0) + res = spk.spike_sync(st1, st2, interval=[3.0, 4.0]) + assert_equal(res, 1.0) + + sync_matrix = spk.spike_sync_matrix([st1, st2, st3], interval=[3.0, 4.0]) + assert_array_equal(sync_matrix, np.ones((3, 3)) - np.diag(np.ones(3))) + + +if __name__ == "__main__": + test_get_non_empty() + test_isi_empty() + test_spike_empty() + test_spike_sync_empty() 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() diff --git a/test/test_generic_interfaces.py b/test/test_generic_interfaces.py new file mode 100644 index 0000000..7f08067 --- /dev/null +++ b/test/test_generic_interfaces.py @@ -0,0 +1,105 @@ +""" test_generic_interface.py + +Tests the generic interfaces of the profile and distance functions + +Copyright 2016, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License + +""" + +from __future__ import print_function +from numpy.testing import assert_equal + +import pyspike as spk +from pyspike import SpikeTrain + + +class dist_from_prof: + """ Simple functor that turns profile function into distance function by + calling profile.avrg(). + """ + def __init__(self, prof_func): + self.prof_func = prof_func + + def __call__(self, *args, **kwargs): + if "interval" in kwargs: + # forward interval arg into avrg function + interval = kwargs.pop("interval") + return self.prof_func(*args, **kwargs).avrg(interval=interval) + else: + return self.prof_func(*args, **kwargs).avrg() + + +def check_func(dist_func): + """ generic checker that tests the given distance function. + """ + # generate spike trains: + t1 = SpikeTrain([0.2, 0.4, 0.6, 0.7], 1.0) + t2 = SpikeTrain([0.3, 0.45, 0.8, 0.9, 0.95], 1.0) + t3 = SpikeTrain([0.2, 0.4, 0.6], 1.0) + t4 = SpikeTrain([0.1, 0.4, 0.5, 0.6], 1.0) + spike_trains = [t1, t2, t3, t4] + + isi12 = dist_func(t1, t2) + isi12_ = dist_func([t1, t2]) + assert_equal(isi12, isi12_) + + isi12_ = dist_func(spike_trains, indices=[0, 1]) + assert_equal(isi12, isi12_) + + isi123 = dist_func(t1, t2, t3) + isi123_ = dist_func([t1, t2, t3]) + assert_equal(isi123, isi123_) + + isi123_ = dist_func(spike_trains, indices=[0, 1, 2]) + assert_equal(isi123, isi123_) + + # run the same test with an additional interval parameter + + isi12 = dist_func(t1, t2, interval=[0.0, 0.5]) + isi12_ = dist_func([t1, t2], interval=[0.0, 0.5]) + assert_equal(isi12, isi12_) + + isi12_ = dist_func(spike_trains, indices=[0, 1], interval=[0.0, 0.5]) + assert_equal(isi12, isi12_) + + isi123 = dist_func(t1, t2, t3, interval=[0.0, 0.5]) + isi123_ = dist_func([t1, t2, t3], interval=[0.0, 0.5]) + assert_equal(isi123, isi123_) + + isi123_ = dist_func(spike_trains, indices=[0, 1, 2], interval=[0.0, 0.5]) + assert_equal(isi123, isi123_) + + +def test_isi_profile(): + check_func(dist_from_prof(spk.isi_profile)) + + +def test_isi_distance(): + check_func(spk.isi_distance) + + +def test_spike_profile(): + check_func(dist_from_prof(spk.spike_profile)) + + +def test_spike_distance(): + check_func(spk.spike_distance) + + +def test_spike_sync_profile(): + check_func(dist_from_prof(spk.spike_sync_profile)) + + +def test_spike_sync(): + check_func(spk.spike_sync) + + +if __name__ == "__main__": + test_isi_profile() + test_isi_distance() + test_spike_profile() + test_spike_distance() + test_spike_sync_profile() + test_spike_sync() diff --git a/test/test_regression/test_regression_15.py b/test/test_regression/test_regression_15.py new file mode 100644 index 0000000..54adf23 --- /dev/null +++ b/test/test_regression/test_regression_15.py @@ -0,0 +1,81 @@ +""" test_regression_15.py + +Regression test for Issue #15 + +Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License + +""" + +from __future__ import division + +import numpy as np +from numpy.testing import assert_equal, assert_almost_equal, \ + assert_array_almost_equal + +import pyspike as spk + +import os +TEST_PATH = os.path.dirname(os.path.realpath(__file__)) +TEST_DATA = os.path.join(TEST_PATH, "..", "SPIKE_Sync_Test.txt") + + +def test_regression_15_isi(): + # load spike trains + spike_trains = spk.load_spike_trains_from_txt(TEST_DATA, edges=[0, 4000]) + + N = len(spike_trains) + + dist_mat = spk.isi_distance_matrix(spike_trains) + assert_equal(dist_mat.shape, (N, N)) + + ind = np.arange(N//2) + dist_mat = spk.isi_distance_matrix(spike_trains, ind) + assert_equal(dist_mat.shape, (N//2, N//2)) + + ind = np.arange(N//2, N) + dist_mat = spk.isi_distance_matrix(spike_trains, ind) + assert_equal(dist_mat.shape, (N//2, N//2)) + + +def test_regression_15_spike(): + # load spike trains + spike_trains = spk.load_spike_trains_from_txt(TEST_DATA, edges=[0, 4000]) + + N = len(spike_trains) + + dist_mat = spk.spike_distance_matrix(spike_trains) + assert_equal(dist_mat.shape, (N, N)) + + ind = np.arange(N//2) + dist_mat = spk.spike_distance_matrix(spike_trains, ind) + assert_equal(dist_mat.shape, (N//2, N//2)) + + ind = np.arange(N//2, N) + dist_mat = spk.spike_distance_matrix(spike_trains, ind) + assert_equal(dist_mat.shape, (N//2, N//2)) + + +def test_regression_15_sync(): + # load spike trains + spike_trains = spk.load_spike_trains_from_txt(TEST_DATA, edges=[0, 4000]) + + N = len(spike_trains) + + dist_mat = spk.spike_sync_matrix(spike_trains) + assert_equal(dist_mat.shape, (N, N)) + + ind = np.arange(N//2) + dist_mat = spk.spike_sync_matrix(spike_trains, ind) + assert_equal(dist_mat.shape, (N//2, N//2)) + + ind = np.arange(N//2, N) + dist_mat = spk.spike_sync_matrix(spike_trains, ind) + assert_equal(dist_mat.shape, (N//2, N//2)) + + +if __name__ == "__main__": + test_regression_15_isi() + test_regression_15_spike() + test_regression_15_sync() diff --git a/test/test_save_load.py b/test/test_save_load.py new file mode 100644 index 0000000..33249b3 --- /dev/null +++ b/test/test_save_load.py @@ -0,0 +1,42 @@ +""" test_save_load.py + +Tests saving and loading of spike trains + +Copyright 2016, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License + +""" + +from __future__ import print_function +from numpy.testing import assert_array_equal + +import tempfile +import os.path + +import pyspike as spk + + +def test_save_load(): + file_name = os.path.join(tempfile.mkdtemp(prefix='pyspike_'), + "save_load.txt") + + N = 10 + # generate some spike trains + spike_trains = [] + for n in range(N): + spike_trains.append(spk.generate_poisson_spikes(1.0, [0, 100])) + + # save them into txt file + spk.save_spike_trains_to_txt(spike_trains, file_name, precision=17) + + # load again + spike_trains_loaded = spk.load_spike_trains_from_txt(file_name, [0, 100]) + + for n in range(N): + assert_array_equal(spike_trains[n].spikes, + spike_trains_loaded[n].spikes) + + +if __name__ == "__main__": + test_save_load() diff --git a/test/test_spikes.py b/test/test_spikes.py new file mode 100644 index 0000000..ee505b5 --- /dev/null +++ b/test/test_spikes.py @@ -0,0 +1,101 @@ +""" test_load.py + +Test loading of spike trains from text files + +Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License +""" + +from __future__ import print_function +import numpy as np +from numpy.testing import assert_equal + +import pyspike as spk + +import os +TEST_PATH = os.path.dirname(os.path.realpath(__file__)) +TEST_DATA = os.path.join(TEST_PATH, "PySpike_testdata.txt") + +TIME_SERIES_DATA = os.path.join(TEST_PATH, "time_series.txt") +TIME_SERIES_SPIKES = os.path.join(TEST_PATH, "time_series_spike_trains.txt") + + +def test_load_from_txt(): + spike_trains = spk.load_spike_trains_from_txt(TEST_DATA, edges=(0, 4000)) + assert len(spike_trains) == 40 + + # check the first spike train + spike_times = [64.886, 305.81, 696, 937.77, 1059.7, 1322.2, 1576.1, + 1808.1, 2121.5, 2381.1, 2728.6, 2966.9, 3223.7, 3473.7, + 3644.3, 3936.3] + assert_equal(spike_times, spike_trains[0].spikes) + + # check auxiliary spikes + for spike_train in spike_trains: + assert spike_train.t_start == 0.0 + assert spike_train.t_end == 4000 + + +def test_load_time_series(): + spike_trains = spk.import_spike_trains_from_time_series(TIME_SERIES_DATA, + start_time=0, + time_bin=1) + assert len(spike_trains) == 40 + spike_trains_check = spk.load_spike_trains_from_txt(TIME_SERIES_SPIKES, + edges=(0, 4000)) + + # check spike trains + for n in range(len(spike_trains)): + assert_equal(spike_trains[n].spikes, spike_trains_check[n].spikes) + assert_equal(spike_trains[n].t_start, 0) + assert_equal(spike_trains[n].t_end, 4000) + + +def check_merged_spikes(merged_spikes, spike_trains): + # create a flat array with all spike events + all_spikes = np.array([]) + for spike_train in spike_trains: + all_spikes = np.append(all_spikes, spike_train) + indices = np.zeros_like(all_spikes, dtype='bool') + # check if we find all the spike events in the original spike trains + for x in merged_spikes: + i = np.where(all_spikes == x)[0][0] # first axis and first entry + # change to something impossible so we dont find this event again + all_spikes[i] = -1.0 + indices[i] = True + assert indices.all() + + +def test_merge_spike_trains(): + # first load the data + spike_trains = spk.load_spike_trains_from_txt(TEST_DATA, edges=(0, 4000)) + + merged_spikes = spk.merge_spike_trains([spike_trains[0], spike_trains[1]]) + # test if result is sorted + assert((merged_spikes.spikes == np.sort(merged_spikes.spikes)).all()) + # check merging + check_merged_spikes(merged_spikes.spikes, [spike_trains[0].spikes, + spike_trains[1].spikes]) + + merged_spikes = spk.merge_spike_trains(spike_trains) + # test if result is sorted + assert((merged_spikes.spikes == np.sort(merged_spikes.spikes)).all()) + # check merging + check_merged_spikes(merged_spikes.spikes, + [st.spikes for st in spike_trains]) + +def test_merge_empty_spike_trains(): + # first load the data + spike_trains = spk.load_spike_trains_from_txt(TEST_DATA, edges=(0, 4000)) + # take two non-empty trains, and one empty one + empty = spk.SpikeTrain([],[spike_trains[0].t_start,spike_trains[0].t_end]) + merged_spikes = spk.merge_spike_trains([spike_trains[0], empty, spike_trains[1]]) + # test if result is sorted + assert((merged_spikes.spikes == np.sort(merged_spikes.spikes)).all()) + # we don't need to check more, that's done by test_merge_spike_trains + + +if __name__ == "main": + test_load_from_txt() + test_merge_spike_trains() diff --git a/test/test_sync_filter.py b/test/test_sync_filter.py new file mode 100644 index 0000000..e259903 --- /dev/null +++ b/test/test_sync_filter.py @@ -0,0 +1,95 @@ +""" test_sync_filter.py + +Tests the spike sync based filtering + +Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net> + +Distributed under the BSD License + +""" + +from __future__ import print_function +import numpy as np +from numpy.testing import assert_equal, assert_almost_equal, \ + assert_array_almost_equal + +import pyspike as spk +from pyspike import SpikeTrain + + +def test_single_prof(): + st1 = np.array([1.0, 2.0, 3.0, 4.0]) + st2 = np.array([1.1, 2.1, 3.8]) + st3 = np.array([0.9, 3.1, 4.1]) + + # cython implementation + try: + from pyspike.cython.cython_profiles import \ + coincidence_single_profile_cython as coincidence_impl + except ImportError: + from pyspike.cython.python_backend import \ + coincidence_single_python as coincidence_impl + + sync_prof = spk.spike_sync_profile(SpikeTrain(st1, 5.0), + SpikeTrain(st2, 5.0)) + + coincidences = np.array(coincidence_impl(st1, st2, 0, 5.0, 0.0)) + print(coincidences) + for i, t in enumerate(st1): + assert_equal(coincidences[i], sync_prof.y[sync_prof.x == t], + "At index %d" % i) + + coincidences = np.array(coincidence_impl(st2, st1, 0, 5.0, 0.0)) + for i, t in enumerate(st2): + assert_equal(coincidences[i], sync_prof.y[sync_prof.x == t], + "At index %d" % i) + + sync_prof = spk.spike_sync_profile(SpikeTrain(st1, 5.0), + SpikeTrain(st3, 5.0)) + + coincidences = np.array(coincidence_impl(st1, st3, 0, 5.0, 0.0)) + for i, t in enumerate(st1): + assert_equal(coincidences[i], sync_prof.y[sync_prof.x == t], + "At index %d" % i) + + st1 = np.array([1.0, 2.0, 3.0, 4.0]) + st2 = np.array([1.0, 2.0, 4.0]) + + sync_prof = spk.spike_sync_profile(SpikeTrain(st1, 5.0), + SpikeTrain(st2, 5.0)) + + coincidences = np.array(coincidence_impl(st1, st2, 0, 5.0, 0.0)) + for i, t in enumerate(st1): + expected = sync_prof.y[sync_prof.x == t]/sync_prof.mp[sync_prof.x == t] + assert_equal(coincidences[i], expected, + "At index %d" % i) + + +def test_filter(): + st1 = SpikeTrain(np.array([1.0, 2.0, 3.0, 4.0]), 5.0) + st2 = SpikeTrain(np.array([1.1, 2.1, 3.8]), 5.0) + st3 = SpikeTrain(np.array([0.9, 3.1, 4.1]), 5.0) + + # filtered_spike_trains = spk.filter_by_spike_sync([st1, st2], 0.5) + + # assert_equal(filtered_spike_trains[0].spikes, [1.0, 2.0, 4.0]) + # assert_equal(filtered_spike_trains[1].spikes, [1.1, 2.1, 3.8]) + + # filtered_spike_trains = spk.filter_by_spike_sync([st2, st1], 0.5) + + # assert_equal(filtered_spike_trains[0].spikes, [1.1, 2.1, 3.8]) + # assert_equal(filtered_spike_trains[1].spikes, [1.0, 2.0, 4.0]) + + filtered_spike_trains = spk.filter_by_spike_sync([st1, st2, st3], 0.75) + + for st in filtered_spike_trains: + print(st.spikes) + + assert_equal(filtered_spike_trains[0].spikes, [1.0, 4.0]) + assert_equal(filtered_spike_trains[1].spikes, [1.1, 3.8]) + assert_equal(filtered_spike_trains[2].spikes, [0.9, 4.1]) + + +if __name__ == "main": + test_single_prof() + test_filter() diff --git a/test/time_series.txt b/test/time_series.txt new file mode 100644 index 0000000..0116c97 --- /dev/null +++ b/test/time_series.txt @@ -0,0 +1,80 @@ +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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