From 43122af0dffb5010ae3e6f8de4da5e8725d68144 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Wed, 14 Nov 2018 10:34:09 -0500 Subject: [PATCH 01/22] Let pearsonr return a tuple instead of trying to convert to float and added test for 0 noise --- mgcpy/independence_tests/rv_corr.py | 3 +-- .../unit_tests/rv_corr_test.py | 16 ++++++++++++++-- 2 files changed, 15 insertions(+), 4 deletions(-) diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py index f737186..e0fcf7f 100644 --- a/mgcpy/independence_tests/rv_corr.py +++ b/mgcpy/independence_tests/rv_corr.py @@ -80,7 +80,6 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None): if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)): corr, covar = pearsonr(data_matrix_X, data_matrix_Y) - corr, covar = corr[0], covar[0] elif (self.which_test == 'rv'): covar = np.trace(np.dot(covar, covar.T)) corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX)) @@ -97,4 +96,4 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None): independence_test_metadata = {"covariance": covar} - return corr, independence_test_metadata + return corr, independence_test_metadata \ No newline at end of file diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py index 383e734..3bfe3d9 100644 --- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py +++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py @@ -23,8 +23,6 @@ def test_local_corr(): assert np.round(test_stat2, decimals=2) == 0.95 assert np.round(test_stat3, decimals=2) == 0.90 - del X, Y, rvcorr, rvcorr2, rvcorr3, test_stat1, test_stat2, test_stat3 - # Against linear simulations np.random.seed(0) X, Y = sims.linear_sim(100, 1) @@ -40,6 +38,20 @@ def test_local_corr(): assert np.round(test_stat1, decimals=2) == 0.24 assert np.round(test_stat2, decimals=2) == 0.49 assert np.round(test_stat3, decimals=2) == 0.24 + + X, Y = sims.linear_sim(100, 1, noise=0) + #savemat('distance matrix data', {'X' : X, 'Y' : Y}) + rvcorr = RVCorr(X, Y, None) + rvcorr2 = RVCorr(X, Y, None, 'pearson') + rvcorr3 = RVCorr(X, Y, None, 'cca') + + test_stat1 = rvcorr.test_statistic()[0] + test_stat2 = rvcorr2.test_statistic()[0] + test_stat3 = rvcorr3.test_statistic()[0] + + assert np.round(test_stat1, decimals=2) == 1.00 + assert np.round(test_stat2, decimals=2) == 1.00 + assert np.round(test_stat3, decimals=2) == 1.00 test_local_corr() From 11a5961191710e11bd24ed7cb14e711605fb39f0 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Wed, 14 Nov 2018 10:34:59 -0500 Subject: [PATCH 02/22] Fixed spacing caused by spyder --- mgcpy/independence_tests/rv_corr.py | 2 +- mgcpy/independence_tests/unit_tests/rv_corr_test.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py index e0fcf7f..baf3d43 100644 --- a/mgcpy/independence_tests/rv_corr.py +++ b/mgcpy/independence_tests/rv_corr.py @@ -96,4 +96,4 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None): independence_test_metadata = {"covariance": covar} - return corr, independence_test_metadata \ No newline at end of file + return corr, independence_test_metadata diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py index 3bfe3d9..25b5ab1 100644 --- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py +++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py @@ -38,7 +38,7 @@ def test_local_corr(): assert np.round(test_stat1, decimals=2) == 0.24 assert np.round(test_stat2, decimals=2) == 0.49 assert np.round(test_stat3, decimals=2) == 0.24 - + X, Y = sims.linear_sim(100, 1, noise=0) #savemat('distance matrix data', {'X' : X, 'Y' : Y}) rvcorr = RVCorr(X, Y, None) From 0d0a991ea06a3214eb0dd89e19eec489a1b028c8 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Thu, 15 Nov 2018 19:27:26 -0500 Subject: [PATCH 03/22] Add HHG test and simulations plot to verify simulations --- mgcpy/benchmarks/simulations.py | 29 ++-- mgcpy/benchmarks/simulations_test.py | 129 +++++++++++++++++- mgcpy/independence_tests/hhg.py | 13 +- .../independence_tests/unit_tests/hhg_test.py | 37 +++++ .../unit_tests/rv_corr_test.py | 4 - 5 files changed, 180 insertions(+), 32 deletions(-) create mode 100644 mgcpy/independence_tests/unit_tests/hhg_test.py diff --git a/mgcpy/benchmarks/simulations.py b/mgcpy/benchmarks/simulations.py index e281c20..8dbcd51 100644 --- a/mgcpy/benchmarks/simulations.py +++ b/mgcpy/benchmarks/simulations.py @@ -256,27 +256,18 @@ def spiral_sim(num_samp, num_dim, noise=0.4, low=0, high=5): :return: the data matrix and a response array """ - if num_dim > 1: - kappa = 1 - else: - kappa = 0 - x = gen_x_unif(num_samp, num_dim, low=low, high=high) - rx = gen_x_unif(num_samp, num_dim, low=low, high=high) - ry = rx - z = rx - sig = np.diag(np.ones(shape=(num_dim))) - gauss_noise = (np.random.multivariate_normal(cov=sig, - mean=np.zeros(num_dim), - size=num_samp)) + uniform_dist = gen_x_unif(num_samp, num_dim=1, low=low, high=high) + the_x = np.array(np.cos(np.pi * uniform_dist)).reshape(num_samp, 1) + y = uniform_dist * np.sin(np.pi * uniform_dist) + x = np.zeros(shape=(num_samp, num_dim)) - ry = np.ones((num_samp, num_dim)) - x[:, 0] = np.cos(z[:, 0].reshape((num_samp)) * np.pi) - for i in range(num_dim - 1): - x[:, i+1] = (x[:, i].reshape((num_samp)) * np.cos(z[:, i+1].reshape((num_samp)) * np.pi)) - x[:, i] = (x[:, i].reshape((num_samp)) * np.sin(z[:, i+1].reshape((num_samp)) * np.pi)) - x = rx * x + if num_dim > 1: + for i in range(num_dim - 1): + x[:, i] = np.squeeze((y * np.power(the_x, i))) + x[:, num_dim-1] = np.squeeze(uniform_dist * the_x) - y = ry * np.sin(z[:, 0].reshape((num_samp, 1)) * np.pi) + kappa*noise*ry*gauss_noise + gauss_noise = np.random.normal(loc=0, scale=1, size=(x.shape[0], 1)) + y = y + noise*num_dim*gauss_noise return x, y diff --git a/mgcpy/benchmarks/simulations_test.py b/mgcpy/benchmarks/simulations_test.py index 25585d4..e118b9e 100644 --- a/mgcpy/benchmarks/simulations_test.py +++ b/mgcpy/benchmarks/simulations_test.py @@ -1,82 +1,159 @@ import numpy as np from mgcpy.benchmarks import simulations as sims +import matplotlib.pyplot as plt def test_simulations(): - num_samps = 100 + num_samps = 1000 num_dim1 = 1 num_dim2 = 300 independent = True + np.random.seed(0) + fig1 = plt.figure(figsize = (50, 80)); + plt.axis('off') + # Linear Simulation returns_low_dim = sims.linear_sim(num_samps, num_dim1) returns_high_dim = sims.linear_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.linear_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 1); + ax1.scatter(x1, y1); + ax1.set_title('Linear', fontweight='bold') + ax1.axis('off'); # Exponential Simulation returns_low_dim = sims.exp_sim(num_samps, num_dim1) returns_high_dim = sims.exp_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.exp_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 2); + ax1.scatter(x1, y1); + ax1.set_title('Exponential', fontweight='bold') + ax1.axis('off'); # Cubic Simulation returns_low_dim = sims.cub_sim(num_samps, num_dim1) returns_high_dim = sims.cub_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.cub_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 3); + ax1.scatter(x1, y1); + ax1.set_title('Cubic', fontweight='bold') + ax1.axis('off'); # Joint-Normal Simulation returns_low_dim = sims.joint_sim(num_samps, num_dim1) returns_high_dim = sims.joint_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.joint_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 4); + ax1.scatter(x1, y1); + ax1.set_title('Joint Normal', fontweight='bold') + ax1.axis('off'); # Step Simulation returns_low_dim = sims.step_sim(num_samps, num_dim1) returns_high_dim = sims.step_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.step_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 5); + ax1.scatter(x1, y1); + ax1.set_title('Step', fontweight='bold') + ax1.axis('off'); # Quadratic Simulation returns_low_dim = sims.quad_sim(num_samps, num_dim1) returns_high_dim = sims.quad_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.quad_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 6); + ax1.scatter(x1, y1); + ax1.set_title('Quadratic', fontweight='bold') + ax1.axis('off'); # W Simulation returns_low_dim = sims.w_sim(num_samps, num_dim1) returns_high_dim = sims.w_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.w_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 7); + ax1.scatter(x1, y1); + ax1.set_title('W-Shaped', fontweight='bold') + ax1.axis('off'); # Spiral Simulation returns_low_dim = sims.spiral_sim(num_samps, num_dim1) returns_high_dim = sims.spiral_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.spiral_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 8); + ax1.scatter(x1, y1); + ax1.set_title('Spiral', fontweight='bold') + ax1.axis('off'); # Uncorrelated Bernoulli Simulation returns = sims.ubern_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.ubern_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 9); + ax1.scatter(x1, y1); + ax1.set_title('Uncorrelated Bernoulli', fontweight='bold') + ax1.axis('off'); # Logarithmic Simulation returns_low_dim = sims.log_sim(num_samps, num_dim1) returns_high_dim = sims.log_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.log_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 10); + ax1.scatter(x1, y1); + ax1.set_title('Logarithmic', fontweight='bold') + ax1.axis('off'); # Nth Root Simulation returns_low_dim = sims.root_sim(num_samps, num_dim1) returns_high_dim = sims.root_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.root_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 11); + ax1.scatter(x1, y1); + ax1.set_title('Fourth Root', fontweight='bold') + ax1.axis('off'); # Sinusoidal Simulation (4*pi) returns_low_dim = sims.sin_sim(num_samps, num_dim1) returns_high_dim = sims.sin_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.sin_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 12); + ax1.scatter(x1, y1); + ax1.set_title('Sinusoidal (4\u03C0)', fontweight='bold') + ax1.axis('off'); # Sinusoidal Simulation (16*pi) returns_low_dim = sims.sin_sim(num_samps, num_dim1, period=16*np.pi) @@ -84,34 +161,84 @@ def test_simulations(): num_samps, num_dim2, period=16*np.pi, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi) + ax1 = fig1.add_subplot(4, 5, 13); + ax1.scatter(x1, y1); + ax1.set_title('Sinusoidal (16\u03C0)', fontweight='bold') + ax1.axis('off'); # Square Simulation returns = sims.square_sim(num_samps, num_dim2, indep=independent) assert np.all(returns[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.square_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 14); + ax1.scatter(x1, y1); + ax1.set_title('Square', fontweight='bold') + ax1.axis('off'); # Two Parabolas Simulation returns_low_dim = sims.two_parab_sim(num_samps, num_dim1) returns_high_dim = sims.two_parab_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 15); + ax1.scatter(x1, y1); + ax1.set_title('Two Parabolas', fontweight='bold') + ax1.axis('off'); # Circle Simulation returns = sims.circle_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.circle_sim(num_samps, 1, noise=0) + ax1 = fig1.add_subplot(4, 5, 16); + ax1.scatter(x1, y1); + ax1.set_title('Circle', fontweight='bold') + ax1.axis('off'); # Ellipse Simulation returns = sims.circle_sim(num_samps, num_dim2, radius=5) assert np.all(returns[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5) + ax1 = fig1.add_subplot(4, 5, 17); + ax1.scatter(x1, y1); + ax1.set_title('Ellipse', fontweight='bold') + ax1.axis('off'); # Diamond Simulation returns = sims.square_sim( num_samps, num_dim2, period=-np.pi/4, indep=independent) assert np.all(returns[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4) + ax1 = fig1.add_subplot(4, 5, 18); + ax1.scatter(x1, y1); + ax1.set_title('Diamond', fontweight='bold') + ax1.axis('off'); # Multiplicative Noise Simulation returns = sims.multi_noise_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.multi_noise_sim(num_samps, 1) + ax1 = fig1.add_subplot(4, 5, 19); + ax1.scatter(x1, y1); + ax1.set_title('Multiplicative Noise', fontweight='bold') + ax1.axis('off'); # Multimodal Independence Simulation returns = sims.multi_indep_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) + + x1, y1 = sims.multi_indep_sim(num_samps, 1) + ax1 = fig1.add_subplot(4, 5, 20); + ax1.scatter(x1, y1); + ax1.set_title('Multimodal Independence', fontweight='bold') + ax1.axis('off'); + +test_simulations() \ No newline at end of file diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py index 3ea0047..29e3d6e 100644 --- a/mgcpy/independence_tests/hhg.py +++ b/mgcpy/independence_tests/hhg.py @@ -1,6 +1,5 @@ import numpy as np from mgcpy.independence_tests.abstract_class import IndependenceTest -from scipy.spatial import distance_matrix class HHG(IndependenceTest): @@ -58,13 +57,11 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None): row_Y, columns_Y = data_matrix_Y.shape[0], data_matrix_Y.shape[1] # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not - if row_X != columns_X or sum(data_matrix_X.diagonal()**2) > 0: - dist_mtx_X = distance_matrix(data_matrix_X, data_matrix_X) + if (row_X != columns_X or sum(data_matrix_X.diagonal()**2) > 0) and \ + (row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0): + dist_mtx_X, dist_mtx_Y = self.compute_distance_matrix(data_matrix_X, data_matrix_Y) else: dist_mtx_X = data_matrix_X - if row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0: - dist_mtx_Y = distance_matrix(data_matrix_Y, data_matrix_Y) - else: dist_mtx_Y = data_matrix_Y n = dist_mtx_X.shape[0] @@ -87,12 +84,12 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None): return corr - def p_value(self, replication_factor=1000): + def p_value(self, replication_factor=100): """ Tests independence between two datasets using HHG and permutation test. :param replication_factor: specifies the number of replications to use for - the permutation test. Defaults to 1000. + the permutation test. Defaults to 100. :type replication_factor: int :return: P-value of HHG diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py new file mode 100644 index 0000000..f1665a2 --- /dev/null +++ b/mgcpy/independence_tests/unit_tests/hhg_test.py @@ -0,0 +1,37 @@ +import mgcpy.benchmarks.simulations as sims +import numpy as np +from scipy.spatial.distance import pdist, squareform +from mgcpy.independence_tests.hhg import HHG + + +def compute_distance_matrix(data_matrix_X, data_matrix_Y): + # obtain the pairwise distance matrix for X and Y + dist_mtx_X = squareform(pdist(data_matrix_X, metric='euclidean')) + dist_mtx_Y = squareform(pdist(data_matrix_Y, metric='euclidean')) + return (dist_mtx_X, dist_mtx_Y) + + +def test_hhg(): + # Against a randomly defined data set + X = np.array([1.1728, 2.4941, 2.4101, 0.1814, 1.1978, 1.5806, 1.2504, + 1.9706, 1.8839, 0.8760])[:, np.newaxis] + Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917, + 7.1748, 6.5792, 2.4012])[:, np.newaxis] + hhg = HHG(X, Y, compute_distance_matrix) + test_stat = hhg.test_statistic() + + assert np.round(test_stat, decimals=2) == 411.88 + + # Against linear simulations + np.random.seed(0) + X, Y = sims.linear_sim(100, 1) + hhg = HHG(X, Y, compute_distance_matrix) + test_stat = hhg.test_statistic() + + assert np.round(test_stat, decimals=2) == 28986.52 + + X, Y = sims.linear_sim(100, 1, noise=0) + hhg = HHG(X, Y, compute_distance_matrix) + test_stat = hhg.test_statistic() + + assert np.round(test_stat, decimals=2) == 950600.00 \ No newline at end of file diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py index 25b5ab1..efdb89b 100644 --- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py +++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py @@ -2,8 +2,6 @@ import numpy as np from mgcpy.independence_tests.rv_corr import RVCorr -#from scipy.io import savemat - def test_local_corr(): # Against a randomly defined data set @@ -26,7 +24,6 @@ def test_local_corr(): # Against linear simulations np.random.seed(0) X, Y = sims.linear_sim(100, 1) - #savemat('distance matrix data', {'X' : X, 'Y' : Y}) rvcorr = RVCorr(X, Y, None) rvcorr2 = RVCorr(X, Y, None, 'pearson') rvcorr3 = RVCorr(X, Y, None, 'cca') @@ -40,7 +37,6 @@ def test_local_corr(): assert np.round(test_stat3, decimals=2) == 0.24 X, Y = sims.linear_sim(100, 1, noise=0) - #savemat('distance matrix data', {'X' : X, 'Y' : Y}) rvcorr = RVCorr(X, Y, None) rvcorr2 = RVCorr(X, Y, None, 'pearson') rvcorr3 = RVCorr(X, Y, None, 'cca') From c09110cdf664cf86b4bb1b1ab8419004e2faced7 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 16 Nov 2018 10:31:13 -0500 Subject: [PATCH 04/22] Removed Extraneous spacing --- mgcpy/independence_tests/hhg.py | 9 +++++---- mgcpy/independence_tests/unit_tests/hhg_test.py | 9 ++++++--- 2 files changed, 11 insertions(+), 7 deletions(-) diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py index 29e3d6e..526fa3b 100644 --- a/mgcpy/independence_tests/hhg.py +++ b/mgcpy/independence_tests/hhg.py @@ -58,7 +58,7 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None): # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not if (row_X != columns_X or sum(data_matrix_X.diagonal()**2) > 0) and \ - (row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0): + (row_Y != columns_Y or sum(data_matrix_Y.diagonal()**2) > 0): dist_mtx_X, dist_mtx_Y = self.compute_distance_matrix(data_matrix_X, data_matrix_Y) else: dist_mtx_X = data_matrix_X @@ -83,7 +83,7 @@ def test_statistic(self, data_matrix_X=None, data_matrix_Y=None): corr = np.sum(S) return corr - + def p_value(self, replication_factor=100): """ Tests independence between two datasets using HHG and permutation test. @@ -110,7 +110,8 @@ def p_value(self, replication_factor=100): test_stats_null = np.zeros(replication_factor) for rep in range(replication_factor): permuted_y = np.random.permutation(self.data_matrix_Y) - test_stats_null[rep] = self.test_statistic(data_matrix_X=self.data_matrix_X, data_matrix_Y=permuted_y) - + test_stats_null[rep] = self.test_statistic( + data_matrix_X=self.data_matrix_X, data_matrix_Y=permuted_y) + # p-value is the probability of observing more extreme test statistic under the null return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py index f1665a2..dbc0730 100644 --- a/mgcpy/independence_tests/unit_tests/hhg_test.py +++ b/mgcpy/independence_tests/unit_tests/hhg_test.py @@ -1,7 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np -from scipy.spatial.distance import pdist, squareform from mgcpy.independence_tests.hhg import HHG +from scipy.spatial.distance import pdist, squareform def compute_distance_matrix(data_matrix_X, data_matrix_Y): @@ -27,11 +27,14 @@ def test_hhg(): X, Y = sims.linear_sim(100, 1) hhg = HHG(X, Y, compute_distance_matrix) test_stat = hhg.test_statistic() - + assert np.round(test_stat, decimals=2) == 28986.52 X, Y = sims.linear_sim(100, 1, noise=0) hhg = HHG(X, Y, compute_distance_matrix) test_stat = hhg.test_statistic() - assert np.round(test_stat, decimals=2) == 950600.00 \ No newline at end of file + assert np.round(test_stat, decimals=2) == 950600.00 + + +test_hhg() From cdf5d1a3ed76886fd0e282acb933f3708494febd Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Tue, 27 Nov 2018 20:46:35 -0500 Subject: [PATCH 05/22] Added simulations edits --- mgcpy/benchmarks/simulations.py | 8 +- mgcpy/benchmarks/simulations_test.py | 190 ++++++++++++++++++--------- 2 files changed, 135 insertions(+), 63 deletions(-) diff --git a/mgcpy/benchmarks/simulations.py b/mgcpy/benchmarks/simulations.py index 8dbcd51..92a332d 100644 --- a/mgcpy/benchmarks/simulations.py +++ b/mgcpy/benchmarks/simulations.py @@ -147,8 +147,12 @@ def joint_sim(num_samp, num_dim, noise=0.5): samp = (np.random.multivariate_normal(cov=sig, mean=np.zeros(2*num_dim), size=num_samp)) - y = samp[:, num_dim: (2*num_dim)] + kappa*noise*gauss_noise - x = samp[:, 0:num_dim] + if num_dim == 1: + y = samp[:, (num_dim):(2*num_dim)] + kappa*noise*gauss_noise + x = samp[:, 0:num_dim] + else: + y = samp[:, (num_dim+1):(2*num_dim)] + kappa*noise*gauss_noise + x = samp[:, 0:num_dim] return x, y diff --git a/mgcpy/benchmarks/simulations_test.py b/mgcpy/benchmarks/simulations_test.py index e118b9e..ac8861a 100644 --- a/mgcpy/benchmarks/simulations_test.py +++ b/mgcpy/benchmarks/simulations_test.py @@ -1,6 +1,7 @@ import numpy as np from mgcpy.benchmarks import simulations as sims import matplotlib.pyplot as plt +from mpl_toolkits.mplot3d import Axes3D def test_simulations(): @@ -10,8 +11,9 @@ def test_simulations(): independent = True np.random.seed(0) - fig1 = plt.figure(figsize = (50, 80)); + fig1 = plt.figure(figsize = (50, 80)) plt.axis('off') + fig2 = plt.figure(figsize = (50, 80)) # Linear Simulation returns_low_dim = sims.linear_sim(num_samps, num_dim1) @@ -20,10 +22,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.linear_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 1); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 1) + ax1.scatter(x1, y1) ax1.set_title('Linear', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.linear_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 1, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Linear', fontweight='bold') + ax2.axis('off') # Exponential Simulation returns_low_dim = sims.exp_sim(num_samps, num_dim1) @@ -32,10 +40,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.exp_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 2); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 2) + ax1.scatter(x1, y1) ax1.set_title('Exponential', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.exp_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 2, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Exponential', fontweight='bold') + ax2.axis('off') # Cubic Simulation returns_low_dim = sims.cub_sim(num_samps, num_dim1) @@ -44,10 +58,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.cub_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 3); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 3) + ax1.scatter(x1, y1) ax1.set_title('Cubic', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.cub_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 3, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Cubic', fontweight='bold') + ax2.axis('off') # Joint-Normal Simulation returns_low_dim = sims.joint_sim(num_samps, num_dim1) @@ -56,10 +76,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.joint_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 4); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 4) + ax1.scatter(x1, y1) ax1.set_title('Joint Normal', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.joint_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 4, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Joint Normal', fontweight='bold') + ax2.axis('off') # Step Simulation returns_low_dim = sims.step_sim(num_samps, num_dim1) @@ -68,10 +94,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.step_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 5); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 5) + ax1.scatter(x1, y1) ax1.set_title('Step', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.step_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 5, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Step', fontweight='bold') + ax2.axis('off') # Quadratic Simulation returns_low_dim = sims.quad_sim(num_samps, num_dim1) @@ -80,10 +112,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.quad_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 6); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 6) + ax1.scatter(x1, y1) ax1.set_title('Quadratic', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.quad_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 6, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Quadratic', fontweight='bold') + ax2.axis('off') # W Simulation returns_low_dim = sims.w_sim(num_samps, num_dim1) @@ -92,10 +130,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.w_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 7); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 7) + ax1.scatter(x1, y1) ax1.set_title('W-Shaped', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.w_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 7, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('W-Shaped', fontweight='bold') + ax2.axis('off') # Spiral Simulation returns_low_dim = sims.spiral_sim(num_samps, num_dim1) @@ -104,20 +148,32 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.spiral_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 8); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 8) + ax1.scatter(x1, y1) ax1.set_title('Spiral', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.spiral_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 8, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Spiral', fontweight='bold') + ax2.axis('off') # Uncorrelated Bernoulli Simulation returns = sims.ubern_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) x1, y1 = sims.ubern_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 9); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 9) + ax1.scatter(x1, y1) ax1.set_title('Uncorrelated Bernoulli', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.ubern_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 9, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Uncorrelated Bernoulli', fontweight='bold') + ax2.axis('off') # Logarithmic Simulation returns_low_dim = sims.log_sim(num_samps, num_dim1) @@ -126,10 +182,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.log_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 10); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 10) + ax1.scatter(x1, y1) ax1.set_title('Logarithmic', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.log_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 10, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Logarithmic', fontweight='bold') + ax2.axis('off') # Nth Root Simulation returns_low_dim = sims.root_sim(num_samps, num_dim1) @@ -138,10 +200,16 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.root_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 11); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 11) + ax1.scatter(x1, y1) ax1.set_title('Fourth Root', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') + + x2, y2 = sims.root_sim(num_samps, 2, noise=0) + ax2 = fig2.add_subplot(4, 5, 11, projection = '3d'); + ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2.set_title('Fourth Root', fontweight='bold') + ax2.axis('off') # Sinusoidal Simulation (4*pi) returns_low_dim = sims.sin_sim(num_samps, num_dim1) @@ -150,10 +218,10 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.sin_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 12); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 12) + ax1.scatter(x1, y1) ax1.set_title('Sinusoidal (4\u03C0)', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Sinusoidal Simulation (16*pi) returns_low_dim = sims.sin_sim(num_samps, num_dim1, period=16*np.pi) @@ -163,20 +231,20 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi) - ax1 = fig1.add_subplot(4, 5, 13); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 13) + ax1.scatter(x1, y1) ax1.set_title('Sinusoidal (16\u03C0)', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Square Simulation returns = sims.square_sim(num_samps, num_dim2, indep=independent) assert np.all(returns[0].shape == (num_samps, num_dim2)) x1, y1 = sims.square_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 14); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 14) + ax1.scatter(x1, y1) ax1.set_title('Square', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Two Parabolas Simulation returns_low_dim = sims.two_parab_sim(num_samps, num_dim1) @@ -185,30 +253,30 @@ def test_simulations(): assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 15); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 15) + ax1.scatter(x1, y1) ax1.set_title('Two Parabolas', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Circle Simulation returns = sims.circle_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) x1, y1 = sims.circle_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 16); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 16) + ax1.scatter(x1, y1) ax1.set_title('Circle', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Ellipse Simulation returns = sims.circle_sim(num_samps, num_dim2, radius=5) assert np.all(returns[0].shape == (num_samps, num_dim2)) x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5) - ax1 = fig1.add_subplot(4, 5, 17); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 17) + ax1.scatter(x1, y1) ax1.set_title('Ellipse', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Diamond Simulation returns = sims.square_sim( @@ -216,29 +284,29 @@ def test_simulations(): assert np.all(returns[0].shape == (num_samps, num_dim2)) x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4) - ax1 = fig1.add_subplot(4, 5, 18); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 18) + ax1.scatter(x1, y1) ax1.set_title('Diamond', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Multiplicative Noise Simulation returns = sims.multi_noise_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) x1, y1 = sims.multi_noise_sim(num_samps, 1) - ax1 = fig1.add_subplot(4, 5, 19); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 19) + ax1.scatter(x1, y1) ax1.set_title('Multiplicative Noise', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') # Multimodal Independence Simulation returns = sims.multi_indep_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) x1, y1 = sims.multi_indep_sim(num_samps, 1) - ax1 = fig1.add_subplot(4, 5, 20); - ax1.scatter(x1, y1); + ax1 = fig1.add_subplot(4, 5, 20) + ax1.scatter(x1, y1) ax1.set_title('Multimodal Independence', fontweight='bold') - ax1.axis('off'); + ax1.axis('off') test_simulations() \ No newline at end of file From 04d5ea8aeda966c986ec070d7f6abc784d59c4f8 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 30 Nov 2018 08:12:39 -0500 Subject: [PATCH 06/22] Add test back --- mgcpy/independence_tests/hhg.py | 131 ++++++++++++++++++ mgcpy/independence_tests/rv_corr.py | 131 ++++++++++++++++++ .../unit_tests/rv_corr_test.py | 49 +++++++ 3 files changed, 311 insertions(+) create mode 100644 mgcpy/independence_tests/hhg.py create mode 100644 mgcpy/independence_tests/rv_corr.py create mode 100644 mgcpy/independence_tests/unit_tests/rv_corr_test.py diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py new file mode 100644 index 0000000..307782e --- /dev/null +++ b/mgcpy/independence_tests/hhg.py @@ -0,0 +1,131 @@ +import numpy as np +from mgcpy.independence_tests.abstract_class import IndependenceTest +from scipy.spatial import distance_matrix + + +class HHG(IndependenceTest): + def __init__(self, compute_distance_matrix=None): + """ + :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix + :type compute_distance_matrix: FunctionType or callable() + """ + IndependenceTest.__init__(compute_distance_matrix) + + def get_name(self): + ''' + :return: the name of the independence test + :rtype: string + ''' + return 'hhg' + + def test_statistic(self, matrix_X, matrix_Y): + """ + Computes the HHG correlation measure between two datasets. + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :test_statistic_: test statistic + - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.hhg import HHG + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> hhg = HHG() + >>> hhg_test_stat = hhg.test_statistic(X, Y) + """ + row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] + row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] + + # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not + if row_X != columns_X or sum(matrix_X.diagonal()**2) > 0: + dist_mtx_X = distance_matrix(matrix_X, matrix_X) + else: + dist_mtx_X = matrix_X + if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0: + dist_mtx_Y = distance_matrix(matrix_Y, matrix_Y) + else: + dist_mtx_Y = matrix_Y + + n = dist_mtx_X.shape[0] + S = np.zeros((n, n)) + + for i in range(n): + for j in range(n): + if i != j: + tmp1 = dist_mtx_X[i, :] <= dist_mtx_X[i, j] + tmp2 = dist_mtx_Y[i, :] <= dist_mtx_Y[i, j] + t11 = np.sum(tmp1 * tmp2) - 2 + t12 = np.sum(tmp1 * (1-tmp2)) + t21 = np.sum((1-tmp1) * tmp2) + t22 = np.sum((1-tmp1) * (1-tmp2)) + denom = (t11+t12) * (t21+t22) * (t11+t21) * (t12+t22) + if denom > 0: + S[i, j] = (n-2) * \ + np.power((t12*t21 - t11*t22), 2) / denom + corr = np.sum(S) + + # no metadata for HHG + self.test_statistic_metadata_ = {} + self.test_statistic_ = corr + + return self.test_statistic_, self.test_statistic_metadata_ + + def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): + """ + Tests independence between two datasets using HHG and permutation test. + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :p_value_: P-value + - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.hhg import HHG + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> hhg = HHG() + >>> hhg_p_value = hhg.p_value(X, Y) + """ + test_stat = self.test_statistic() + # estimate the null by a permutation test + test_stats_null = np.zeros(replication_factor) + for rep in range(replication_factor): + permuted_y = np.random.permutation(self.matrix_Y) + test_stats_null[rep] = self.test_statistic(matrix_X=self.matrix_X, matrix_Y=permuted_y) + + # p-value is the probability of observing more extreme test statistic under the null + self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor + self.p_value_metadata_ = {} + + return self.p_value_, self.p_value_metadata_ diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py new file mode 100644 index 0000000..a207bb4 --- /dev/null +++ b/mgcpy/independence_tests/rv_corr.py @@ -0,0 +1,131 @@ +import numpy as np +from mgcpy.independence_tests.abstract_class import IndependenceTest +from numpy import matlib as mb +from scipy.sparse.linalg import svds +from scipy.stats import pearsonr + + +class RVCorr(IndependenceTest): + def __init__(self, compute_distance_matrix=None, which_test='rv'): + """ + :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix + :type compute_distance_matrix: FunctionType or callable() + + :param which_test: specifies which test to use, including 'rv', 'pearson', and 'cca'. + :type which_test: str + """ + IndependenceTest.__init__(self, compute_distance_matrix) + self.which_test = which_test + + def get_name(self): + ''' + :return: the name of the independence test + :rtype: string + ''' + return self.which_test + + def test_statistic(self, matrix_X=None, matrix_Y=None): + """ + Computes the Pearson/RV/CCa correlation measure between two datasets. + - Default computes linear correlation for RV + - Computes pearson's correlation + - Calculates local linear correlations for CCa + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :test_statistic_: test statistic + - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.rv_corr import RVCorr + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> rvcorr = RVCorr() + >>> rvcorr_test_stat = rvcorr.test_statistic(X, Y) + """ + row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] + row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] + + mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0), + matrix_X.shape[0], 1) + mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0), + matrix_Y.shape[0], 1) + + covar = np.dot(mat1.T, mat2) + varX = np.dot(mat1.T, mat1) + varY = np.dot(mat2.T, mat2) + + if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)): + corr, covar = pearsonr(matrix_X, matrix_Y) + elif (self.which_test == 'rv'): + covar = np.trace(np.dot(covar, covar.T)) + corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX)) + * np.trace(np.dot(varY, varY)))) + else: + if varX.size == 1 or varY.size == 1 or covar.size == 1: + covar = np.sum(np.power(covar, 2)) + corr = np.divide(covar, np.sqrt(np.sum(np.power(varX, 2)) + * np.sum(np.power(varY, 2)))) + else: + covar = np.sum(np.power(svds(covar, 1)[1], 2)) + corr = np.divide(covar, np.sqrt(np.sum(np.power(svds(varX, 1)[1], 2)) + * np.sum(np.power(svds(varY, 1)[1], 2)))) + self.test_statistic_ = corr + self.test_statistic_metadata_ = {"covariance": covar} + + return self.test_statistic_, self.test_statistic_metadata_ + + def p_value(self, matrix_X, matrix_Y, replication_factor=1000): + """ + Tests independence between two datasets using the independence test. + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :p_value_: P-value + - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.rv_corr import RVCorr + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> rvcorr = RVCorr() + >>> rvcorr_p_value = rvcorr.p_value(X, Y) + """ + if matrix_X is None: + matrix_X = self.matrix_X + if matrix_Y is None: + matrix_Y = self.matrix_Y + self.p_value_ = self.test_statistic(matrix_X, matrix_Y) + self.p_value_metadata_ = {} + + return self.p_value_, self.p_value_metadata_ diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py new file mode 100644 index 0000000..27b3e2b --- /dev/null +++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py @@ -0,0 +1,49 @@ +import mgcpy.benchmarks.simulations as sims +import numpy as np +from mgcpy.independence_tests.rv_corr import RVCorr + +# from scipy.io import savemat + + +def test_local_corr(): + # Against a randomly defined data set + X = np.array([1.1728, 2.4941, 2.4101, 0.1814, 1.1978, 1.5806, 1.2504, + 1.9706, 1.8839, 0.8760])[:, np.newaxis] + Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917, + 7.1748, 6.5792, 2.4012])[:, np.newaxis] + rvcorr = RVCorr(None) + rvcorr2 = RVCorr(None, 'pearson') + rvcorr3 = RVCorr(None, 'cca') + + test_stat1 = rvcorr.test_statistic(X, Y)[0] + test_stat2 = rvcorr2.test_statistic(X, Y)[0] + test_stat3 = rvcorr3.test_statistic(X, Y)[0] + + assert np.round(test_stat1, decimals=2) == 0.90 + assert np.round(test_stat2, decimals=2) == 0.95 + assert np.round(test_stat3, decimals=2) == 0.90 + + del X, Y, rvcorr, rvcorr2, rvcorr3, test_stat1, test_stat2, test_stat3 + + # Against linear simulations + np.random.seed(0) + X, Y = sims.linear_sim(100, 1) + # savemat('distance matrix data', {'X' : X, 'Y' : Y}) + rvcorr = RVCorr(None) + rvcorr2 = RVCorr(None, 'pearson') + rvcorr3 = RVCorr(None, 'cca') + + assert rvcorr.get_name() == 'rv' + assert rvcorr2.get_name() == 'pearson' + assert rvcorr3.get_name() == 'cca' + + test_stat1 = rvcorr.test_statistic(X, Y)[0] + test_stat2 = rvcorr2.test_statistic(X, Y)[0] + test_stat3 = rvcorr3.test_statistic(X, Y)[0] + + assert np.round(test_stat1, decimals=2) == 0.24 + assert np.round(test_stat2, decimals=2) == 0.49 + assert np.round(test_stat3, decimals=2) == 0.24 + + +test_local_corr() From ae83c07365ae91606ea3e9b977482aa6c355ba82 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 30 Nov 2018 11:15:29 -0500 Subject: [PATCH 07/22] Edited the test and added demo --- demos/mcorr_dcorr_mantel.ipynb | 2 +- demos/rv_cca_hhg.ipynb | 264 ++++++++++++++++++ mgcpy/independence_tests/hhg.py | 15 +- mgcpy/independence_tests/kendall_spearman.py | 38 ++- mgcpy/independence_tests/rv_corr.py | 21 +- .../independence_tests/unit_tests/hhg_test.py | 27 +- .../unit_tests/kendall_spearman_test.py | 35 +++ .../unit_tests/rv_corr_test.py | 17 +- 8 files changed, 347 insertions(+), 72 deletions(-) create mode 100644 demos/rv_cca_hhg.ipynb create mode 100644 mgcpy/independence_tests/unit_tests/kendall_spearman_test.py diff --git a/demos/mcorr_dcorr_mantel.ipynb b/demos/mcorr_dcorr_mantel.ipynb index 1f7727b..04fff1d 100644 --- a/demos/mcorr_dcorr_mantel.ipynb +++ b/demos/mcorr_dcorr_mantel.ipynb @@ -435,7 +435,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.4" + "version": "3.6.6" } }, "nbformat": 4, diff --git a/demos/rv_cca_hhg.ipynb b/demos/rv_cca_hhg.ipynb new file mode 100644 index 0000000..3a064f3 --- /dev/null +++ b/demos/rv_cca_hhg.ipynb @@ -0,0 +1,264 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 174, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.spatial.distance import pdist, squareform\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 175, + "metadata": {}, + "outputs": [], + "source": [ + "from mgcpy import RVCorr, HHG\n", + "from mgcpy.benchmarks.power import power\n", + "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, ubern_sim, exp_sim, w_sim, joint_sim, spiral_sim" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Statistic" + ] + }, + { + "cell_type": "code", + "execution_count": 176, + "metadata": {}, + "outputs": [], + "source": [ + "def test_stats_vs_dimension(corr_type, simulation_type, dim_range):\n", + " test_stats = []\n", + " for d in range(1, dim_range+1):\n", + " x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n", + " if corr_type == 'rv' or corr_type == 'cca':\n", + " corr = RVCorr(which_test=corr_type)\n", + " #else:\n", + " #corr = HHG()\n", + " test_stats.append(corr.test_statistic(x, y)[0])\n", + " return test_stats" + ] + }, + { + "cell_type": "code", + "execution_count": 177, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_test_stats(simulation_type, dim_range, simulation_name):\n", + " rv_test_stats = test_stats_vs_dimension('rv', simulation_type, dim_range)\n", + " cca_test_stats = test_stats_vs_dimension('cca', simulation_type, dim_range)\n", + " #hhg_test_stats = test_stats_vs_dimension('hhg', simulation_type, dim_range) \n", + " plt.plot(rv_test_stats, label='RV')\n", + " plt.plot(cca_test_stats, label='CCA')\n", + " #plt.plot(hhg_test_stats, label='HHG')\n", + " plt.xlabel('Dimensions')\n", + " plt.ylabel('Test Statistics')\n", + " plt.legend()\n", + " plt.gca().set_xlim(1, dim_range+1)\n", + " plt.xticks(np.arange(0, dim_range+1, 5))\n", + " plt.title('Test Statistics \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 178, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_test_stats(quad_sim, 20, 'Quadratic')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## P-value" + ] + }, + { + "cell_type": "code", + "execution_count": 184, + "metadata": {}, + "outputs": [], + "source": [ + "def pvalue_vs_dimension(corr_type, simulation_type, dim_range):\n", + " p_value = []\n", + " for d in range(1, dim_range+1):\n", + " x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n", + " if corr_type == 'rv' or corr_type == 'cca':\n", + " corr = RVCorr(which_test=corr_type)\n", + " #else:\n", + " #corr = HHG()\n", + " p_value.append(corr.p_value(x, y)[0])\n", + " return p_value" + ] + }, + { + "cell_type": "code", + "execution_count": 185, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_p_value(simulation_type, dim_range, simulation_name):\n", + " rv_pvalue = pvalue_vs_dimension('rv', simulation_type, dim_range)\n", + " cca_pvalue = pvalue_vs_dimension('cca', simulation_type, dim_range)\n", + " #hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\n", + " plt.plot(rv_pvalue, label='RV')\n", + " plt.plot(cca_pvalue, label='CCA')\n", + " #plt.plot(hhg_pvalue, label='HHG')\n", + " plt.xlabel('Dimensions')\n", + " plt.ylabel('pvalue')\n", + " plt.legend()\n", + " plt.gca().set_xlim(1, dim_range+1)\n", + " plt.xticks(np.arange(0, dim_range+1, 5))\n", + " plt.title('P-value \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 186, + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "float() argument must be a string or a number, not 'dict'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_p_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlinear_sim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Linear'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mplot_p_value\u001b[0;34m(simulation_type, dim_range, simulation_name)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mcca_pvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpvalue_vs_dimension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'cca'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msimulation_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;31m#hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'RV'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcca_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'CCA'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;31m#plt.plot(hhg_pvalue, label='HHG')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 2747\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2748\u001b[0m return gca().plot(\n\u001b[0;32m-> 2749\u001b[0;31m *args, scalex=scalex, scaley=scaley, data=data, **kwargs)\n\u001b[0m\u001b[1;32m 2750\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2751\u001b[0m \u001b[0;31m# Autogenerated by boilerplate.py. 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\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36masarray\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m 499\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 500\u001b[0m \"\"\"\n\u001b[0;32m--> 501\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 502\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 503\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: float() argument must be a string or a number, not 'dict'" + ] + }, + { + "data": { + "image/png": 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dist_mtx_X = distance_matrix(matrix_X, matrix_X) + dist_mtx_X = self.compute_distance_matrix(matrix_X) else: dist_mtx_X = matrix_X if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0: - dist_mtx_Y = distance_matrix(matrix_Y, matrix_Y) + dist_mtx_Y = self.compute_distance_matrix(matrix_Y) else: dist_mtx_Y = matrix_Y @@ -84,7 +83,7 @@ def test_statistic(self, matrix_X, matrix_Y): self.test_statistic_metadata_ = {} self.test_statistic_ = corr - return self.test_statistic_, self.test_statistic_metadata_ + return corr, {} def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): """ @@ -117,15 +116,15 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): >>> hhg = HHG() >>> hhg_p_value = hhg.p_value(X, Y) """ - test_stat = self.test_statistic() + test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0] # estimate the null by a permutation test test_stats_null = np.zeros(replication_factor) for rep in range(replication_factor): - permuted_y = np.random.permutation(self.matrix_Y) - test_stats_null[rep] = self.test_statistic(matrix_X=self.matrix_X, matrix_Y=permuted_y) + permuted_y = np.random.permutation(matrix_Y) + test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0] # p-value is the probability of observing more extreme test statistic under the null self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor self.p_value_metadata_ = {} - return self.p_value_, self.p_value_metadata_ + return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {} \ No newline at end of file diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py index acf2b68..10c0cce 100644 --- a/mgcpy/independence_tests/kendall_spearman.py +++ b/mgcpy/independence_tests/kendall_spearman.py @@ -49,30 +49,27 @@ def test_statistic(self, matrix_X, matrix_Y): >>> kendall_spearman = KendallSpearman() >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y) """ - if matrix_X is None: - matrix_X = self.matrix_X - if matrix_Y is None: - matrix_Y = self.matrix_Y assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape" assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape" - - if self.which_test == 'kendall': - self.test_statistic_ = kendalltau(matrix_X, matrix_Y)[0] + + if self.which_test == 'kendall': + test_statistic_ = kendalltau(matrix_X, matrix_Y)[0] else: - self.test_statistic_ = spearmanr(matrix_X, matrix_Y)[0] + test_statistic_ = spearmanr(matrix_X, matrix_Y)[0] + self.test_statistic_ = test_statistic_ self.test_statistic_metadata_ = {} - return self.test_statistic_, self.test_statistic_metadata_ + return test_statistic_, {} def p_value(self, matrix_X, matrix_Y, replication_factor=1000): """ Tests independence between two datasets using the independence test. - :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :param matrix_X: a [n*1] data matrix, a square matrix with n samples in p dimensions :type matrix_X: 2D `numpy.array` - :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in q dimensions :type matrix_Y: 2D `numpy.array` :param replication_factor: specifies the number of replications to use for @@ -96,18 +93,17 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): >>> kendall_spearman = KendallSpearman() >>> kendall_spearman_p_value = kendall_spearman.p_value(X, Y) """ - if matrix_X is None: - matrix_X = self.matrix_X - if matrix_Y is None: - matrix_Y = self.matrix_Y - assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape" - assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape" - + row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] + row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] + assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape" + assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape" + if self.which_test == 'kendall': - self.p_value_ = kendalltau(matrix_X, matrix_Y)[1] + p_value_ = kendalltau(matrix_X, matrix_Y)[1] else: - self.p_value_ = spearmanr(matrix_X, matrix_Y)[1] + p_value_ = spearmanr(matrix_X, matrix_Y)[1] + self.p_value_ = p_value_ self.p_value_metadata_ = {} - return self.p_value_, self.p_value_metadata_ + return p_value_, {} \ No newline at end of file diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py index a207bb4..1ac1b27 100644 --- a/mgcpy/independence_tests/rv_corr.py +++ b/mgcpy/independence_tests/rv_corr.py @@ -70,7 +70,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None): varX = np.dot(mat1.T, mat1) varY = np.dot(mat2.T, mat2) - if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)): + if (self.which_test == 'pearson'): + assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape" + assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape" corr, covar = pearsonr(matrix_X, matrix_Y) elif (self.which_test == 'rv'): covar = np.trace(np.dot(covar, covar.T)) @@ -88,9 +90,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None): self.test_statistic_ = corr self.test_statistic_metadata_ = {"covariance": covar} - return self.test_statistic_, self.test_statistic_metadata_ + return corr, {"covariance": covar} - def p_value(self, matrix_X, matrix_Y, replication_factor=1000): + def p_value(self, matrix_X, matrix_Y, replication_factor=None): """ Tests independence between two datasets using the independence test. @@ -101,7 +103,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): :type matrix_Y: 2D `numpy.array` :param replication_factor: specifies the number of replications to use for - the permutation test. Defaults to 1000. + the permutation test. Defaults to None. :type replication_factor: int :return: returns a list of two items, that contains: @@ -121,11 +123,8 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): >>> rvcorr = RVCorr() >>> rvcorr_p_value = rvcorr.p_value(X, Y) """ - if matrix_X is None: - matrix_X = self.matrix_X - if matrix_Y is None: - matrix_Y = self.matrix_Y - self.p_value_ = self.test_statistic(matrix_X, matrix_Y) + test_stat = self.test_statistic(matrix_X, matrix_Y)[0] + self.p_value_ = np.abs(test_stat) self.p_value_metadata_ = {} - - return self.p_value_, self.p_value_metadata_ + + return np.abs(test_stat), {} diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py index dbc0730..5379450 100644 --- a/mgcpy/independence_tests/unit_tests/hhg_test.py +++ b/mgcpy/independence_tests/unit_tests/hhg_test.py @@ -1,14 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np -from mgcpy.independence_tests.hhg import HHG -from scipy.spatial.distance import pdist, squareform - - -def compute_distance_matrix(data_matrix_X, data_matrix_Y): - # obtain the pairwise distance matrix for X and Y - dist_mtx_X = squareform(pdist(data_matrix_X, metric='euclidean')) - dist_mtx_Y = squareform(pdist(data_matrix_Y, metric='euclidean')) - return (dist_mtx_X, dist_mtx_Y) +from mgcpy import HHG +import pytest def test_hhg(): @@ -17,24 +10,22 @@ def test_hhg(): 1.9706, 1.8839, 0.8760])[:, np.newaxis] Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917, 7.1748, 6.5792, 2.4012])[:, np.newaxis] - hhg = HHG(X, Y, compute_distance_matrix) - test_stat = hhg.test_statistic() + hhg = HHG() + test_stat = hhg.test_statistic(X, Y) assert np.round(test_stat, decimals=2) == 411.88 # Against linear simulations np.random.seed(0) X, Y = sims.linear_sim(100, 1) - hhg = HHG(X, Y, compute_distance_matrix) - test_stat = hhg.test_statistic() + hhg = HHG() + test_stat = hhg.test_statistic(X, Y) assert np.round(test_stat, decimals=2) == 28986.52 X, Y = sims.linear_sim(100, 1, noise=0) - hhg = HHG(X, Y, compute_distance_matrix) - test_stat = hhg.test_statistic() + hhg = HHG() + test_stat = hhg.test_statistic(X, Y) assert np.round(test_stat, decimals=2) == 950600.00 - - -test_hhg() +test_hhg() \ No newline at end of file diff --git a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py new file mode 100644 index 0000000..c9fa50f --- /dev/null +++ b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py @@ -0,0 +1,35 @@ +import mgcpy.benchmarks.simulations as sims +import numpy as np +from mgcpy import KendallSpearman +import pytest + + +def test_kendall_spearman(): + # Against a randomly defined data set + X = np.array([1.1728, 2.4941, 2.4101, 0.1814, 1.1978, 1.5806, 1.2504, + 1.9706, 1.8839, 0.8760])[:, np.newaxis] + Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917, + 7.1748, 6.5792, 2.4012])[:, np.newaxis] + kspear = KendallSpearman(None) + kspear2 = KendallSpearman(None, 'spearman') + + test_stat1 = kspear.test_statistic(X, Y)[0] + test_stat2 = kspear2.test_statistic(X, Y)[0] + + assert np.round(test_stat1, decimals=2) == 1.00 + assert np.round(test_stat2, decimals=2) == 1.00 + + # Against linear simulations + np.random.seed(0) + X, Y = sims.linear_sim(100, 1) + kspear = KendallSpearman(None) + kspear2 = KendallSpearman(None, 'spearman') + + assert kspear.get_name() == 'kendall' + assert kspear2.get_name() == 'spearman' + + test_stat1 = kspear.test_statistic(X, Y)[0] + test_stat2 = kspear2.test_statistic(X, Y)[0] + + assert np.round(test_stat1, decimals=2) == 0.33 + assert np.round(test_stat2, decimals=2) == 0.48 \ No newline at end of file diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py index 27b3e2b..439e3ee 100644 --- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py +++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py @@ -1,8 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np -from mgcpy.independence_tests.rv_corr import RVCorr - -# from scipy.io import savemat +from mgcpy import RVCorr +import pytest def test_local_corr(): @@ -14,21 +13,17 @@ def test_local_corr(): rvcorr = RVCorr(None) rvcorr2 = RVCorr(None, 'pearson') rvcorr3 = RVCorr(None, 'cca') - + test_stat1 = rvcorr.test_statistic(X, Y)[0] test_stat2 = rvcorr2.test_statistic(X, Y)[0] test_stat3 = rvcorr3.test_statistic(X, Y)[0] - assert np.round(test_stat1, decimals=2) == 0.90 assert np.round(test_stat2, decimals=2) == 0.95 assert np.round(test_stat3, decimals=2) == 0.90 - del X, Y, rvcorr, rvcorr2, rvcorr3, test_stat1, test_stat2, test_stat3 - # Against linear simulations np.random.seed(0) X, Y = sims.linear_sim(100, 1) - # savemat('distance matrix data', {'X' : X, 'Y' : Y}) rvcorr = RVCorr(None) rvcorr2 = RVCorr(None, 'pearson') rvcorr3 = RVCorr(None, 'cca') @@ -40,10 +35,6 @@ def test_local_corr(): test_stat1 = rvcorr.test_statistic(X, Y)[0] test_stat2 = rvcorr2.test_statistic(X, Y)[0] test_stat3 = rvcorr3.test_statistic(X, Y)[0] - assert np.round(test_stat1, decimals=2) == 0.24 assert np.round(test_stat2, decimals=2) == 0.49 - assert np.round(test_stat3, decimals=2) == 0.24 - - -test_local_corr() + assert np.round(test_stat3, decimals=2) == 0.24 \ No newline at end of file From 574ad5f96617d4146ea91dfdc0f5b086988858ff Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 30 Nov 2018 11:31:11 -0500 Subject: [PATCH 08/22] Fixed docstrings --- mgcpy/independence_tests/hhg.py | 22 +++++++-------- mgcpy/independence_tests/kendall_spearman.py | 28 +++++++++++--------- mgcpy/independence_tests/rv_corr.py | 24 ++++++++++------- 3 files changed, 41 insertions(+), 33 deletions(-) diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py index 4edb962..80751c9 100644 --- a/mgcpy/independence_tests/hhg.py +++ b/mgcpy/independence_tests/hhg.py @@ -1,3 +1,7 @@ +""" + **HHG Class** +""" + import numpy as np from mgcpy.independence_tests.abstract_class import IndependenceTest @@ -6,7 +10,7 @@ class HHG(IndependenceTest): def __init__(self, compute_distance_matrix=None): """ :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix - :type compute_distance_matrix: FunctionType or callable() + :type compute_distance_matrix: ``FunctionType`` or ``callable()`` """ IndependenceTest.__init__(compute_distance_matrix) @@ -21,16 +25,12 @@ def test_statistic(self, matrix_X, matrix_Y): """ Computes the HHG correlation measure between two datasets. - :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions :type matrix_X: 2D `numpy.array` - :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions :type matrix_Y: 2D `numpy.array` - :param replication_factor: specifies the number of replications to use for - the permutation test. Defaults to 1000. - :type replication_factor: int - :return: returns a list of two items, that contains: - :test_statistic_: test statistic - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, @@ -89,21 +89,21 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): """ Tests independence between two datasets using HHG and permutation test. - :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions :type matrix_X: 2D `numpy.array` - :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions :type matrix_Y: 2D `numpy.array` :param replication_factor: specifies the number of replications to use for the permutation test. Defaults to 1000. - :type replication_factor: int + :type replication_factor: integer :return: returns a list of two items, that contains: - :p_value_: P-value - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, that the independence tests computes in the process - :rtype: float, dict + :rtype: list **Example:** >>> import numpy as np diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py index 10c0cce..16a583b 100644 --- a/mgcpy/independence_tests/kendall_spearman.py +++ b/mgcpy/independence_tests/kendall_spearman.py @@ -1,3 +1,7 @@ +""" + **Kendall and Spearman Class** +""" + from mgcpy.independence_tests.abstract_class import IndependenceTest from scipy.stats import kendalltau, spearmanr @@ -6,10 +10,10 @@ class KendallSpearman(IndependenceTest): def __init__(self, compute_distance_matrix=None, which_test='kendall'): """ :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix - :type compute_distance_matrix: FunctionType or callable() + :type compute_distance_matrix: ``FunctionType`` or ``callable()`` - :param which_test: specifies which test to use, including 'kendall' or 'spearman' - :type which_test: str + :param which_test: specifies which test to use, including ``'kendall'`` or ``'spearman'`` + :type which_test: string """ IndependenceTest.__init__(self, compute_distance_matrix) self.which_test = which_test @@ -26,17 +30,17 @@ def test_statistic(self, matrix_X, matrix_Y): Computes the Spearman's rho or Kendall's tau measure between two datasets. - Implments scipy.stats's implementation for both - :param matrix_X: a [n*1] data matrix, a square matrix with n samples in 1 dimension - :type matrix_X: 1D numpy.array + :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension + :type matrix_X: 1D `numpy.array` - :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in 1 dimension - :type matrix_Y: 1D numpy.array + :param matrix_Y: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension + :type matrix_Y: 1D `numpy.array` :return: returns a list of two items, that contains: - :test_stat_: test statistic - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, that the independence tests computes in the process - :rtype: float, dict + :rtype: list **Example:** >>> import numpy as np @@ -66,21 +70,21 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): """ Tests independence between two datasets using the independence test. - :param matrix_X: a [n*1] data matrix, a square matrix with n samples in p dimensions + :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension :type matrix_X: 2D `numpy.array` - :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in q dimensions + :param matrix_Y: a ``[n*1] data`` matrix, a square matrix with ``n`` samples in ``1`` dimensions :type matrix_Y: 2D `numpy.array` :param replication_factor: specifies the number of replications to use for the permutation test. Defaults to 1000. - :type replication_factor: int + :type replication_factor: integer :return: returns a list of two items, that contains: - :p_value_: P-value - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, that the independence tests computes in the process - :rtype: float, dict + :rtype: list **Example:** >>> import numpy as np diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py index 1ac1b27..61afb14 100644 --- a/mgcpy/independence_tests/rv_corr.py +++ b/mgcpy/independence_tests/rv_corr.py @@ -1,3 +1,7 @@ +""" + **RVCorr Class** +""" + import numpy as np from mgcpy.independence_tests.abstract_class import IndependenceTest from numpy import matlib as mb @@ -9,10 +13,10 @@ class RVCorr(IndependenceTest): def __init__(self, compute_distance_matrix=None, which_test='rv'): """ :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix - :type compute_distance_matrix: FunctionType or callable() + :type compute_distance_matrix: ``FunctionType`` or ``callable()`` - :param which_test: specifies which test to use, including 'rv', 'pearson', and 'cca'. - :type which_test: str + :param which_test: specifies which test to use, including ``'rv'``, ``'pearson'``, and ``'cca'``. + :type which_test: string """ IndependenceTest.__init__(self, compute_distance_matrix) self.which_test = which_test @@ -31,10 +35,10 @@ def test_statistic(self, matrix_X=None, matrix_Y=None): - Computes pearson's correlation - Calculates local linear correlations for CCa - :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions :type matrix_X: 2D `numpy.array` - :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions :type matrix_Y: 2D `numpy.array` :param replication_factor: specifies the number of replications to use for @@ -45,7 +49,7 @@ def test_statistic(self, matrix_X=None, matrix_Y=None): - :test_statistic_: test statistic - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, that the independence tests computes in the process - :rtype: float, dict + :rtype: list **Example:** >>> import numpy as np @@ -96,21 +100,21 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None): """ Tests independence between two datasets using the independence test. - :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p``` dimensions :type matrix_X: 2D `numpy.array` - :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions :type matrix_Y: 2D `numpy.array` :param replication_factor: specifies the number of replications to use for the permutation test. Defaults to None. - :type replication_factor: int + :type replication_factor: integer :return: returns a list of two items, that contains: - :p_value_: P-value - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, that the independence tests computes in the process - :rtype: float, dict + :rtype: list **Example:** >>> import numpy as np From acf1d66afa3af0e12b3198c0e92d9e34a3a89d2f Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 30 Nov 2018 11:38:16 -0500 Subject: [PATCH 09/22] Fixed docstrings --- mgcpy/independence_tests/hhg.py | 6 +++--- mgcpy/independence_tests/kendall_spearman.py | 5 +++-- mgcpy/independence_tests/rv_corr.py | 6 +++--- 3 files changed, 9 insertions(+), 8 deletions(-) diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py index 80751c9..42365e1 100644 --- a/mgcpy/independence_tests/hhg.py +++ b/mgcpy/independence_tests/hhg.py @@ -1,5 +1,5 @@ """ - **HHG Class** + **HHG Independence Test Module** """ import numpy as np @@ -38,9 +38,9 @@ def test_statistic(self, matrix_X, matrix_Y): :rtype: float, dict **Example:** + >>> import numpy as np >>> from mgcpy.independence_tests.hhg import HHG - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, @@ -106,9 +106,9 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): :rtype: list **Example:** + >>> import numpy as np >>> from mgcpy.independence_tests.hhg import HHG - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py index 16a583b..9ee438b 100644 --- a/mgcpy/independence_tests/kendall_spearman.py +++ b/mgcpy/independence_tests/kendall_spearman.py @@ -1,5 +1,5 @@ """ - **Kendall and Spearman Class** + **Kendall and Spearman ndependence Test Module** """ from mgcpy.independence_tests.abstract_class import IndependenceTest @@ -43,6 +43,7 @@ def test_statistic(self, matrix_X, matrix_Y): :rtype: list **Example:** + >>> import numpy as np >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman @@ -87,9 +88,9 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): :rtype: list **Example:** + >>> import numpy as np >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py index 61afb14..ac0c70e 100644 --- a/mgcpy/independence_tests/rv_corr.py +++ b/mgcpy/independence_tests/rv_corr.py @@ -1,5 +1,5 @@ """ - **RVCorr Class** + **RVCorr Independence Test Module** """ import numpy as np @@ -52,9 +52,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None): :rtype: list **Example:** + >>> import numpy as np >>> from mgcpy.independence_tests.rv_corr import RVCorr - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, @@ -117,9 +117,9 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None): :rtype: list **Example:** + >>> import numpy as np >>> from mgcpy.independence_tests.rv_corr import RVCorr - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, From 3d0e977a7d11694972b1dc3ce33d7717907d7145 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 30 Nov 2018 12:03:46 -0500 Subject: [PATCH 10/22] Pep8 --- mgcpy/independence_tests/hhg.py | 10 +++++----- mgcpy/independence_tests/kendall_spearman.py | 12 ++++++------ mgcpy/independence_tests/rv_corr.py | 12 ++++++------ mgcpy/independence_tests/unit_tests/hhg_test.py | 6 ++++-- .../unit_tests/kendall_spearman_test.py | 4 ++-- mgcpy/independence_tests/unit_tests/rv_corr_test.py | 6 +++--- 6 files changed, 26 insertions(+), 24 deletions(-) diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py index 42365e1..7d9998b 100644 --- a/mgcpy/independence_tests/hhg.py +++ b/mgcpy/independence_tests/hhg.py @@ -38,7 +38,7 @@ def test_statistic(self, matrix_X, matrix_Y): :rtype: float, dict **Example:** - + >>> import numpy as np >>> from mgcpy.independence_tests.hhg import HHG >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, @@ -82,7 +82,7 @@ def test_statistic(self, matrix_X, matrix_Y): # no metadata for HHG self.test_statistic_metadata_ = {} self.test_statistic_ = corr - + return corr, {} def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): @@ -106,7 +106,7 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): :rtype: list **Example:** - + >>> import numpy as np >>> from mgcpy.independence_tests.hhg import HHG >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, @@ -126,5 +126,5 @@ def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): # p-value is the probability of observing more extreme test statistic under the null self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor self.p_value_metadata_ = {} - - return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {} \ No newline at end of file + + return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {} diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py index 9ee438b..096bb13 100644 --- a/mgcpy/independence_tests/kendall_spearman.py +++ b/mgcpy/independence_tests/kendall_spearman.py @@ -43,7 +43,7 @@ def test_statistic(self, matrix_X, matrix_Y): :rtype: list **Example:** - + >>> import numpy as np >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman @@ -56,8 +56,8 @@ def test_statistic(self, matrix_X, matrix_Y): """ assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape" assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape" - - if self.which_test == 'kendall': + + if self.which_test == 'kendall': test_statistic_ = kendalltau(matrix_X, matrix_Y)[0] else: test_statistic_ = spearmanr(matrix_X, matrix_Y)[0] @@ -88,7 +88,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): :rtype: list **Example:** - + >>> import numpy as np >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, @@ -102,7 +102,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape" assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape" - + if self.which_test == 'kendall': p_value_ = kendalltau(matrix_X, matrix_Y)[1] else: @@ -111,4 +111,4 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): self.p_value_ = p_value_ self.p_value_metadata_ = {} - return p_value_, {} \ No newline at end of file + return p_value_, {} diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py index ac0c70e..3dca185 100644 --- a/mgcpy/independence_tests/rv_corr.py +++ b/mgcpy/independence_tests/rv_corr.py @@ -1,7 +1,7 @@ """ **RVCorr Independence Test Module** """ - + import numpy as np from mgcpy.independence_tests.abstract_class import IndependenceTest from numpy import matlib as mb @@ -52,7 +52,7 @@ def test_statistic(self, matrix_X=None, matrix_Y=None): :rtype: list **Example:** - + >>> import numpy as np >>> from mgcpy.independence_tests.rv_corr import RVCorr >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, @@ -66,9 +66,9 @@ def test_statistic(self, matrix_X=None, matrix_Y=None): row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0), - matrix_X.shape[0], 1) + matrix_X.shape[0], 1) mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0), - matrix_Y.shape[0], 1) + matrix_Y.shape[0], 1) covar = np.dot(mat1.T, mat2) varX = np.dot(mat1.T, mat1) @@ -117,7 +117,7 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None): :rtype: list **Example:** - + >>> import numpy as np >>> from mgcpy.independence_tests.rv_corr import RVCorr >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, @@ -130,5 +130,5 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None): test_stat = self.test_statistic(matrix_X, matrix_Y)[0] self.p_value_ = np.abs(test_stat) self.p_value_metadata_ = {} - + return np.abs(test_stat), {} diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py index 5379450..9c65b9b 100644 --- a/mgcpy/independence_tests/unit_tests/hhg_test.py +++ b/mgcpy/independence_tests/unit_tests/hhg_test.py @@ -1,7 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np -from mgcpy import HHG import pytest +from mgcpy import HHG def test_hhg(): @@ -28,4 +28,6 @@ def test_hhg(): test_stat = hhg.test_statistic(X, Y) assert np.round(test_stat, decimals=2) == 950600.00 -test_hhg() \ No newline at end of file + + +test_hhg() diff --git a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py index c9fa50f..1937704 100644 --- a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py +++ b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py @@ -1,7 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np -from mgcpy import KendallSpearman import pytest +from mgcpy import KendallSpearman def test_kendall_spearman(): @@ -32,4 +32,4 @@ def test_kendall_spearman(): test_stat2 = kspear2.test_statistic(X, Y)[0] assert np.round(test_stat1, decimals=2) == 0.33 - assert np.round(test_stat2, decimals=2) == 0.48 \ No newline at end of file + assert np.round(test_stat2, decimals=2) == 0.48 diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py index 439e3ee..4aee659 100644 --- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py +++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py @@ -1,7 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np -from mgcpy import RVCorr import pytest +from mgcpy import RVCorr def test_local_corr(): @@ -13,7 +13,7 @@ def test_local_corr(): rvcorr = RVCorr(None) rvcorr2 = RVCorr(None, 'pearson') rvcorr3 = RVCorr(None, 'cca') - + test_stat1 = rvcorr.test_statistic(X, Y)[0] test_stat2 = rvcorr2.test_statistic(X, Y)[0] test_stat3 = rvcorr3.test_statistic(X, Y)[0] @@ -37,4 +37,4 @@ def test_local_corr(): test_stat3 = rvcorr3.test_statistic(X, Y)[0] assert np.round(test_stat1, decimals=2) == 0.24 assert np.round(test_stat2, decimals=2) == 0.49 - assert np.round(test_stat3, decimals=2) == 0.24 \ No newline at end of file + assert np.round(test_stat3, decimals=2) == 0.24 From 8f3f39f6be9048a65b206a9d30d4da685271fac0 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Mon, 3 Dec 2018 14:24:39 -0500 Subject: [PATCH 11/22] Fix rv_corr permutation test --- mgcpy/independence_tests/rv_corr.py | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py index 3dca185..024481a 100644 --- a/mgcpy/independence_tests/rv_corr.py +++ b/mgcpy/independence_tests/rv_corr.py @@ -127,8 +127,15 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=None): >>> rvcorr = RVCorr() >>> rvcorr_p_value = rvcorr.p_value(X, Y) """ - test_stat = self.test_statistic(matrix_X, matrix_Y)[0] - self.p_value_ = np.abs(test_stat) + test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0] + # estimate the null by a permutation test + test_stats_null = np.zeros(replication_factor) + for rep in range(replication_factor): + permuted_y = np.random.permutation(matrix_Y) + test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0] + + # p-value is the probability of observing more extreme test statistic under the null + self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor self.p_value_metadata_ = {} - return np.abs(test_stat), {} + return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {} From e04b1deafe128a3b6a8328eb790541507820712f Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Mon, 3 Dec 2018 14:39:38 -0500 Subject: [PATCH 12/22] Removed old tests --- mgcpy/independence_tests/hhg.py | 130 ----------------- mgcpy/independence_tests/kendall_spearman.py | 114 --------------- mgcpy/independence_tests/rv_corr.py | 141 ------------------- 3 files changed, 385 deletions(-) delete mode 100644 mgcpy/independence_tests/hhg.py delete mode 100644 mgcpy/independence_tests/kendall_spearman.py delete mode 100644 mgcpy/independence_tests/rv_corr.py diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py deleted file mode 100644 index 7d9998b..0000000 --- a/mgcpy/independence_tests/hhg.py +++ /dev/null @@ -1,130 +0,0 @@ -""" - **HHG Independence Test Module** -""" - -import numpy as np -from mgcpy.independence_tests.abstract_class import IndependenceTest - - -class HHG(IndependenceTest): - def __init__(self, compute_distance_matrix=None): - """ - :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix - :type compute_distance_matrix: ``FunctionType`` or ``callable()`` - """ - IndependenceTest.__init__(compute_distance_matrix) - - def get_name(self): - ''' - :return: the name of the independence test - :rtype: string - ''' - return 'hhg' - - def test_statistic(self, matrix_X, matrix_Y): - """ - Computes the HHG correlation measure between two datasets. - - :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions - :type matrix_X: 2D `numpy.array` - - :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions - :type matrix_Y: 2D `numpy.array` - - :return: returns a list of two items, that contains: - - :test_statistic_: test statistic - - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, - that the independence tests computes in the process - :rtype: float, dict - - **Example:** - - >>> import numpy as np - >>> from mgcpy.independence_tests.hhg import HHG - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, - 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) - >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, - 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) - >>> hhg = HHG() - >>> hhg_test_stat = hhg.test_statistic(X, Y) - """ - row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] - row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] - - # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not - if row_X != columns_X or sum(matrix_X.diagonal()**2) > 0: - dist_mtx_X = self.compute_distance_matrix(matrix_X) - else: - dist_mtx_X = matrix_X - if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0: - dist_mtx_Y = self.compute_distance_matrix(matrix_Y) - else: - dist_mtx_Y = matrix_Y - - n = dist_mtx_X.shape[0] - S = np.zeros((n, n)) - - for i in range(n): - for j in range(n): - if i != j: - tmp1 = dist_mtx_X[i, :] <= dist_mtx_X[i, j] - tmp2 = dist_mtx_Y[i, :] <= dist_mtx_Y[i, j] - t11 = np.sum(tmp1 * tmp2) - 2 - t12 = np.sum(tmp1 * (1-tmp2)) - t21 = np.sum((1-tmp1) * tmp2) - t22 = np.sum((1-tmp1) * (1-tmp2)) - denom = (t11+t12) * (t21+t22) * (t11+t21) * (t12+t22) - if denom > 0: - S[i, j] = (n-2) * \ - np.power((t12*t21 - t11*t22), 2) / denom - corr = np.sum(S) - - # no metadata for HHG - self.test_statistic_metadata_ = {} - self.test_statistic_ = corr - - return corr, {} - - def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): - """ - Tests independence between two datasets using HHG and permutation test. - - :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions - :type matrix_X: 2D `numpy.array` - - :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions - :type matrix_Y: 2D `numpy.array` - - :param replication_factor: specifies the number of replications to use for - the permutation test. Defaults to 1000. - :type replication_factor: integer - - :return: returns a list of two items, that contains: - - :p_value_: P-value - - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, - that the independence tests computes in the process - :rtype: list - - **Example:** - - >>> import numpy as np - >>> from mgcpy.independence_tests.hhg import HHG - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, - 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) - >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, - 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) - >>> hhg = HHG() - >>> hhg_p_value = hhg.p_value(X, Y) - """ - test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0] - # estimate the null by a permutation test - test_stats_null = np.zeros(replication_factor) - for rep in range(replication_factor): - permuted_y = np.random.permutation(matrix_Y) - test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0] - - # p-value is the probability of observing more extreme test statistic under the null - self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor - self.p_value_metadata_ = {} - - return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {} diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py deleted file mode 100644 index 096bb13..0000000 --- a/mgcpy/independence_tests/kendall_spearman.py +++ /dev/null @@ -1,114 +0,0 @@ -""" - **Kendall and Spearman ndependence Test Module** -""" - -from mgcpy.independence_tests.abstract_class import IndependenceTest -from scipy.stats import kendalltau, spearmanr - - -class KendallSpearman(IndependenceTest): - def __init__(self, compute_distance_matrix=None, which_test='kendall'): - """ - :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix - :type compute_distance_matrix: ``FunctionType`` or ``callable()`` - - :param which_test: specifies which test to use, including ``'kendall'`` or ``'spearman'`` - :type which_test: string - """ - IndependenceTest.__init__(self, compute_distance_matrix) - self.which_test = which_test - - def get_name(self): - ''' - :return: the name of the independence test - :rtype: string - ''' - return self.which_test - - def test_statistic(self, matrix_X, matrix_Y): - """ - Computes the Spearman's rho or Kendall's tau measure between two datasets. - - Implments scipy.stats's implementation for both - - :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension - :type matrix_X: 1D `numpy.array` - - :param matrix_Y: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension - :type matrix_Y: 1D `numpy.array` - - :return: returns a list of two items, that contains: - - :test_stat_: test statistic - - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, - that the independence tests computes in the process - :rtype: list - - **Example:** - - >>> import numpy as np - >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman - - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, - 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) - >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, - 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) - >>> kendall_spearman = KendallSpearman() - >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y) - """ - assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape" - assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape" - - if self.which_test == 'kendall': - test_statistic_ = kendalltau(matrix_X, matrix_Y)[0] - else: - test_statistic_ = spearmanr(matrix_X, matrix_Y)[0] - - self.test_statistic_ = test_statistic_ - self.test_statistic_metadata_ = {} - - return test_statistic_, {} - - def p_value(self, matrix_X, matrix_Y, replication_factor=1000): - """ - Tests independence between two datasets using the independence test. - - :param matrix_X: a ``[n*1]`` data matrix, a square matrix with ``n`` samples in ``1`` dimension - :type matrix_X: 2D `numpy.array` - - :param matrix_Y: a ``[n*1] data`` matrix, a square matrix with ``n`` samples in ``1`` dimensions - :type matrix_Y: 2D `numpy.array` - - :param replication_factor: specifies the number of replications to use for - the permutation test. Defaults to 1000. - :type replication_factor: integer - - :return: returns a list of two items, that contains: - - :p_value_: P-value - - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, - that the independence tests computes in the process - :rtype: list - - **Example:** - - >>> import numpy as np - >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, - 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) - >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, - 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) - >>> kendall_spearman = KendallSpearman() - >>> kendall_spearman_p_value = kendall_spearman.p_value(X, Y) - """ - row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] - row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] - assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape" - assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape" - - if self.which_test == 'kendall': - p_value_ = kendalltau(matrix_X, matrix_Y)[1] - else: - p_value_ = spearmanr(matrix_X, matrix_Y)[1] - - self.p_value_ = p_value_ - self.p_value_metadata_ = {} - - return p_value_, {} diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py deleted file mode 100644 index 024481a..0000000 --- a/mgcpy/independence_tests/rv_corr.py +++ /dev/null @@ -1,141 +0,0 @@ -""" - **RVCorr Independence Test Module** -""" - -import numpy as np -from mgcpy.independence_tests.abstract_class import IndependenceTest -from numpy import matlib as mb -from scipy.sparse.linalg import svds -from scipy.stats import pearsonr - - -class RVCorr(IndependenceTest): - def __init__(self, compute_distance_matrix=None, which_test='rv'): - """ - :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix - :type compute_distance_matrix: ``FunctionType`` or ``callable()`` - - :param which_test: specifies which test to use, including ``'rv'``, ``'pearson'``, and ``'cca'``. - :type which_test: string - """ - IndependenceTest.__init__(self, compute_distance_matrix) - self.which_test = which_test - - def get_name(self): - ''' - :return: the name of the independence test - :rtype: string - ''' - return self.which_test - - def test_statistic(self, matrix_X=None, matrix_Y=None): - """ - Computes the Pearson/RV/CCa correlation measure between two datasets. - - Default computes linear correlation for RV - - Computes pearson's correlation - - Calculates local linear correlations for CCa - - :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p`` dimensions - :type matrix_X: 2D `numpy.array` - - :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions - :type matrix_Y: 2D `numpy.array` - - :param replication_factor: specifies the number of replications to use for - the permutation test. Defaults to 1000. - :type replication_factor: int - - :return: returns a list of two items, that contains: - - :test_statistic_: test statistic - - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, - that the independence tests computes in the process - :rtype: list - - **Example:** - - >>> import numpy as np - >>> from mgcpy.independence_tests.rv_corr import RVCorr - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, - 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) - >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, - 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) - >>> rvcorr = RVCorr() - >>> rvcorr_test_stat = rvcorr.test_statistic(X, Y) - """ - row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] - row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] - - mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0), - matrix_X.shape[0], 1) - mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0), - matrix_Y.shape[0], 1) - - covar = np.dot(mat1.T, mat2) - varX = np.dot(mat1.T, mat1) - varY = np.dot(mat2.T, mat2) - - if (self.which_test == 'pearson'): - assert row_X == 1 or columns_X == 1, "Data matrix should be (n, 1) shape" - assert row_Y == 1 or columns_Y == 1, "Data matrix should be (n, 1) shape" - corr, covar = pearsonr(matrix_X, matrix_Y) - elif (self.which_test == 'rv'): - covar = np.trace(np.dot(covar, covar.T)) - corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX)) - * np.trace(np.dot(varY, varY)))) - else: - if varX.size == 1 or varY.size == 1 or covar.size == 1: - covar = np.sum(np.power(covar, 2)) - corr = np.divide(covar, np.sqrt(np.sum(np.power(varX, 2)) - * np.sum(np.power(varY, 2)))) - else: - covar = np.sum(np.power(svds(covar, 1)[1], 2)) - corr = np.divide(covar, np.sqrt(np.sum(np.power(svds(varX, 1)[1], 2)) - * np.sum(np.power(svds(varY, 1)[1], 2)))) - self.test_statistic_ = corr - self.test_statistic_metadata_ = {"covariance": covar} - - return corr, {"covariance": covar} - - def p_value(self, matrix_X, matrix_Y, replication_factor=None): - """ - Tests independence between two datasets using the independence test. - - :param matrix_X: a ``[n*p]`` data matrix, a square matrix with ``n`` samples in ``p``` dimensions - :type matrix_X: 2D `numpy.array` - - :param matrix_Y: a ``[n*q]`` data matrix, a square matrix with ``n`` samples in ``q`` dimensions - :type matrix_Y: 2D `numpy.array` - - :param replication_factor: specifies the number of replications to use for - the permutation test. Defaults to None. - :type replication_factor: integer - - :return: returns a list of two items, that contains: - - :p_value_: P-value - - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, - that the independence tests computes in the process - :rtype: list - - **Example:** - - >>> import numpy as np - >>> from mgcpy.independence_tests.rv_corr import RVCorr - >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, - 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) - >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, - 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) - >>> rvcorr = RVCorr() - >>> rvcorr_p_value = rvcorr.p_value(X, Y) - """ - test_stat = self.test_statistic(matrix_X=matrix_X, matrix_Y=matrix_Y)[0] - # estimate the null by a permutation test - test_stats_null = np.zeros(replication_factor) - for rep in range(replication_factor): - permuted_y = np.random.permutation(matrix_Y) - test_stats_null[rep] = self.test_statistic(matrix_X=matrix_X, matrix_Y=permuted_y)[0] - - # p-value is the probability of observing more extreme test statistic under the null - self.p_value_ = np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor - self.p_value_metadata_ = {} - - return np.where(test_stats_null >= test_stat)[0].shape[0] / replication_factor, {} From 691951e985a5462341d6430bb68c61c4a94f29df Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Thu, 6 Dec 2018 19:02:21 -0500 Subject: [PATCH 13/22] Add updated tests --- mgcpy/independence_tests/hhg.py | 114 ++++++++++++++++++ mgcpy/independence_tests/kendall_spearman.py | 92 +++++++++++++++ mgcpy/independence_tests/rv_corr.py | 117 +++++++++++++++++++ 3 files changed, 323 insertions(+) create mode 100644 mgcpy/independence_tests/hhg.py create mode 100644 mgcpy/independence_tests/kendall_spearman.py create mode 100644 mgcpy/independence_tests/rv_corr.py diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py new file mode 100644 index 0000000..0125d3f --- /dev/null +++ b/mgcpy/independence_tests/hhg.py @@ -0,0 +1,114 @@ +import numpy as np +from mgcpy.independence_tests.abstract_class import IndependenceTest +from scipy.spatial import distance_matrix + + +class HHG(IndependenceTest): + def __init__(self, compute_distance_matrix=None): + """ + :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix + :type compute_distance_matrix: FunctionType or callable() + """ + IndependenceTest.__init__(compute_distance_matrix) + self.which_test = "hhg" + + def test_statistic(self, matrix_X, matrix_Y): + """ + Computes the HHG correlation measure between two datasets. + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :test_statistic_: test statistic + - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.hhg import HHG + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> hhg = HHG() + >>> hhg_test_stat = hhg.test_statistic(X, Y) + """ + row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] + row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] + + # use the matrix shape and diagonal elements to determine if the given data is a distance matrix or not + if row_X != columns_X or sum(matrix_X.diagonal()**2) > 0: + dist_mtx_X = distance_matrix(matrix_X, matrix_X) + else: + dist_mtx_X = matrix_X + if row_Y != columns_Y or sum(matrix_Y.diagonal()**2) > 0: + dist_mtx_Y = distance_matrix(matrix_Y, matrix_Y) + else: + dist_mtx_Y = matrix_Y + + n = dist_mtx_X.shape[0] + S = np.zeros((n, n)) + + for i in range(n): + for j in range(n): + if i != j: + tmp1 = dist_mtx_X[i, :] <= dist_mtx_X[i, j] + tmp2 = dist_mtx_Y[i, :] <= dist_mtx_Y[i, j] + t11 = np.sum(tmp1 * tmp2) - 2 + t12 = np.sum(tmp1 * (1-tmp2)) + t21 = np.sum((1-tmp1) * tmp2) + t22 = np.sum((1-tmp1) * (1-tmp2)) + denom = (t11+t12) * (t21+t22) * (t11+t21) * (t12+t22) + if denom > 0: + S[i, j] = (n-2) * \ + np.power((t12*t21 - t11*t22), 2) / denom + corr = np.sum(S) + + # no metadata for HHG + self.test_statistic_metadata_ = {} + self.test_statistic_ = corr + + return self.test_statistic_, self.test_statistic_metadata_ + + def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000): + """ + Tests independence between two datasets using HHG and permutation test. + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :p_value_: P-value + - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.hhg import HHG + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> hhg = HHG() + >>> hhg_p_value = hhg.p_value(X, Y) + """ + return super(HHG, self).p_value(matrix_X, matrix_Y) diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py new file mode 100644 index 0000000..24a0670 --- /dev/null +++ b/mgcpy/independence_tests/kendall_spearman.py @@ -0,0 +1,92 @@ +from mgcpy.independence_tests.abstract_class import IndependenceTest +from scipy.stats import kendalltau, spearmanr + + +class KendallSpearman(IndependenceTest): + def __init__(self, compute_distance_matrix=None, which_test='kendall'): + """ + :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix + :type compute_distance_matrix: FunctionType or callable() + + :param which_test: specifies which test to use, including 'kendall' or 'spearman' + :type which_test: str + """ + IndependenceTest.__init__(self, compute_distance_matrix) + self.which_test = which_test + + def test_statistic(self, matrix_X, matrix_Y): + """ + Computes the Spearman's rho or Kendall's tau measure between two datasets. + - Implments scipy.stats's implementation for both + + :param matrix_X: a [n*1] data matrix, a square matrix with n samples in 1 dimension + :type matrix_X: 1D numpy.array + + :param matrix_Y: a [n*1] data matrix, a square matrix with n samples in 1 dimension + :type matrix_Y: 1D numpy.array + + :return: returns a list of two items, that contains: + - :test_stat_: test statistic + - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> kendall_spearman = KendallSpearman() + >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y) + """ + if matrix_X is None: + matrix_X = self.matrix_X + if matrix_Y is None: + matrix_Y = self.matrix_Y + assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape" + assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape" + + if self.which_test == 'kendall': + self.test_statistic_ = kendalltau(matrix_X, matrix_Y)[0] + else: + self.test_statistic_ = spearmanr(matrix_X, matrix_Y)[0] + + self.test_statistic_metadata_ = {} + + return self.test_statistic_, self.test_statistic_metadata_ + + def p_value(self, matrix_X, matrix_Y, replication_factor=1000): + """ + Tests independence between two datasets using the independence test. + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :p_value_: P-value + - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.kendall_spearman import KendallSpearman + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> kendall_spearman = KendallSpearman() + >>> kendall_spearman_p_value = kendall_spearman.p_value(X, Y) + """ + return super(KendallSpearman, self).p_value(matrix_X, matrix_Y) diff --git a/mgcpy/independence_tests/rv_corr.py b/mgcpy/independence_tests/rv_corr.py new file mode 100644 index 0000000..7fec1fa --- /dev/null +++ b/mgcpy/independence_tests/rv_corr.py @@ -0,0 +1,117 @@ +import numpy as np +from mgcpy.independence_tests.abstract_class import IndependenceTest +from numpy import matlib as mb +from scipy.sparse.linalg import svds +from scipy.stats import pearsonr + + +class RVCorr(IndependenceTest): + def __init__(self, compute_distance_matrix=None, which_test='rv'): + """ + :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix + :type compute_distance_matrix: FunctionType or callable() + + :param which_test: specifies which test to use, including 'rv', 'pearson', and 'cca'. + :type which_test: str + """ + IndependenceTest.__init__(self, compute_distance_matrix) + self.which_test = which_test + + def test_statistic(self, matrix_X=None, matrix_Y=None): + """ + Computes the Pearson/RV/CCa correlation measure between two datasets. + - Default computes linear correlation for RV + - Computes pearson's correlation + - Calculates local linear correlations for CCa + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :test_statistic_: test statistic + - :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.rv_corr import RVCorr + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> rvcorr = RVCorr() + >>> rvcorr_test_stat = rvcorr.test_statistic(X, Y) + """ + row_X, columns_X = matrix_X.shape[0], matrix_X.shape[1] + row_Y, columns_Y = matrix_Y.shape[0], matrix_Y.shape[1] + + mat1 = matrix_X - mb.repmat(np.mean(matrix_X, axis=0), + matrix_X.shape[0], 1) + mat2 = matrix_Y - mb.repmat(np.mean(matrix_Y, axis=0), + matrix_Y.shape[0], 1) + + covar = np.dot(mat1.T, mat2) + varX = np.dot(mat1.T, mat1) + varY = np.dot(mat2.T, mat2) + + if (self.which_test == 'pearson') and ((row_X == 1 or columns_X == 1) and (row_Y == 1 or columns_Y == 1)): + corr, covar = pearsonr(matrix_X, matrix_Y) + elif (self.which_test == 'rv'): + covar = np.trace(np.dot(covar, covar.T)) + corr = np.divide(covar, np.sqrt(np.trace(np.dot(varX, varX)) + * np.trace(np.dot(varY, varY)))) + else: + if varX.size == 1 or varY.size == 1 or covar.size == 1: + covar = np.sum(np.power(covar, 2)) + corr = np.divide(covar, np.sqrt(np.sum(np.power(varX, 2)) + * np.sum(np.power(varY, 2)))) + else: + covar = np.sum(np.power(svds(covar, 1)[1], 2)) + corr = np.divide(covar, np.sqrt(np.sum(np.power(svds(varX, 1)[1], 2)) + * np.sum(np.power(svds(varY, 1)[1], 2)))) + self.test_statistic_ = corr + self.test_statistic_metadata_ = {"covariance": covar} + + return self.test_statistic_, self.test_statistic_metadata_ + + def p_value(self, matrix_X, matrix_Y, replication_factor=1000): + """ + Tests independence between two datasets using the independence test. + + :param matrix_X: a [n*p] data matrix, a square matrix with n samples in p dimensions + :type matrix_X: 2D `numpy.array` + + :param matrix_Y: a [n*q] data matrix, a square matrix with n samples in q dimensions + :type matrix_Y: 2D `numpy.array` + + :param replication_factor: specifies the number of replications to use for + the permutation test. Defaults to 1000. + :type replication_factor: int + + :return: returns a list of two items, that contains: + - :p_value_: P-value + - :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value, + that the independence tests computes in the process + :rtype: float, dict + + **Example:** + >>> import numpy as np + >>> from mgcpy.independence_tests.rv_corr import RVCorr + + >>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045, + 0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1) + >>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312, + 1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1) + >>> rvcorr = RVCorr() + >>> rvcorr_p_value = rvcorr.p_value(X, Y) + """ + return super(RVCorr, self).p_value(matrix_X, matrix_Y) From 53227a28ac8f8e4a1b3360ce9cfb438ad4cacbd0 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Thu, 6 Dec 2018 23:10:06 -0500 Subject: [PATCH 14/22] Add demo and fixed abstract class to include p-value for scipy tests --- demos/other_tests.ipynb | 840 +++++++++++++++++++ demos/rv_cca_hhg.ipynb | 264 ------ mgcpy/independence_tests/abstract_class.py | 8 +- mgcpy/independence_tests/kendall_spearman.py | 4 - 4 files changed, 847 insertions(+), 269 deletions(-) create mode 100644 demos/other_tests.ipynb delete mode 100644 demos/rv_cca_hhg.ipynb diff --git a/demos/other_tests.ipynb b/demos/other_tests.ipynb new file mode 100644 index 0000000..229220c --- /dev/null +++ b/demos/other_tests.ipynb @@ -0,0 +1,840 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tutorial for Tests other than MGC" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.spatial.distance import pdist, squareform\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, import the simultions utilizing the import statement below (for this tutorial only 4 out of 20 were imported):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, w_sim, spiral_sim" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the readme. Visualizations of the 4 simulations imported above are shown below with and without the noise:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 4, num=1, figsize=(20,5))\n", + "\n", + "x_normal, y_normal = linear_sim(100, 1)\n", + "x_no_noise, y_no_noise = linear_sim(1000, 1, noise=0)\n", + "ax[0].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", + "ax[0].plot(x_no_noise, y_no_noise, 'ro')\n", + "ax[0].set_xlim([-1, 1])\n", + "ax[0].set_ylim([-1, 1])\n", + "\n", + "x_normal, y_normal = quad_sim(100, 1)\n", + "x_no_noise, y_no_noise = quad_sim(1000, 1, noise=0)\n", + "ax[1].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", + "ax[1].plot(x_no_noise, y_no_noise, 'ro')\n", + "ax[1].set_xlim([-1, 1])\n", + "ax[1].set_ylim([-1, 2])\n", + "\n", + "x_normal, y_normal = w_sim(100, 1)\n", + "x_no_noise, y_no_noise = w_sim(1000, 1, noise=0)\n", + "ax[2].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", + "ax[2].plot(x_no_noise, y_no_noise, 'ro')\n", + "ax[2].set_xlim([-1, 1])\n", + "ax[2].set_ylim([-1, 2])\n", + "\n", + "x_normal, y_normal = spiral_sim(100, 1)\n", + "x_no_noise, y_no_noise = spiral_sim(1000, 1, noise=0)\n", + "ax[3].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", + "ax[3].plot(x_no_noise, y_no_noise, 'ro')\n", + "ax[3].set_xlim([-4, 4])\n", + "ax[3].set_ylim([-4, 4])\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## DCorr, MCorr, Mantel" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, import the `DCorr` class from the mgcpy package:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "ename": "ModuleNotFoundError", + "evalue": "No module named 'mgcpy.independence_tests.mgc.distance_transform'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdcorr\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/dcorr.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabstract_class\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mIndependenceTest\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmgc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistance_transform\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtransform_distance_matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'mgcpy.independence_tests.mgc.distance_transform'" + ] + } + ], + "source": [ + "from mgcpy.independence_tests.dcorr import DCorr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### DCorr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Put description here..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `DCorr` object with `'dcorr'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Dcorr's test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x, y = quad_sim(100, 1)\n", + "\n", + "dcorr = DCorr(which_test='dcorr')\n", + "test_stat = dcorr.test_statistic(x, y)[0]\n", + "print(\"DCorr's test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p_value = dcorr.p_value(x, y)[0]\n", + "print(\"DCorr p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### MCorr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Put description here..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `DCorr` object with `'mcorr'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the MCorr's test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x, y = quad_sim(100, 1)\n", + "\n", + "mcorr = DCorr(which_test='mcorr')\n", + "test_stat = mcorr.test_statistic(x, y)[0]\n", + "print(\"MCorr's test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p_value = mcorr.p_value(x, y)[0]\n", + "print(\"MCorr p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Mantel" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Put description here..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `DCorr` object with `'mantel'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Mantel's test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x, y = quad_sim(100, 1)\n", + "\n", + "mantel = DCorr(which_test='mantel')\n", + "test_stat = mantel.test_statistic(x, y)[0]\n", + "print(\"Mantel's test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p_value = mantel.p_value(x, y)[0]\n", + "print(\"Mantel p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## HHG" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The HHG test statistic was developed as specified in Heller, et. al. (2012). For more information about the test statistic, refer to the documentation specified in the R package here: https://cran.r-project.org/web/packages/HHG/vignettes/HHG.html.\n", + "\n", + "Essentially, the test takes the distance between two points, $P_{0}$ and $P_{1}$, and calculates how far each of the other data points in the data set are from $P_{0}$ and $P_{1}$ and organizes it in the following table:\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
$d_{y}(P_{0},\\cdot) \\leq d_{y}(P_{0},P_{1})$
$d_{y}(P_{0},\\cdot) > d_{y}(P_{0},P_{1})$
$d_{x}(P_{0},\\cdot) \\leq d_{x}(P_{0},P_{1})$
$A_{11}(P_{0}, P_{1})$
$A_{12}(P_{0}, P_{1})$
$A_{1\\cdot}(P_{0}, P_{1})$
$d_{x}(P_{0},\\cdot) > d_{x}(P_{0},P_{1})$
$A_{21}(P_{0}, P_{1})$
$A_{22}(P_{0}, P_{1})$
$A_{2\\cdot}(P_{0}, P_{1})$
$A_{\\cdot 1}(P_{0}, P_{1})$
\n", + "
$A_{\\cdot 2}(P_{0}, P_{1})$
\n", + "
$N-2$
\n", + "\n", + "A Chi square test statistic is then computed from table and the HHG test statistic is simply the sum of all the test statistics calculated:\n", + "\n", + "$$S(i, j)=\\frac{(N-2)(A_{12}A_{21}-A_{11}A_{22})}{A_{1\\cdot}A_{2\\cdot}A_{\\cdot 1}A_{\\cdot 2}}$$\n", + "\n", + "$$T=\\sum_{i=1}^{N}\\sum_{j=1, i \\neq j}^{N}S(i, j)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, import the `HHG` class from the mgcpy package:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "from mgcpy.independence_tests.hhg import HHG" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `HHG` object and then call the test statistic method. This is done below, by utilizing a simulation and calculating the HHG test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "HHG test statistic: 36.88\n" + ] + } + ], + "source": [ + "x, y = w_sim(10, 1)\n", + "\n", + "hhg = HHG()\n", + "test_stat = hhg.test_statistic(x, y)[0]\n", + "print(\"HHG test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "HHG p-value: 0.92\n" + ] + } + ], + "source": [ + "p_value = hhg.p_value(x, y)[0]\n", + "print(\"HHG p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Kendall, Spearman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, import the `KendallSpearman` class from the mgcpy package. Note that these tests utilize the `scipy.stats` implementation of the kendall and spearman tests and were included out of convenience:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "from mgcpy.independence_tests.kendall_spearman import KendallSpearman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Kendall" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Kendall tau coefficient was calculated utilizing the `scipy.stats` implementation. Further explanation this test can be found here: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kendalltau.html. Note: The inputs for this test must be 1 dimensional." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `KendallSpearman` object with `'kendall'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Kendall's test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Kendall's test statistic: -0.05\n" + ] + } + ], + "source": [ + "x, y = quad_sim(100, 1)\n", + "\n", + "kendall = KendallSpearman(which_test='kendall')\n", + "test_stat = kendall.test_statistic(x, y)[0]\n", + "print(\"Kendall's test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pearson's p-value: 0.74\n" + ] + } + ], + "source": [ + "p_value = kendall.p_value(x, y)[0]\n", + "print(\"Pearson's p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Spearman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Spearman rho coefficient was calculated utilizing the `scipy.stats` implementation. Further explanation this test can be found here: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.spearmanr.html. Note: The inputs for this test must be 1 dimensional." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `KendallSpearman` object with `'spearman'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Spearman's test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spearman's test statistic: 0.09\n" + ] + } + ], + "source": [ + "x, y = spiral_sim(100, 1)\n", + "\n", + "spearman = KendallSpearman(which_test='spearman')\n", + "test_stat = spearman.test_statistic(x, y)[0]\n", + "print(\"Spearman's test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pearson's p-value: 0.15\n" + ] + } + ], + "source": [ + "p_value = spearman.p_value(x, y)[0]\n", + "print(\"Pearson's p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Pearson's, RV, and CCA" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, import the `RVCorr` class from the mgcpy package:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "from mgcpy.independence_tests.rv_corr import RVCorr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Pearson's" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\newcommand{\\cov}{\\mathrm{cov}}$The Pearson's correlation was calculated utilizing the `scipy.stats` implementation. Further explanation this test can be found here: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.pearsonr.html.\n", + "\n", + "This is a test returns a statistic between -1 and 1 and measures the linear correlation between two vectors. Note: The inputs for this test must be 1 dimensional.\n", + "\n", + "The correlation is calculated via the following formula:\n", + "\n", + "$$\\rho _{X, Y}=\\frac{\\cov(X, Y)}{\\sigma _{X}\\sigma _{Y}}$$\n", + "\n", + "where $\\cov$ is the covariance, $\\sigma _{X}$ is the standard deviation of $X$, and $\\sigma _{Y}$ is the standard deviation of $Y$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `RVCorr` object with `'pearson'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the Pearson's test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pearson's test statistic: 0.46\n" + ] + } + ], + "source": [ + "x, y = linear_sim(100, 1)\n", + "\n", + "pearson = RVCorr(which_test='pearson')\n", + "test_stat = pearson.test_statistic(x, y)[0]\n", + "print(\"Pearson's test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pearson's p-value: 0.00\n" + ] + } + ], + "source": [ + "p_value = pearson.p_value(x, y)[0]\n", + "print(\"Pearson's p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### RV" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\newcommand{\\COVV}{\\mathrm{COVV}}$$\\newcommand{\\Tr}{\\mathrm{Tr}}$$\\newcommand{\\VAV}{\\mathrm{VAV}}$$\\newcommand{\\RV}{\\mathrm{RV}}$This test is essentially the a multivariate generalization of the square pearson's correlation coefficient. It returns values between 0 and 1. If $X$ and $Y$ are matrices of centered column vectors with covariance:\n", + "\n", + "$$\\Sigma _{XY}=E(X^{T}Y)$$\n", + "\n", + "Then the scaled covariance ($\\COVV$) is:\n", + "\n", + "$$\\COVV(X,Y)=\\Tr(\\Sigma _{XY}\\Sigma _{YX})$$\n", + "\n", + "Then the scaled-valued variance is defined similarly ($\\COVV$):\n", + "\n", + "$$\\VAV(X)=\\Tr(\\Sigma _{XX}^{2})$$\n", + "\n", + "Then, the RV Coefficient is defined as:\n", + "\n", + "$$\\RV(X,Y)=\\frac{\\COVV(X,Y)}{\\sqrt{\\VAV(X)\\VAV(Y)}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `RVCorr` object with `'rv'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the RV test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RV test statistic: 0.00\n" + ] + } + ], + "source": [ + "x, y = quad_sim(100, 3)\n", + "\n", + "rv = RVCorr(which_test='rv')\n", + "test_stat = rv.test_statistic(x, y)[0]\n", + "print(\"RV test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RV p-value: 0.88\n" + ] + } + ], + "source": [ + "p_value = rv.p_value(x, y)[0]\n", + "print(\"RV p-value: %.2f\" % p_value)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### CCA" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\newcommand{\\cov}{\\mathrm{cov}}$This test infers information from the cross-covariance matrices of random variables. It is a generalization of the RV test and can be considered the most general case of almost all statistical tests.\n", + "\n", + "If $\\Sigma _{XX}=\\cov(X, X)$ and $\\Sigma _{YY}=\\cov(Y, Y)$, then:\n", + "\n", + "$$\\frac{a^{T}\\Sigma _{XX}b}{\\sqrt{a^{T}\\Sigma _{XX}a}\\sqrt{b^{T}\\Sigma _{YY}b}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the other tests, simply create an `RVCorr` object with `'cca'` as the `which_test` parameter and then call the test statistic method. This is done below, by utilizing a simulation and calculating the CCA test statistic from that data:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CCA test statistic: 0.28\n" + ] + } + ], + "source": [ + "x, y = spiral_sim(100, 6)\n", + "\n", + "cca = RVCorr(which_test='cca')\n", + "test_stat = cca.test_statistic(x, y)[0]\n", + "print(\"CCA test statistic: %.2f\" % test_stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "P-values are calculated via permutation tests as with other packages. This is done by permutting $y$ and calculating the test statistic. The number of times that the test statistics are greater than or equal to null divided by the replication factor is equal to the p-value. This is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CCA p-value: 0.00\n" + ] + } + ], + "source": [ + "p_value = cca.p_value(x, y)[0]\n", + "print(\"CCA p-value: %.2f\" % p_value)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/demos/rv_cca_hhg.ipynb b/demos/rv_cca_hhg.ipynb deleted file mode 100644 index 3a064f3..0000000 --- a/demos/rv_cca_hhg.ipynb +++ /dev/null @@ -1,264 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 174, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from scipy.spatial.distance import pdist, squareform\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 175, - "metadata": {}, - "outputs": [], - "source": [ - "from mgcpy import RVCorr, HHG\n", - "from mgcpy.benchmarks.power import power\n", - "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, ubern_sim, exp_sim, w_sim, joint_sim, spiral_sim" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Test Statistic" - ] - }, - { - "cell_type": "code", - "execution_count": 176, - "metadata": {}, - "outputs": [], - "source": [ - "def test_stats_vs_dimension(corr_type, simulation_type, dim_range):\n", - " test_stats = []\n", - " for d in range(1, dim_range+1):\n", - " x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n", - " if corr_type == 'rv' or corr_type == 'cca':\n", - " corr = RVCorr(which_test=corr_type)\n", - " #else:\n", - " #corr = HHG()\n", - " test_stats.append(corr.test_statistic(x, y)[0])\n", - " return test_stats" - ] - }, - { - "cell_type": "code", - "execution_count": 177, - "metadata": {}, - "outputs": [], - "source": [ - "def plot_test_stats(simulation_type, dim_range, simulation_name):\n", - " rv_test_stats = test_stats_vs_dimension('rv', simulation_type, dim_range)\n", - " cca_test_stats = test_stats_vs_dimension('cca', simulation_type, dim_range)\n", - " #hhg_test_stats = test_stats_vs_dimension('hhg', simulation_type, dim_range) \n", - " plt.plot(rv_test_stats, label='RV')\n", - " plt.plot(cca_test_stats, label='CCA')\n", - " #plt.plot(hhg_test_stats, label='HHG')\n", - " plt.xlabel('Dimensions')\n", - " plt.ylabel('Test Statistics')\n", - " plt.legend()\n", - " plt.gca().set_xlim(1, dim_range+1)\n", - " plt.xticks(np.arange(0, dim_range+1, 5))\n", - " plt.title('Test Statistics \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 178, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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sF5FfReT4YMVijDH5MjMziYmJqXUJAUBEiImJqdBVUDDrFN7CjXZYnBG40Qg74+bKfTmIsRhjTIHamBDyVfS5BS0pqOosvFnJijEKeFudeUAjEWlR2nHT9+wsbRNjjDHlVJWtj1py5NR9iRQ9NR4icpOILBSRhRGZu8nLs/GajDE1V2hoKAkJCfTs2ZPzzjuPffvcXELt27dnzZo1R2x711138cwzz1RabFWZFIq6xiny215VX1XVfqraL5wc1m3aFOTQjDEmeOrUqcOSJUtYvnw5TZo0YcKECQCMHj2aiRMPTwaXl5fHxx9/zOWXX15psVVlUkjkyPlcW+Hn3LebfrUh1Y0xtcOAAQPYts1NFT1mzJgjksKsWbNo164dbdu2LW73gKvKJqmTgXEiMhE3BWSqqu7wZ8f0zYuAa4IZmzHmGPDolBWs3L4/oMfsHt+AP5/Xw69tc3Nz+fbbb7n++usB6N27NyEhISxdupQ+ffowceJExoyp3Inmgtkk9QPc/KZdRSRRRK4XkVtE5BZvk6m4OVzX4+aqvbWYQx0hJySCBvtWkJWTF5S4jTEm2A4ePEhCQgIxMTHs2bOHM888s2Bd/tVCTk4On3/+OZdeemmlxha0K4XS5lFVN7vPbWU+blhdurGJxb/tpX+HmHLHZ4wx/v6iD7T8OoXU1FTOPfdcJkyYwB133AG4pHDWWWcxdOhQevfuTdOmTSs1tho39lFoZF1aSTKLVm+o6lCMMaZCGjZsyPPPP8+zzz5LdnY2AB07diQmJob777+/0ouOoAYmhZCIugAkr51fxZEYY0zF9e3bt6D+IN+YMWNYvXo1F154YaXHU+OSAuEuKdRJXkZaZnYVB2OMMWV34MCBIx5PmTKFq6++uuDx3XffTWZmJg0bNqzs0GpgUggJ5WD9NvSQTczfWFKHaWOMMWVV85ICENHqeHqFbGbOhuSqDsUYY2qVGpkUQlsm0Fp28eta69lsjDGBVCOTAi0SAIhKWc6u/bVzogxjjKkKNTQp9AGgl2yyIiRjjAmgmpkU6jZBG7Whb/gW5qxPqepojDGm1qiZSQGQFgleUkjGdY42xpiaY+fOnYwePZqOHTvSvXt3Ro4cydq1a1m7di0jR46kU6dOdOvWjcsuu4ykpKSC/e68805atmxJXl5whvqpsUmB+ASaZm8nPTWFjcnpVR2NMcb4TVW58MILGTZsGBs2bGDlypU88cQTJCUlcc455zB27FjWr1/PqlWrGDt2LLt37wbcUNqfffYZrVu3ZtasWUGJreYmBa9eoUfIZuast3oFY0zNMXPmTMLDw7nlllsKliUkJLBu3ToGDBjAeeedV7D81FNPpWfPngX79ezZk7Fjx/LBBx8EJbaqHDq7Ylr0BWBQ3UTmrE/mmgHtqjYeY0zN89X9sHNZYI/ZvBeMeKrETZYvX84JJ5zg9/J8H3zwAWPGjGHUqFE8+OCDZGdnEx4eXuGQfdXcK4XoGGjYmoHRiczdkEKuTdFpjKnFsrKymDp1KhdccAENGjSgf//+zJgxI+DnqblXCgAt+tApcTlpmTks25ZKQutGVR2RMaYmKeUXfbD06NGDjz/+uMjlP/zwQ5H7TJs2jdTUVHr16gVARkYGdevW5ZxzzglobDX3SgGgRQL1DmymHhlWr2CMqTFOO+00Dh06xGuvvVawbMGCBXTq1Im5c+fy5ZdfFiyfNm0ay5Yt44MPPuD1119n8+bNbN68mU2bNjFjxgwyMjICGltQk4KIDBeRNSKyXkTuL2J9WxH5VkR+FZHvRaRVmU4Q73o2j4zdbUnBGFNjiAifffYZX3/9NR07dqRHjx6MHz+e+Ph4vvjiC1544QU6d+5M9+7deeutt2jQoAHTp08/4qogOjqaQYMGMWXKlIDGFrTiIxEJBSYAZwKJwAIRmayqK302exZ4W1X/KyKnAU8CVx99tGJ4LZDObLSD2zbt5WBWLnUiQgP1FIwxJmji4+OZNGlSkeumTZt21LI9e44eFfrTTz8NeFzBvFI4CVivqhtVNQuYCIwqtE134Fvv/swi1pesXlOoH0+v0M1k5eaxcIsNpW2MMRURzKTQEtjq8zjRW+ZrKXCxd/9CoL6IHDXxsojcJCILRWRhfieOAvEJND2wivBQ4UcrQjLGmAoJZlKQIpYVbjf6B2CoiCwGhgLbgJyjdlJ9VVX7qWq/uLi4I1e2SCAkZT0DWkYy18ZBMsb4oTYPjVPR5xbMpJAItPZ53ArY7ruBqm5X1YtUtS/wkLcstUxnadEHUM5rtofl21PZm55VsaiNMbVaVFQUKSkptTIxqCopKSlERUWV+xjB7KewAOgsIu1xVwCjgSt8NxCRWGCPquYBDwBvlPksXgukk+v8hupx/LQxhZG9WlQwdGNMbdWqVSsSExM5qii6loiKiqJVq7I15PQVtKSgqjkiMg6YDoQCb6jqChF5DFioqpOBYcCTIqLALOC2Mp+ofnOo15yWB9dQL7Inc9YnW1IwxhQrPDyc9u3bV3UY1VZQezSr6lRgaqFlj/jc/xg4ultfWbXoQ8jOpfRvf6P1VzDGmAqo2T2a88UnQPJahraPZnNKBlv3BLaHnzHGHCtqR1JokQCax7BGbiKKuTZFpzHGlEvtSApeZXPrg2uIqx9pU3QaY0w51Y6kUL8FRMchO39lYMcY5qxPJs+G0jbGmDKrHUlBxBUhbV/CwE6xpKRnsSYpraqjMsaYGqd2JAVwRUi7VzOwXTSAtUIyxphyqD1JoUUf0FziMzfSIS7akoIxxpRDLUoKrrKZ7YsZ2DGW+Zv2kJWTV7UxGWNMDVN7kkLDVlA3Bna4eoWMrFyWbN1X1VEZY0yNUnuSgogrQtq+lAEdYggRbChtY4wpo9qTFMAVIe1eRcPwXHq1bMhcSwrGGFMmtSspxCdAXg7sWsHATrEs3rqPtMzsqo7KGGNqjNqVFLw5m9m+hEGdYsnNU37eZFN0GmOMv2pXUmjUFqIawY6lHN+2MZFhIVavYIwxZVC7koKIK0LasYSo8FBObNfEpug0xpgyCGpSEJHhIrJGRNaLyP1FrG8jIjNFZLGI/CoiIyt80hYJkLQScg4xsFMsa5LS2JWWWeHDGmPMsSBoSUFEQoEJwAigOzBGRLoX2uxhYJI3R/No4KUKn7hFH8jLhl2rGNQpFsCuFowxxk/BvFI4CVivqhtVNQuYCIwqtI0CDbz7DYHtFT6rN4w2O5bQPb4BjeqGW72CMcb4KZhJoSWw1edxorfM13jgKhFJxE3beXtRBxKRm0RkoYgsLHWy7cbtIbIhbF9CaIgwoEMMc9cno2pDaRtjTGmCmRSkiGWFv5nHAG+paitgJPCOiBwVk6q+qqr9VLVfXFxcKWcVaNEbdiwBYGCnWLanZrIpOb08z8EYY44pwUwKiUBrn8etOLp46HpgEoCq/gREAbEVPnN8AiStgNzsgnoFGzXVGGNKF8yksADoLCLtRSQCV5E8udA2vwGnA4hIN1xSKKV8yA8tEiA3C3atom1MXVo2qmNTdBpjjB+ClhRUNQcYB0wHVuFaGa0QkcdE5Hxvs3uBG0VkKfABcK0GovC/xeHKZhFhYKcY5m5IJtem6DTGmBKFBfPgqjoVV4Hsu+wRn/srgYEBP3GTDhBRH3YsBVy9wqSFiSzflkqf1o0CfjpjjKktaleP5nwhId4w2q6y+ZSOrl7BmqYaY0zJamdSAJcUkpZDbg5x9SM5rnl95m6wpGCMMSWpvUkhPgFyMiF5DeCKkBZs3ktmdm4VB2aMMdVX7U0KBXM2uyKkQZ1iycrJY+HmvVUYlDHGVG+1NynEdIKIegWd2E5q34SwELF6BWOMKUHtTQohIdC8V8GVQnRkGH3bNOLH9RXvBmGMMbVV7U0K4IqQdi6DPFePMLhzHCu27yflwKEqDswYY6qn2p0U4hMg5yAkrwVgSJc4VK1pqjHGFKd2JwWfOZsBerVsSKO64fyw1oqQjDGmKLU7KcR2gfC6BT2bQ0OEQZ1imb3OhtI2xpii1O6kEBLqKpu9FkjgipB2px1i1Y60KgzMGGOqp1KTgoicLCJ1vftjROQZEWld2n7VRos+sOPXgsrmIZ3dfAyz11kRkjHGFObPlcKrwEER6Q08CCQB7wY1qkBqkQDZ6ZCyAYDmDaPo2qw+sywpGGPMUfxJCjnecNajgOdU9e9A/eCGFUA+czbnG9w5lgWb9pKRlVNFQRljTPXkT1JIF5E/AlcBX3rTZYYHN6wAiu0KYVEFLZDA1Stk5eYxf+OeKgzMGGOqH3+SwuW4+ZZvUdUduGk1/+HPwUVkuIisEZH1InJ/Eev/KSJLvNtaEdlXpuj9ERoGzXoecaVwUvsmRIaFWNNUY4wpxJ9JdsKAF1T1oPd4N/BNaTuJSCgwATgTN1/zAhGZ7E2sA4Cq3u2z/e1A3zLE7r/4BFj6IeTlQUgIUeGh9O8QY/UKxhhTiD9XCp8CvuNN5wGf+LHfScB6Vd2oqlnARFy9RHHG4KbkDLwWCZCVBns2Fiwa0jmWjbvTSdybEZRTGmNMTeRPUgjzvtQBUNVDQKQf+7UEtvo8TvSWHUVE2gLtge/8OG7Z5fds9ilCGtolv2mqDXlhjDH5/EkKKSIyMv+BiJwL+FNDK0UsK64b8WjgY1UtcgYcEblJRBaKyMLdu8tR5NO0G4RGHpEUOjWtR4uGUcyyegVjjCngT1IYCzwmIptEZBPwCHCzH/slAr6d3FoB24vZdjQlFB2p6quq2k9V+8XFxflx6kJCw6FZjyNaIIkIgzvH8uP6ZHJy88p+TGOMqYVKTQqqulZV++Eqgfuq6kmqutaPYy8AOotIexGJwH3xTy68kYh0BRoDP5Ut9DLK79nsM+bRkC5xpGXmsDQx8I2ejDGmJiq29ZGIjFHVD0TkjkLLAVDV50s6sKrmiMg4YDoQCryhqitE5DFgoarmJ4gxwEQN9gh18Qmw6E3YuwmadADcFJ0hAj+sTeaEtk2CenpjjKkJSmqS2tj7W1R5jV9f4Ko6FZhaaNkjhR6P9+dYFeY7Z7OXFBrVjaB3q0bMWrube87sUilhGGNMdVZsUlDVl7y7X6rqPN91InJyUKMKhqbdICTcVTb3vKhg8ZAucbz43Tr2ZWTRqG5EFQZojDFVz5+K5peKWDYh0IEEXVikq2xe9gls/KFg8dAuseQpzFmfUoXBGWNM9VBsUhCRk0TkTiBORO7wuT1MTRr7yNfwJyEkBN4+HyZdA/u20qdVI+pHhVnTVGOMoeQrhWggFlfEFOdzywIuDX5oQdD2FLjtZzj1IVg7A148kbDZf2NYezeUts3GZow51pVUpzATmCkib6rqRgBxTY/qqmp6ZQUYcOF1YOh90Gc0zPgTfP8ET9Zpyb1pl7E+6UQ6N29Q1REaY0yV8adOYbyINPBmX1sBbBKRe4IcV/A1agOX/ReumUxk3Xr8O+Kf1Jl0KexeU9WRGWNMlfEnKfRS1f3ABcAMXM/ka4MZVKXqMJTwW+fyQuSNNN67HF4+BaY/BJmpVR2ZMcZUOn+SQoSIhOFGOP2fNzhe7RoXIjSMlB7XcUbOP8jpfQX8NAFe6AeL33PDbRtjzDHCn6TwOvAbrjPbDyLSBjgQ1KiqwNAucezIrsdPPR6BG7+Dxm3h81vhP2fCtkVVHZ4xxlQKf8Y++qeqxqvqWd5QFFuB04IfWuXq36EJEaEhrmlqy+Ph9zPgglcgdSu8djp8Pg4OWLNVY0ztVuaxj3yUOPZRTVM3Iox+7Roza20yD52D68+QMAaOOwdm/Q3mvQwrJ8OoF6B7SXMFGWNMzVXSlYLv2EeFb7FBjqtKDOkSx5qkNHamZh5eGNUAznocbv0JGrV2ldDWn8EYU0sVmxQKjX30J98bhQa5qy2GdHZj/xU5d3NsZxgwzhUnWR2DMaaWOnbGPvJDtxb1iasfWfwUnV1HuEH1VnxWuYEZY0wlKalO4SRgAN7YRz6rGlBTxz4qRf5sbDNX7yI3TwkNKTSjaJ1G0Ol0WPE/OOsvIEXNOGqMMTXXsTX2kR+Gdoljb0Y2y7cV03mtx4WwPxESF1ZuYMYYUwnKNPZRWYnIcOA53Mxrr6vqU0VscxkwHjdxz1JVvaI85wqUQZ1iEYFZa3fTp3XHUDHfAAAgAElEQVSjozfoOgJCI2Dl/6D1iZUfoDHGBJE/dQr7ReRJEZksIjPyb6XtJCKhuLqHEUB3YIyIdC+0TWfgAWCgqvYA7ir7UwismHqR9IxvWHRlM0BUQ+joFSFZb2djTC3jT1J4F9gMdAGeBnYCS/zY7yRgvapu9IbGmIgbKsPXjcAEVd0LoKq7/Iw7qAZ3juWX3/axPzO76A3yi5C2WRGSMaZ28ScpxKnqv4EsVf0W+B3uC780LXG9n/Mlest8dQG6iMgcEZnnFTcdRURuEpGFIrJw9+7g9yoe0iWO3Dzlpw3FzMbWdQSERlorJGNMreNPUsj/ubxTRM4GegKt/divqKY5hXt9hQGdgWHAGOB1ETmqIF9VX1XVfqraLy4uzo9TV8zxbRoTHRFa/GxsUQ1cK6SVn1sRkjGmVvEnKTwhIg2BPwAP44qT/uDHfokcmTxaAduL2OZzVc1W1U3AGlySqFIRYSEM6Bhb8mxsPS6E/dsgcUHlBmeMMUHkT1LYpaqpqvqrqg5W1T7ADj/2WwB0FpH2IhIBjAYmF9rmf8CpACISiytOKldLp0Ab2iWWrXsOsjklo+gNugy3IiRjTK0TtB7NqpoDjAOmA6uASaq6QkQeE5Hzvc2mAykishKYCfxRVYspyK9cQ7p4Q16UWIR0hhUhGWNqlaD2aFbVqRQaJ0lVH/G5r8A93q1aaRsTTduYusxau5vfndKu6I16XAhrvoTEn6HNyZUanzHGBIP1aC7B4M6x/LQxhaycYq4EuloRkjGmdilTj2YRqa+qaZUWXRUb0jmOd+f9xqItexnQMeboDSLrQ+czXRHS2U+6ORiMMaYGK/ZbTEQeEpHjVHWjiER4vZgTRSRJRGrdzGtFGdAxhrAQKb53M7gipLQdsHV+5QVmjDFBUtJP2ytwTUQBrgEigRjcVJxPBjmuaqF+VDjHt21cfGUzQJezISzKipCMMbVCSUkhSw830h8OfKCqOaq6glo6dHZRhnaJY8X2/exOO1T0Br5FSNYKyRhTw5WUFA6JSDcRyb868B0Er25ww6o+8mdj+3F9CVcL3S+AAzth67xKisoYY4KjpKRwL66z2XrgeZ/K5pHAr5UQW7XQI74BTaIjmLW2mNnYwHVksyIkY0wtUNIczXNUtbOqNlbV8T7Lp6rqZZUSXTUQEiIM6hTL7HXJ5OUVM+RFZD3ofJZXhJRbuQEaY0wAWRtKPwzpEkfygUOs2rm/+I16XAgHkuC3nyovMGOMCTBLCn4Y0jkWoJQipLMhrI6bfMcYY2qoUpOCiBzVwa2oZbVZ0wZRHNe8fslNUyOioUuQi5CWfwK7Vgfn2MYYg39XCj/7uaxWG9oljoVb9pB+KKf4jXpcCOm7YMvcwAew5iv4+Pcw5c7AH9sYYzwl9WhuKiJ9gDoi0ktEenu3QRxDTVLzDekSR3auMm9jCYO4dj7LFSGtDHAR0oFd8Pk4CI1wzV6T1wf2+MYY4ynpSuEc4EXc5DgTfG4PAn8KfmjVS792jYkKD+Gr5TuLn3gnItrVLQSyCEkVPr8Nsg7AlR+BhMKS9wJzbGOMKaSkJqlvqupg4HpVHeJNsDNYVUeq6keVGGO1EBkWysXHt+LjRYk88vkKcnKL6b3c40JI3w1b5gTmxAteh3Uz4MzHocMwN4fD0onW9NUYExT+1Ck0FZEGACLyioj8LCKn+3NwERkuImtEZL2I3F/E+mtFZLeILPFuN5Qx/kr1+Kie3Dy0A+/M28J1by0g9WD20Rt1PgvC6wamI9uu1TDjYeh0Jpx0o1vW90pI2w4bZlb8+MYYU4g/SeEmVd0vImfhipLGAs+UtpOIhOKKm0YA3YExItK9iE0/VNUE7/Z6GWKvdCEhwgMjuvH0xb34aUMKF788l98KT9cZUdcVIa2aArklVEqXJucQfHqDK5IaNQFE3PIuI6BOE1jybvmPbYwxxfAnKeQXoI8A3lTVRX7udxKwXlU3qmoWMBEYVb4wq5fLT2zDO9f3Z3faIS54aQ4LNu85coNAFCF99xfYucwlhPrNDi8Pi4Del8HqLyFjT/H7G2NMOfjz5b5URKYC5wFfiUg9DieKkrQEtvo8TvSWFXaxiPwqIh+LSOuiDiQiN4nIQhFZuHt3CX0FKtGAjjH877aBNKwTzpWvzefTXxIPr+x0JoRHl78IaeMPMPcFOOE66Dri6PUJV0Buluu3YIwxAeRPUrgOGA+cpKoZQBRwvR/7SRHLCieTKUA7Ve0NfAP8t6gDqeqrqtpPVfvFxcX5cerK0T42ms9uPYXj2zbinklLeXb6Gjc+UkWKkDL2wGe3QExHOPuvRW/Tog806wWLrQjJGBNYpSYFVc0FOuDqEgDq+LMf7srA95d/K2B7oWOnqGr+RAWvASf4cdxqpVHdCN7+fX8u69eKF2eu5/YPFnMwK9cVIWUkw5Yf/T+YKnxxt+sAd/Hrrj6hOH2vhB1LIGlFxZ+EMcZ4/Bnm4kXgVOAqb1E68Iofx14AdBaR9iISAYzGDcXte+wWPg/PB1b5E3R1ExEWwtMX9+bBkccxdfkORr/6E7uaDy57EdLSD1zHt1MfhPi+JW/b6zIICYfF1mfBGBM4/vziP0VVbwYyAVR1DxBR2k6qmgOMA6bjvuwnqeoKEXlMRM73NrtDRFaIyFLgDuDacjyHakFEuGlIR1656gTWJh3ggn//Qmqb0/0vQtqzCab+EdoOhIF3lb59dAx0HQ6/fgi5RTSNNcaYcvAnKWSLSAhefYA3E5tf8056cy90UdWOqvpXb9kjqjrZu/+AqvZQ1T6qeqqq1vjR3s7u0ZyPbhlAnsKf1nWGjBTYPLvknXJz4NObXG/lC1+BkFD/TpZwlSuiWjej9G2NMcYPJY19lD8S6gTgEyBORB4FfgSeroTYaqyeLRvy+biBbIsdyAGNYvW3bxc/NAbA7L9D4s9w7j+gURv/T9TpDKjXzIqQjDEBU9KVws8Aqvo28DDwLLAXuFRVJ1ZCbDVaswZRvHvLMFbWH0jTbTN4+NMlZBc1NMbWBfDD066OoNclZTtJaBj0vhzWTYcD1aOprjGmZitpXoSCJqWqugKwZi5lVCcilH4jryNk0rf8tmga1+49xB/O6kp2rpKZnUt2Rionf/17iGrGlLg7SJu1kUM5uWRm55GZnUum7/3sPLJy87iyfxvO7tH88En6XgVzn3d1C6eMq7ona4ypFaS4Yg0RSQT+UdyOqlrsumDq16+fLly4sCpOXT7ZmfC3jmxsfjZnb7iE7NzDr/fTYa9ySegPjM76Ewv0uILlIQJR4aHuFhZCVHgokeGhpGZkkZKexeRxg+javP7hc7x2OmRnwNi5h4fDMMYYHyKySFX7lbZdSVcKoUA9iu6EZvwVHgVdR9Jh/dd8Ne7vbNqbRVR4CC22f02nmd+z5/jb+cegsUSGh3hJIJTwUEGK+HLfnXaIEc/NZtz7vzB53CDqRHgV0n2vdP0bti+GlsdX8hM0xtQmJSWFHar6WKVFUpv1uACWTaJT+iI6dT8D9m+HT11fhCbn/JkmoeF+HSaufiT/ujyBq9+Yz6NTVvDUxb3dip4Xw7QH3DwLlhSMMRVQUkWzXSEESsfTIaI+rPgf5OXB/8a6UVAveh38TAj5BnWOZezQjkxcsJXJS70O4lENodt5sOwjV1xljDHlVFJS8GvOBOOH8Cg4bqTryDb3edj4PZz9BMR2Ktfh7j6zCye0bcyDny5jS0q6W5hwBWSmwpovAxe3MeaYU9LMazYucyB1vwAy98E3f4au58AJ15b7UOGhITw3OoEQgds/WExWTh60HwoNWlmfBWNMhfjTo9kEQsfTILKB62x2/vMVbiXUqnFdnrmkD78mpvLMtNWuF3TCGNjwHaRuC1DQxphjjSWFyhIeBZe/C1d9AtGxATnk8J7NuWZAW17/cRPfrU5yRUioG1jPGGPKwZJCZeowFJr3CughHxzZjW4tGnDvpKXsDI13A+otec8Nw22MMWVkSaGGiwoP5cUr+nIoJ487Jy4mr88VsGcj/DavqkMzxtRAlhRqgY5x9XhsVE/mb9rDK7t7uXkcltisbMaYsrOkUEtcckIrLurbkme/T2RXmxGuT0RWelWHZYypYSwp1CKPXdCTtjHR/GlLAmQdgJWfV3VIxpgaJqhJQUSGi8gaEVkvIveXsN0lIqIiUupgTaZ49SLDeGFMX2Ye7EhSWEt0sRUhGWPKJmhJQURCcRP0jAC6A2NEpHsR29XHTcU5P1ixHEt6tmzIgyO78fbBgciWOW6aT2OM8VMwrxROAtar6kZVzQImAqOK2O5x4Bm8OaBNxf3ulHbs7ngheSokzX6zqsMxxtQgwUwKLYGtPo8TvWUFRKQv0FpVvyjpQCJyk4gsFJGFu3fbDGOlEREeHH0GC0L6kLfkfdIOHqrqkJyDe63/hDHVXDCTQlHjOBR8I4hICPBP4N7SDqSqr6pqP1XtFxcXF8AQa69GdSOIHXwdLXQ3/33vnZLniA6mrAxY+iG8dS483Q6++0vVxGGM8Uswk0Ii0NrncStgu8/j+kBP4HsR2QycDEy2yubA6Tj4cg6F1qPllk/5aGFi5Z1YFRIXwZS74O9d4bObIDUR2g6C2X93o8QaY6qlkibZqagFQGcRaQ9sA0YDV+SvVNVUoGAQIBH5HviDqtaguTarufA6hCdcxjmL3uWUyT/Tt00jOjerX/p+5ZWe7OaKXvwu7FoJYXXcBEN9r3LDb2RnwKvD4NObYeycgI0BZYwJnKBdKahqDjAOmA6sAiap6goReUxEzg/Wec2RQvpeRQRZXBA2n3HvLyYzOzewJ8jNgbUz4MOr4O/HwfQHIbwunPsv+MMauPAVaDfIjQobEQ2XvOHqFv43tlLrFzYnp/PolBVMW76D3Dyr16hxFvwHPrnRTVJlgkqqrKy5nPr166cLF9rFhN9U4aWTSc2Los+2+2hUN5wT2zWhf/smnNS+Cd1bNCAstBy/DVI2uIH3lrwPaTugbiz0Ge2uCpp2K3nf+a/CV3+Es5+EAbeW73n5SVX5aFEi4yevICPLJcR2MXW5fnAHLj2hFVHhoUE9vwmA7Yvh9TMgLwcueMUNEW/KTEQWqWqpxfOWFI4Fc56Hr//EvBFT+eS3evy8eQ9bUjIAiI4I5QSfJNG7VUMiw4r5osxKd72kF78LW+aAhEDns1wi6Hw2hEX4F48qTLwC1n0NN3wD8QkBeqJHSs3I5sHPlvHlsh2c3KEJz17q5p/496yNLN26jybREVwzoC3XDGhHk2g/YzeVKzsTXh3qZhWs1xQO7IbbF7qrTlMmlhTMYWlJ8I9ucMo4OPMxAHamZvLz5j38vCmFnzftYW3SAQAiwkLo3yqKs5vu58R6yXQgkfC962D3Wjf6al42NOnoEkGfMdCgRfliytgDLw+E8Dpw8yyIrBeoZwvAvI0p3PPhEnalHeKes7pw85COhIa4BnGqys+b9vDa7I18s2oXUeEhXHJCK24Y1IF2sfZlU63MeBjmvuDmIYmoB2+cDcMehGH/V9WR1TiWFMyR3h8N23+Bu1dCqNe+IGMPJK+F3Ws4uGMVBxKXE75nHY2ydhbslqMhJIW1IL1+RyJaHEeLfqOI7DCwwjPHAbBpNvz3PDc50AUvVfx4QHZuHv/6Zi0vfb+BdjHR/OvyBPq0blTs9ut3pfHarE18tngb2Xl5DO/RnJuGdKBvm8YBicdUwOY58NY50O86OPefbtmk38G6GXD7L+X/QXKMsqRgjrRqiqsMPu5cOLgPktdAuk9HwLAoiO0MsV0hrisHG3ZkWVZzZifX56ctB1iauI/sXKVFwyhuP60zl/ZrRXh56iIK++6vMOsZuOh16H1phQ61OTmdOycuZmliKpf1a8Wfz+tBdKR/Dex27c/krbmbeXfeFvZn5nBSuybcOKQDpx/XlJCQACRAUzaH0tyVpAjcMufwleSeTTDhJOh1GVwwoWpjrGEsKZgj5WS5f6aDe7wv/i4Qd9zh+w3bQEjxX/KZ2bn8tCGF579bx+Lf9tE2pi53ndGZ8/u0LCiWKZfcHPdrMGkF3DILmnQo8yF8K5PDQoSnLu7NyF7l+xWZfiiHDxds5T8/bmLbvoN0jIvmxsEduKBvS6uUrkxT7oRF/4XfT4M2Jx+5bsafXJHSzT9Aiz5VE18NZEnBHC0vz/3yqkDRj6ry3epdPDtjLat27KdLs3rcc2YXzu7RHCnvcff9Bq8McnUVv5/uf4U1R1Ym92/fhH9enkB8ozrli8NHTm4eXy7bwauzNrJi+35i60Vy3cB2XD+ovSWHYFv3Nbx3CQy8s6AO7AgH98ELx0PT7vC7KYEpyjwG+JsUbD6FY0lISIX/gUSE07s148vbB/HiFX3JyVNuefcXzn9xDt+v2VW+4TQatYHzX3B1HjP9HwZj/sYURjw3i+krdnLf8K68f+PJRScEVVj4BvyrN6yZ5texw0JDGJXQki9uH8T7N/SnR3wD/jZ9Dee/+COrd+73O8ZqY/knrv7m4N6qjqRkGXvg83HuC//Uh4repk4jGPYAbJ4Na76q3PiOAXalYCokJzePzxZv47lv15G49yAntmvMH87qSv8OMWU/2JS7YNGbcNWn0On0YjfzrUxu26Quz43uW3xl8r6tMHmcG1ojPNo1o73xW4jrWubwfli7m3snLWV/ZjYPjezGNQPalv/qqDKtnQ4fjAHNhZNugpF/q+qIivfx72HlZLjxO2jRu/jtcnPg5VNc34Vb55Xp6vJYZVcKplKEhYZwab/WfHfvMB4f1YMtKRlc/uo8rv7PfJZu3Ve2g539BMR1g89ugQO7itxkc3I6l7zyExNmbuDSE1rx5R2Di04IqvDL2/DSAEhc6Fqv3DYfwqPcF+TBMsYGDO0Sx7S7BjOwYwx/nryC6/+7kOQD1WQE2uJsmQuTroHmvSDhKljwOuxcXtVRFW35J+427P9KTgjgWtCd9RfYswEW/qdy4jtG2JWCCaiDWbm8M28zL3+/gb0Z2ZzVvRn3ntWVrs39HHMpaSW8dqobK+nKjzmUp+xJzyLlQBaLt+7jqamrCA0RnryoN+f0LqYyOXUbTLkD1n8D7QbDqAnQuK1bt+UnV4zSYRhc8SGElL1+QFX579zNPPHVahpEhfP3y/owtEs1HL135zJ48xzX6ev309xV0gsnuB7n135Zvcri03bCSycfrlcK9aPVmCq8c6Hr8XzHYqjbJPhx1mBW0WyqVFpmNm/8uJnXZ2/kQFYO5/eJ5+4zutCycR32pmeR4n3Rp6QfKvi7Jz2L5ANZ9Nv1KTcfmMDf9GomHBpxxHFLrExWdcNuTHvAdbI78zHod/3RraoWvgFf3A2D7oYzxpf7Oa7euZ87PljM2qQD3DCoPX8c3rX43uCVbc9GeGM4hIS5L9lG3oDFC9+EL+6Ci/8DvS6p2hjzqcL7l7l+K7fMdk2j/ZW0wjVS6H8LDH8yeDHWApYUTLWwLyOLf8/ayFtzNpOZk1vsGHihIUKT6AhioiOIiQ7nvtS/0jP9Jz5JeIOc5n2JqRdB0/qR9G7VqOgmsPt3uGaM66a7q4xRL5bcvDW//uKSN6DnxeV+fpnZuTwxdRVv/7SF7i0a8PyYvnRqGtje2WWWttP1/M3c764QfOtP8nLdlVh1Gi5i0X/dld2IZ6D/zWXff/IdbhyuW+dDbKfAx1dLWFIw1cqutEw+/HkreQpN6kUQGx3hkkC9SGLrRdAgKvzITmIZe+CVwRAa7obBiGpQ9IFV3XDdX93n+mKcMd5VppbQ5wJw2759PmxfAtdPr3B7969XJnHfx0s5mJ3Ln8/rwegTW1dNJfTBva7IaO9m11yz1QlHb/PbfHjjLBh8L5z+SKWHeIS9m10ntZbHw9Wfl/6+FSUtyTVR7TAMRr8X4ABrD0sKpubbMtd1bOt1KVz06tHr05JcUciaqdD6ZDdURkxH/49/YJeb30FC4KbvKzy/Q9L+TO6dtJQf1yczvEdznrq4F43qVmKrmKwMV8a+bRFc+RF0PLX4bT+9GVZ86lrulOU1C6S8PPjvua7uY+zcw0Vc5THrWfjucfjdF9B+cOBirEWs9ZGp+dqeAkP/z10JLPng8HJVWPYxvNQfNnwHZ/0Vrpta9i+3ek3h8nfdcB+Tfge52RUKt1mDKN7+/Uk8OPI4vl2dxPB/zeanDSkVOqbfcrPho9/B1vlw8eslJwSAMx+F0Eg3/0VVmfeSG213+FMVSwgAA26Dhq3d87E5FyokqElBRIaLyBoRWS8i9xex/hYRWSYiS0TkRxHpHsx4TA005I+ujuDLeyF5vSsLn3Q1fHK9a6ly82w3+ms5WhEBrtjivOdhy48B+YIMCRFuGtKRT8cOpG5EKFe8Po9npq0mO9e/L6q8PGVXWiZLt+5j2vIdvPHjJv765Upue/8Xbn5nIcu3pRa1E/zvVjdQ3Ln/dLPdlaZ+cxh6H6yd5iZJqmy7VsO3j0HXc9yAiBUVXscVHe78FX6dWPHjHcOCVnwkIqHAWuBM3HzNC4AxqrrSZ5sGqrrfu38+cKuqDi/puFZ8dAxKTXTlzvWaQkYKHDoApz4Ip9xe/mRQ2PSH4KcX4fwX4firA3LI9EM5PDZlJR8u3Eqf1o147vIEGtQJZ/u+g+xMzWRH6kG2p2ayY5/3N/UgSamHyCqUQCLCQohvGEXqwWz2Z+Zwy9AO3H5aZzfchip89X/w879d/cDge/0PMCfLdQDTXK8DWGRAnnepcrPdpDmpW13lcL0ANedVdcfdvw1uX1Q9KtGrEX+Lj4I5R/NJwHpV3egFNBEYBRQkhfyE4IkGalYFh6kcDVu5+oKJV0D88XDBy9D0uMCe44xHXfPGL+9xAwW2PrHCh4yODOPpS3ozpEscD3z6K8Oe/f6obcJChOYNo4hvWIe+rRvTope736JhFPGN3N8m0RGICPsysnj8i1VMmLmB6SuSeOaS3hy/6TWXEAaMg0H3lC3AsAgY8TS8exH8NAEGl3H/8pr1LOxYApe9E7iEAK7fxdlPuEr0uS/AsKMKJ4wfgnmlcAkwXFVv8B5fDfRX1XGFtrsNuAeIAE5T1XVFHOsm4CaANm3anLBly5agxGyquT0b3Wiu/nRsKo+MPa65Znamq3gO4Hj92/YdZNKCrTSoE058wyhaNKpDfMMoYutFlnlo7plrdvHQp8s4/cAUHg9/k5xeYwi78KXytdwBmHglbJjpmqg2iC/fMfy17Rf3a77XJUU3HgiEj651Q3vcvij4z6cGqQ4VzUV90o/KQKo6QVU7Av8HPFzUgVT1VVXtp6r94uKqYc9RUzmadAheQgDXI3b0B24s/w+vcskhQFo2qsPdZ3bh+kHtGdGrBQmtG9G0QVS55mo4tWtTvj07mUfD3+Lr3BM4c/0lzN20p/zBnf1XN4bQjD+V/xj+yD7ohjCp18z1SQiWM8a75/Od/4MrmsOCmRQSAd8mBa2A7SVsPxHwo4bMmCBq1h0u+jdsW+gqt6tjk+1131Dni1sJaXsKDa56h7yQUK54bT4PfbaMtMxytKBq3M4NU738YzfbWbB8+7ib3OmCCW6k02Bp3A5OHut6t29fErzz1FLBTAoLgM4i0l5EIoDRwGTfDUTEtz/7OcBRRUfGVLpu57mmsEvehZ+DVMRRXlt/dq2v4rrBmA/o37Ul0+4cwg2D2vP+z79x9j9nMXNN0YMJlmjQ3a5J51f3uRFIA0hVWf79R+i8l8g94XroeFpAj1+kwfe6K78ZD1fPxF6NBS0pqGoOMA6YDqwCJqnqChF5zGtpBDBORFaIyBJcvcLvghWPMWUy9H7XXHLaA7BpVlVH4ySthPcudc1Jr/4UohoCUCcilIfP7c4nY0+hbmQY1725gHsmLWFfRpb/x46o60YdTVruhv8IgEM5uXz88ybee+oWus+8kTV5rTh39Vn8sHZ36TtXVFRD10Jt82zXudH4zXo0G1OczP2uUjR9N9w00xVL+CMv1w3fsGsV7F7l/u5a7ZZJiBu6IzTC3cK8vwXLIn3ue3/DvGX5/Qmun15sLIdycnnh2/W8/MMGGteN4C8X9GB4Tz8rzFXd0B87foXbf4HocsyJAexNz+K9+Vv4au4vPJL1D/qHrGZzq1Fs6T+e8dN/Y1NyOiN6Nufhc7vTMgCz5BWrYM6FbNf09Rifc8GGuTAmEFI2uBZJDVvD9TOObPuu6tra71p1+LZ7FexeAzk+ldQN27jhqvN7XOdmebds9zfn0OH7BX99l3nLoxrCJW+6eo9SLN+Wyn0f/8rKHfs5p1cLxp/fg7j6fvRD2LXK9Qk5/mo477kyvVQbdx/gjTmb+HhRIqfkLuS5qFepG5JDyLn/QBLGAC5pvT57Ey98tw5BGHdaJ24Y3D54o8vmT+159pMw4NbgnKOGsKRgTKCs/8YV23QZAe0G+iSANZCVdni7+vGu/0RcN5cEmnZzI5RG+jmXRIBl5+bx6qyNPPfNOupGhnL/8OMY3CWO+IZRJQ/WN+0BmPeyuzqK71viOVSV+Zv28PrsjXy7ehd1Q/J4pfnnDE75yE3sc8lbRY5cmrg3g8e/WMn0FUm0j41m/Pk9gjMnharrh7HtlwrNuaCqNWOWvRJYUjAmkOY8B197I4pGx7kObk27uyTQtLv78q/TuGpjLMa6pDTu++RXFv/mZptrEBVGtxYN6NaiAd29v52b1XM9pAEyU91kPI3bu7kYiuj/kJ2bx9RlO3ht9kaWb9tPk+gIxvUJ4eptjxKetNSNVHvm426muxJ8v2YX4yevYHNKRvCKlPLnXOgyHHpcBDEd3BApRbSAUlV2px1iTVIaa3amsTYpjTVJB1iXlEaP+Aa8ed1J1IsMZp/f4LGkYEygpWxwRTgVHE21KuTmKUu27mPljv2s8m5rdqaRkZULuPksOsRGFySLUw9O57j5D6AXvIz4jE2UejCbiT//xltzN7MjNZMOcdHcMKgDl0TOI6GJW1kAAAtWSURBVGLqPW7YkVEToNu5fsd2KCeX12Zt5MWZ64NXpPTtYzD7H/h2lcqrE0NGvTYkhbdkc15zlmXGMj+1EcsPxpJGXQBi60XQpVl9Wjeuy8e/JDKwUyz/+V0/wkNr3liilhSMMSXKy1O27MkoSBLulsa2fQcR8vgs4s+0Cknhgfg3adeyOVk5eXy8KJH0rFwGdIjhxiHtGdYumpDp98Pid6B1fzejWzlHPC1cpPTo+T0YEoAipX0ZWWxKTmfjjhSSt67h4M51hOzdQOyhRNrJTtqF7CRejuz8lx3ZBGI6Eh7X2XWajOnAlOTm3D5tH6NPbM2TF/WqccVJlhSMMeWSmpHNqp372b16Duf9fDWfRl3E/QcuIy9POb9PPL8f1J6eLRu6JrIfXQvJa924ScMecK2kKqg8RUoZWTlsSk5nU3I6m5PT2ehzf2/G4Q59kWEhdG5Wjy7N6tO1WX26NHd/W9TNQ/ZugT0b3BXhng2QstH9TdtRsP/O6G68tu94Wg26gutGDKrwc61MlhSMMRX3+W2wdCI5N8/hUKNOREeGucrbRW/BtPshsoHrAR7gDmn/396dx1hVnnEc//4cQGBQVBjrArIoaHGpCNIqLqDUYNuIO9qSWG1ibTUt2sQQaWpjYrXaWou1UmtFY1GjAmqta62CcamgIpuyBK2yQ6osyjo8/eMcruP1Mgwzc++ZA79PMrn3nnPPOc+8OXOfue857/OW6lK65MTuLFu9If3wX8cHqz5PHz9j+ZqNX9r+gL3b0qNzNT1qqunRqZoenavpWVNNt07Vpadzrc+mz5K6WwtfJmY+hpYmo6RXdepH529eDH3Obt7CfmXipGBmTbduZXLRuUs/GDERNq5J5sKePQl6Dk6K2nXYv2yHr9ulVGy/6jZ079SeHp070LOmmu7ph3/3zu1p36Z8F4M3rZjP4w/cQd81/6KXFoOqoOepyVzfR3yvvCU8msBJwcyaxxt3Jd8KBo+Gd/6ezG9x2i9h4MjGV2bdSVPmreTtjz6hW6f2hQ//ik51WmT1+s1cMPY1qj+dxz3H/ZdOH/4jGZxY1QYOG5IkiMPPbFFzOjgpmFnzqN0MY09OBuZ17Arn3wtdB2QdVeYWf7qec+58lao9xKSfnMgBn82BWROTn7VLoHX75DbYo85LEsUObs8tNycFM2s+S2fAzEeTC8otdDxGFmYvWc2FY1/nkE7VPHrFCckYhq1b4aPXYdYEmPN4MlvgnntD3xEw9KbMYnVSMDOrgMnzVnLZfVNLj2Go3QIfTE4SRLt9k7krMtISJtkxM9vlndq7ht+ccxRT5q1k9KSZfOkf7apWcNjpyXSyGSaEnZHP8dpmZi3I8OMPYfEn6xnz7wV02bc9Pzu91443aqGcFMzMmsHV3+7Nok/Wc9sL8zhon3ac369L1iE1ipOCmVkzkMTN5x3D8rUbGDVhBgd2bMvAw/JXJ6us1xQkDZU0V9ICSaNKrL9G0hxJMyS9KKlbOeMxMyunNq324K4R/Ti0pgNXPPAW7y9bk3VIO61sSUFSFXAncCbQB7hYUvHsIO8A/SPiGOAx4JZyxWNmVgl7t23NuEuPp/2eVVw6bipLV6/POqSdUs5vCgOABRGxMCI2AQ8Dw+q+ISJeiojP05dvAPnshDMzq+Ogfdox7ocDWLthC5eOm8raDZt3vFELUc6kcDDwcZ3Xi9Jl2/Mj4JlSKyRdLmmapGkrV1Zg0m8zsybqc9De/PkHxzF/xTp+Ov5tNtduzTqkBilnUihVirDkSDlJI4D+wK2l1kfE3RHRPyL619S0/GqEZmYAp/Su4aZzj+aV+au4bmLRGIYWqpx3Hy0C6s620QVYUvwmSUOA0cCpEbGxeL2ZWZ5d2L8rSz5d37wzyZVROZPCVKCXpB7AYuAi4Pt13yCpL/AXYGhErChjLGZmmRk5pHfWITRY2bqPImILcBXwHPAe8EhEzJZ0g6Sz0rfdCnQAHpU0XdKT5YrHzMx2rKyD1yLiaeDpomW/qvN8SDmPb2ZmO8cF8czMrMBJwczMCpwUzMyswEnBzMwKnBTMzKzAScHMzApyN0ezpLXA3KzjyLHOwKqsg8gxt1/jue2apqnt1y0idlgnKI+T7MxtyOTTVpqkaW6/xnP7NZ7brmkq1X7uPjIzswInBTMzK8hjUrg76wByzu3XNG6/xnPbNU1F2i93F5rNzKx88vhNwczMysRJwczMCnKVFCQNlTRX0gJJo7KOJ08kfShpZjpvxbSs42npJN0raYWkWXWW7SfpBUnz08d9s4yxJdtO+/1a0uL0HJwu6TtZxthSSeoq6SVJ70maLenn6fKKnH+5SQqSqoA7gTOBPsDFkvpkG1XuDI6IY32veIPcBwwtWjYKeDEiegEvpq+ttPv4avsB/CE9B49N51uxr9oC/CIivg58C7gy/ayryPmXm6QADAAWRMTCiNgEPAwMyzgm20VFxBTgf0WLhwH3p8/vB86uaFA5sp32swaIiKUR8Xb6fC3JzJUHU6HzL09J4WDg4zqvF6XLrGECeF7SW5IuzzqYnPpaRCyF5A8X2D/jePLoKkkz0u4ld7/tgKTuQF/gP1To/MtTUlCJZb6ftuEGRsRxJN1vV0o6JeuAbLdzF3AocCywFPh9tuG0bJI6ABOAkRGxplLHzVNSWAR0rfO6C7Ako1hyJyKWpI8rgEkk3XG2c5ZLOhAgfVyRcTy5EhHLI6I2IrYCf8Xn4HZJak2SEMZHxMR0cUXOvzwlhalAL0k9JLUBLgKezDimXJBULWmvbc+BM4BZ9W9lJTwJXJI+vwR4IsNYcmfbB1rqHHwOliRJwN+A9yLitjqrKnL+5WpEc3oL2+1AFXBvRNyYcUi5IKknybcDSCrjPui2q5+kh4BBJOWKlwPXA48DjwCHAB8BF0SEL6aWsJ32G0TSdRTAh8CPt/WR2xcknQS8AswEtqaLryO5rlD28y9XScHMzMorT91HZmZWZk4KZmZW4KRgZmYFTgpmZlbgpGBmZgVOCrbLklSbVuOcLeldSddI2iNd11/SmIziei2L45o1hG9JtV2WpHUR0SF9vj/wIPBqRFyfbWRmLZe/KdhuIS3vcTlJQTZJGiTpKSjU+b9f0vPpvBPnSrolnX/i2bTkAJL6SZqcFhV8rk7JgZcl/VbSm5LmSTo5XX5kumx6WgSuV7p8XfooSbdKmpUea3i6fFC6z8ckvS9pfDrKFUk3S5qT7u93lW5H2/W1yjoAs0qJiIVp91Gp6pKHAoNJ5up4HTgvIq6VNAn4rqR/AncAwyJiZfoBfiNwWbp9q4gYkI66vx4YAlwB/DEixqelWaqKjnkuyQjfb5CM/J0qaUq6ri9wJEl9r1eBgZLmkJSHOCIiQtI+TW4UsyJOCra7KVVtF+CZiNgsaSbJh/ez6fKZQHfgcOAo4IX0n/Yqkkqf22wrWvZW+n5IkstoSV2AiRExv+iYJwEPRUQtSbGzycDxwBrgzYhYBCBperrPN4ANwD1pknpqp35zswZw95HtNtIaULWUri65ESCt4Lk5vrjYtpXknycBs+vMGnZ0RJxRvH26/1bpvh4EzgLWA89JOq04pHrC3VjneS3JN5EtJJVFJ5BMsPJsqQ3NmsJJwXYLkmqAscCfonF3V8wFaiSdkO6vtaQjd3DMnsDCiBhDUuHymKK3TAGGS6pK4zsFeLOe/XUAOqbTWI4k6Xoya1buPrJdWbu066U1yby3DwC31b9JaRGxSdL5wBhJHUn+dm4HZtez2XBghKTNwDLghqL1k4ATgHdJKodeGxHLJB2xnf3tBTwhqS3Jt4yrG/O7mNXHt6SamVmBu4/MzKzAScHMzAqcFMzMrMBJwczMCpwUzMyswEnBzMwKnBTMzKzg/+vbpHju4xWeAAAAAElFTkSuQmCC\n", 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\n", 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gS5w3As+hlasnv0H/cRtE5Ps+9l+Nns1VoeX/uXX8UChAR+b4YxvalJOH/l7aOXT3+zfgGWAzuhz7c9YylFJd6LDay9Dn+QrgPGu5N3HoC2MV2hR7CrpUOwQ/N5HwBvq/9yq6hPpL3htYSngVepZeg/79/cCSNZC8BRz6L4SFdWN2KbqhVS2wEljp55ydCWyxfrd/AS6xfFaB5A6Hn6NNubvR5+sPSqkXwv1M4WBKlI9AROQ+9MVhhZ8fqmEUIDrnYRPaxNM91PJEG+tuvwxIVEr1ROkYPwFqlFJ/i8b4oxmjLEYg1hT4u+iQWtO4xjAqiIWyMESOURYGg2FYYJTF8MYoC4PBYDAExTi4DQaDwRCUmBWFizZjx45VU6dOHWoxDAaDYUSxfv36WivpNSCjRllMnTqVdevWDbUYBoPBMKIQEV8VGwZgzFAGg8FgCIpRFgaDwWAIilEWBoPBYAjKqPFZGAwGw2Dp7u6msrKSjo6OoRbFcVJSUsjPzycxMTGi/Y2yMBgMBovKykoyMjKYOnUqMjxb3EeEUoq6ujoqKyuZNm1aRGMYM5TBYDBYdHR0kJubO6oUBYCIkJubO6gZk1EWBoPB4MFoUxQ2g/1cRlkYDIPkhU+qqW4cfTZug8EToywMhkHQ2tnDNQ+u5553y4ZaFMMoID4+nkWLFjF//nxWrlxJQ4PumzRt2jS2bdvWb9tvf/vb/P73g27tEjJGWRgMg6CsthWloOJg21CLYhgFpKamsnHjRj755BNycnK4/fbbAbjkkkt4+OGH+7Zzu908/vjjXHzxxTGTzSgLg2EQlNe1AlBxsH2IJTGMNo477jj27tUN/VavXt1PWbz55ptMnTqVKVMGdCOOGiZ01mAYBOW1WllU1puZxWjjF89s4dOqJkfHnDt5DD9fOS/odr29vbz66qtceeWVACxYsIC4uDg2bdrEwoULefjhh1m9erWjsgXDzCwMhkFQVquVRH1bNy2dpl+PYXC0t7ezaNEicnNzOXjwIKeffnrfOnt20dPTw1NPPcWFF14YU9nMzMJgGAS2GQr07GL2xDFDKI3BSUKZATiN7bNobGzknHPO4fbbb+e6664DtLI444wzOOWUU1iwYAHjx4+PqWxmZmEwDILy2lbmTtIKwvgtDE6RmZnJLbfcwk033UR3dzcARUVF5Obm8qMf/SjmJigwysJgiJjG9m7qWrs4aeZYwEREGZxl8eLFff4Jm9WrV1NSUsL5558fc3mMGcpgiBDbub24MBtXUjyV9WZmYRgcLS0t/d4/88wz/d5/5zvf4Tvf+U4sRerDzCwMhgix/RXTx6VRkO2iwkREGUYxRlkYDBFSVtuKCBTmuCjISTVmKMOoxigLgyFCymtbmZyZSkpiPPnZLvbWt6OUGmqxDIaoYJSFwRAhZXVtTB3rAiA/O5Xmzh4a27uHWCqDIToYZWEwRIBSirKaFqbmpgFQkKOVhgmfNYxWjLIwGCKgvq2bpo4epo3VyiI/OxUwZT8MoxejLAyGCCizwmYPKQtrZmGUhWGQVFdXc8kll1BUVMTcuXNZsWIF27dvZ/v27axYsYIZM2YwZ84cLrroIvbv39+337e+9S3y8vJwu91RkSuqykJEzhSRbSJSKiI/8rE+WUQesdZ/ICJTPdYtEJH3RGSLiGwWkZRoymowhIOdYzHVUhaZqYmMSUkwZijDoFBKcf7553Pqqaeyc+dOPv30U2688Ub279/P2WefzTXXXENpaSlbt27lmmuuoaamBtAly5988kkKCgp48803oyJb1JSFiMQDtwNnAXOB1SIy12uzK4F6pdQM4Gbgd9a+CcADwNVKqXnAqYDxHBqGDeV1rcQJFFgzCtB+C2OGii2lB5q59K4PaO4YHZeHtWvXkpiYyNVXX923bNGiRezYsYPjjjuOlStX9i3/zGc+w/z58/v2mz9/Ptdccw0PPfRQVGSLZgb3MqBUKbULQEQeBlYBn3psswq4wXr9OHCb6EaxZwAfK6U2ASil6qIop8EQNmW1reRnu0hKOHS/VZDtorSmJcBeBqdZs7mat0tr2VLVxLHTc50d/PkfQfVmZ8eceCSc9Vu/qz/55BOWLFkS8nKbhx56iNWrV7Nq1Squv/56uru7SUxMdERkm2iaofKACo/3ldYyn9sopXqARiAXOAJQIvKiiHwkIj/0dQARuUpE1onIOns6ZjDEgvK61j4TlE1+diqV9W0jKteisb2bL/79fXaOUCW3YU89AHsO44TIrq4u1qxZw3nnnceYMWM45phjeOmllxw/TjRnFuJjmfe/yN82CcCJwNFAG/CqiKxXSr3ab0Ol7gTuBFi6dOnI+YcaRjQ6bLaVJYXZ/ZYX5Ljo6HZT29LFuIzkIZIuPNbvPsi7O+t4t7SWonHpQy1OWCil2Fihe1RHJXs+wAwgWsybN4/HH3/c5/I33njD5z4vvPACjY2NHHnkkQC0tbXhcrk4++yzHZUtmjOLSqDA430+UOVvG8tPkQkctJa/oZSqVUq1AWuAo6Ioq8EQMjUtnbR29fZFQtkU5Ojw2ZEUEVVS3QxAZcPIc8zvrmujvk37KkbLzGL58uV0dnby97//vW9ZcXExM2bM4N133+W5557rW/7CCy+wefNmHnroIe666y7Ky8spLy+nrKyMl156ibY2Z89JNJVFMTBTRKaJSBJwCfC01zZPA1+xXl8AvKb0HP5FYIGIuCwlcgr9fR0Gw5BRbnXHG2iG0s7ukVR9tmSfVhZ7R5DMNvasYlxG8qhRFiLCk08+ycsvv0xRURHz5s3jhhtuYPLkyTz77LPceuutzJw5k7lz53LvvfcyZswYXnzxxX6ziLS0NE488cQBFWsHS9TMUEqpHhG5Fn3hjwfuVkptEZFfAuuUUk8D/wDuF5FS9IziEmvfehH5E1rhKGCNUuo5nwcyGGJMuVeOhY2dmDeSCgpus2YWe0fgzGLDnnpcSfF8ZtY4Xis5MNTiOMbkyZN59NFHfa574YUXBiw7ePDggGVPPPGE43JFtZ+FUmoN2oTkuexnHq87AJ+NZJVSD6DDZw2GYUVZXSsJcUJeVmq/5a6kBMamJ42Y8NmuHnefY3skziw2VDSwID+TqWPTqG3porWzh7Rk06InWpgMboMhTMprWynMcZEQP/Dvk5ftGjFmqJ01LfS4FUXj0jjQ3ElnT+9QixQyHd29fFrVxOLCbApzTPZ8LDDKwmAIk7LagWGzNgXZI6evRUl1EwCfnTMBgH0NHUMpTlhsqWqkx61YXJDVpyz21Dlz3kdS6HM4DPZzGWVhMISB260or2sd4K+wyc92sbehnV738L/glFQ3kxQfx4lWD/GR5LfYsEc7txcVZjElR38XTji5U1JSqKurG3UKQylFXV0dKSmRV00yBj6DIQz2N3fQ0e32P7PISaW7V3GguYNJmak+txkulOxrpmh8et/FdiT5LTZUNJCXlcr4DH3xG5OS4IiyyM/Pp7KyktGY5JuSkkJ+fn7E+xtlYTCEQV+12Vx/ZqhDfS2Gu7LYVt3McUW5TMxMQWRk5Vps3NPAosKsvveFuS5HlEViYiLTpk0b9DijEWOGMhjC4FCOhcvn+pESPtvQ1kV1UwezJ2aQlBDHhIyUETOzONDcwd6GdhYXeCiLHGeUhcE/RlkYDGFQXtdKUkIck/3MGvKyU/Vd+jC/8NqZ27MmZgBa7r0NI+Niu9HyVyz2mFkU5LioPNiOewT4ikYqRlkYDGGwq6aVKTku4uJ8lTWD5IR4JmSkDPswTjsZb86kMQDkZaWOGAf3hooGEuOFeZMz+5YV5rjo6nWzv3nkRHSNNIyyMEBFMZRFp2HKaCNQJJSNXX12OFNS3USWK5HxVsHDvOxU9jV0jIgoro17GpgzaQwpifF9y5wOnzUMxCgLAzz/A3jiGzDKwgWdptet2FPXFlRZFOS4hn3HvJLqZmZPzEC3j9Ezix63juIazvS6FZsqG/r5K8BDWRi/RdQwyuJwp7tdN3hproKabUMtzbCmqqGdrl7/YbM2+dmp7Gtsp7s3Or2QB4vbrdhW3czsiWP6luVZjvnh7uTevr+Ztq7efpFQAJOzUomT4R9YMJIxyuJwZ98mcPfo1ztfG1pZhjnldVbfbT9hszYF2S7cCqobh+ddemV9O21dvcy2nNsA+Vadq+Hut7ArzS4u6N9LJDE+jslZqWZmEUWMsjjcqSzWz+kTjbIIgr9qs97k5wzv8NmtVpmPWR7Kwp5ZDPcorg176sl2JTIld2DosgmfjS5GWRzuVBZDViHMOw/K34aezqGWaNiyq7aV1MR4JowJ3AWvLzFvmDq5t1U3IwJHTDikLFxJCWS7EkfEzGJRQVafr8UTrSyGt/wjGaMsDncq10H+0VC0HHraYc97Qy3RsKXcKiDo60LlyaTMFOLjZNjepZdUN1GY4xpQzjsvO3VY+yyaO7rZcaCFxV7tbG0Kc13UtnTS2tkTY8kOD4yyOJxpqoKmvVpZTDkB4hIPL1NUdwe8dzv8YSa8/eegm5fXtTHNT+a2JwnxcUzKTBm2Zig7Esqb4Z5r8XFlI0rBIq9IKBtTqjy6GGVxOFO5Tj/nHw3J6VB47OGhLHp7YMMDcOsSePF66GqFj+4LGDrc0+um4mBbUOe2TX52KhWh3KUrBR/9E5r2hSr9oOjo7qW8tpVZHpFQNnlZLvbWtw/biqsb9tQDsDCIsjC5FtHBKIvDmcpiiE+CiUfq90Wf0WG0LaOnRWU/lIKtz8D/HQ9P/TdkTIDLnobP/RoO7oL9W/zuWlnfTo9bBQ2btSnIdoWWmLdvEzz9Ta2sYsCO/S24FczxNbPITqW9u5f6tu6YyBIuGysaKBqXRmZqos/1JtciuhhlcThTuQ4mLYQEy2FbtFw/73p9yESKGmVvwl2nwSOXAgouuh++9ipMPwVmnwMSB58+5X/3utAioWwKclzsb+qkoztI97ktT+rnutKQxh0sviKhbOw2scPRb6GUYsOeBr/+CoDM1EQyUhKGrflvpGOUxeFKbzdUbdAmKJuJCyE1Z3SZoqo2wv3nw30robkazr0NrnkP5p4LtqM6fZz22Wx92u8wZTWh5VjY2NVnqwL5AJSKubLYVt1MSmIcU3x8Dlvm4VhQsLK+nbrWLr/+CgARMeGzUcQoi8OV/Vt09FP+0kPL4uK0KWrnayO/9EfdTnjsq3DnKVopnvFr+OZHcNSXId5HG5e5q6CmxG8We3ldK+nJCYxNTwrp8AV9ztYAyqLqI2jYDa6xWt4YnPOS6iaOmJBBvI9CiPbMYjhGcX1k+SsWF/pXFmByLaKJURaHK3YynufMArQpqmU/HPg09jI5QdM+eObbcNvRsP0FOPkH8K1NcPy1kBigpeTsc/Tzp75nF2W1uoBgsLBZm5D6Wmx5UkegLbsKOpugNfrd2bb5iYQCyHIl4kqKH5YRURsrGkhNjGfWBN+y2xTmuKioN6XKo4FRFocrlesgfQJkFvRfPv0z+nmkmaLa6+Hln8Mti3Wk09FXaiWx/CeQkhl8/zGToOBYv36L8rrWkJ3bABMyUkiKj/N/l64UbPmPnsnlL9HLomyKqmnupLaly2ckFGgzTl7W8My12LCngSPzM0mID3zJKshx0dXj5kCzSS51mqgqCxE5U0S2iUipiPzIx/pkEXnEWv+BiEy1lk8VkXYR2Wg97oimnIcllcWQt/SQ3d4mMw/GzR5ZymL9vfCXhfDOX7Qv4tpiWPEHSB8f3jhzz4X9m7VJyIOuHjd769uZ5qPEhD/i4oS87FT/Mf9710NjBcw7H3Jn6GVRVhZ9PSz8zCzAboI0vJRFZ08vn1Y1BTVBgYmIiiZRUxYiEg/cDpwFzAVWi8hcr82uBOqVUjOAm4HfeazbqZRaZD2ujpachyVtB+Hgzv7+Ck+KlsPud3VF2uFOczU89z0YPw+ufhs+fyfkRNhDec5K/ezl6N5zsA23IqyZBVh9LfxdtGwT1KwVenYXnwy1OyKROmRKAkRC2QzHxLxPq5ro6nUPKEvuC6Msokc0ZxbLgFKl1C6lVBfwMLDKa5tVgB1g/jhwmoRqFDZEzt71+tnbX2FTtBx6OkZG6Y+P/qmr5q66DSbOH9xYWYUw+agBfgu7gGD4ysLl2wzldmsIax6hAAAgAElEQVQT1IzTIDUL4uIhZ/qAGY3TlFQ3MzY9mdx0/7Wt8rJTaWjrHlYlMzb0tVH1HzZrY5cqN8rCeaKpLPKACo/3ldYyn9sopXqARiDXWjdNRDaIyBsiclIU5Tz8qCzWeQWTF/teP+V4naw33E1RvT2w7h6t3HKLnBlz7rlWlNKevkVldrXZEMNmbQpyUqlr7Rp44d27DpoqtQnKJrco6maokuom5kwK7CDOG4alyjdWNDApM4UJYwIEKFgkJVilyq28GINzRFNZ+JoheIco+NtmH1ColFoMfBf4l4gM8MqJyFUisk5E1tXURD+SZNRQWazNNsnpvtcnpenSH6XDXFlsf143bTr6a86NOedc/bz1mb5FZXWtZLkSyU4LLWzWJt+qPjtgdrHlSW12mrXi0LLcGTqL3B0kiS9Cenrd7NjfEjSaKH8YNkHaUFEfkr/CxoTPRodoKotKwDPUJh+o8reNiCQAmcBBpVSnUqoOQCm1HtgJHOF9AKXUnUqppUqppePGjYvCRxiFuN1Qud6/v8Km6DQ4sEX7BIYrxXfBmHyY+TnnxswtgglH9ouKKq9tDTkZz5OCvh4RHheuPhPUZyHF4/4ndwa4u/vNaJykvK6Nzh43syf5joSyycuyFNwwmVnUtnRScbA9YDKeN6ZUeXSIprIoBmaKyDQRSQIuAbyD2J8GvmK9vgB4TSmlRGSc5SBHRKYDM4FdUZT18KFuB3Q2+vdX2NilP3aujb5MkVC7Q5clWXq57yS7wTB3FVR8oKvyopVFqGU+POlLzPO8y638UM+GPE1Q4BERFR2/hR0J5S/HwmZ8RjKJ8TJsZhYbw/BX2BTk6FLlbV3Dx+8yGoiasrB8ENcCLwJbgUeVUltE5JciYs31+QeQKyKlaHOTHV57MvCxiGxCO76vVkodjJashxX+kvG8mTAf0sYNX7/Furt1NNHiy5wfe65tinqWju5eqho7IppZ5KYlkZoY3z+Lu88EdabXxtENny2pbiJOYMZ4P6ZHi7g4YVLm8ImI2ljRQHycMH9yCLkyFn2lys3swlEcviXrj1JqDbDGa9nPPF53ABf62O/fwL+jKdthS2WxTlKzL07+iIvTCXq71mrTSdwwyt/saoUND+qLesYE58cfN0vnmmx9mt1TVgMwNYQ+Ft6IiA6ftc1Q7l5tgpp5OiR73eGnjYXkzCgqi2amjU0jJTE+6LY6MW942Pw3VNQzZ1IGqUnB5bbxDJ8NFCZsCI9hdAUwxITKdToZL5SLf9FyXYJi/yfRlyscPvm3NqU56dj2Zs65sPsd9lbuBkKvNutNfnbqoTvcPe9DS/VAExTo5MgoRkSVVDcF9VfYDJfEvF63YlNFY1j+CjC5FtHCKIvDic4WXfMpmHPbpmgYlv5QCj78O4yfC4XHRe84c1eBchO3XU+Mw82xsCnI8ehrseVJSEiBI870vXHujKj4LFo6e6g42M7sIJFQNnlZqRxo7qSzJzqRWaGys6aFls4eFheE7q8AXeMqI9mUKncaoywOJ6o2gHIH91fYZEzUIbbDSVnsXQ/VH+vaT9HM35wwD3KmM7nqJcamJzEmxXfDnWAUZLto6uihsbVDR1jNPMN/yHLuDF0CxOHM+e37Led2GDMLpWBfQ4ejcoTLhhArzXojIhSY8FnHMcricMJ2buctCX2fos/oTO6uYfLHK74LktJhwcXRPY4IzF3F9JaPmJ/tjngYO2/h4KevQ+sB3yYom9wiQOl8Cwcp2RdaJJRN/jBJzNtY0UBmamJEJkCTa+E8RlkcTlSu03evrpzQ9ylaDr1dulbUUNNaB588AQsvGeggjgZzziWBXs5M3BDxEHb4bPzW/0CiC44IkBMydqZ+dthvsa26ifTkhL7s7GDkDZPEvA17GlhUkBVyWXhPCnNdVBxsM6XKHcQoi8MFpfTMIlQTlM2U43Wo53AwRW18AHo7YemVMTlca+6RVKqxHNvxVsRjFGS7iKeXcRUvakWRFOAuOccqWeKwstha3cwRE9KJ89HwyBeTMlMRGdrEvJbOHrbvbw7buW1TkOOi05QqdxSjLA4XGvZoM0iozm2bxFStMIZaWbjdUPwP3f50gnfx4uhQVtfG873LKGj4ADoaIxpjTGoCpybvILX7YGATFGhfRsYkR53cSind8ChEfwXo+koTMlKGdGbxcWUDbhW+v8JmiomIchyjLA4XQk3G80XRcqjZ2pfRPCTsfFW3ID06NrMK0A2Pnu9dRry7G7a/GNEYIsLnkz+kQ1JgxunBd8id4ejMorqpg8b27pD9FTY6fHboLrQbK3TmdqQzCxM+6zxGWRwuVK6DhFQd3RQuw6H0R/E/IG08zF4Zs0OW17ayQc3AnT7Rbwe9oPT2cHLPe7yXcDQkhZDY53CuRUlfmY/QZxYw9H0tNuxpYPrYNLJc4RVvtDGlyp0nqLIQkWNFxGW9Xi0ivxeRgmD7GYYZlcWQd1RkdZQmzNMX6p2vOi9XKNTv1v20l3wFEiK7eERCWW0b48ekEjf3XCh9ReephEv5W2S4G3miYxlKheBszZ0BbXW6QZUD2JFQwarNepOXncq+hg56h8BBrJRiY0VDxLMK0Ka0SZmpJtfCQUKZWdwJtIvIAuB6YD/wQFSlMjhLT6fOTQjXX2EjomcXO63SH7Fm/b1ahiWXx/Sw5XVWtdm5q3QzqNKXwx9kyxN0x7t4qftIDrZ2Bd/eLsPiUPjstuomJmemkOkKL08kLyuVHrfiQHPscy32NrRT09wZsb/CxoTPOksoyqJH6VuiVcBflFJ/BEzBlZFE9WYd/hqJv8KmaDm0H4TqTc7JFQo9nbob3qwVkJkf00P3VZstPE4XVQzXFNXbDVufoTbvNDpJ6l9Q0B8OFxQsqW6OqD7SUIbPHvJXhJe57Y1RFs4SirJoFZEfAJcCz4lIHBBZOqthaOhLxotwZgEw/VT9HOuoqE+fhrbamDq2ARrbu6lr7dJlPuLiYfY5sP2l8LKry96A9np65+huwpWhFOfLmgIS74iy6Opxs7OmhVlh+itgaBPzNuxpIDkhjtlBuvoFozDXRU1zJ+1dQ1u2ZLQQirK4GN3R7mql1D50E6M/RVUqg7NUFusmQWMmRT5GxgTdFCjWTu7iu3T+wbRTY3pYu+92X/bw3HOhuxVKw/DbbHkSkseQteAsIMSS2QlJkD3FEWWxq7aF7l4VtJWqL/L6GjcNhbKoZ0F+Jonxg4u/6esnMkwq6I50Qvk2EoBblVL2VaIGeCV6Ihkcp7I4cn+FJzOW68qpkTh6I6F6M1S8r2cVMS6RXl7npSymngSp2bDVu3+XH3q6YOuzMGsF6WnpZLsSQ79o5c6A2sErC7vhUSRmKFdSAtmuxJjPLLp63HxS1TQo57ZNX/hsnVEWThDKP/AJwHMe58b0mhg5NO/XCXmD8VfYFC3XrT93vzP4sUKh+B863HfRF2NzPA/KalsROXTBIT4RZp0N257XfpSgA7wBHQ19iXi6+myIF97cmXBw56CDCbbuayYxXpg+NnDDI3/kZafG3GexdV8TXT3usDrj+cPkWjhLSDMLpVRfGIdSqhNIjp5IBkfZu04/O6EsCo7VF+9Y+C06GuHjR+HIL+g7+hhTXtvK5MzU/s2C5q6CzibY9UbwAbY8qZsZWWXeC7JdVIZ60cotgu42aN4XgeSH2FbdRNG4dJISIpuVDUWuxWCT8TzJdiWSnpxglIVDhPIrqhORFfYbETkHMC1ORwqVxbr96KQFgx8rMQWmnhAbZbHpEe0jiGaDowCU1bUN7I43/RRIHhM8Kso2Qc0+GxL0fZXumNceWmE7hyKiSqqbw87c9iQvy8Xe+vbQ8kMcYsOeeiaMSWZSZsqgxzKlyp0lFGVxDfBLESkTkTLgZ8A3oiuWwTEq18HEI3WNJycoWg6126GhwpnxfKGUdmznLYHJi6N3HL+HV5TVtAzsu52QrBsXbXtOh8X6Y9da3cnPoxZUfo6Lrl43NS0hmLAcUBaNbd3sa+yIKBLKJi87lfbuXurbAnxWh7GT8SKpNOuLKUZZOEZQZaGU2q6UWgosBhYrpZYppbZHXzTDoOntgb0fOWOCsrFLf+yKYlRU+dtQu23IZhX1bd00dfT47qMwdxW010N5gEq0W57Ufc6nn9q3yO5rEVJGccYkXc58EAUFS6qbAAYVfmqXNI+V3+JgaxfldW2O+CtsTKly5/CrLERktfV8nYhcB1wGXObx3jDcqdmqTTlOKotxs/XFLJqmqOK7tJ8iWJXWKFHmHTbryYzTIDFN53/4orsDSp7TNaw8SpMUZIcRxhkXp8OFBzGz2LY/vIZHvrAVXKwKCm5y0F9hY5cqD2lGZwhIoJmFrd7H+XiMjbJcBieotJ3bDoTN2tilP3a9Du4oJDs17YOSZ2Hxpc6ZzsLEzrHw2Xc7MRWOOEPL6Ovz73xNO8G9FJ194a0MJdcCBl1QcOu+ZjJTE5k4JnLbvz2ziFWuxYY99cQJLMjPdGxMExHlHH6VhVLqr9bL55RSP/V8AGtiI55hUFSuA1cuZE91dtyi5doUs2+js+OCLu3h7oGlVzg/doiU17USJ4dmAwOYcy601uh2s95seVLPiqaf0m9xSmI84zKSw8u1qC8P7BsJwLbqJmZNzBiU7T/LlYgrKT5mEVEbKhqYNXEMrqQIil36weRaOEcoDu6/+lh2u9OCGKKA3RnPIWdhH9NP1c+lDpuierth/T0w47OQM93ZscOgrLaV/GyX/5DTmWdAQsrAqKjudti2Buas1HkZXhRkp4aWxQ1aWaheXXE3TNxu3fBoziBMUKCjifKyYpNr4XbrSrODLR7oTV6W7vo3nGcW3b1DUJwzAgL5LJaJyLeAcbafwnr8hBBrQ4nImSKyTURKReRHPtYni8gj1voPRGSq1/pCEWkRke+H97EMtDdoJ7GTJiibtLEwaaHzfottz+vcgiFybNuU17X6NkHZJKdrhbb1mf6Jc6WvQleLX19LQY6LylDt/4OIiNrb0E5rV++gIqFsdBOk6CuLXbUtNHf0sNhBfwXoUuWTh3Gp8keLK/jC/70bWkXiISbQzCIN7ZtIoL+/ogu4MNjAIhKPnoGcBcwFVouIdz/MK4F6pdQM4Gbgd17rbwaeD/4xDAPYu14/O+nc9qRoOVR+CB1Nzo1ZfBdkFug79yFCh822Mi03SKOiuau0YrOLNIJlgsqBqSf73CU/O5Wqhg56QrmTzLX7ce8IUfJDbN03+Egom1gl5m3Yo53bTs8sAApyUoflzKK4/CA//s9mMlMTGZPinOktWgTyWay1/BMnePgqfgbcrpTaFsLYy4BSpdQuKwP8YXSZc09WAfdZrx8HThPLyCoi5wG7gC1hfSKDpnIdIDD5qOiMX7Rc+xbK33ZmvJrtukTGkst1ldchoqalk9auXt+RUJ4c8Tmd7GjXiupu1zOjuef6bTBVkO2i162obgqhR4QrRyueCGYWdk2oI8JseOSLvOxUGtq6ae3sGfRYgdhQ0UBGSkLEpUkCMRxLlVfWt3H1/evJz3Zx2+qjSBhk0cRYEIqEN4jIGKtb3hagTES+G8J+eYBn5laltcznNkqpHqARyBWRNOB/gF8EOoCIXCUi60RkXU1NTQgiHUZUFsP4OZAyeFOETwqO0bkATpmi1t2tL75HXebMeBFSXqsvKgHNUKDzKIqW6xBapWDHyzpMOUC4b18V1FD9FmNnRpRrUVLdTGGOi/Tkwd+t5sWoVPnGPToZLy7OYf8aWlkcGEalyls7e/j6P9fT1evm75ctDbsx1VARirI4UinVBJwHvIQuUX55CPv5+ta9M2P8bfML4GalVMDypkqpO5VSS5VSS8eNGxeCSIcJSjlXadYfCckw9URnlEVXK2z8lzbtpI8f/HiDYEBp8kDMPRca90DVBm2Cco2FKSf63bwvMS+ciKgIZhYlViSUE+THoAlSW1cPJdVNjvsrbIZTqXK3W/G9RzexrbqJW1cvZsZ452dS0SIUZZEkIglok9F/LJNSKO77SsCzV3c+UOVvG+sYmei6U8cAvxeRcuDbwPUicm0IxzSAvhvtaIiev8KmaLmujlpfPrhxNj+uy2MMsWMboKyulYQ46bujDsisFbpR0ceP6B7hAUxQAJMyU4mTMPIWcou0XySMkvAd3b2U1bYOOhLKJi9LX2groziz2FzZiFvBoij4K2B4hc/++dUdvLClmutXzOHUWUN7YxQuocxT7wL2AJ8Ab4hIIRDKr7cYmCki04C9wCWAd63pp4GvAO8BFwCvWS1cT7I3EJEbgBal1G0hHNMAzlaaDYRd+mPnWlj61fD2bTsIpa/oi+z2F2H8PCg81nkZw6S8tpXCHFdoNmRXDkw7GT78uw5zDZJxnpQQx8QxKWFUn7X7ce/U0WchUHqgBbfCkUgogPEZySTGS1RnFhscaqPqjylWja+h9ls8+3EVt7y6gwuX5HPlidOGVJZICKoslFI3o6OSABCRCmB5CPv1WLOBF4F44G6l1BYR+SWwTin1NPAP4H4RKUXPKC6J7GMY+lFZrKujjp0V3eOMPQLG5GlTVDBloZQuQLjtea0cKt4H5Ya08TDvPDj+OufzQSKgrDZI2Kw3c8/VdbLSxsOUE4Junp/jCs8MBdoUFaKyKLGc205EQgHExQmTMqMbEbVxTwNTcl3kpCUF3zgChkOp8k/2NvL9xzaxZEo2/3v+fMcKJcYSv8pCRFYrpR4KUAfqlmCDK6XW4JXtrZT6mcfrDoKE4Sqlbgh2HIMXlcW6Wmu0u8vZpT+2Pq2LFnqbYHq6dKOk7S/C9ucPmasmHgknfV9XcI2FnCHidivK61o5YUYY1Wxmr4Q1P9AKL4QoroJsF+/urA1tbDsxMQwnd8m+JpIT4gZWzB0EOjEvehfaDRX1HDc9N2rj26XKo5Jr0Vyt+5ssuMjvzc6B5g6+/s915LiSuOPSJSQnDF2032AINLPwrA3ljSnhOFzpaoPqT+DE78TmeEXLYcP92slbcDS01urIoO3P6wzvrmaIT9blL46/ToecZubHRrYw2d/cQUe3O7yZRfo4uPLlQ3kRQcjPTqW6qYPOnt7gF43EVJ13EoaTe9v+ZmZOSCfewaiivOxU3toRnWjDfY3t7G/qdLR4oC8Kc1LZVdPq/MDP/w98+h8YP9vn7K+ju5dv3L+ehrZuHr/mOMZljNy+cX6VhVdtqPc914nI0BuXDb7Zt1Hbz6Ptr7CZfiog8NqvoKcDKj4EFKRPhPmf17OH6adAknN3utGir9psuHfleaHnshTkuFAKqho6Qou4CrOg4NZ9zZw6y9nIwLysVA40d9LV4464654/isvrARwtS+6LwhwXr2+rQSnlnAnowNZDJV82PjRAWSiluP7JzWzY08D/feko5k12rkDiUGBqQ4027IziaIbNeuLK0Y7psje0sjjlf+Dra+G7W+HcW2D2ihGhKMAzxyJI9vYgKLCrz4YbPhtCt7ralk5qWzoHVZbcF3nZqSilZwFO825pLRkpCczPi+6FtNAuVd7sYKnyN/+gf9vTT4XNj2qzqwd/f2sXT3y0l29/diZnHTnJueMOEYF8FsuA47BqQ3msGkOItaEMQ0BlMWRP0/WbYsXqh7WiyJgYu2NGgfK61r5aQtEiP9zEvNwZuh95a602eQXAztye7VAklE2+RxOkKQ76QpRSvLWjluOLch01m/miwKNU+fhBlG3vo2YbfPKENvcWHgv/ugh2vARzzgFgbckBfvN8CSuOnMh1y2cO/njDgKjVhjIMAUpBRXHsTFA2qVkjXlEA7KppZUqOKypZxDYTx6SQECfhzSwgJFOUHQnlVEKeTZ49G3I4ImrPwTb2NrRzYjgBBRHieF+LN/+gKxgcdy0Unaaj4TY9BEDpgWaue2gDcyaO4aYLF0b19xRLAvks1gJrReQepdSuGMpkiJSmvdBSHXtlMUoor2tlejjO7QiIjxMmZ6VSEXJinoeymHJcwE1L9jUxNj3JcSfqpExd5tvpXIu3S3VUWFjRZxGSl+1gqfLaHfDJv+H4b0KaFcW14CL44A4aa6u48r5tJCfG8/evLHW0N8dQE4rPoklEfiMiT4vIS/Yj6pIZwicanfEOE3rdij11baE5nQdJQU4YJbOzCnXNrBBmFtv2Nzs+qwCdTDg+I9nxXIt3SmuZnJkSk3OenBDPpDEpzmRxv3mT7mdy3DcPLVv0RXD38NT9f2FfQwd/+/KS0KoAjCBCURYPAOXAEegS4tVAFFqkGQZNZbH+EU+YP9SSjDiqGtrp6g0zbDZCCrJdoZf8iIvX+RZBlEWv1fDIaX+FjdNNkHrdind31nHCjLExS1ArcKL6bN1O7cxeekV/H9KEeexNncVR9S9w4+ePZMmU6EZ3DQWhKItxSqm/AV1KqVfR5TmWRVcsQ0RUroNJiyAhOpmwo5nyOqvvtoMOXH/kZ6dS2xJGFdTcGUET83bXtdLZ447KzAIgL9vl6Mzi06omGtq6OXFm7AIxHClV/tYfIT5J5wx58OAHu7mz6Vjmx5VzQV794I4xTAlFWdhNgKtF5HPAfPoXCDQMB3q6dI6FMUFFRFjVZgeJHZkTupO7CA7uArd/5WI7t+dEcWaxr7Edt9uZfFzbX3F8UeyUxZTcQZYqP1gGmx7Ws4qMCX2L39tZx8+f2kLdtJWouESdczEKCUVZ3CgimcD3gZ+gzVKmzelwY/8nOnzVKIuI2FXbSmpiPBPGRD/DNj/bVhZhOLl7O6Gx0u8mJdXNxAnMnBCdktd52al09yoOOJSn8E5pLbMnZsQ0ozlsJe3NW3+EuIR+s4qKg23814PrmZLr4sZLT0VmnanNVL3dAQYamYSiLA4opRqVUh8rpU5SSi0E9kVbMEOYVMao0uwopdwqIBgL+3lBJH0tIKDfomRfE1PHppGSGJ26Q325FqH2EA9AR3cvH5YfjEkUlCeDCp+t361DY5dcDmMOJdjd/Mp2Onvc3PWVoxmTkggLvwitNbqi8ijDZHCPFiqLIWOSrgJrCJvyujamRTFz25NxGckkJ8SFHhHVpyz8+y227W92PHPbk75cCwec3Ot319PV445JfoUng1IWb/8JJA5O+FbfogPNHTyzqYqLlhYcMl/OPF03wdr4oBMiDytMBvdowe6MNwJLHw81Pb1uKg62cdb82CQWigj52amhX3jTx0NSht+ZRWtnD7vr2vjCUdEr0Ohke9W3S2tJiBOWTcsZ9FjhkJOWRFpSfPjKoqECNjwIS74CmYduxh54bzc9bsVXjp96aNv4RFhwMXx4p+7Z4ortZ4wmJoN7NNBaC/VlxgQVIZX17fS4VUzCZm3ys8PoayFiFRTc4XP19v3Rydz2JC05gSxXoiPhs++U1nJUYTZpDvQID4eIS5W/bbXzOeHbfYs6unt54IM9nDZ7/MCgiEWrwd2tO0COIsLK4BaRDKVUc8ykM4TG3vX62SiLiCiri10klE1BTiobrQ5xIZE7Ayo/9Lkq2pFQNnlZPpogdbXqToGFx0LBMUFntg1tXWze28i3TzsiipL6pzDH1RcmHRKNe3UJ/sWXQtahINCnN1ZxsLWLK07w0fFu4pH6sfFBOOYqB6QeHvidWYjIj0VktlJql4gkWVnblSKyX0SCdsozxJDKYt0LetKioZZkRFJWE7scC5v8bBeN7d00dYQYNZM7Q5tDujsGrNpW3YwrKZ787OhmDOdneyXmKQX/uQZe+Tnc/Tm49Sh44/faGeyH93fVoRScMCN6zY4CYedaqBCq+ALwzp91R0eP/jBKKe5+p4zZEzM4rsjP51j0JR3Kvv9TB6QeHgQyQ30R2Ga9vgxIBnLRLVV/E2W5DOGw+z19J5MUGwftaKO8rpX05ATGpscumbHADp8Ntfrs2JmA0uZGL7bua2LWxIyoF6zLy9KJeX0X2rf/pPs5fObHsOqvOrhi7a/hLwvgnrNhwwPQ2d8Q8XZpLWlJ8SyMcrMjfxTmuujoDrFUedM+WH+fLuWRPaVv8bs76yipbuaKE6f5j5478kIdZrvpXw5JPvQEUhZd6pD6PRN4SCnVo5TagnFwDx+62rR5YtrJEQ/R3tVLW1ePg0KNLMpqW5kWo7BZm4KccPtaWJ34vJzcSqmoR0LZ5GWn0tbVS0Nbt+6G+OqvYP4X4OQfwOIvweXPwrc3w2d+As1V8NR/wx9mwr+/rvu0u3t5p7SOY6fnkhg/NK10C8KJiHrnL+DugRO/22/x3W+XkZuWxLkLJ/vfN20szPwcbHpEtxweBQT6xjpFZI6I2LMJz+KB5hZ2uLDnPejt0t3oIuSbD33E1+5b56BQI4syK8ciltiJeSFXn83xrSzWbK6moa2buZOi66+AQxFRNbu3wr+v1DXIzr21v58iqxBO+QF88yO44iVYeInuwX7/+fT8aT4XNvyDFZOGzu0ZcvhsczWsvwcWroacQ36JstpWXi05wJeOnRI8p2XRF6H1gFaUo4BAyuJ7wNNAKXCLh5N7BfBxDGQzhELZm7oqaWHg8tX+qGnu5LWSA3y0p55eh0o5jCQ+LDtIZX07S2Nc+C3blUhaUnzokTkpYyB9Qj9l8cymKq57eANLp2Tz+SiGzdrkZ6eSRjuTXrhS5xxc8oD/LogiUHgMrPwzfH87XHAPB1KLuCr+Wb7w3vnw9+XaMd52MOpye3+GkEqVv3urzsI+qf+s4t53ykiKj+PSYwuDH2zmGeDKHTU5F36VhVLqHaXUTKVUtlLqBo/la5RSF8VEOkNwyt7QUVARti5ds3kfbgUd3W52hxMlMkq49bUdjE1P4qKlsS13ZodxhpXk5lFQ8KmNe/nWwxtYMiWb+65YFpMw1LzMFG5KvIO0pp1wwT2QPTW0HRNTYP7n+W3Orzgn8U7UGf8LPZ2w5vtw0xHwyJfhQElUZbfpK1UeSFm0HIDif+geFbb5D2hs7+ax9ZWsXDiZ8RkhdNtLSNK+i21rYq4Uo4EEfiYAACAASURBVMHQGA4NztBeD/s2DcoE9cymKtKtC40dgnm48NGeet7aUctVJ08nNSk6ZTICoRPzwoj5zy2CulL+vb6S7zyykWOm5XLvV4+OWb5C1vpbOCu+mFfyr4Wiz4S1r9uteKe0ljkzZyLHfxOueQe+8RYsu0rf8NxxArz00wEO8WgQNNfi3Vt1La6T+pfAe6R4D21dvXz1hKmhH2zRF7WZeMsTkQk7jIiqshCRM0Vkm4iUisiPfKxPFpFHrPUfiMhUa/kyEdloPTaJyPnRlHPEUv6ODuuL0Lm9t6GddbvrueKEqcSJri90OHHrqzvIdiXypWOmBN84CuRn64tWyGGcuTOgtYZfPP4uxxeN5e7Lj45dJ7btLyJrf80riafw76Rzw9592/5m6lq7+teDmrQAzrxR+zcWroZ3b4HblukudKGekwgIWKq8tRaK74L5F8DYGX2Le3rd3Pfubo6ZlsP8vMzQDzZxgfbtbBz5UVFBlYWIDPg1+lrmY5t4dA2ps4C5wGoRmeu12ZVAvVJqBnAzurkSwCfAUqXUInQk1t9COeZhR9kbug9wXmSVZp/dVAXAF5bkM31cOlsPo5nFx5UNrN1Ww9dOmh7zTGKbghwXrXZ0UQi8UacvUucXdnLXV5bGbjZUt1NHNE2cz6MTv09lw8Bcj2C809dC1UdeQtpYWHUbXPmyfv34FfDPVVCzfbCS+6Qwx8X+pk46un2UKn/vNuhuh5P7zype+nQ/exvaufJEH0l4gRDRinDveqjZFnz7YUwoMwtfaaO+U0n7swwoVUrtUkp1AQ8Dq7y2WQXcZ71+HDhNREQp1aaUsuPNUoDDz/MaCmVvwpTjI2529PSmKhYWZDElN405k8aw9TCaWdz6WimZqYlcdtzQzCqAviS6UMp+3P9eOb98rwuAHx+TELXqsgPobIaHVuuOfRc/yLic7IjqQ71dWkvRuDQmZQZIHCxYBle9Ditu0glt/3c8vPxz6GyJWHxfFOb6KVXedlA73ed/HsbN6rfq7rfLKMxxcdqcCYTNgot00uwIn10EyuAeLyILgVQROVJEFliPEwktdDYPqPB4X2kt87mNpRwa0Yl/iMgxIrIF2Axc7aE8PGW8SkTWici6mpqaEEQaRTRXQ01JxCaonTUtbKlqYuUCXW559sQMKuvbQ88oHsF8WtXEy5/u54oTppGRMnQpQ3ZiXkWQxLx73injp09tYeas+SiJI6lhVyzEA7cbnrxaR2BdeC9kTyEvO5WGtm5aO0PPHejqcfPBroOhVZmNi4dlX4dr1+uCfO/8GW5fBluedMw05TfX4r3bdfmSk3/Qb/GmigbW7a7n8uOnEh9J4mP6eB0Z9fEjARtYDXcCzSzOBm4D8tHmJPtxPfDTEMb2dVa9v22/2yilPlBKzQOOBv6fiAwIP1BK3amUWqqUWjpu3Djv1aObsjf187TInNvPbKpCBM5ZoBOL5kzSSV3bDwNT1G1rd5CRnMDl4Tgqo0B+CIl5d721i1888ylnzpvILZcei2QVBu3H7Rhv3QQlz8IZ/9sXRBFJ9dkNe+pp7+4Nr39F+jg473adq+HKgccuh/vPc8Q01ZdrUedx3tsOwgd/g7mrYPycftvf/U4Z6ckJXLh0EOHJi1ZD8z7YuTbyMYaYQKGz9yilTgKuVEqdbDU+OkkptUIp9VgIY1fSv/1qPlDlbxvLJ5EJ9IsxU0ptBVrR7VwNNmVvQEqWLvMRJkopntlUxbKpOUzM1Dp4tlWEbrT7Lbbvb2bN5mouP2EqmalDW4hgTEoimamJfs1Qd7yxk/99bitnHzmJW7+4mKSEOMidGRtlse0FWHujvrs/9pq+xbbpLJzqs++U1hIncKy/OkqBKDwGvv46nPUH2LtBm6ZeuUHPACIkNy0JV1I8ezxndB/cAV3NcMoP+21b3djBcx/v4+KjCwY3Cz3iTEjNHtHlP0LxWYwXkTEAInKHiHwoIqeFsF8xMFNEpolIEnAJOsnPk6eBr1ivLwBeU0opa58E65hTgFlAeQjHPDxQCna9CdNO0tP2MNm6r5mdNa2cu+hQuYJJmSmMSUkY9RFRt71WSlpSvO9qoUNAQU6qTzPU7WtL+e3zJaxcOJm/XLLoUHkMO9ciitFC1O6AJ76uo5VW/qVfhnZelmXvD2Nm8XZpLQsLsnQnuUiIT9DVW7+5Ttv/375ZR019+lRE50FErIgoS+G0N8D7d8CclTBhXr9t73+/HLdSXO7ZsyISEpJ1zsXWZ/XxRiChKIurlFJNInIGenZwDfD7YDtZPoZrgReBrcCjSqktIvJLEbFj7/4B5IpIKfBdwA6vPRHYJCIbgSeB/1JK1YbzwUY19WXQuCdiE9TTm6pIiBPOmn+oPaSIMHuUO7l31rTwzMdVfPm4qWSnxa5oYCDys1wDzFB/eWUHf3hxG+cvzuPmixaS4FlHKbcIulu1zyoadDTBw1+E+CS4+EFI7O+QHp+RTGK8hDyzaO7oZlNlozNd8dLHw3l/hStehNQsePQyeODzOsrI7Q5rqALP8NkP7oDORji5/6yivauXBz/Yw+lzJ/T5OQbFwtU6f2OE5lyEEjNoq+6zgHuUUutFJKT8DKXUGmCN17KfebzuwEcjJaXU/cD9oRzjsGQQ/grbBHXizLHkeF0w504aw2PrKnC7VdQrmA4Ft68tJTkhjq+dNDxmFaBnFmu3HejLtbj55e3c8lopFyzJ53dfWDDQoerZj9ujF7QjuN3w5Df0zOWyp/r1b7CJixMmZfroa+GHD3YdpNetOL7IwRaqhcfCVW/ofIi1v9YOcERXMUhKh+R06znD63267jiYnM65vc28Vt+KKmlF3v8rzDpbz6Q8eHLDXhraup2bhU5eDOPmwMaHYOkVzowZQ0JRFptEZA1wBPBjEUnHhLIOLbve0P22x84Me9eP9jSwt6Gd754+sPnM7IkZtHb1Ulnf3hdeOFoor23lqY1VfPX4qYxNTx5qcfooyHHR2aNLZt/7bjl/fX0nlxxdwI3nH+lbYXsqi2knOSvMm7/XpSnO/F3AsfOyUtkbYub526W1pCTGcdQUh0uSxyfAsVfz/9u77+i46iuB49+rLqvasqzmIjcsd2EcgwtgYwKGYEQJEEgIARIgCyFtlyQkG9LLJhs2BJIAwaGXYALIpiVgkC33JrngJksukixLsmz1OvrtH2/GGFllZjRVup9zfDR688rPc0Zz5/3KvUy9FnYtt7p22hqsqb5tDdZ027YGqC21xiIcv3dYa0SWAktDgJcfAcRKfngGR82KaRnxniv/KmKt6P73f1tdfW78/fqTM8HiduA8rDUTTSIyHGsxnfKHzk7rzmLCpW7V215RWE5EWAiXTT17vnhWmmOQu27ABYs/f1REaIhw10Xj/N2UT3EMGP/X8h3k7a/ii+eP5uc503q+s4vPgLAozw9y730bPvo1zLwFzr+7110zhkaz5oBzU9XXFlUzZ2wSkWFeWhcSlwJz73V+f1sHtDWwbs9hfvzqBv50/QQmj0yB1E/Pn1lzoJqiygb+cONMz6aun3GjNUBf8CJc+pDnzusDfXYnGWNswDissQqAaGeOU15StQeaqt1aX2HrNLy18xiXTBrR7cyOc1JiEYG9xwbWjKijNU38c1sZt8wZzYh4JxLA+ZBjrUXe/ipumzuGX1zTS6AACAmx0pXbEwp6RNV++OddVjfJVQ/3+SUkIzGayvpW2jp6Hyc4XtfCgcoGFvipKl63QsMgOpGUUeMpMiPZGzrprEAB8FR+CclxkXxuhoe7+uJSYcLioFxz4Uy6j0eBRcCX7Jsagb96s1GqF8V51k83kgduLD5BVX0rS3so2jIkIozMpJgBN8j9l7yDhIhw98WBdVcBVjfU8NhIvrpgLD+5eqpz32LtCQU9orXeGtAOj4Kbnrd+9iFjaDTGwLHa3sctPknx4cHxCg/JSLSnKj9x9v+hqLKevP1V3HrBGO/cEWXfAnVl1vT3IOJMN9Q8Y8wsEdkOYIypsU+FVf5Qstr6Zpng+gKh3MJyYiJCuSRrRI/7TE6L4+PygRMsyk818+qWo9w4e1TvqSb8JCo8lE0PLnZtQkHSBGtswdYOof1cK/LeD6HmINy2wun31MjET9ZajOmlbnl+UTXDYiKYnOr9wkyuigoPJbWHVOV/X3uIiLAQbjnfiZoV7jjnCmuNVMGLMP4S71zDC5zpTmq3z34yAPbKea7NU1OeYeuAw2vd6oJq6+jknV0VfHZKSq8J6LJS4zlc0+RSOodA9njeQYyBry8c3/fOfuLyzLOkCVa5z1NH+nfh/e/Btmdg3v2QucDpwzLs4yy9rbUwxkpJPm98UsDOrOsuVfmppjZe21bKtdkZ3psIER5llaPdsxJaar1zDS/oLTeU467jMeA1IFlEfgrk80l2WOVL5duhtc6tLqj8oipqm9s/tRCvO1mpcRhjrXQOdpV1Lby0+SjXzxp5uozpgHDmjCh3NdVA7jdgxFRY9KBLh6YlWF04va21OFjVwPG6Vs+sr/CS7lKVv7jpCC3tndy+INO7F8/+InQ0w+43vHsdD+rtzmITgDHmWeBHwO+Bk8ANxpiXfdA21ZWjjzPT9SmTuQXlJESHs2BC7zm0JttnRA2EQkiPry7G1mn4j0WBe1fhFk8Ei7e+YwWM6x63Vhe7ICIshBFxkb2utcg/ELjjFQ6jhw2hoq7ldKrydlsnz647zPwJSafT33hNxiwYPimoMtH2FixO3zsaY3YbY/5ojPk/Y8wuH7RLdackD1KmWzn/XdDcZuPfHx/nyumpVn6hXmQkRhMbGRb0g9zVDa28sPEwOdnpvfarB6WYJCvPkLvBYudyK4vroh+4lVsMHGstegkWRScYkzTEMyufvcSRUNCxgv6dXRVU1LX4JhWMiJVc8OgGz85s86LePjmSReQ7Pf3zWQuVpb0Zjmx0qwtq1d5KGttsLJ3RexcUWP3nWalxQT999sk1xbR1dHLvogl97xyMkia4FyzqjsFb37Xqts/7ptuXzxg6pMc7iw5bJxuKTwT0XQWcnap8WX4JY4fHsGhSzxNAPGrGTSAhUPiSb67XT70Fi1AgFojr4Z/ypaObrLwybgxurygsJzkukvPHOTffPSstjj0Vdc6X+wwwNY1tPLf+MFfNSGd8cqy/m+MdjoSCrjAGcu+Djla49nFrzYGbMhKjOVbbTGfn2e+RwtJaGlo7Anq8Aj6dqnzbkZMUHD3F7fMzfTcgH59uzYYqfNnl3Fb+0Nu75Zgx5mc+a4nqXUkehIRZlfFcUNfSzqp9ldwyZ7TThVuyUuN5vuUI5bUtp+sXBJNl+SU0t9u475IBelcB1lqLwpesVN0RTnazbX0ait63KtEl9W8cJ2NoNO02Q2V96+k09w5ri6oRgblOfjnxl+GxEUSHW6nKNx8+SVxUGNfP6kfNCnecdzvsf9dKSRLlQm1vP3BqzEIFgOI8yDjPSo7mgn/vPk5bR2ePC/G64yiEtCcI11vUNrXzzLpDXDEtlXNSBvANsGOQu8bJqnk1JdaainELYXb/s/WcXmtx6ux1CvlF1UxLTwiYzL49caQq31hygnd3VXDznNG+r8c++Sqr/niABwroPVg4U7NC+UJLLZRvc6sLKrewnIzEaGaNdj6Rm+NDdm9F8AWLv68rob61g/sWBVeSNpe5MiOq0wZvfN26M815zEoZ0k+n11p0GeRubO1g+5GTzAukFB+9GJ00hN32L0W39bdmxQDXW6W8mp6eUz52eB2YTpdTktc0tpFfVM3SmekuJUOLiwpn1LDooKuaV9/SzrL8Ej47JYUp6YG3atijhtlTlzgTLNY/BkfWw5X/49bK/+70VF5106Ea2m0m4McrHBzjFkumpgZll6svaULAYFCcZ2UaHTXHpcPe2XUMW6fhahe6oBwmp8YHXdW8Z9cfpq6lg/svGeB3FWCNU8RnQHUfweL4x7Dq55B1lTX7xkNiIsNIHBJ+1vTZdUXVRISF8JlMD6X19rKxw63xnju8vQhvAPBxB51yS8lqq+CLi4uncgvKGZ8cc3oMwhVZafG8v+c4Le02osK9lF7agxpbO/jbmmIWTUpm+sjA7//1iL4SCna0WcWMohLOKo/qCRmJZxdByi86wewxQ4PiPQNw/ayRTBwRy3ljgiO4+ZPeWQS6hiqo3O1yF1RFbQubDtVw9cwMt/LxT06NozOI0n48v+EwJ5va+cbiQXBX4ZA0AU4c6LkO9erfQcUOK1C4uJDTGV0X5lU3tLLnWF3Ar684U3REqNNTygc7DRaB7pB7JVRX7ijHGLhqpnv5+B2FkIJhcV5zm40n1xRz4cThzBo91N/N8Z2kCdbkh6ZuhhdLt8Ka/7WKGWV9ziuXzxhq3Vk41uOsO3gCIGjGK5RrNFgEuuI8iEyA9GyXDlux4xhT0+PdXpQ2etgQosND2RMEM6Je3HSE6oY27h9MdxUASfb/b9euqLYmq/spLg2u+I3XLp+RGE1Tm41TTe0ArD1QTXxUGNMyBkk34CCjwSLQleRZ6aNDnO8DPnyikcKjp9wa2HYIDREmBUHaj7aOTp5YfZALxg0LmkFVj3EsrOsaLD74qdU9dc2fvTp/31ES1nF3kV9Uzbzxw51e/KmCiwaLQHbyMJw85PL6ipU7jgFwVT+CBViL8/YGeNqPFYXlHK9r5Z6LB1hmWWckjrHWTpwZLIrzYONf4fx73Moj5oqMREcivmYOn2ii7FQz8ydqF9RApcEikJXYxytc/KPPLShn9pih/Z43npUaz8mmdo7XtfbrPN5ijOHJNcWckxLLxef0nnp9QAoNg6FjPwkWLbXw5r3WWMbih7x++Ywz7izy7SVUdbxi4PJqsBCRJSKyT0SKROT73TwfKSKv2J/fKCKZ9u2fFZGtIrLT/jN4ag96UkkexIyA5CynD9lXUc++4/UupffoSVaqPe1HgI5brC06wd6Ker66YJxbM74GhDMTCr77A6u287WPQ4T3U4MPHRJOdHgoZSebWVtUTUZiNJlJgZuSXPWP14KFiIRiVdm7ApgC3CwiU7rsdidw0hgzAXiYTyrwVQNLjTHTgduA57zVzv4yxvDMukP88PWdnu2uMca6sxh7kUvz41cUlhMicOV092ZBnclRACZQxy2eXFPM8NhIcs7tf2AMWknjrRrae1ZCwQtw4Xdh5GyfXFpEyBgazdGTTaw7eIL5E5IGb9AeBLx5ZzEHKDLGFBtj2oCXgZwu++QAz9gfLwcWi4gYY7YbY8rt23cDUSLipYK47mtpt/Gfr+7godzdvLDxCLvKPPgNvGofNBx3qQvKGMOKHeXMGz+c5Lj+v1wJQ8LJSIwOyBxR+4/Xk7e/itvmjiEyLDgWgHlF0gToaIHX74HUGXDRAz69fEZiNGuLqqltbg+q9RXKdd4MFhnA0TN+L7Vv63YfY0wHUAt0XSFzPbDdGHNWx7mI3CUiW0RkS1VVlcca7ozKuha+8MQGXttWyt0XjyMiNIQ3Cso8dwFHCVUX1lfsLKvl8Immfs2C6ipQCyE9taaEqPAQvnjBGH83xb8cCQVt9hoVYb7N9Jox1Jo+CzBvvAaLgcybwaK7+9Gu/TS97iMiU7G6pu7u7gLGmCeMMbONMbOTk303wFl49BRLH81n//F6/vqlWfzgisksnJTMisJybN0Ug3FLyWprtstQ5z8McwvKCQ8VLp+a6pk2YBVCOljVQGuHzWPn7K+q+lZe317G9bNGMizA02B73YgpEBYNl/4EUrr28nqfY/psVmqcR+5mVeDyZrAoBUad8ftIoLynfUQkDEgAauy/jwReB75sjAmYIrWvby/lhsfXEx4awj//Yx5LplljAznZGVTWt7Kx+ET/L9Jpg0NrXOqC6uw0rNxxjIvPGUHCkPD+t8EuKzWejk5DUWWDx87ZX8+tP0R7Zyd3LvBBreRAF5ME3yuBuff65fKOGXfaBTXweTNYbAYmishYEYkAvgDkdtknF2sAG+DzwCpjjBGRROAt4AfGmLXOXMzbKwFsnYZfvb2Hb79SyKzRieTet+D0ADDA4skjiI0M80xX1LFCaxqkC11Qmw/VUFHXwlI303v0xJGEMFC6oprbbDy34TCLs1IYN1BLproq3H+ptSfZZ8wtnuyjutXKb7wWLOxjEPcB7wF7gH8YY3aLyM9E5Gr7bk8BSSJSBHwHcEyvvQ+YAPy3iBTY//X6btx3rJ6/fHSQWnvqAU+qbW7njqc388TqYr48dwzP3Xn+Wd0fUeGhXD41lXd2VdDS3s8um9PjFc4vxluxo5yo8BAunZzSv2t3kZkUQ0RYSMAMcr+2rZSTTe187UK9qwgEWanxbHpwsY5XDAJeTVFujHkbeLvLth+f8bgFuKGb434B/MKVa0WGh/Dbd/fyp1UHuHH2KO6YP5bRHpjzXVTZwF3PbuHoySZ+fd10bp4zusd9c7LTeW1bKR/tqzzdPeWW4jyrLzrWuW9r7bZO3t5ZwaWTUzxeFjIsNIRJKXHsDYBCSJ2dhmX5JcwYmcCcsYMstUcAGxEf1fdOKugNmBXcY4fH8Nb9C1gyLZUXNh5m4e8/5J7ntrL1sPsF/z7cW8m1j62ltrmdF792Qa+BAmDe+CSGx0byZkHXoRkXdLTCkQ0u3VWsO3iCmsY2jyzE605Wahx7AqAQ0qq9lRRXN3LngrE6n18pHxswwQJganoCf7gxmzUPXMLdF49n3cFqrv/Leq7981re2nGMDlunU+cxxvDXvIPc8cxmRicNIfcbC5xKUhcWGsJVM9L4YG8ldS1udoeVboaOZpfGK97YXkZcZBgLJ3lnRlhWWjzVDW1U1fs37ceTa4pJT4jyyIJDpZRrBlSwcEhNiOJ7S7JY/4PF/CxnKjWNbdz74jYW/v4jnsovoaG1o8djW9ptfOuVAn7zzl6unJ7G8nvmuZRjKSc7nbaOTt7dVeFe44vzQEIgc75Tu1fWt7ByRznXzcrw2uK0yfZBTH+OW+wsrWVjSQ23zx9LeOiAfNsqFdAG9F9dTGQYX56byarvLuTxW88jLSGKn6/8mLm/+oBfvb2H8i4lIY/VNnPj4+vJLSznvy6fxKM3n0t0hGsfwNmjEhmTNIRcd7uiSlZD+rlOp5Z+fsMROjoNX5nvvQHfQCiE9OSaYmIjw7hpzqi+d1ZKedygqMEdGmItVLt8aioFR0/xtzXFPJVfwlP5JXxuehpfu3AcbbZO7n5uKy3tNp68dTaXTnFvVpGIkDMznUc/LKKyrsW1wb/WBijbAvPud2r3lnYbL2w4zOKsEacLz3vDsJgIUuIj/ZZQsPxUM2/tPMbt8zKJj/LcGhKllPMGRbA4U/aoRB69ZRalJ5t4eu0hXt58lFx78r1Rw4bw0tfOZ2JKXL+ucXV2Bo+sKmLFjmOuLRw7vA46O5xejJdbUM6Jxjbu8OJdhUNWajx7/HRn8fS6QwB8ZX6mX66vlBqEwcJh5NAh/OiqKdx/6URe2XSU4uoGvrcki8Qh/U8fMWFELNMy4nmzoMy1YFGSB6GRMOr8Pnc1xrBsbQlZqXHMHe/9gvNZaXGsO1hNu63Tp2MG9S3tvLTxCFdMS2XkUE1/rZS/DOgxC2fER4XztYvG8evrZngkUDjkzMxgR2ktxVUupMkoyYNRc5xakbv+oFXL4Q4fTSOdnBpPu81QXNXo9Wud6ZXNR6lv7eBrF47z6XWVUp826IOFtyydmY4Izq+5aDwBFTudnjK7bG0JSTERHs0w25usNN/PiOqwdfL3tYeYkzmMmaMSfXZdpdTZNFh4SWpCFBeMTSK3sNy5okiH1lg/nRivKKlu5IO9lXzxgjFEhfumlsP45FjCQ8Wn4xbv7Kqg7FQzX9XUHkr5nQYLL7rm3HRKqhvZWVbb984leRARB+mz+tz16bUlhIeE8KULel9R7knhoSFMGOG7ldzGGP62ppjMpCEez3ellHKdBgsvWjI1zSqKtN2JrqiS1TBmHoT2PuegtrmdV7eWsnRmOiPifJuTZ3JqnM+6obYcPklhaS13LhhLSIim9lDK3zRYeFHCkHCrKNKOPooi1ZbBiSKnuqD+sfkoTW02bvfDNNKstDiO17VS09jm9Ws9ubqYxCHhfP48XYSnVCAYtFNnPapkDWz4s5WmIyzSmv4aFgGhkXw/tJ23mmsofWMNY0YMtT8f8en9yrZZ5+ljcLvD1snT6w5x/thhTMtwboW3Jznqd+ytqPNqSuqS6kb+vec49y6c4PIKeqWUd2iw6K/Ganj1KyACMSOsWsgdbdDRArZWxna08R+hLYTu6GOQOy7NSkvei399fJyyU838eKnvy2cCTD4j7Yc3g8WyfGtM5svzBnl9baUCiAaL/nrne1ZVu7tXd1sDWYDvvVrI+7vK2PDAAqKkA2xtViry0z9brWAR0nuv4LL8EkYP89+Ab3JcJMNjI7w6yH2qqY1Xtx4lJ9v3YzJKqZ5psOiPvW/BruWw6IfdBgqHnOx0lm8t5cPiRq5wM7124dFTbDl8kh9fNYVQPw74ZqXGe7UQ0gsbj9DS3slXdRGeUgFFB7jd1XwSVn4HUqbDgm/3uuu88cP7XRTp72tLiI0M44bZI90+hydkpcax/3i907VBXNHaYePpdYe4cOLw07WdlVKBQYOFu977ETRWQc6jENp7JtTQEGHpzDRW7a2kttn1okjH61pYueMYN84eRZyfs65mpcXT2tHJoRNNHj93bkE5VfWtmtpDqQCkwcIdRe9DwfOw4FuQnu3UITnZGbTZOnnPjaJIz64/hM0YvjIv0+VjPS3LS4WQjDE8lW8lRrxwovcGz5VS7tFg4aqWOsj9JgyfBBc94PRhM0cmkJk0hDcKyly6XHObjRc3HuGyKSmMTvJ/1tWJKbGEhojHB7nXHKhmb0W91tdWKkBpsHDV+z+BujLIeQzCnZ+tIyJcnZ3B+uITHK9rcfq4NwrKONnU7pOaFc6IDAtlfHKMx6vm/S2/gMSkEQAADV1JREFUhOS4SK7O9k1iRKWUazRYuKJkDWx5CubeC6M+4/LhOdnpGAMrCp0b6DbGsCy/hKnp8cwZO8zl63mLp2dE7auoZ/X+Kr4yL9NrdcSVUv3j1WAhIktEZJ+IFInI97t5PlJEXrE/v1FEMu3bk0TkQxFpEJFHvdlGp7U1Qu59MHSsNVXWDeOTY5mekeD0rKg1B6o5UNnAHfMDq2smKy2OslPNbg3Wd+fx1QeJCg/hljm+S4yolHKN14KFiIQCjwFXAFOAm0Wk62KEO4GTxpgJwMPAb+3bW4D/Bv7TW+1z2apfwslD1uynCPfHDnKy09lZVstBJ4oiLVtrdc1cNdO9tRneMtme9mOfB+4ucgvL+ee2Mm6bm8nQGM8Vn1JKeZY37yzmAEXGmGJjTBvwMpDTZZ8c4Bn74+XAYhERY0yjMSYfK2j439FNVu6nz3wVMhf061TOFkUqqmzgo31V3HrBmIDrmnGk/ejvIPfu8loeWF7IZzKH8t3LJnmiaUopL/FmsMgAjp7xe6l9W7f7GGM6gFrA6YLSInKXiGwRkS1VVVX9bG4P2lvgzXshYSRc+pN+ny4lPoq545LILSjrtSjS0+tKiAgL4ZbzA69rJiU+ksQh4f2aPlvT2MZdz25l6JAI/vzF84gI0+EzpQKZN/9Cu+tk7/rp6Mw+PTLGPGGMmW2MmZ2cnOxS45yW91uo3g9L/wiRnllVfE12BodONFFY2n1RpFNNbby2tYxrstMZHhvpkWt6koiQlRrndtW8Dlsn976wjaqGVh6/9TyS4wLv/6iU+jRvBotS4MxiBCOBrn0vp/cRkTAgAahx62o2zwy2fkr5dlj7Rzj3SzBhscdOe/m0VCJCQ3izhzUXL206SnO7jTsWBMZ02e5kpcazr6Kezt7qdPTgl2/vYX3xCX597XRmjNTa2koFA28Gi83ARBEZKyIRwBeA3C775AK32R9/HlhlnCpY3Y3Kj601EM2n3GxuFx1t8OZ9EJMMl/3SM+e0S4gOZ1FWMisKj52VY6nd1smz6w8xf0LS6foRgWhyWhzN7TaO1LiW9mP51lL+vvYQd8wfy/Xn+TfPlVLKeV4LFvYxiPuA94A9wD+MMbtF5GcicrV9t6eAJBEpAr4DnJ5eKyKHgD8AXxGR0m5mUn1aVCLkPwyPZMP6x6zU3/2R/zAc3wVXPQzRnv/2e012BtUNrawvPvGp7e/uquBYbUvALMLriTuD3IVHT/Hg6zuZNz6JB6/M8lbTlFJe4NVRRWPM28aYc4wx440xv7Rv+7ExJtf+uMUYc4MxZoIxZo4xpviMYzONMcOMMbHGmJHGmI97vdjQMVZNifRz4b0H4U+zofAV6HQjO+rx3bD6dzD9Bsi60vXjnbAoawRxkWFn1edetraEscNjWDRphFeu6ykTR8QRIrDHyemzVfWt3P3cVkbERfLoLbMIC9UBbaWCycD6i02bCbe+Dre+Yd0NvH4XPHERFH3g/DlsHdbsp6gEWPLbvvd3U1R4KEumpfLe7gpa2m0AbDtyku1HTnH7/ExC/FizwhnREaFkDo9hrxN3Fm0dnXz9+a2cam7jiVtnM0zXUygVdAZWsHAYvwjuyoPrn7IS/z1/HTybYw1Y92X9o9Z+n/s9xDg9i9ctOdkZNLR2sGpvJWBVwouLCuP6WcHRlz/ZybQfP12xmy2HT/K7z89kSnrgjsMopXo2MIMFWCVKp38e7tsMS34Dx3bAEwth+Z1QU9L9MdUH4MNfweSlMOUarzdx7vgkkuMieWN7GeWnmnlnVwU3zxlNTGRwFDDMSo3jSE0TDa0dPe7z4sYjvLDxCPdcPJ6lMzVJoFLBauAGC4ewSLjg6/DNArjwu1Yp1Ec/Y9XObqz+ZL9Om9X9FB4NV/4v+CAXU2iIsHRGOh/tq+JPq4owxvDluWO8fl1PyUpzpP3ovitq6+EaHsrdxcXnJPNfl+sKbaWC2cAPFg5RCbD4x3D/dsi+BTY9AX/Mtgay2xph05NwdCNc8VuIS/FZs3Ky02mzdfLSpiNcMS2NkUP9X7PCWZPTrEWK3S3Oq6ht4Z7nt5GRGM0jXzjXr3XDlVL9Fxz9HZ4UnwZXP2KlGX//p7DqF7Dpb9BaBxMvgxk3+bQ5M0YmMHZ4DCXVjdyxINOn1+6vjMRo4iLDzkr70dJu4+7nt9LU2sELXz2fhCH+LQWrlOq/wXNn0VXyJLj5RbjjPWvabXi0tabCx6nARYRvXDKBm2aPYtbooT69dn+JCFlpcZ8qhGSM4Udv7KLw6Cn+cFM256R4JkWKUsq/Bt+dRVejL4A7/2VNmQ31z8tx3ayRXBckM6C6ykqN5/XtVlJEEeHZ9YdZvrWUby6eyOVTU/3dPKWUh2iwcPBToAh2WWlxNGzooPRkM6Unm/nZyo+5dHIK31w80d9NU0p5kH5Cqn5xpP14f89x/rSqiMykITx808yAX1SolHLN4B2zUB4xyT4m8fOVH9Nu6+TJL88mLkoHtJUaaDRYqH6JiQxjTNIQDPDIF85lXHKsv5uklPIC7YZS/fbtS8/B1mlYlBXYyQ+VUu7TYKH67Zpzu1bLVUoNNNoNpZRSqk8aLJRSSvVJg4VSSqk+abBQSinVJw0WSiml+qTBQimlVJ80WCillOqTBgullFJ9EmOMv9vgESJSD+zzdzuC2HCgus+9VE/09XOfvnb909/Xb4wxJrmvnQbSCu59xpjZ/m5EsBKRLfr6uU9fP/fpa9c/vnr9tBtKKaVUnzRYKKWU6tNAChZP+LsBQU5fv/7R1899+tr1j09evwEzwK2UUsp7BtKdhVJKKS/RYKGUUqpPAyJYiMgSEdknIkUi8n1/tyfYiMghEdkpIgUissXf7Ql0IrJMRCpFZNcZ24aJyL9F5ID951B/tjFQ9fDa/UREyuzvvwIRudKfbQxkIjJKRD4UkT0isltEvmnf7vX3X9AHCxEJBR4DrgCmADeLyBT/tiooLTLGZOt8d6c8DSzpsu37wAfGmInAB/bf1dme5uzXDuBh+/sv2xjzto/bFEw6gO8aYyYDFwD32j/vvP7+C/pgAcwBiowxxcaYNuBlIMfPbVIDmDFmNVDTZXMO8Iz98TPANT5tVJDo4bVTTjLGHDPGbLM/rgf2ABn44P03EIJFBnD0jN9L7duU8wzwLxHZKiJ3+bsxQSrFGHMMrD9oYISf2xNs7hORHfZuKu3Cc4KIZALnAhvxwftvIAQL6Wabzgd2zXxjzCysrrx7ReQifzdIDSp/AcYD2cAx4H/925zAJyKxwGvAt4wxdb645kAIFqXAqDN+HwmU+6ktQckYU27/WQm8jtW1p1xzXETSAOw/K/3cnqBhjDlujLEZYzqBJ9H3X69EJBwrULxgjPmnfbPX338DIVhsBiaKyFgRiQC+AOT6uU1BQ0RiRCTO8Ri4DNjV+1GqG7nAbfbHtwFv+rEtQcXxIWd3Lfr+65GICPAUsMcY84cznvL6+29ArOC2T7X7PyAUWGaM+aWfmxQ0RGQc1t0EWFmIX9TXr3ci8hKwECs19HHgIeAN4B/AaOAIcIMxRgdyu+jhtVuI1QVlgEPA3Y7+d/VpIrIAWAPsBDrtmx/EGrfw6vtvQAQLpZRS3jUQuqGUUkp5mQYLpZRSfdJgoZRSqk8aLJRSSvVJg4VSSqk+abBQg46I2OzZTXeLSKGIfEdEQuzPzRaRR/zUrnX+uK5SztCps2rQEZEGY0ys/fEI4EVgrTHmIf+2TKnApXcWalCzpzi5CyuRnYjIQhFZCafrLDwjIv+y1/y4TkT+x17741172gVE5DwRybMnYnzvjLQLH4nIb0Vkk4jsF5EL7dun2rcV2JPnTbRvb7D/FBH5nYjssl/rJvv2hfZzLheRvSLygn1FLyLyGxH52H6+3/v6dVQDX5i/G6CUvxljiu3dUN1l6hwPLMKqlbIeuN4Y84CIvA58TkTeAv4E5Bhjquwf7L8E7rAfH2aMmWPPMvAQcClwD/BHY8wL9hQ1oV2ueR3WiuaZWCudN4vIavtz5wJTsfKfrQXmi8jHWGkysowxRkQS+/2iKNWFBgulLN1lLwZ4xxjTLiI7sT7U37Vv3wlkApOAacC/7V/yQ7Eypzo4Er1tte8PVtD5oYiMBP5pjDnQ5ZoLgJeMMTasBHF5wGeAOmCTMaYUQEQK7OfcALQAf7MHr5Uu/c+VcoJ2Q6lBz54fy0b3mTpbAewZUdvNJ4N8nVhftgTYfUaVt+nGmMu6Hm8/f5j9XC8CVwPNwHsicknXJvXS3NYzHtuw7lw6sDK1voZV9Obd7g5Uqj80WKhBTUSSgb8Cjxr3ZnvsA5JFZK79fOEiMrWPa44Dio0xj2BlC53RZZfVwE0iEmpv30XApl7OFwsk2MuRfgurC0spj9JuKDUYRdu7cMKxaho/B/yh90O6Z4xpE5HPA4+ISALW39T/Abt7Oewm4Esi0g5UAD/r8vzrwFygECsT6wPGmAoRyerhfHHAmyIShXVX8m13/i9K9UanziqllOqTdkMppZTqkwYLpZRSfdJgoZRSqk8aLJRSSvVJg4VSSqk+abBQSinVJw0WSiml+vT/GjwutJjFz4QAAAAASUVORK5CYII=\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plot_test_stats(quad_sim, 20, 'Quadratic')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## P-value" - ] - }, - { - "cell_type": "code", - "execution_count": 184, - "metadata": {}, - "outputs": [], - "source": [ - "def pvalue_vs_dimension(corr_type, simulation_type, dim_range):\n", - " p_value = []\n", - " for d in range(1, dim_range+1):\n", - " x, y = simulation_type(num_samp=100, num_dim=d, noise=0)\n", - " if corr_type == 'rv' or corr_type == 'cca':\n", - " corr = RVCorr(which_test=corr_type)\n", - " #else:\n", - " #corr = HHG()\n", - " p_value.append(corr.p_value(x, y)[0])\n", - " return p_value" - ] - }, - { - "cell_type": "code", - "execution_count": 185, - "metadata": {}, - "outputs": [], - "source": [ - "def plot_p_value(simulation_type, dim_range, simulation_name):\n", - " rv_pvalue = pvalue_vs_dimension('rv', simulation_type, dim_range)\n", - " cca_pvalue = pvalue_vs_dimension('cca', simulation_type, dim_range)\n", - " #hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\n", - " plt.plot(rv_pvalue, label='RV')\n", - " plt.plot(cca_pvalue, label='CCA')\n", - " #plt.plot(hhg_pvalue, label='HHG')\n", - " plt.xlabel('Dimensions')\n", - " plt.ylabel('pvalue')\n", - " plt.legend()\n", - " plt.gca().set_xlim(1, dim_range+1)\n", - " plt.xticks(np.arange(0, dim_range+1, 5))\n", - " plt.title('P-value \\n Data: {} Simulation, 100 samples, noise=0'.format(simulation_name))\n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 186, - "metadata": {}, - "outputs": [ - { - "ename": "TypeError", - "evalue": "float() argument must be a string or a number, not 'dict'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_p_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlinear_sim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'Linear'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[0;32m\u001b[0m in \u001b[0;36mplot_p_value\u001b[0;34m(simulation_type, dim_range, simulation_name)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mcca_pvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpvalue_vs_dimension\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'cca'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msimulation_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;31m#hhg_pvalue = pvalue_vs_dimension('hhg', simulation_type, dim_range)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'RV'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcca_pvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'CCA'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;31m#plt.plot(hhg_pvalue, label='HHG')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 2747\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2748\u001b[0m return gca().plot(\n\u001b[0;32m-> 2749\u001b[0;31m *args, scalex=scalex, scaley=scaley, data=data, **kwargs)\n\u001b[0m\u001b[1;32m 2750\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2751\u001b[0m \u001b[0;31m# Autogenerated by boilerplate.py. 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\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36masarray\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m 499\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 500\u001b[0m \"\"\"\n\u001b[0;32m--> 501\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 502\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 503\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mTypeError\u001b[0m: float() argument must be a string or a number, not 'dict'" - ] - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plot_p_value(linear_sim, 20, 'Linear')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.6" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/mgcpy/independence_tests/abstract_class.py b/mgcpy/independence_tests/abstract_class.py index 3174d3f..c3a68a4 100644 --- a/mgcpy/independence_tests/abstract_class.py +++ b/mgcpy/independence_tests/abstract_class.py @@ -7,7 +7,7 @@ import numpy as np from scipy.spatial.distance import pdist, squareform -from scipy.stats import t +from scipy.stats import kendalltau, pearsonr, spearmanr, t def EUCLIDEAN_DISTANCE(x): return squareform(pdist(x, metric='euclidean')) @@ -129,6 +129,12 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): "p_local_correlation_matrix": p_local_correlation_matrix, "local_correlation_matrix": local_correlation_matrix, "optimal_scale": independence_test_metadata["optimal_scale"]} + elif self.get_name() == "kendall": + p_value = kendalltau(matrix_X, matrix_Y)[1] + elif self.get_name() == "spearman": + p_value = spearmanr(matrix_X, matrix_Y)[1] + elif self.get_name() == "pearson": + p_value = pearsonr(matrix_X, matrix_Y)[1] else: # estimate the null by a permutation test test_stats_null = np.zeros(replication_factor) diff --git a/mgcpy/independence_tests/kendall_spearman.py b/mgcpy/independence_tests/kendall_spearman.py index 24a0670..96d7cac 100644 --- a/mgcpy/independence_tests/kendall_spearman.py +++ b/mgcpy/independence_tests/kendall_spearman.py @@ -42,10 +42,6 @@ def test_statistic(self, matrix_X, matrix_Y): >>> kendall_spearman = KendallSpearman() >>> kendall_spearman_stat = kendall_spearman.test_statistic(X, Y) """ - if matrix_X is None: - matrix_X = self.matrix_X - if matrix_Y is None: - matrix_Y = self.matrix_Y assert matrix_X.shape[1] == 1, "Data matrix should be (n, 1) shape" assert matrix_Y.shape[1] == 1, "Data matrix should be (n, 1) shape" From 2decdcb25a6117af8e1f80ffe7e8fb5c5d0f0337 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Thu, 6 Dec 2018 23:44:52 -0500 Subject: [PATCH 15/22] Fix unit tests --- mgcpy/independence_tests/unit_tests/hhg_test.py | 2 +- mgcpy/independence_tests/unit_tests/kendall_spearman_test.py | 2 +- mgcpy/independence_tests/unit_tests/rv_corr_test.py | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py index 9c65b9b..75acd6e 100644 --- a/mgcpy/independence_tests/unit_tests/hhg_test.py +++ b/mgcpy/independence_tests/unit_tests/hhg_test.py @@ -1,7 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np import pytest -from mgcpy import HHG +from mgcpy.independence_tests.hhg import HHG def test_hhg(): diff --git a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py index 1937704..b5a3a13 100644 --- a/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py +++ b/mgcpy/independence_tests/unit_tests/kendall_spearman_test.py @@ -1,7 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np import pytest -from mgcpy import KendallSpearman +from mgcpy.independence_tests.kendall_spearman import KendallSpearman def test_kendall_spearman(): diff --git a/mgcpy/independence_tests/unit_tests/rv_corr_test.py b/mgcpy/independence_tests/unit_tests/rv_corr_test.py index 4aee659..59d97f4 100644 --- a/mgcpy/independence_tests/unit_tests/rv_corr_test.py +++ b/mgcpy/independence_tests/unit_tests/rv_corr_test.py @@ -1,7 +1,7 @@ import mgcpy.benchmarks.simulations as sims import numpy as np import pytest -from mgcpy import RVCorr +from mgcpy.independence_tests.rv_corr import RVCorr def test_local_corr(): From 5c94dbffd02b2fab52da5fda15ac2708d9e77fcb Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 7 Dec 2018 07:28:24 -0500 Subject: [PATCH 16/22] Fixed issues with hhg --- .../benchmarks/unit_tests/simulations_test.py | 95 ++++++++++--------- mgcpy/independence_tests/hhg.py | 2 +- 2 files changed, 49 insertions(+), 48 deletions(-) diff --git a/mgcpy/benchmarks/unit_tests/simulations_test.py b/mgcpy/benchmarks/unit_tests/simulations_test.py index ac8861a..a143847 100644 --- a/mgcpy/benchmarks/unit_tests/simulations_test.py +++ b/mgcpy/benchmarks/unit_tests/simulations_test.py @@ -1,6 +1,6 @@ +import matplotlib.pyplot as plt import numpy as np from mgcpy.benchmarks import simulations as sims -import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D @@ -11,24 +11,24 @@ def test_simulations(): independent = True np.random.seed(0) - fig1 = plt.figure(figsize = (50, 80)) + fig1 = plt.figure(figsize=(50, 80)) plt.axis('off') - fig2 = plt.figure(figsize = (50, 80)) + fig2 = plt.figure(figsize=(50, 80)) # Linear Simulation returns_low_dim = sims.linear_sim(num_samps, num_dim1) returns_high_dim = sims.linear_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.linear_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 1) ax1.scatter(x1, y1) ax1.set_title('Linear', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.linear_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 1, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 1, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Linear', fontweight='bold') ax2.axis('off') @@ -38,15 +38,15 @@ def test_simulations(): returns_high_dim = sims.exp_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.exp_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 2) ax1.scatter(x1, y1) ax1.set_title('Exponential', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.exp_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 2, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 2, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Exponential', fontweight='bold') ax2.axis('off') @@ -56,15 +56,15 @@ def test_simulations(): returns_high_dim = sims.cub_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.cub_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 3) ax1.scatter(x1, y1) ax1.set_title('Cubic', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.cub_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 3, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 3, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Cubic', fontweight='bold') ax2.axis('off') @@ -74,15 +74,15 @@ def test_simulations(): returns_high_dim = sims.joint_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.joint_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 4) ax1.scatter(x1, y1) ax1.set_title('Joint Normal', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.joint_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 4, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 4, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Joint Normal', fontweight='bold') ax2.axis('off') @@ -92,15 +92,15 @@ def test_simulations(): returns_high_dim = sims.step_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.step_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 5) ax1.scatter(x1, y1) ax1.set_title('Step', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.step_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 5, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 5, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Step', fontweight='bold') ax2.axis('off') @@ -110,15 +110,15 @@ def test_simulations(): returns_high_dim = sims.quad_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.quad_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 6) ax1.scatter(x1, y1) ax1.set_title('Quadratic', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.quad_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 6, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 6, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Quadratic', fontweight='bold') ax2.axis('off') @@ -128,15 +128,15 @@ def test_simulations(): returns_high_dim = sims.w_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.w_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 7) ax1.scatter(x1, y1) ax1.set_title('W-Shaped', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.w_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 7, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 7, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('W-Shaped', fontweight='bold') ax2.axis('off') @@ -146,15 +146,15 @@ def test_simulations(): returns_high_dim = sims.spiral_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.spiral_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 8) ax1.scatter(x1, y1) ax1.set_title('Spiral', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.spiral_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 8, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 8, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Spiral', fontweight='bold') ax2.axis('off') @@ -162,15 +162,15 @@ def test_simulations(): # Uncorrelated Bernoulli Simulation returns = sims.ubern_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.ubern_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 9) ax1.scatter(x1, y1) ax1.set_title('Uncorrelated Bernoulli', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.ubern_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 9, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 9, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Uncorrelated Bernoulli', fontweight='bold') ax2.axis('off') @@ -180,16 +180,16 @@ def test_simulations(): returns_high_dim = sims.log_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.log_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 10) ax1.scatter(x1, y1) ax1.set_title('Logarithmic', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.log_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 10, projection = '3d'); - ax2.scatter(x2[:, 0], x2[:, 1], y2) + ax2 = fig2.add_subplot(4, 5, 10, projection='3d') + ax2.scatter(x2[:, 0], x2[:, 1], y2[:, 0]*y2[:, 1]) ax2.set_title('Logarithmic', fontweight='bold') ax2.axis('off') @@ -198,15 +198,15 @@ def test_simulations(): returns_high_dim = sims.root_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.root_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 11) ax1.scatter(x1, y1) ax1.set_title('Fourth Root', fontweight='bold') ax1.axis('off') - + x2, y2 = sims.root_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 11, projection = '3d'); + ax2 = fig2.add_subplot(4, 5, 11, projection='3d') ax2.scatter(x2[:, 0], x2[:, 1], y2) ax2.set_title('Fourth Root', fontweight='bold') ax2.axis('off') @@ -216,7 +216,7 @@ def test_simulations(): returns_high_dim = sims.sin_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.sin_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 12) ax1.scatter(x1, y1) @@ -229,7 +229,7 @@ def test_simulations(): num_samps, num_dim2, period=16*np.pi, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi) ax1 = fig1.add_subplot(4, 5, 13) ax1.scatter(x1, y1) @@ -239,7 +239,7 @@ def test_simulations(): # Square Simulation returns = sims.square_sim(num_samps, num_dim2, indep=independent) assert np.all(returns[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.square_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 14) ax1.scatter(x1, y1) @@ -251,7 +251,7 @@ def test_simulations(): returns_high_dim = sims.two_parab_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 15) ax1.scatter(x1, y1) @@ -261,7 +261,7 @@ def test_simulations(): # Circle Simulation returns = sims.circle_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.circle_sim(num_samps, 1, noise=0) ax1 = fig1.add_subplot(4, 5, 16) ax1.scatter(x1, y1) @@ -271,7 +271,7 @@ def test_simulations(): # Ellipse Simulation returns = sims.circle_sim(num_samps, num_dim2, radius=5) assert np.all(returns[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5) ax1 = fig1.add_subplot(4, 5, 17) ax1.scatter(x1, y1) @@ -282,7 +282,7 @@ def test_simulations(): returns = sims.square_sim( num_samps, num_dim2, period=-np.pi/4, indep=independent) assert np.all(returns[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4) ax1 = fig1.add_subplot(4, 5, 18) ax1.scatter(x1, y1) @@ -292,7 +292,7 @@ def test_simulations(): # Multiplicative Noise Simulation returns = sims.multi_noise_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.multi_noise_sim(num_samps, 1) ax1 = fig1.add_subplot(4, 5, 19) ax1.scatter(x1, y1) @@ -302,11 +302,12 @@ def test_simulations(): # Multimodal Independence Simulation returns = sims.multi_indep_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - + x1, y1 = sims.multi_indep_sim(num_samps, 1) ax1 = fig1.add_subplot(4, 5, 20) ax1.scatter(x1, y1) ax1.set_title('Multimodal Independence', fontweight='bold') ax1.axis('off') -test_simulations() \ No newline at end of file + +test_simulations() diff --git a/mgcpy/independence_tests/hhg.py b/mgcpy/independence_tests/hhg.py index 0125d3f..47890a6 100644 --- a/mgcpy/independence_tests/hhg.py +++ b/mgcpy/independence_tests/hhg.py @@ -9,7 +9,7 @@ def __init__(self, compute_distance_matrix=None): :param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix :type compute_distance_matrix: FunctionType or callable() """ - IndependenceTest.__init__(compute_distance_matrix) + IndependenceTest.__init__(self, compute_distance_matrix) self.which_test = "hhg" def test_statistic(self, matrix_X, matrix_Y): From 30ccbde32881fd077d7b56341907d3c9f8b78d7d Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 7 Dec 2018 07:40:51 -0500 Subject: [PATCH 17/22] Fix hhg and sims test --- mgcpy/benchmarks/unit_tests/simulations_test.py | 3 --- mgcpy/independence_tests/unit_tests/hhg_test.py | 8 +++----- 2 files changed, 3 insertions(+), 8 deletions(-) diff --git a/mgcpy/benchmarks/unit_tests/simulations_test.py b/mgcpy/benchmarks/unit_tests/simulations_test.py index a143847..555f7d5 100644 --- a/mgcpy/benchmarks/unit_tests/simulations_test.py +++ b/mgcpy/benchmarks/unit_tests/simulations_test.py @@ -308,6 +308,3 @@ def test_simulations(): ax1.scatter(x1, y1) ax1.set_title('Multimodal Independence', fontweight='bold') ax1.axis('off') - - -test_simulations() diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py index 75acd6e..f185bc7 100644 --- a/mgcpy/independence_tests/unit_tests/hhg_test.py +++ b/mgcpy/independence_tests/unit_tests/hhg_test.py @@ -11,21 +11,19 @@ def test_hhg(): Y = np.array([3.2311, 12.1113, 11.1350, 1.1989, 3.3127, 4.8580, 3.4917, 7.1748, 6.5792, 2.4012])[:, np.newaxis] hhg = HHG() - test_stat = hhg.test_statistic(X, Y) + test_stat = hhg.test_statistic(X, Y)[0] assert np.round(test_stat, decimals=2) == 411.88 # Against linear simulations np.random.seed(0) X, Y = sims.linear_sim(100, 1) - hhg = HHG() - test_stat = hhg.test_statistic(X, Y) + test_stat = hhg.test_statistic(X, Y)[0] assert np.round(test_stat, decimals=2) == 28986.52 X, Y = sims.linear_sim(100, 1, noise=0) - hhg = HHG() - test_stat = hhg.test_statistic(X, Y) + test_stat = hhg.test_statistic(X, Y)[0] assert np.round(test_stat, decimals=2) == 950600.00 From 246eabf432505a5113da286f6546a2cdb987fbba Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 7 Dec 2018 07:58:05 -0500 Subject: [PATCH 18/22] Update hhg_test.py --- mgcpy/independence_tests/unit_tests/hhg_test.py | 3 --- 1 file changed, 3 deletions(-) diff --git a/mgcpy/independence_tests/unit_tests/hhg_test.py b/mgcpy/independence_tests/unit_tests/hhg_test.py index f185bc7..f887d66 100644 --- a/mgcpy/independence_tests/unit_tests/hhg_test.py +++ b/mgcpy/independence_tests/unit_tests/hhg_test.py @@ -26,6 +26,3 @@ def test_hhg(): test_stat = hhg.test_statistic(X, Y)[0] assert np.round(test_stat, decimals=2) == 950600.00 - - -test_hhg() From 99cff38f7b4917e9e4970fd0a070149e2708eb7b Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 7 Dec 2018 08:25:49 -0500 Subject: [PATCH 19/22] Fix p-value for class --- mgcpy/independence_tests/abstract_class.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/mgcpy/independence_tests/abstract_class.py b/mgcpy/independence_tests/abstract_class.py index c3a68a4..8c619d1 100644 --- a/mgcpy/independence_tests/abstract_class.py +++ b/mgcpy/independence_tests/abstract_class.py @@ -131,10 +131,13 @@ def p_value(self, matrix_X, matrix_Y, replication_factor=1000): "optimal_scale": independence_test_metadata["optimal_scale"]} elif self.get_name() == "kendall": p_value = kendalltau(matrix_X, matrix_Y)[1] + p_value_metadata = {} elif self.get_name() == "spearman": p_value = spearmanr(matrix_X, matrix_Y)[1] + p_value_metadata = {} elif self.get_name() == "pearson": p_value = pearsonr(matrix_X, matrix_Y)[1] + p_value_metadata = {} else: # estimate the null by a permutation test test_stats_null = np.zeros(replication_factor) From 2e163708aba16e50a36a7ef0c5f0b517e7d31d86 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 7 Dec 2018 10:06:14 -0500 Subject: [PATCH 20/22] Remove matplotlib --- .../benchmarks/unit_tests/simulations_test.py | 194 +----------------- 1 file changed, 1 insertion(+), 193 deletions(-) diff --git a/mgcpy/benchmarks/unit_tests/simulations_test.py b/mgcpy/benchmarks/unit_tests/simulations_test.py index 555f7d5..fd5bee5 100644 --- a/mgcpy/benchmarks/unit_tests/simulations_test.py +++ b/mgcpy/benchmarks/unit_tests/simulations_test.py @@ -1,7 +1,6 @@ -import matplotlib.pyplot as plt import numpy as np +import pytest from mgcpy.benchmarks import simulations as sims -from mpl_toolkits.mplot3d import Axes3D def test_simulations(): @@ -10,219 +9,76 @@ def test_simulations(): num_dim2 = 300 independent = True - np.random.seed(0) - fig1 = plt.figure(figsize=(50, 80)) - plt.axis('off') - fig2 = plt.figure(figsize=(50, 80)) - # Linear Simulation returns_low_dim = sims.linear_sim(num_samps, num_dim1) returns_high_dim = sims.linear_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.linear_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 1) - ax1.scatter(x1, y1) - ax1.set_title('Linear', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.linear_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 1, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Linear', fontweight='bold') - ax2.axis('off') - # Exponential Simulation returns_low_dim = sims.exp_sim(num_samps, num_dim1) returns_high_dim = sims.exp_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.exp_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 2) - ax1.scatter(x1, y1) - ax1.set_title('Exponential', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.exp_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 2, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Exponential', fontweight='bold') - ax2.axis('off') - # Cubic Simulation returns_low_dim = sims.cub_sim(num_samps, num_dim1) returns_high_dim = sims.cub_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.cub_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 3) - ax1.scatter(x1, y1) - ax1.set_title('Cubic', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.cub_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 3, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Cubic', fontweight='bold') - ax2.axis('off') - # Joint-Normal Simulation returns_low_dim = sims.joint_sim(num_samps, num_dim1) returns_high_dim = sims.joint_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.joint_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 4) - ax1.scatter(x1, y1) - ax1.set_title('Joint Normal', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.joint_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 4, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Joint Normal', fontweight='bold') - ax2.axis('off') - # Step Simulation returns_low_dim = sims.step_sim(num_samps, num_dim1) returns_high_dim = sims.step_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.step_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 5) - ax1.scatter(x1, y1) - ax1.set_title('Step', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.step_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 5, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Step', fontweight='bold') - ax2.axis('off') - # Quadratic Simulation returns_low_dim = sims.quad_sim(num_samps, num_dim1) returns_high_dim = sims.quad_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.quad_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 6) - ax1.scatter(x1, y1) - ax1.set_title('Quadratic', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.quad_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 6, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Quadratic', fontweight='bold') - ax2.axis('off') - # W Simulation returns_low_dim = sims.w_sim(num_samps, num_dim1) returns_high_dim = sims.w_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.w_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 7) - ax1.scatter(x1, y1) - ax1.set_title('W-Shaped', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.w_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 7, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('W-Shaped', fontweight='bold') - ax2.axis('off') - # Spiral Simulation returns_low_dim = sims.spiral_sim(num_samps, num_dim1) returns_high_dim = sims.spiral_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.spiral_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 8) - ax1.scatter(x1, y1) - ax1.set_title('Spiral', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.spiral_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 8, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Spiral', fontweight='bold') - ax2.axis('off') - # Uncorrelated Bernoulli Simulation returns = sims.ubern_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.ubern_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 9) - ax1.scatter(x1, y1) - ax1.set_title('Uncorrelated Bernoulli', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.ubern_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 9, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Uncorrelated Bernoulli', fontweight='bold') - ax2.axis('off') - # Logarithmic Simulation returns_low_dim = sims.log_sim(num_samps, num_dim1) returns_high_dim = sims.log_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.log_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 10) - ax1.scatter(x1, y1) - ax1.set_title('Logarithmic', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.log_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 10, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2[:, 0]*y2[:, 1]) - ax2.set_title('Logarithmic', fontweight='bold') - ax2.axis('off') - # Nth Root Simulation returns_low_dim = sims.root_sim(num_samps, num_dim1) returns_high_dim = sims.root_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.root_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 11) - ax1.scatter(x1, y1) - ax1.set_title('Fourth Root', fontweight='bold') - ax1.axis('off') - - x2, y2 = sims.root_sim(num_samps, 2, noise=0) - ax2 = fig2.add_subplot(4, 5, 11, projection='3d') - ax2.scatter(x2[:, 0], x2[:, 1], y2) - ax2.set_title('Fourth Root', fontweight='bold') - ax2.axis('off') - # Sinusoidal Simulation (4*pi) returns_low_dim = sims.sin_sim(num_samps, num_dim1) returns_high_dim = sims.sin_sim(num_samps, num_dim2, indep=independent) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.sin_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 12) - ax1.scatter(x1, y1) - ax1.set_title('Sinusoidal (4\u03C0)', fontweight='bold') - ax1.axis('off') - # Sinusoidal Simulation (16*pi) returns_low_dim = sims.sin_sim(num_samps, num_dim1, period=16*np.pi) returns_high_dim = sims.sin_sim( @@ -230,81 +86,33 @@ def test_simulations(): assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.sin_sim(num_samps, 1, noise=0, period=16*np.pi) - ax1 = fig1.add_subplot(4, 5, 13) - ax1.scatter(x1, y1) - ax1.set_title('Sinusoidal (16\u03C0)', fontweight='bold') - ax1.axis('off') - # Square Simulation returns = sims.square_sim(num_samps, num_dim2, indep=independent) assert np.all(returns[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.square_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 14) - ax1.scatter(x1, y1) - ax1.set_title('Square', fontweight='bold') - ax1.axis('off') - # Two Parabolas Simulation returns_low_dim = sims.two_parab_sim(num_samps, num_dim1) returns_high_dim = sims.two_parab_sim(num_samps, num_dim2) assert np.all(returns_low_dim[0].shape == (num_samps, num_dim1)) assert np.all(returns_high_dim[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.two_parab_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 15) - ax1.scatter(x1, y1) - ax1.set_title('Two Parabolas', fontweight='bold') - ax1.axis('off') - # Circle Simulation returns = sims.circle_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.circle_sim(num_samps, 1, noise=0) - ax1 = fig1.add_subplot(4, 5, 16) - ax1.scatter(x1, y1) - ax1.set_title('Circle', fontweight='bold') - ax1.axis('off') - # Ellipse Simulation returns = sims.circle_sim(num_samps, num_dim2, radius=5) assert np.all(returns[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.circle_sim(num_samps, 1, noise=0, radius=5) - ax1 = fig1.add_subplot(4, 5, 17) - ax1.scatter(x1, y1) - ax1.set_title('Ellipse', fontweight='bold') - ax1.axis('off') - # Diamond Simulation returns = sims.square_sim( num_samps, num_dim2, period=-np.pi/4, indep=independent) assert np.all(returns[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.square_sim(num_samps, 1, noise=0, period=-np.pi/4) - ax1 = fig1.add_subplot(4, 5, 18) - ax1.scatter(x1, y1) - ax1.set_title('Diamond', fontweight='bold') - ax1.axis('off') - # Multiplicative Noise Simulation returns = sims.multi_noise_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - x1, y1 = sims.multi_noise_sim(num_samps, 1) - ax1 = fig1.add_subplot(4, 5, 19) - ax1.scatter(x1, y1) - ax1.set_title('Multiplicative Noise', fontweight='bold') - ax1.axis('off') - # Multimodal Independence Simulation returns = sims.multi_indep_sim(num_samps, num_dim2) assert np.all(returns[0].shape == (num_samps, num_dim2)) - - x1, y1 = sims.multi_indep_sim(num_samps, 1) - ax1 = fig1.add_subplot(4, 5, 20) - ax1.scatter(x1, y1) - ax1.set_title('Multimodal Independence', fontweight='bold') - ax1.axis('off') From 61c2caaee562c90dec1e1468a26e56229f1f60ed Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 7 Dec 2018 11:08:56 -0500 Subject: [PATCH 21/22] Remove simulations from other_tests.ipynb and added new simulations demo --- demos/other_tests.ipynb | 218 +++++---- demos/simulations.ipynb | 1012 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 1128 insertions(+), 102 deletions(-) create mode 100644 demos/simulations.ipynb diff --git a/demos/other_tests.ipynb b/demos/other_tests.ipynb index 229220c..d508d36 100644 --- a/demos/other_tests.ipynb +++ b/demos/other_tests.ipynb @@ -9,9 +9,20 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 20, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "(None, )" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "import numpy as np\n", "from scipy.spatial.distance import pdist, squareform\n", @@ -19,13 +30,6 @@ "%matplotlib inline" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simulations" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -35,72 +39,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from mgcpy.benchmarks.simulations import linear_sim, quad_sim, w_sim, spiral_sim" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the readme. Visualizations of the 4 simulations imported above are shown below with and without the noise:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(1, 4, num=1, figsize=(20,5))\n", - "\n", - "x_normal, y_normal = linear_sim(100, 1)\n", - "x_no_noise, y_no_noise = linear_sim(1000, 1, noise=0)\n", - "ax[0].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", - "ax[0].plot(x_no_noise, y_no_noise, 'ro')\n", - "ax[0].set_xlim([-1, 1])\n", - "ax[0].set_ylim([-1, 1])\n", - "\n", - "x_normal, y_normal = quad_sim(100, 1)\n", - "x_no_noise, y_no_noise = quad_sim(1000, 1, noise=0)\n", - "ax[1].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", - "ax[1].plot(x_no_noise, y_no_noise, 'ro')\n", - "ax[1].set_xlim([-1, 1])\n", - "ax[1].set_ylim([-1, 2])\n", - "\n", - "x_normal, y_normal = w_sim(100, 1)\n", - "x_no_noise, y_no_noise = w_sim(1000, 1, noise=0)\n", - "ax[2].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", - "ax[2].plot(x_no_noise, y_no_noise, 'ro')\n", - "ax[2].set_xlim([-1, 1])\n", - "ax[2].set_ylim([-1, 2])\n", - "\n", - "x_normal, y_normal = spiral_sim(100, 1)\n", - "x_no_noise, y_no_noise = spiral_sim(1000, 1, noise=0)\n", - "ax[3].plot(x_normal, y_normal, 'bo', alpha=0.5)\n", - "ax[3].plot(x_no_noise, y_no_noise, 'ro')\n", - "ax[3].set_xlim([-4, 4])\n", - "ax[3].set_ylim([-4, 4])\n", - "\n", - "plt.show()" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -117,19 +62,61 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 23, "metadata": {}, "outputs": [ { - "ename": "ModuleNotFoundError", - "evalue": "No module named 'mgcpy.independence_tests.mgc.distance_transform'", + "name": "stderr", + "output_type": "stream", + "text": [ + "/anaconda3/lib/python3.6/site-packages/Cython/Compiler/Main.py:367: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/mgc/distance_transform.pyx\n", + " tree = Parsing.p_module(s, pxd, full_module_name)\n" + ] + }, + { + "ename": "ImportError", + "evalue": "Building module mgcpy.independence_tests.mgc.distance_transform failed: [\"distutils.errors.CompileError: command 'gcc' failed with exit status 1\\n\"]", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmgcpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindependence_tests\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdcorr\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mDistutilsExecError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m 117\u001b[0m self.spawn(compiler_so + cc_args + [src, '-o', obj] +\n\u001b[0;32m--> 118\u001b[0;31m extra_postargs)\n\u001b[0m\u001b[1;32m 119\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/distutils/ccompiler.py\u001b[0m in \u001b[0;36mspawn\u001b[0;34m(self, cmd)\u001b[0m\n\u001b[1;32m 908\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mspawn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcmd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 909\u001b[0;31m \u001b[0mspawn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdry_run\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdry_run\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 910\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/distutils/spawn.py\u001b[0m in \u001b[0;36mspawn\u001b[0;34m(cmd, search_path, verbose, dry_run)\u001b[0m\n\u001b[1;32m 35\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'posix'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 36\u001b[0;31m \u001b[0m_spawn_posix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcmd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msearch_path\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdry_run\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdry_run\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 37\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'nt'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/distutils/spawn.py\u001b[0m in \u001b[0;36m_spawn_posix\u001b[0;34m(cmd, search_path, verbose, dry_run)\u001b[0m\n\u001b[1;32m 158\u001b[0m \u001b[0;34m\"command %r failed with exit status %d\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 159\u001b[0;31m % (cmd, exit_status))\n\u001b[0m\u001b[1;32m 160\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mWIFSTOPPED\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mDistutilsExecError\u001b[0m: command 'gcc' failed with exit status 1", + "\nDuring handling of the above exception, another exception occurred:\n", + "\u001b[0;31mCompileError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mload_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, is_package, build_inplace, language_level, so_path)\u001b[0m\n\u001b[1;32m 214\u001b[0m so_path = build_module(module_name, pyxfilename, pyxbuild_dir,\n\u001b[0;32m--> 215\u001b[0;31m inplace=build_inplace, language_level=language_level)\n\u001b[0m\u001b[1;32m 216\u001b[0m \u001b[0mmod\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mimp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_dynamic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyximport.py\u001b[0m in \u001b[0;36mbuild_module\u001b[0;34m(name, pyxfilename, pyxbuild_dir, inplace, language_level)\u001b[0m\n\u001b[1;32m 190\u001b[0m \u001b[0minplace\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minplace\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 191\u001b[0;31m reload_support=pyxargs.reload_support)\n\u001b[0m\u001b[1;32m 192\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mso_path\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"Cannot find: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mso_path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/pyximport/pyxbuild.py\u001b[0m in \u001b[0;36mpyx_to_dll\u001b[0;34m(filename, ext, force_rebuild, build_in_temp, pyxbuild_dir, setup_args, reload_support, inplace)\u001b[0m\n\u001b[1;32m 101\u001b[0m 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everything.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 339\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_extensions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 340\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/Cython/Distutils/old_build_ext.py\u001b[0m in \u001b[0;36mbuild_extensions\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 193\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcython_sources\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msources\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 194\u001b[0;31m 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574\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcc_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_postargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpp_opts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 575\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m 119\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m \u001b[0;32mraise\u001b[0m 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sources, output_dir, macros, include_dirs, debug, extra_preargs, extra_postargs, depends)\u001b[0m\n\u001b[1;32m 572\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 573\u001b[0m \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 574\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcc_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_postargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpp_opts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 575\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 576\u001b[0m \u001b[0;31m# Return *all* object filenames, not just the ones we just built.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/anaconda3/lib/python3.6/distutils/unixccompiler.py\u001b[0m in \u001b[0;36m_compile\u001b[0;34m(self, obj, src, ext, cc_args, extra_postargs, pp_opts)\u001b[0m\n\u001b[1;32m 118\u001b[0m extra_postargs)\n\u001b[1;32m 119\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mDistutilsExecError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mCompileError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 121\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 122\u001b[0m def create_static_lib(self, objects, output_libname,\n", + "\u001b[0;31mImportError\u001b[0m: Building module mgcpy.independence_tests.mgc.distance_transform failed: [\"distutils.errors.CompileError: command 'gcc' failed with exit status 1\\n\"]" ] } ], @@ -160,9 +147,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'DCorr' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquad_sim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mdcorr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDCorr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwhich_test\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'dcorr'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0mtest_stat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdcorr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtest_statistic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"DCorr's test statistic: %.2f\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mtest_stat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mNameError\u001b[0m: name 'DCorr' is not defined" + ] + } + ], "source": [ "x, y = quad_sim(100, 1)\n", "\n", @@ -298,7 +297,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -348,7 +346,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -364,14 +362,14 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "HHG test statistic: 36.88\n" + "HHG test statistic: 56.76\n" ] } ], @@ -392,14 +390,23 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "HHG p-value: 0.92\n" + "HHG p-value: 0.51\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/anaconda3/lib/python3.6/site-packages/mgcpy/independence_tests/abstract_class.py:154: UserWarning: The p-value is greater than 0.05, implying that the results are not statistically significant.\n", + "Use results such as test_statistic and optimal_scale, with caution!\n", + " \"Use results such as test_statistic and optimal_scale, with caution!\")\n" ] } ], @@ -424,7 +431,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -454,14 +461,14 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Kendall's test statistic: -0.05\n" + "Kendall's test statistic: 0.05\n" ] } ], @@ -482,14 +489,14 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Pearson's p-value: 0.74\n" + "Pearson's p-value: 0.49\n" ] } ], @@ -521,14 +528,14 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Spearman's test statistic: 0.09\n" + "Spearman's test statistic: -0.04\n" ] } ], @@ -549,14 +556,14 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Pearson's p-value: 0.15\n" + "Pearson's p-value: 0.72\n" ] } ], @@ -581,7 +588,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -619,14 +626,14 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Pearson's test statistic: 0.46\n" + "Pearson's test statistic: 0.53\n" ] } ], @@ -647,7 +654,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -700,14 +707,14 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "RV test statistic: 0.00\n" + "RV test statistic: 0.02\n" ] } ], @@ -728,14 +735,14 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "RV p-value: 0.88\n" + "RV p-value: 0.43\n" ] } ], @@ -771,7 +778,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -799,7 +806,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -814,6 +821,13 @@ "p_value = cca.p_value(x, y)[0]\n", "print(\"CCA p-value: %.2f\" % p_value)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/demos/simulations.ipynb b/demos/simulations.ipynb new file mode 100644 index 0000000..9a576e7 --- /dev/null +++ b/demos/simulations.ipynb @@ -0,0 +1,1012 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tutorial for Simulations" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, import the simultions utilizing the import statement below:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from mgcpy.benchmarks import simulations as sims" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the documentation. Visualizations of the 4 simulations imported above are shown below with and without the noise. Each simulation is also shown in 2D." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Linear Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.linear_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.linear_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Linear', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exponential Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.exp_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.exp_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Exponential Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cubic Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.cub_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.cub_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Cubic Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Joint-Normal Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.joint_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.joint_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Joint-Normal Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.step_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.step_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Step Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quadratic Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.quad_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.quad_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Quadratic Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## W-Shaped Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.w_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.w_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('W-Shaped Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Spiral Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.spiral_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.spiral_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Spiral Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Uncorrelated Bernoulli Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.ubern_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.ubern_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Uncorrelated Bernoulli Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Logarithmic Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.log_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.log_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Logarithmic Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fourth-Root Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.root_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.root_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Fourth-Root Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sinusoidal (4$\\pi$) Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.sin_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.sin_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Sinusoidal (4$\\pi$) Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sinusoidal (16$\\pi$) Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.sin_sim(100, 1, period=16*np.pi)\n", + "x_no_noise, y_no_noise = sims.sin_sim(1000, 1, noise=0, period=16*np.pi)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Sinusoidal (16$\\pi$) Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Square Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.square_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.square_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Square Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Diamond Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.square_sim(100, 1, period=-np.pi/4)\n", + "x_no_noise, y_no_noise = sims.square_sim(1000, 1, noise=0, period=-np.pi/4)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Diamond Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Two Parabolas Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.two_parab_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.two_parab_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Two Parabolas Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Circle Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.circle_sim(100, 1)\n", + "x_no_noise, y_no_noise = sims.circle_sim(1000, 1, noise=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Circle Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ellipse Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "x_normal, y_normal = sims.circle_sim(100, 1, radius=5)\n", + "x_no_noise, y_no_noise = sims.circle_sim(1000, 1, noise=0, radius=5)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Note change in X axis compared to circle simulation\n", + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal (with noise)')\n", + "ax1.scatter(x_no_noise, y_no_noise, c='r', label='No noise')\n", + "ax1.set_title('Ellipse Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multiplicative Noise Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "# Note that this simulation has no noise parameter\n", + "x_normal, y_normal = sims.multi_noise_sim(1000, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal')\n", + "ax1.set_title('Multiplicative Noise Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multimodal Independence Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [], + "source": [ + "# Note that this simulation has no noise parameter\n", + "x_normal, y_normal = sims.multi_indep_sim(1000, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 4))\n", + "ax1 = fig.add_subplot(1, 1, 1)\n", + "ax1.scatter(x_normal, y_normal, c='b', label='Normal')\n", + "ax1.set_title('Multimodal Independence Simulation', fontweight='bold')\n", + "ax1.set_xlabel('X Vector')\n", + "ax1.set_ylabel('Y Vector')\n", + "plt.legend(bbox_to_anchor=(1.3, 0.9), bbox_transform=plt.gcf().transFigure)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.6" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 9588020a1c5ee05f28dd3173691c28fb5a98ca55 Mon Sep 17 00:00:00 2001 From: Sambit Panda Date: Fri, 7 Dec 2018 13:24:24 -0500 Subject: [PATCH 22/22] Added equations for each sim --- demos/simulations.ipynb | 268 ++++++++++++++++++++++++++++++++++++---- 1 file changed, 244 insertions(+), 24 deletions(-) diff --git a/demos/simulations.ipynb b/demos/simulations.ipynb index 9a576e7..4b136b1 100644 --- a/demos/simulations.ipynb +++ b/demos/simulations.ipynb @@ -38,7 +38,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the documentation. Visualizations of the 4 simulations imported above are shown below with and without the noise. Each simulation is also shown in 2D." + "Simultions are randomly generated with an $x$ which is $(n\\cdot d)$ and $y$ which is $(n\\cdot 1)$ that have 2 required parameters: `num_samp` or the number of samples, and `num_dim` or the number of dimensions. Optional parameters can be set based on the documentation. Visualizations of the 4 simulations imported above are shown below with and without the noise. Each simulation is also shown in 2D.\n", + "\n", + "For all the below simulations, $(X, Y) \\overset{i.i.d}{\\sim} F_{XY}=F_{Y|X}F_{X}$ where $X$ and $Y$ are independently identically distributed." ] }, { @@ -48,9 +50,20 @@ "## Linear Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Linear $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n", + "\n", + "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n", + "\n", + "$$Y=w^{T}X+\\kappa \\epsilon$$" + ] + }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -60,12 +73,12 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { - "image/png": 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ev8pBRMmJ1/TqZmBL9N51dVYtuL3d+suBcOQXP0f5jgfwZQDrROQ1e9u/qOrTPpaJiGIoL4/e9Brur3RzVDdHjFM28HOU719UVVT1E6p6vp0YTIkMMX1faB5O1tHe3t4ufheCgsP+PbTHej4Qo3yJyCw3JjwIVH+lN9bv2bPndAZVAqxgumfPntMBrI+1j++jfFPBUb5EyYk3MjbTUbe5KNoo31WrVvUvKCh4EMC5YOWDrJrp+ra2tpuqq6t3R9uB66ES5aDATHiQxeyT5hV+l4OyB6+6KGcEYpL0gAjMhAdEeYQBldIStOAVmEnSAyIPBxAR+Y4BlVIWxODl5lyy2SgPBxAR+Y4BlVIWxODFPsPOvJ7wIGitFkReY0CllAUxeLHP0F9BbLUg8hoDKqUsiMGLfYb+CmKrBZHXGFApZUEMXuwz9FcQWy2IvMaASikLavDiJOn+CWKrBZHXGFApLQxe5BTEVgsirzGgZjmOrEwfPztzgtpqQeQlBtQsxpGV6cuVzy5IFwVstaB8x4CaxZIZWRmkE26Q5MKo1EwvCvjbIDKLq81ksVDIOpFGErFqCeETrjNwlJayKQ5I/Nllg0xWlOFvo6Noq80QpYo11CyWaGRlLtTC3JILo1IzuVWFvw0i8xhQs1iikZW8NzC2XBiVmslFAX8bROYxoGaxRCMrc6EW5pZcGJWayUUBfxtE5jGgZrl4IytzoRbmpmwflZrJRQF/G0TmMaDmsFyohVF86V4U8LdBZB5H+RIloanJGrCzbZvVLDp7NoNPLuEoXzLB1xqqiDwkIrtFZL2f5SCKJ1cmgcg5l1xiVa+dafp0v0tFeczvJt9fAbjM5zIQxcVbTAIiMoA+/3znfebMYVAl3/gaUFV1BYAP/SwDUSK8xcS8pGdpGjkyfgCNZv58Q6UkSk2B3wVIRESmApgKAOUc008+KC+PPiMRf47piZylKdyEDgB13xsMvP9+ZhmcOJHZ64nS5HeTb0KqOl9Va1S1pl+/fn4Xh/IQbzExK9yEfj+m4wQE7RAcahVcN0UyD6YA0KVL5u9BlIbAB1Qiv/EWE0OamoCCArzdYgXRb2AOQgDEkYwIV3eJPBb4Jl+iIKirYwBNS69ewL59HTYZC5zR1NcDDzzgZg5EMfl928wiAC8BGC4i74rI1/wsDxFlKHIkbkQwdU1trXVPE4Mp+cjXGqqqXutn/kSUoenTrVtV/MDaKAUMm3yJKHlNTcCNNwIff+x6VuE53E42ETOAUsAxoBJRbCNHAhs3epJV5CSoB9EVPaU1axZ8J+Io3ziSvvmcKFc4J1IQ8TSYvo4qhKAn0+lo5b2+lFUYUGPg/K2UFwYP9iWAAjg1kEgVCxsVF5Vu6PA07/WlbMOAGgPnb81ded3y0NQE9O17KoCamEghGSJWH6gdQKEKLFly8mne60u5gAE1Brfnb83rk7qP8q7lIbIJd8oUYO9eb/IuKzsVPNvb0TT+gbi/+Wxf8J2IATWGWH03Jvp08u6kHiC50PIQ92LMzybcqqqONdD33utQZv7mKddxgfEYIifwBqw+HRPNUJWV0Sdbr6iwrszJPaGQdUKPJIKsGE0a+bu8H9MxHXPMTt2XitraDk23sQT9N88FxskE1lBjcLNPh8uBZS7dJnM3Wx688Mq3m7CntRjt6Dwfruscg4ii9YPGw9885QMG1Djc6tPJ9pO63zJpPsy6lWMipvL7r71TUIqPzU8oH02XLkBjY8rBMxr+5ikfMKD6ICgn9WwdGJVJP2jgR5NGzoUbsai2qwG0oKBjAG1rM/bBBOU3T+QqVc2aVF1drbmisVG1okJVxPrb2Oh9/qWlHdvvSku9L0c6RCLbHa0k4nfJ0tDYqFpUFP2AvEgefuGp/ua9/D8CYKUG4BzHlN3J9wKkknIpoPqtokKjnl8rKvwuWWKmy+7pxU1VVfTCu50KCrLjasnm9QUfAyqTicQm3zzl9SARk83LJpsPPbmdo6jIs9tYFBFz4oYnUzh+PEDt2onlwu1NlH8YUPOUl4NETActk/2grpy4I+8FPX48gzeLTx2pHcAvUI8zKxwVuyxdnSXaLTYARwVTsDGg5ikvB4m4EbRMjcA2UlN31kA9nM5PAcwP1Z+cTL4LFN8vfSDrB/o0NVkfYzQcFUxBxoAaRbaOfk2Fl6Ndg3wPYlo19cjp/FysgXbimI1IVNH9kQeCO2I5TQ0NsSffyPaLBcpxfnfippK8GJSUyWAIv0fuBlWQB0Al9X17OJCo3ZFUJC9/RLFGcQPu5QkOSmIykFhDjZBu8yTnKo0tyPcgRtbUb+nThP3HilE3xbv5cMN9oB+jAHVoRAiK7qWKpgXt2V/dTEOs1oGKCm/LQZQyvyN6KsmLGmq69zgGuRYWBF7X3pPOr74++hfnRSoqUm1s5G8ngh/3SIM1VCYDyfcCpJK8CKh9+mhaJzcvJxtg03J8CU/IhYXRvywvUn19p/Lm1EQVhnj9G2dAZTKR2OTr0NQEHDzYeXthYefmyciBS717R39P06MS2bScWGSz/f2YjoOtguum+DuICKpRb2Pxc57boA7A49qolJX8jOYALgPwBoAtAH6QaH+3a6ixmt769Om4X7QaUFFR54qPG81UbB5MrAVlHQb3tHtV+6yqSqu8fk0DmWy+btYWg9LaAtZQmQwk/zIGugDYCuAsAEUA1gKoivcatwNqsk1v8QKv2yeHIDQPBuUkeFJEP6hnATRGE246/PhMk7k4czPYB2k+aQZUJhPJv4yBcQCedTy+A8Ad8V7jVw01svaXKKi5eXJMtYaaTlnivSYQJ8GysugfghfJ96sHc5K5OHOzRSRIrS0MqEwmkn8ZA1cDeNDx+MsAfh7vNW4H1GSDRbwTgdsBJ5X3T6csiV7jy0mwtjZ6pl6k2loXD8xfyXyXbraIBKG1JYwBlclE8i9j4JooAfX+KPtNBbASwMry8nJ1WzI1unhBx4uAk2ytM52yJHqNJyfBxkbVkpLoGbmd0uwHzfRw/WhCT+aCizVUJqbkU/wnrX7Oe1zJOIBNvqmIdRIM0lV3OmVJ9BpXToJ+3sZSVpZBwTPndxN6omDOPlQmpuRT4h2AFwCI8YyBAgBvATjTMShpZLzXmAyobtUKgnTV7UYN1chJ0K8mXBFjg4hMifV5hz/zIHTZBm2UrxvlYUBlMpES7wD8B4DFdpPsVeFkJHPgcwCa7dG+DYn2NxVQ3bwyrq/vXMvz66rbjT7U8D7RTmgxT3QeB84Oo3x79nTls40nlRN+vHlr/fztuCWZGrEfNWYGVCYTKfEOwMNR0kN+FNZUQHWrFhntP7vflSKvagDOY/8jaj29BzTyntNfdfPvA0/1hB+vhmrqdxkUiT4bP/t0GVCZTCTfC5BKMhVQ3ernDFJzb6oyakarqvJlIoV2QE8Aei0aM/oeTTYhpnNbU2QQMf27DIpEn42fo44ZUJlMpMQ7AEMA/A7AbgC7APwWwBA/Chv0GmqQBiSlIuVmNA+XM+uUHIOITHyPppsQ0/kNxBsdni0XZMlI9Nn4eV8sAyqTiZR4B+A5AF+1BxEVALgBwHN+FDbofajZWkNNWG4/J1KIcx+oie/R9HeW7vs1NkZfmCGX+lBN1FDZh8oU5JR4B+C1ZLZ5kYI+yjdItwFEk+ytPteiUQ+jyNsp/JzVkRQ+MOcx9eljpVS+U9OtCqYGggHWsQTlt2OCiT7U8H4c5csUxJR4B2AJgCn2Pald7H8/70dh/bgPNdX/vJn+Z3frFoV4J6tb+jTqbvTxfjJ5wNhECulezLjRqpDqd5itLRvpyHSUr1sYUJlMpMQ7AOX2bTN77H7U3wMo96OwXgdUr2ucbuYXedK+Fo16FF28D6CAK8OeM2lq9btVIVv73nMJAyqTiZR4B2B8Mtu8SF4HVK9rDpnkF/fKPsooXM+CqEdz4WYSlPyqFYVlw+QOuY4BlclEElVFPCKyWlXHJNrmhZqaGl25cqVn+YVC1mktkoi18HFQ8gsvOh5eVPt+TMd0zIEAEPPF7CRcZAGsBbU3bPAg144qK63F1iNVVFgLVAdZ5PcXqbQUmD+fi2y7SURWqWqN3+Wg7BaK9YSIjBOR2wD0E5EZjvQjWH2pOa+8PLXtfuX3yrebsKO1B9ohaIfgG5iDENwLphqRfoF6nFlhV6riBNOmJivwhULW36Ymc2WaPdsKPE6lpdb2oKurswJmRUX051tbgYYGb8tERKmLGVBhza/bHdatMj0c6QCspdeyTqondK9P0knn19QEFBdbVVcR/NfeKTgNh07WSE0HUmfwbEUx6tCIEPRk+n7pAwk/k3AtrKXFirstLdbjdINq5HcJnApKItbfbKrV1dVZNWmJ8eVt2+ZpcYgoHYnahAFU+N0uHU6Z9KGmO/jE6/61qPnV12vMTjYP0qba+g5lqq9P/TMx2R8dhIFE4XKY/m3k04jfIAH7UJkMpMQ7WBM79HQ87gXHsmtepkwCaqwTVZcuwRv00dioegSF/tzGAriyJqjJkaxBCDpuBfWgXCzkGwZUJhMpXpNvWF9V3eeo0X4EoL/pmrLbYjWZnTiRWdOjMXbzrYrguimCYhx3rQm3g27dgMZGNDUqKisUIVFUHt5g/PMw2R8d67v0slm0oaHzICITfZ3O/lTTTddu9mETEZKqoa6C475TABUAVvsR/d2oofrWpNbYqFpUFL9QbqWIRbW9qBWZzCMINdRsu3eUNd/4wBoqk4GUeAfgMgDbACywUwuAz/pRWNN9qJ6eCAM6H66qdwHKVJ9jEIJDEIJ6KrKtvF5jQGUykZLbCegL4PMALofVBOxLYTOd2KGx0eozTefEknIwqK2NnpHbKcW5cFVTq235PQlCUMoRhKCeimyrUXuNAZXJREq8g9WFNwXATPtxOYCxfhTWxExJpiYv7/QavwIooFpYmNFnkmztxWQQ8TsgmihDEI4hWayhxseAymQiJd4BmAPgFwA22Y97AfibH4U1uXxbppOX/xG1ni6kffJxSYnxM3eygdLUSTkItbsglMFL+Xa8qWJAZTKREu9gD0ACsMaxba0fhfVjtRlVK/C+gzJ/5sJ1IYBGk8xFhqlmwyDUloJQBq9lU43aawyoTCZSMnP5vgLgIrtWOkZE+gH4k6qOTndkcbo8nct3+nRgzhwA6DhXrQs08r1ra4ElS1zKLX2m5sv1eo7koJaBgoNz+ZIJydyH+t8Afgegv4jMBvAXAHe5Wio/DB588l5QiJwMpoD5e0HVkVpRjBsLrftAoXaKEUz9vo/Q1FSMXs+RHNQyEFGOSaYaC2AEgG8A+CaAc/yqThtt8vVwOr/IpuLd6JlyU2NQ+sBMNBsG4ViCUAYKDrDJl8lAiv0E8AcAdQC6+V3IcMoooHo8CjccPA+jWK9F48mTdbr9kLnW5xeE/rwglIGCgQGVyUSK1+Q7H9a9p++IyG9E5EoRKTJRKxaRa0Rkg4i0i4j7/Ra9egHPP+96Nid164YX6xtxZoWiuxzFXyvqTk4fl25TYxCm2zMpvLpKe7v1149VYeKVwe/mdSLKPjEDqqo+qarXwrrv9AkA1wPYJiIPichnMsx3PYCrAKzI8H0Su+QSYN++xPulq7gYaGzsWHE8dAgXP1AX9WSdbj8k+/xOcTvYmV5qjojyRCrVWQCfALAGwAkT1WMAywDUJLt/Wk2+bjTppjEbkVM6TY1u9PllY5OnF32fuda8TomBTb5MBlLiHYABAG4B8CKAtwD8FMD5RjJPIqACmApgJYCV5eXlmjITAbS+PvV8I5gazGMqAGbroBwvgh2n6cs/DKhMJlLM+1BF5GYA1wIYDqvJ91FVfTHZmq+ILAEwMMpTDar6pL3PMgDfVdWkbi5N6z5USeOGl6Ii4KGHjHXshZsQnct9lZaaW5YrHabuKfWaF/ePZutnQ+njfahkQrxBSRcBuBvAGap6SyrBFABU9RJVPTdKejKjEqeqtja5/Zz9oMeOGY10bq2dmYlsHeTkRV+yqfttiSi/xBuU9FVV/ZOqZve8MUuWdA6qRUWdBxK5WFUMYvDK1kFOXgQ7Nxf5JqLclcxMScaJyD+JyLsAxgH4g4g862qGS5Z0DJ6Ga6CJBDF4ZWstzKtgF4Tbeogou8QMqCLytIjtT1QIAAAPZklEQVRUupGpqv5OVYeoarGqDlDVz7qRj0mZ3KoRxOCVzbUwBjsiCqJ4NdRfAfiTiDSISKFH5QmkTO9LTDZ4eT2ZAANTZ5zQgYjSFXe1GRHpBmAmgMsALABwsj9VVe91vXQRPF1txsGLUZ9BHAmcb/gd5C+O8iUTEvWhHgdwGEAxgB4RKW94MagoiCOB8w2/AyLKREGsJ0TkMgD3AlgMYIyqtsbaN9eVl0evoZocVBTEkcD5ht8BEWUiXg21AcA1qvqDfA6mgDeDioI4Ejjf8DsgokzEuw/1k6q6wcvCBJUXI2KDOBI43/A7IKJM+HIfajZye0RsNt/Gkiu8+g44kpgoN8Ud5Rs0fo3yJcpUU5M1uKmlxQrWzv92HEnsP47yJRNYQyVymfM+ZqDz5P4cSUyUGxhQiVwW7XacSBxJTJT9GFCJXJZMsORIYqLsx4AaQBy0klsSBUuOJCbKDQyoAZPpvMEUPNFuxwmve8/R3ES5gwE1YDj9Xe6JdjvOggXWBRMXJSDKHbxtJmBCoc6jQAHrRNye3Uu9EwUWb5shE1hDDZhsmv4uH/p68+EYicgMBtSAyZbp7/KhrzcfjpGIzGFANSzTGk22TEGYD329+XCMRGQOA6pBpmo0bs8bbIKppc6C3KTK5dyIKBUMqAblU43GRF9v0JtUs6k/m4j8x4BqUD7VaEz09Qb9AiRb+rOJKBgYUA3KpxqNib7eoF+AZEt/NhEFgy8BVUTuEZHNIvK6iPxORHr6UQ7T3K7RBK2/MdO+3my4AMmG/mwiCga/aqjPAThXVT8BoBnAHT6Vwyg3azRB729MR7QLkKIi4NCh4Fw0EBEly5eAqqp/UtU2++HLAIb4UQ43pFujSVT7DHp/YzoiL0D69LEuFvbuzZ2LBiLKH75PPSgiTwH4jao2xnh+KoCpAFBeXl7dEl6lOYeEa5/OgFla2rF2mw9TElZWnlqE26miwro4IXILpx4kE1wLqCKyBMDAKE81qOqT9j4NAGoAXKVJFCRX5/JNJpDkQ7DJh4sGCiYGVDKhwK03VtVL4j0vItcD+DyA2mSCaS5LZrTr7NnRa7G5dAtHeXn0i4YgDVIiIorFr1G+lwH4PoArVLU10f65LpnRrvlwCwfv+ySibObXKN+fA+gB4DkReU1E5vpUjkBINpDk+i0c+XDRQES5y7Um33hU9Ww/8g2qcMBoaLCaecvLrWCaj4Gkri4/j5uIsp8vAZU6YyAhIspunHqQiIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABlYiIyAAGVCIiIgMYUImIiAxgQKW0BW3BcyIiP3FiB0pL5JJz4bVLAU5QQUT5iTVUSksuLnhORJQJBtQ05XtzZzJLzhER5RMG1DSEmztbWqwFscPNnfkUVJNZco6IKJ8woKaBzZ1cu5SIKBIDahrY3Mm1S4mIInGUbxrKy61m3mjb8wmXnCMiOoU11DSwuZOIiCIxoKaBzZ1ERBSJTb5pYnMnERE5sYZKRERkAAMqERGRAQyoREREBjCgEhERGeBLQBWRH4vI6yLymoj8SUTK/CgHERGRKX7VUO9R1U+o6vkA/g/ATJ/KQUREZIQvAVVVDzgedgOgfpSDiIjIFN/uQxWR2QC+AmA/gE/H2W8qgKkAUJ5vc/sREVHWEFV3KocisgTAwChPNajqk4797gBQoqr/mug9a2pqdOXKlQZLSUQEiMgqVa3xuxyU3VyroarqJUnuuhDAHwAkDKhERERB5dco36GOh1cA2OxHOYiIiEzxqw/1bhEZDqAdQAuAaT6Vg4iIyAhfAqqqftGPfImIiNzCmZKIiIgMYEAlIiIygAGViIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABlYiIyAAGVCIiIgMYUImIiAxgQCUiIjKAAZWIiMgABlQiIiIDGFCJiIgMYEAlIiIygAGViIjIAAZUFzQ1AZWVQChk/W1q8rtERETkNl8WGM9lTU3A1KlAa6v1uKXFegwAdXX+lYuIiNzFGqphDQ2ngmlYa6u1nYiIchcDqmHbtqW2nYiIcgMDqmHl5altJyKi3MCAatjs2UBpacdtpaXWdiIiyl0MqIbV1QHz5wMVFYCI9Xf+fA5IIiLKdb4GVBH5roioiPT1sxym1dUB77wDtLdbfxlMiYhyn28BVUTOAPAZAByuQ0REWc/PGup9AL4HQH0sAxERkRG+BFQRuQLAe6q6Nol9p4rIShFZuWfPHg9KR0RElDrXZkoSkSUABkZ5qgHAvwC4NJn3UdX5AOYDQE1NDWuzREQUSK4FVFW9JNp2ETkPwJkA1ooIAAwBsFpExqrqTrfKQ0RE5CbP5/JV1XUA+ocfi8g7AGpU9QOvy0JERGSKqPrbippKQBWRPQBa0syqLwC/gjbzZt7MO9j5V6hqP5OFofzje0D1ioisVNUa5s28mXfu5R2E/Ik4UxIREZEBDKhEREQG5FNAnc+8mTfzztm8g5A/5bm86UMlIiJyUz7VUImIiFzDgEpERGRATgVUEblGRDaISLuIxBw+LyKXicgbIrJFRH7g2H6miLwiIm+KyG9EpCiFvHuLyHP2a58TkV5R9vm0iLzmSEdF5Er7uV+JyNuO5843mbe93wnH+y/28LjPF5GX7O/mdRH5kuO5lI871vfneL7YPo4t9nFVOp67w97+hoh8NtnjTCHvGSKy0T7O50WkwvFc1M/fYN43iMgeRx43OZ673v6O3hSR613I+z5Hvs0iss/xXKbH/ZCI7BaR9TGeFxH5b7tsr4vIGMdzGR03UUpUNWcSgHMADAewDNZkEdH26QJgK4CzABQBWAugyn7uMQCT7X/PBVCfQt7/DuAH9r9/AOCnCfbvDeBDAKX2418BuDrN404qbwCHYmx39bgBDAMw1P53GYAdAHqmc9zxvj/HPtMBzLX/PRnAb+x/V9n7F8Oa/nIrgC6G8/604zutD+cd7/M3mPcNAH4e47f2lv23l/3vXibzjtj/FgAPmThu+/X/AGAMgPUxnv8cgGcACIALAbxi4riZmFJNOVVDVdVNqvpGgt3GAtiiqm+p6scAHgXwBRERABMBPG7v92sAV6aQ/Rfs1yT72qsBPKOqrSnkYSrvk7w4blVtVtU37X+/D2A3gHRnpYn6/cUp0+MAau3j/AKAR1X1mKq+DWCL/X7G8lbVpY7v9GVYc1WbkMxxx/JZAM+p6oeq+hGA5wBc5mLe1wJYlML7x6WqK2BdfMbyBQCPqOVlAD1FZBAyP26ilORUQE3SYADbHY/ftbf1AbBPVdsitidrgKruAAD7b/8E+09G55PObLvJ6j4RKXYh7xKxlsJ7OdzUDI+PW0TGwqrlbHVsTuW4Y31/Ufexj2s/rONM5rWZ5u30NVg1p7Bon7/pvL9of5aPi8gZaZY73bxhN3GfCeAFx+ZMjjuT8mV63EQp8Xxy/ExJnGXhVPXJZN4iyjaNsz2pvJPI1/k+gwCcB+BZx+Y7AOyEFWzmA/g+gFmG8y5X1fdF5CwAL4jIOgAHouzn5nEvAHC9qrbbm+Med7S3SVTeOPsk89p4kn69iEwBUAPgU47NnT5/Vd0a7fVp5v0UgEWqekxEpsGqpU9MpdwZ5B02GcDjqnrCsS2T486kfJkeN1FKsi6gaoxl4VLwLoAzHI+HAHgf1qTaPUWkwK7VhLcnlbeI7BKRQaq6ww4cu+OU4Z8B/E5Vjzvee4f9z2Mi8jCA75rO225uhaq+JSLLAIwG8Ft4cNwichqAPwD4od0sl9RxRxHr+4u2z7siUgDgdFhNhsm8NtO8ISKXwLrY+JSqHgtvj/H5JxtYEuatqnsdD38J4KeO106IeO2yJPNNKm+HyQC+EVGuTI47k/JletxEKcnHJt+/ARgq1sjWIlgngMWqqgCWwurbBIDrASRT4w1bbL8mmdd26mOyg1G4T/NKAFFHNKabt4j0CjenikhfAOMBbPTiuO3P+Xew+rn+N+K5VI876vcXp0xXA3jBPs7FACaLNQr4TABDAbya1FEmmbeIjAYwD8AVqrrbsT3q528470GOh1cA2GT/+1kAl9pl6AXgUnRsHck4bzv/4bAG/7zk2JbpcSdjMYCv2KN9LwSw375Qy/S4iVLj96gokwnAP8G6Kj0GYBeAZ+3tZQCeduz3OQDNsK6SGxzbz4J1gt0C4H8BFKeQdx8AzwN40/7b295eA+BBx36VAN4DEIp4/QsA1sEKKI0AupvMG8BF9vuvtf9+zavjBjAFwHEArznS+eked7TvD1Yz8RX2v0vs49hiH9dZjtc22K97A8CkNH5jifJeYv/2wse5ONHnbzDvfwOwwc5jKYARjtfeaH8eWwB81XTe9uMfAbg74nUmjnsRrJHhx2H9//4agGkAptnPC4Bf2GVbB8cI/0yPm4kplcSpB4mIiAzIxyZfIiIi4xhQiYiIDGBAJSIiMoABlYiIyAAGVCIiIgMYUMl3InKGWCvO9LYf97IfV0Tst0wiVogRke+IyANp5HmliFRlVnIiolMYUMl3qrodwBwAd9ub7gYwX1VbInZdBGtSAadocyIn40pYq88kzZ51iYgoKt6HSoEgIoUAVgF4CMDNAEartbKJc58+ADYDGKLWfLWVAFYAqFBVFZHbYU3rWAxrasd/tV/3FVhTGiqA12EF7/+DNWn+fgBfBNAD1tJ1pbAmCLhRVT+yp8r7K6wZfhar6n+49RkQUXbjFTcFgqoetwPiHwFcGhlM7X32isirsJbgehKn1jpVEbkU1lSCY2HNnLNYRP4BwF5YsyONV9UPRKS3qn4o1kLX/6eqjwOAiLwO4BZVXS4iswD8K4Dv2Fn3VFXnJPdERJ2wyZeCZBKsKebOjbOPs9nX2dx7qZ3WAFgNYASsADsR1uonHwCAqnZaV1NETocVNJfbm34Na1HrsN+kczBElF8YUCkQROR8AJ8BcCGAWyMmenf6PawFw8cA6Kqqq8NvAeDfVPV8O52tqv9jb8+0X+Nwhq8nojzAgEq+s1eamQPgO6q6DcA9AH4WbV9VPQRrCa6H0HEw0rMAbhSR7vZ7DhaR/rAm7P9nu/8V4ZHEAA7C6jeFqu4H8JGIfNJ+7ssAloOIKAUMqBQENwPYpqrP2Y8fADBCRGL1Wy4CMArAo+ENqvonAAsBvGQvnP44gB6qugHAbADLRWQtgHvtlzwK4HYRWSMifwdrubd77L7U8xF/kXMiok44ypeIiMgA1lCJiIgMYEAlIiIygAGViIjIAAZUIiIiAxhQiYiIDGBAJSIiMoABlYiIyID/B1FWtwXytR3YAAAAAElFTkSuQmCC\n", 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\n", 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" ] @@ -95,6 +108,17 @@ "## Exponential Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Exponential $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n", + "\n", + "$$X \\sim \\mathcal{U}(0,3)^{p}$$\n", + "\n", + "$$Y=\\exp(w^{T}X)+10\\kappa \\epsilon$$" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -112,7 +136,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -142,6 +166,17 @@ "## Cubic Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Cubic $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n", + "\n", + "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n", + "\n", + "$$Y=128\\left(w^{T}X-\\frac{1}{3}\\right)^{3}+48\\left(w^{T}X-\\frac{1}{3}\\right)^{2}-12\\left(w^{T}X-\\frac{1}{3}\\right)+80\\kappa \\epsilon$$" + ] + }, { "cell_type": "code", "execution_count": 7, @@ -159,7 +194,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -189,6 +224,18 @@ "## Joint-Normal Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Joint normal $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Let $\\rho=1/2p$, $I_{p}$ be the identity matrix of size $p\\times p$, $J_{p}$ be the matrix of ones of size $p\\times p$, and $\\Sigma =\\begin{bmatrix}\n", + " I_{p} & \\rho J_{p} \\\\\n", + " \\rho J_{p} & (1+0.5\\kappa)I_{p}\\\\\n", + "\\end{bmatrix}$. Then\n", + "\n", + "$$(X,Y) \\sim \\mathcal{N}(0,\\Sigma)$$" + ] + }, { "cell_type": "code", "execution_count": 9, @@ -206,7 +253,7 @@ "outputs": [ { "data": { - "image/png": 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zRERWi8jqDRs2NL6QFtQaragaqo3wo7QYGmEkU3IVTGPMsDFmPrAPcKiIzA3Z5jpjzAJjzAJvTHRN1OFrW020Ij+NjPCjtBgaYSRbjDGFSMBlwOfitjn44INNkBdeeGHCukgqFWO6uoxxvrVO6upy1tdAd3e32bRpkymXy+YPf/iDueKKK8xll11mjDHm5JNPNjfffLMxxpgbbrjBnHLKKRP2v+yyy8wRRxxhtm/fbjZs2GBmzpxpduzYYVavXm3mzp1rhoaGzObNm80HPvAB88QTT4we0xhjvvnNb5qvfOUrxhhjdu3aZd5++22zYcMGc/TRR5uhoSFjjDFf+9rXzOWXX17TOTYbqZ6LyYzI+OfdSyJ5l6xQAKuNhU7l6SWfLSJ7uP9PA44DXqrrQev4ta0mWpGfRkb4UVoIjTCSKXlWyfcC7hORZ4DHcNow44M71kqd43mljVbkp5ERfpQWQiOMZEqeXvJnjDEHGmPmGWPmGmO+XPeD1vlrm3W0onpF+FFaCI0wkimtNdKnAV/bLKMV1SPCj9KCNDD82WSn9aIV9fc7bZZr1zqW5fLl+gBNQjRakZIG22hFrRd8o7dXBVJRlKporSq5oihKDUwKwWymZgWl/ujzoNSLpq+ST506lcHBQUqlUmSXHaUJGByE3/0OduyAzk7Ye28olVJnY4xhcHCQqVOn1qGQSqvT9IK5zz77sG7dOoo6zlyxYMsWRzD9luEbbziCGZhZ04apU6eyzz77ZFjABNSR2DI0vWB2dHSw77775l0MJQ1BgRkacgQzSLnsdIMpMl5wC28EmRfcAlQ0JyGTog1TaSLCoueEiSVkNgKrrmQx3FbDrzUNTW9hKk1GmMBE0QzjnWsdbqsWalOhFqbSWGyFpFnGO9c63LbZwq+1uDWsgqk0lighKZWac7xzrcNt6xkQJmtx02DExYmHaZPC4mEqTUadYpI2hErFmHLZiSVZLo+VOWq9DeVyeLzKcrn2smZ9netV1gKAZTzM3EUwTVLBnCTUIjCNxF/OUsmYzs7shd5W2NJes3qI2yQORqyCqbQmWYlxmJDVy7pKKnM11mI9xE0tTBVMZRKRZTU0ShzysK6qEap6iFszN6ckYCuY6vRRJg9RHuezzx5zfFxwgZ0jxNbp0oiuT9U4huoR+1WDEauFqRSMWqrUUdXQuBRlIdlYmCLG9PVldOIxVGstNktbcQFAq+RK05G2yhcUhFIpvWBGCU9YWdra7AU3S/KoCreY2KpgKs1HGksqTEQ6OqoTzKh2SFtBLpfD9SVL0WmkgE3itsooCi+YwHuA+4AXgeeBi5P2UcGc5KTx7No6ZdJYmEmiFFG+EWSCvpzTUTE7O5tUdCaxNzyKZhDMvYCD3P9nAC8DH4jbRwVzkpPmRa2mvTIseSJmY1VFlO+19vKE1a+S4lyqoZ4W5yTubxlF4QVzQkHgduBDcduoYE4S4kbM2FYFq7Uwp04d+79UGss7Lj+vjBHlO4PKhF2GSRAdW8GrVMY3BZRKjqOpnlVmtTCLLZhAD7AW2D3ktyXAamD1nDlz6nGtlEaSJIpphCSYT1qr03/chH13dvos0UD5wvQl1sJMM7onTbtsltartmEWUzCB6cDjwGlJ26qFOQnI0noJilc1FmepFF8uX9pcCi9jpeK0Wb5K2Qwj5lXK5rttfdFtmLbXIO05ZVllVi95aMp1XnIR6QDuAO42xlyZtH3YvORKk9HW5rzeQURgZKS2vHt6nAg6aalUnL/+uJQhjCC0mZAy9vez69wlTNkxtu+uzi6mnHc23HXXxKkrbK9B1HZRNEOE+oJiOy95biN9xJmx7AbgRRuxVCYJtcaPjCNsdIsNS5eOG8USJVEjtIWPFFq6dJxYAkzZsZV1191F29o1XDTzBwwNAWed5ewzc2b4AYLXIO6aBCf8a5b4oc2OjRlajwQcBRjgGeApN50Ut49WyScB1bSPpake9vUZ095uRsDsos1sotsMI2Y9JTNiWZW9sFQxQ1gE3vDKHvHbMJjFhOTV0TEh8tEQXWYxlXF+qMg2zM5O5zxbqMpcb2iWNsw0SQVzkpBGANMIbMi2nhCBMZuYHi5ugbZDr01yJ+12ohkpmI5QR7Wdbi6NtXku9nnaOzoCohn0kqs4Zo4KppIfWToMbBwkcY4UGBWkbYRYa1OmhFprlUpM16AUKc6q9Rd5MZ7TCLMTx0JWy7FxqGAq+VCpTAy029lZ/Yuf1InaIm7liCtCkdsEq71J3uwsBLNcHj210Gp7NdeuxTzbWaKCqeRD1Hhrr/tOWuIszErFmPbaqs2RKaq/ZMq0ntJEMXQF2Tu1yD6bgWsXq4ct2HcyS1QwlXyIe/GrIa7zdlbDI6Py9o6fJpiwb3mLOKOALixVnD6cAaXzjHGbqv/mUtmc0zF+RNE4Pazn6JwWsFxVMJV8SBLMtC9fWBXfIkVWhW1TqZQudFyVnutKxZi1bWWrMg0jZhjGOYlG9bBe47+jrOxJ5nxSwVTyIa5KHjWcMS4IbxXtiFukK9o7bZNCuv0YCI+H6aXu7uquV9ALbpk87/8ZWFjAtViFcXlPoiq/CqaSD2FVaK+fTDUvdspq907azWIqoY6UIboccU4qQ7WBiG3Ew29hl0rVx/DEaR/dIin6i0aMhY8l6fpPkoAcKphKfoS9lJVKuhfbI4WF6VldwS46XjX2wpKbb0wgYGNM1W2j26aX4rXI1olkefzUzQ6lUnTAkijxTLr+kyTkmwqmUhzSepuDfSwt9t1FW6xleU5HZSwKelh1299bvMruRCMwrgP6hBprlkGPqxHMpBQVMSnu+quFWdykgtmk1Bp1x2+xxogHRHfRGe0IbtPtKanaHpPWU4rWkyy9+p2d9eklEDUdSNh1a8E2TJ1mV6k/tlPWegSDTvT2OlF4LKIZzSH8WAJOJKPBwfAd33pr7P9/+ierYoYxi/H5j556fz8jUuPr1t7uBN0olcZky5auLme/JMLuVW8vbNzoRHVq5Sl2yTFakdJCVBt1p79/YmSgiJd+kJL7NyISUBJtbWPHiRLVKpgzh9Hwb20jw9VnJOKEnxsZgenTYefO+O1LpYnidvXVydGc4u6V/8O1Zk3LiSWgVfKmpxk6FceNQkk7XUVfX6gXflWf00F8O+n7bGaZ/FXyczrcDutZ5e9ds6SqeFeXWdVXCX8s/L0VgvlMoip2WtA2zBagmYbDpRX2pCGRYXll7FRJm0bAXFhy+kZulJhwcrWkpKGg5bJZ1Vexeyya4WPbIFQwW4FmmKyq2pcywooaRqKzqOdQSdsUNkFZI49twh+LxVTMa+1V3IcWQQWzFSj6dKh9fdVX+yI+Bq9Sjs4iZwvTQP2Cgdgk90MZvOSh0ZCKWhPJCVvBVKdPM1PP6R5qpb8fvvtd5/X0s3WrMyVEEiHTTWyhi79jeXQWJ51UfXmzYrgGx06tuB7u4O3/KkvpJjBXke19UMahgtnMhM1h06i5XcI82H6WLp0olh423YzcOXbWUGYEYQ1lzuc6bqU3OosaugMVklLJSSJOl6IkXKUMPhZRXa1Sd/dSVDCbGt/EXZn2jUsSw/5+p4vLwIAjigMDzrJ/u7iXcc6c5GO4TInQiVAjOsPuQDVRzURsQUolpxvQxo1ON55bbonNd6t00TuwnJ4eZ9n/WLzeXuCaCFg/C4XApt5elKRtmBkRNdbbtruJjbMpahsvOlHQMdLZ6Ywm8coUso03Vjyy+S3v9ksvVRPYeOrUieuCJxoM3FEqmRHEDMhYuLfFVMyAlM0IgXtb1N4UBSkb6vRRQgl7QKPCmUWJoY2zKS6UWw3OmV20mVV9ES9TtVGGsk5hzq6kFCGwr7WXYx3b/lOOde4UtQtRQXp6NIVgAjcC64HnbLZXwcyAasXKL4a2D3nUjIe1dv/xBcrw68CFpUp9+j6mSbvtlml+w8gE7fNfXv/mkVNd1Co+9RTbgvT0aBbBXAgcpILZQKoVq6QIQraRbrq6srEEy+XQ7L/b1udUR/MQy87O+CDDcSnCwnyVcuRtCH63Iqe6CE63kUb46l1lVgsztWj2qGA2kGoszCgxTHr5oo5VKlU17URQBKKyv7CUzYyPNmnETZtLZfuYn2GCtmhRaJvttfS5sT2d+cvPYOw6+799i4mZRz1qQre4+d29exvVFpuVoGkbZraCCSwBVgOr58yZU4dL1WLYtmEmBZa1Ia66VauV6U5TOxYsWEbnuhEx45xYu2ira1V9Gx1jwYmr7bjujZN3heq19rK5lr4JbZJbZExMvG9C7DS9SVMGhzWj2AY5zooCtK9OGsH0J7UwMyLOS57lQxv3kkaIqZWwuW2YF5bCgwXf3D3Rw15v0VyPG0+zhliafvGqVIwZkIjr195uTKUyqm2RbZfudsYY+7ZCW8u8SMNvM0AFU8mfuKGRES/mekrxEYe6u42ZPt3EietwW+OHJ47A+PP2LE2R0fJaC5H70YoVePc6VioJ0/TaBCbxfyBt2riL0iUpQ1QwlXyJ61YUEcHbPyfPaKAIt7/h6P4NFsKqBDPuGqRJthOQxTVveOKWZPkmVd3b24vXJSlDmkIwgVuBN4CdwDrgvLjtVTCbgKTZIUNEYATHsvTPhzPaDlmN4FTrqa41dXePHbu93VmOElfLFGs9eqKZlE+5bL9dQZwwjSYTwQTagStsMmpEUsEsGMF2zxpCm62nNM55U5Onu729di98HVM6wSTa+21rcYvYbVtL96Mmx1Ywxdk2GhG5F1hkkjZsAAsWLDCrV6/OuxitS3+/E1Rj7VqYORPefnv8VAkizqtXBQZ33h2XEWmnzeQQ+ae9ve4Rh7ayG9N4B0nelF20812W8EluGR9xKM21LpWcaS0GBuK3K5edqSdaEBF53BizIGk7m+AbTwK3i8hZInKal2ovolJYwoIhBANuDA5OnFemhm9qUDxyEUuou1iOINZiCTCFYc7nBoYRDM6HZVBK6a91WGQrP42KctXk2AjmTGAQ+Evgv7jp5HoWSqmSLKK+REUiuvhiJ4ZiHci96tJABGMtlh67sYPd2YLgfFj2aHs7XQZvvTUxspU/dFyLzgBZFTb19qIkbcOMIavG+hyiluc+/nuyp+Cw1mC7c4u1V4ZBVl5yYB/gJzhBMt4EbgP2sck866SCGUNWY3Jz6rrTVKJZ4O5NE5L/o2nT66AFPOJh2AqmTZX8JuBnwLuBvYF/cdcpRSIqYG/aqNop5hB/h042UMqkSp22mmp8qd6MuO2HlMtQqTjSUgWNKOs42trg7LPHqtpLlyY3q+jUFbHYCOZsY8xNxphdbroZmF3ncilpyWp+nzjngDGjojlUKvOpjhu5mKuraJWrHfGleuEJ8o7pM5FKZcyDbDNdRIARhF1ZlbajAzo7x6/r7ITu7sBB3UjtXlt2kpfcQ6euiMRGMDeKyJki0u6mM3GcQEqRsJzfJ9Ev5HcOhGEMlMtM37iG427q5asspc3WdiqXHUdDCt6mOzenkCfIU4cG4dxz4YIL4JOfTO9JL5d5edGnGKEjm4Ltvjucd974qUluvBFmzZq4rd9iFEvBLsrUFUUkqc4OzMGpkm/Aacf8KTDHpr6fddI2zAQSOhz7m7D8UX5GQ5MFsQjYEDUSJdgmOYTlED1f2kZH/Ljyoid/e2DWzrSwtsa4+2Ubek7bMGNT8gbwQZt1jUgqmDFYjM5IDAfmRUT3iBqj7HMkbS6VQ7fZxHSzk3YzghMpaBPdYy+vxYvr7Ze76FWbpk8f74GOOc+q44MGHXpxjr+48eaTfJy4DVkK5hM26xqRVDAjsOxS5L23keHA/PtFWYK+6SG8Y+/sHH/s7XSabXTkJ1ZNlIYRs216lbFBg3MohYmiF2czLp8WFUk/NQsmcATwWeA14FJfWgY8bZN51kkFMwKbLkUVJwLQMJLchcedjTDqtwn4rNvfTy07sSELIEbNkqruUuXd36juQl6NIa45IOx+tiC2ghnn9OkEpgNTgBm+9Dbw15k0oCrZkNSlyB29s8/wAG0WPm0zOOh1pJlI2Nzfvb2OB/kHP+CP/xhm5egTDCt1xJk0P55DL6q70PTpzt847/jVV2dfrslMkqICZRvlbURSCzOCJAszpcMh1uLxHAhBKhWnut5oKyvoMWvmAAAcK0lEQVQhDSPmX1lkNtFd2M7xm+ie0KyRmKZPH7v2ce3CcR3V1bochQw7rn9PRPbwFkTkXSJyd70EXKmCpC5FafrVdXWxkZiuP8aEd2y++OKJwThSUK/+lG0YjuIhHuLwOh2hdqazhV9xxFhXrjaL1/Kdd8b6hEV1A2pvj+6o3tWl1mU1JCkq8KTNukYktTBjiPOSx1mgIfuFzZUzwcr0s2hRJpZWPS3AolqXXhr2rMY0+8W1YSYNgVRHzzjI0Ev+OL5+l0AZ9ZI3F2EvVGenUyULEdhKxZhzOhKmbfVII5Zu1TEP8Sq6YFaVgl5y78Pnn9Yj6f4pxhiTqWCeAKwFfuCmAeDDNplnnVQwayD4QgXbGwPdkCoVE25pBqffzVs0Wlkww4QvKcBGi3ZMTyIzwXTyYhZODMz/Asyy2aceSQWzCsKq6mnmqE6aYCtv0UghmJNKNKOEz3Z2SGUcWVqYApwJfMldngMcapN51kkFMyVR09xGvVDBKl4TCWJLJW8K37A55W3vbR4xMAs8V1CWgvkPwN8DL7rL7wIes8ncIu8TgF8DrwD/I2l7FcwUVCrRL1B7eNvkYFtp9FmOGvKoKYNUKo2fu9w2dXRMHELZ2WnXnSvJQVRv8Sr4bJRZCuYT7t8nfetqHumDMyPlb4D34nSSfxr4QNw+KpgpSOp7GTJ2eRsdo1PdDuctKk2ehtvCxXAEHEeZrfXutybjmkfikk0QkHo7gvI6riW2gmnTD3OniLSDM2BCRGYDIxb7JXEo8Iox5rfGmB3Aj4BTMshXgfi+l+UyzJgxYfVUdnI1F7OeWTlEuJxctI0Mh44wEoB777WbH0kEdu1ypGXNGmdunrSUSuPn68kq0HRa8jpuxtgI5jU4U1TsKSLLgQeAr2Zw7L1xxql7rHPXjUNElojIahFZvWHDhgwOO8nxAl6asNcV5yVcvjzy5ZvFILMZVMHMgMhrGHVvggQ7pFcTp3LbNrs8so6BGQy8OnNmY45bb2zMUOD9wKeBzwD72+xjkefpwPd8y2cB18bto1Vyl6jG8yRHjYjTdmZMLpOdaUqZgu17Uf1pk9owg5Og1bst0back6kNE7gT6AW6bTJKm3CiId3tW/5b4G/j9im0YDbKAxj3wKfpUhKSz6TqdlPwZHWto8bsB5+zpHsfHJlV72c1qiyl0uT1kuO0J96KE2n9H4FTgU6bTK0O7ERB+i2wL2NOnz+P26ewgtlID2DUwxjncQ2+ML5yby45Id9eRcOy5SWWkeKZ1iFSFMeKRaT+olGzYI5uANOA/4bTjvl74EbgQzaZW+R9EvAyjrd8adL2hRJM/1c6Sqzq8aAm9bWrohzeqZwREol9BCd6+mjEdE3VJe/epOlKZCswfgszrN9toy25ogh3CjITzHEbwzzgSWA4zX5ZpcIIpm2n7np8UZPaHsNeGP9UCQlVoQtLY3P9vEp5tJtRuWzyF51mS8EO5sakm9PcRmDCnsXg8NVGU/A+l2FkaWH+MXAh8KBbhf46MN8m86xTYQTTtj9cPb6oNmLtF8e+vlQvlJe9f5K0ASmbFxdV0dG6yVJd2nCDQhHxwZtwbFuBKao1V+BRPWFk0YZ5PnAv8DvgWnKa+MyfCiGYRZh9r1KJFq/2djtHQEw5V/VVzBbRYZGZpYCXOkqYh9tiJiOLEqA4i1WxJgvBvAk4HmizyagRqRCCGSdCWc2+Z/N1jrM0w4bQ2b7QSefoT21t6WM4pkiTxmsfHMcdt23U85C2Z0RUZHwllLq0YeadCiGYcV/0LB7QNO0/cZZmtS900jk2QSqc0Po/SEnT3ZqJ38vIcf1JIfbyrpY3EbaCaTPSR/ETNTKhVBobflYLYRNabd0aPi1Eby8MD9d+zCxGlBSIQo1S8qYK6e+HWbPCJ5HzGB725qtjYMBRvYEB6Bqsclhhkw07bAYiBVNE7hKRnsYVpUmImj8nq/lR0oy57e93hjqmIbi9f+4fj5NOSp+vEs60afDgg44KxoklQLkc+r1cS8xwxrAPqf93JVuiTE/gYzh9JJcCHTbmar1TIarkxlTnAbTdJ43XM66tMdiG6VXr/e1eYd1eNA5mumQTps2miaOz05i+vtAuXYtD+seO3s96NxG1CGTRhgl043Qjehr4HHCpl2wyzzoVRjDTkrZdMm5bm2Cx3ssSJdDVDq/UND554/KThMs2r8A9GaJrVDQvLEXcz7hhiIo1WQlmJ/Al4CXgcuAyL9lknnVqWsFM21eu2uAatvlG7VdtvMVWTnWe2+hVyvE91Jqwk3gRqVkwcaKhvwB8DeiyyazeqWkFM4uxtX19di9ZlDUaNvGZpmxSV1fdPjbDSLL2NVkn8SKShWCuIiEYRqNT0wpmraMxbMSyWmtUUzapVKrP9dauQQ3BVjAjveTGmKONMc9n515qYaI860HvdBTXXRf/e7kMIyNOVG6va1OYu1WpH2+95dyncjl+u1LJ2camF0KaZ0RpCNoPsxH09o69TCLOX/+0AWH4I1bH9bWMeqnS9MErl6G72357ZSJz5jj3c80axzasVKK7n61Z43zg4sTV5hnxE4xw3t9f3Xko8diYoUVJTVslT4tldXoEoturLNrURsCY7m519oRVr9NsH9fjIa5tMc5hk6ZdUh0/NYMOjWxiLLr2jID5bltf+DtRqYQ6eEZ8KXdRKmqKm442SlyzjhsQJYBRYfoKErGomX1PKphFJunJsujT9w5tZjGV8Hciy76UKfoXTgoh9jvN/JZmUnBmG2vSVk3iAmoERTSuD2gDI5w3u5GrgllUbJ4sS8HbSbs5g5AnMqvgGf7qoWWXpKYXzah7FJW8qEBJgw3SqEnaIMMFsDALUISaUMEsKjZPVqViHZ5ti4S8eFlYmJ4VZNv/0yeYTS2aXrU3S8GKahONUpM0x7cR7AZQACO3JlQwi4rNk5XCogt98Wrpg+l/0VKK5aQQzjTWnU2VOGkUkO3w2FqbBOqMWpgFTLkKZrUPZHC/OGuj2rHcYZ/x4CifoMUqYkbAvE232UWbGcGN+N3Xl9mY8lSC2d7ueOzrJYSlkv0HICqYhl+0/M6eOLVIuo62HvawqUYK1EhYACO3JgotmMDpwPPACLDAdr/cBLPapyFsv7Bo6J4HtFqr0HayLN8LuKqvYs7pmBgFZ1d7ymjtWYmZzZQLtaSk6nEwTZkS/7vfax0UU/95ZXX/Qu5h0dSo4MWLpeiCuT/wZ8DKphDMausbcZFkgk+WjUU3fXpmn/Fy2ZhXsThmvcQrbXg7m2Qhttu6S9k1FdiIu+02Sq4UWjBHD94sgllti3aa/WxeLM8Si4pk5K7fXCqbC0uV2C+9iDHD5DQVRdpO2LbJJjYlObStJt3bejf0NbPp1yBUMLMkawszbTDg4L4WI0b8sRTDjNBcLcy40SzB/o+2yYv/WIOjqq4pqupe74a+Zm9cbBC5CyZwD/BcSDrFt02iYAJLgNXA6jlz5tTvisWRZRtmmsDBSYLjESG2r1KO1OhVfRWzgQyrp9WkoHikne0y7Hrk1Gk/USz997mR1l6zu68bRO6CaXXwRliYWT2gWXnJk6qjcU6EqAc+YtthZNy7P+449Qz95jlE6hR/cwTMekpOk0LwmlYpcsEPxxDOOWwulSM/KsH124lw6OVpzTV7B8kGoYJpTHNXR5IcQf4HPq2FmaUV5qadtE8UsEolm2mAfWkYMdfSZxZTcZoUgtX5Ko43AuZaxubTWU/JDLaVzAhiBqRs1hPeRLCe0rg5eM4gZdCMRqAWphWFFkzgo8A64B3gTeBum/1SC+ZkeFgizuG19vLoO7mqr2J2dqZow6yxqhm0rIYRM+yWySoiTxXH89J6SuZa+iZOCtbZWbVF6/+wXEvfBGfYdjrNNsbn7Z2zf7KyQj5WzWw0NJBCC2a1KbVgFr064vfqtrePTaplTGz13C+G4OjEWe2VCdaO9xJPeDcysjBDR/OEvYx9fZn2r8yy3XUEzPWdfaZcNuYMKpE9B8asSSZsM0SXOaejUlwNKprVW0BUMI3J1sLM+qGL8uZ6I20ihsa91l4eJ5ZxKfQ0+/qMaWvLTHCsDlyHJoAs087O5BkzvfbgqJ4Fm0thF1tpFlQwjcmuOlKPak1UW1t7e6zQJxlqXtueZ2mOK2OjutwELfgCiGJi8j6GEb971fbYvqtqwTUtKpgeWViG9WgLrVKI4oy1xUwc6jhO2DN2wESm9vbx17lRx60lec9HyG/DiDnDjT26uRRzA8KuudIUqGBmSdZtoUkRbKKSOwZ8QMYsyMVURrsvxlUXy2XT2D6XImNtsnmLoW0Km4rYfx7evatlbnilkKhgZknWFmY1bXoRATq2SJdZ1ec4HOL6C75K2ewioe3SG3pZqWTTzumFN0s633q3qfrLkzQ/e2ens01cjcTGiVUUx6Jiha1g6qyRNtQ6TW6QNDM6wtgMgnfdNWHq3C6zlaPuWkov/UjE1K0C9DDACIKJO8706c7fJUucWQ0DxO4bhjHOdL9h189PyLFGaW8PzzptWbypiDduhJtuip6xcccO5zoEpy32c9ddzrnFMWdO2hIqzYCNqhYlNWU8zDDSRvT2iGsasMxzE92xlqjtqJZUybNaq90/xKr+P/SZnaRoG42KQFKNdZhkXWobZtOBVskLjG07mFel9YgLF2cpHKPe85SiVZNgetXcavYtlcbvW0XszGFk9LL7v3mRDpxqg6p4+6pYNh22gqlV8jzo7XWq2OUyRFSjAecV9FcJw6q2nZ3w9tvWh17LHJaynC3EVJFDGCa8amzFjh0wOJh+v44O2Lx5/L5vvQUPPuj8b1ntFQwXXOC0NBw50M9vTQ+/HWhj++AQIxI4r46O5KaWqCaaSiW6Gq9MDmxUtSipEBZmPUZNpHEq2U55EZKG6DIXlpxO7/7+mknW4xBd4cMR65na2qLPzbO8KxWr6EavUjbt7eHdriace2dn9D0NTvuR5BxSmga0Sl4HqunAbiOwSfnG5WE75NBXlQ3qc5J33RtZ5BfZVO2H9UjedQh4vMOiDnnlt26KiPpQ6ZjsSYsKZj1I270obTzMqEjqcXnYOpB8+wSzjIrGY7q7I7NPHPFSb8H0rLyQ37zISX6xb29PGWG+1nuvNBUqmPUgrVc1i5csKY803mffcf2BzRdTMe+E9dHs7DSr+iqhep044qXeo3timiL8cUC98vb1GTMgCWX2l73We680FbaCqU4fS/r7YV1bhJMhyvkQ1d8yTT/MpDx6e6FUqiqvbducv7fSyybeNXH7HTs46q6l4/xTXpfQ6Vcvj3ZYlctwyy3xfS/9dHTE/myCKxLy3VqaM6G83/kOrP3UcraKRZmGhyeui7rH2t+ytbBR1aKkvCxMrwqbOFY7SCMsTH8BU1iYwWwjq6txFlTYiJeottc4a87dLqotdT0hs2zGnadtm3KUFaxtmC0HWiXPDr+4+B0foQFz/WTxktnmEfTgBof/BfY5IxDVaBPd1Yl7sO3Vm6s7GAk9Stx847QvLE38IG2jwwy2hXijo8SurS37axt1riqWkwYVzAypqfmqxpesUnGExBO3zSXLPBKCE2+RhO41weTvMB5X2DAB6o4Q487OCbuf01EZN1XEdiLmyIkra9oLrCLY8qhgZkheDtKqDdSoKrp/XvMkgQxLHR3xB68m35Cie/r1WntEfuWy/U1RQVQsUMHMkLyarzxNCAYFvrCUcOA44ap1tsg4QaomvzjiTPukj4JXNm13VCxQwcyYPAwVkXBH0xAJL32SeNUaTi2urTRK4MLWl0rxF8CmS1VY9yLveGmcOkpLo4LZCOqsouVyzOiUuJe+nnPoVGNJdnZOHMIYNwTRw8ZCrOZcte+kEqDQgglcAbwEPAP8BNjDZr9CCWYDqnuVSpXdfWy7GUXlWypl3/G82o9L0n7VCLhamEqAogvm8cAU9/+vA1+32a9QgtkgT1DVIciiqqu2QhLcv9rwbDge+LoZ4mnLpW2YSgi2gpnLSB9jzC+MMbvcxYeBffIoR01kMYrHgulXp4z23t8PPT1w1llO5PC+vrFhOkkjgvx59vY60ck9qdm4MTpKeQKDlBgYcLIZGHDCrPX3V5XVePr77ULbtbePH/aj4deUarFR1Xom4F+AM2N+XwKsBlbPmTMn8y9L1TSyr5FtdbaWQB1JDpio/P1z4JRKxkyZMu73d+gMnUc9k8tk036pFqViAXlXyYF7gOdC0im+bZbitGGKTZ6FqpIXsctKkojHtfdl1aYY+P2MELGEiCbYtO2cceej/S6VFOQumIkHhrOBh4Au230KJZjGFK9TdNKQpAhBHWwr1a3o1oZ4NR8gDbmmZEShBRM4AXgBmJ1mv8IJZtGw6bfYNbFP52Iq2RjHIcMxrXWwGvGrh5VftI+g0hCKLpivAK8BT7npuzb7qWAmYCMglYp5rb08IcBuzYZZX1+44LmimahB1Q7YD/PmVytyRWxmURpCoQWz2lRYwSySVWJRlrrEwo3qtxkWjDeMaqvXWYqcVvFbFhXMRtGEVklddCHK+QJ2+1d7HSNOZnOpipPRqOoti61gasT1Wlm6FLZuHb9u61ZnfUGJmiU2aXbZWNojpuGNWu+nv3/sOnrb2/aZjOj32jW4Nn1fT42qriSgglkrDerAniXBadEz6c+9ZEn4+mnToK3N6UwfpmD9/c6+AwPO8vDwmHrbFChCzNYyJ/03qy5fEmVSYWOGFiUVskqu7V5j+L3kIhM6sYdWsWu9fpXwaE6LqVRXky5Se7TSMNA2zAZRaxtmXi9ovY9rK4QZtBv6I9L7Pf+t+M1SqkMFs5HUEoknD4dRI45rO6ooAwu9Cf1uSsFQwWwG8qrOR0X4yfK4SVHfM46KrjVppRZsBVOdPnmSh8Oovx8GB8N/GxiId9CkIcyB4uHvRZCRB6q3F9asgZER568GJFLqgTji2hwsWLDArF69Ou9iZEdPz5h32E+57Lz1jTxmkK6u2l3n/f1w5pnhv4k46qYoBUBEHjfGLEjaTi3MPMmjG4ut9ZpFX9Le3ugYmtq3UWlCVDDzpC4dIhNII1RZNA1o30ZlEqGCmTf1bnzzIrB7bZMnnTRRwETC983CCszjo6AodUIFczLjH0VjjPP3llvg7LPHC9inPlVfK1A9MsokYUreBVDqSNQ497vumuhU+uAHne3XrnUsS9uhiYrSQqiXfDLT1uZYlkHUQ60o41AvuaLRdxQlY1QwJzPqoVaUTFHBnMyoh1pRMkWdPpOd3l4VSEXJCLUwFUVRLMlFMEXkf4nIMyLylIj8QkTenUc5FEVR0pCXhXmFMWaeMWY+cAfwpZzKoSiKYk0ugmmMedu32A00T2dQRVFaltzaMEVkuYi8BvQSY2GKyBIRWS0iqzds2NC4AhaJ4HjwWmNVKopSFXUb6SMi9wB/EvLTUmPM7b7t/haYaoy5LCnPlhzp440H9w9xzCJWpaIoo9iO9Ml9aKSIlIE7jTFzk7ZtScHMI8iworQYhR4aKSLv8y3+FfBSHuVoCppw3nNFmazk1XH9ayLyZ8AIMAB8KqdyFJ85c8ItTB0PrigNJxfBNMb81zyO25QsXx7ehqnjwRWl4ehIn6Kj48EVpTDoWPJmQMeDK0ohUAtTURTFEhVMRVEUS1QwFUVRLFHBVBRFsUQFU1EUxRIVTEVRFEtUMBVFUSxRwVQURbEk92hFaRCRDThjzxvFLGBjA4+XRNHKA8UrU9HKA8UrU9HKA/mXqWyMmZ20UVMJZqMRkdU2IZ8aRdHKA8UrU9HKA8UrU9HKA8UsUxhaJVcURbFEBVNRFMUSFcx4rsu7AAGKVh4oXpmKVh4oXpmKVh4oZpkmoG2YiqIolqiFqSiKYokKpqIoiiUqmAmIyP8SkWdE5CkR+YWIvDvn8lwhIi+5ZfqJiOyRZ3ncMp0uIs+LyIiI5NY1REROEJFfi8grIvI/8iqHrzw3ish6EXku77IAiMh7ROQ+EXnRvV8X51yeqSLyqIg87Zbn8jzLY4O2YSYgIrsbY952/78I+IAxJrdJ20TkeOBeY8wuEfk6gDHmi3mVxy3T/jgT2v1f4HPGmIbPhSwi7cDLwIeAdcBjwGJjzAuNLouvTAuBIeD7NtNIN6A8ewF7GWOeEJEZwOPAqXldIxERoNsYMyQiHcADwMXGmIfzKI8NamEm4ImlSzeQ6xfGGPMLY8wud/FhYJ88ywNgjHnRGPPrnItxKPCKMea3xpgdwI+AU/IskDHmfuCtPMvgxxjzhjHmCff/zcCLwN45lscYY4bcxQ43FdqCU8G0QESWi8hrQC/wpbzL4+Nc4Od5F6Ig7A285lteR45iUHREpAc4EHgk53K0i8hTwHrg34wxuZYnCRVMQETuEZHnQtIpAMaYpcaY9wD9wGfyLo+7zVJgl1umumNTppyRkHWFtlbyQkSmA7cBlwRqUA3HGDNsjJmPU1M6VERyb7qIQ2eNBIwxx1lu+kPgTuCyOhYnsTwicjZwMrDINKgROsU1yot1wHt8y/sAr+dUlsLithXeBvQbY36cd3k8jDF/EJGVwAlAIZxkYaiFmYCIvM+3+FfAS3mVBRxPMPBF4K+MMVvzLEvBeAx4n4jsKyKdwMeBn+VcpkLhOlluAF40xlxZgPLM9np5iMg04Dhyfr+SUC95AiJyG/BnOF7gAeBTxpjf5VieV4DdgEF31cN5eu0BROSjwLXAbOAPwFPGmA/nUI6TgKuAduBGY8zyRpchUJ5bgWNwQpe9CVxmjLkhx/IcBawCnsV5ngH+zhhzV07lmQfcgnO/2oB/MsZ8OY+y2KKCqSiKYolWyRVFUSxRwVQURbFEBVNRFMUSFUxFURRLVDAVRVEsUcFUcseNovOqiMx0l9/lLpcD260UkQ8H1l0iIt+p4pinisgHaiu50mqoYCq5Y4x5DfgH4Gvuqq8B1xljglMq34rTId3Px931aTkVSCWYIqIj41oc7YepFAJ3yN7jwI3A+cCBbtQh/zYlnJEg+xhj3nEDSNyPM6e0EZHPAx/D6dj/E2PMZe5+nwA+hzO2/Bkccb4D2OSm/wrMAL4LdAG/Ac41xvyHO1zvV8AHgZ8ZY75Vr2ugFB/9YiqFwBiz0xW8fwWOD4qlu82giDyKM974dhzr8h9dsTweeB9OmDcBfubGoxwElgIfNMZsFJGZxpi3RORnwB3GmBUAIvIMcKEx5pci8mWceAGXuIfewxjzn+t5/kpzoFVypUicCLwBxEWs8VfL/dXx4930JPAE8H4cAf1LYIUxZiOAMWZCfEoR+SMcUfylu+oWYKFvk3+s5mSUyYcKplIIRGQ+TrT0w4H/7kYHD+OnwCIROQiY5gXExbEq/7cxZr6b9nPHbQu1h3nbUuP+yiRBBVPJHTeKzj/gxGdcC1wBfDNsWzdC90qctk6/s+du4Fw31iMisreI7An8P+Bjbvsnnice2IzTbokxZhPwHyJytPvbWcAvUZQAKphKETgfWGuM+Td3+TvA+0Ukqt3wVuAvcKahAJypO3DilT4kIs8CK4AZxpjngeXAL0XkacALa/Yj4PMi8qSI/ClwNnCF25Y5Hyh01BwlH9RLriiKYolamIqiKJaoYCqKoliigqkoimKJCqaiKIolKpiKoiiWqGAqiqJYooKpKIpiyf8H04eyuNdpTjAAAAAASUVORK5CYII=\n", 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bv/999Bx5JPYTAUceif3f/z565s/H9qiOsXDhws1vv/32gX7cH/3oRxvuvPPOcVOnTp22fPny/M0337wx6L7HjRtX6uzs3Dpt2rTjZ82adfQJJ5yw22+bj370ozseffTRMeb7s846q6+3t7f1rLPO6gOAadOm7TnmmGP2mC1PK3Pnzt02a9asKdagpKCceeaZ/RdffHHvySeffNz06dOPmzNnzlZrdy8APPTQQ2OmTZt2/HHHHTft5z//+aFf/vKX35wwYcLgLbfcsv6iiy5659SpU6dNnz792BdffHEkAGzcuLFlxIgRXCgUtKKSEivfRkQjATwGYASMsdx7mfl6r21mzJjBkstXSA2ZjNEytUME+ERICumCiFYz8wzrshdeeGH9CSecsC0pn+qB6dOnH/PQQw+9Nm7cuFLSvkTJ17/+9cMOOuig8tVXX111/1944YVxJ5xwQofTdkm2UPcBOJuZTwBwIoDziOi0BP0RBD0mT9ZbLggNxg033PDG66+/HjrwKm0ccsghpS984QvaP6YSE1Q2MPv8WysmeTOF+mHxYiBni6rP5YzlgtAEnH322btPPfXUPf5r1hdXXnllb2urVoAvgITHUIkoS0TPA9gC4NfM/LTDOvOIaBURrdq6dWvtnRQENzo7gaVLgULB6OYtFIz3nZ1JeyYIQgIkKqjMXGLmEwFMAnAKEVWVxWHmpcw8g5lnjB/vONdXEJKjsxNYv94YM12/XsRUEJqYVET5MvPbAB4BcF7CrgiCIAhCIBITVCIaT0SHVP4eBeAcAIESGQuCIDQiSVSbCVqhRUi2hXokgJVE9AcAv4cxhvrLBP0RBEFIFWGrzQQhaIUWIdko3z8w80nM/B5mfhczL0rKF0EQhNAsWTIWEya8G5nMdEyY8G4sWRK6fFuQajNWalmhRUjJGKogRIrk1xVqzZIlY3H11QVs2tQGo35bG66+uhCFqAapNmOlVhVaBBFUodGQ/LpCEixaNBH2ZPJ792awaFHo8m3WajPW5c8991z7vHnztgNGtZnVq1ePdtrerNBy5JFHOlZoOfjgg8tmhRbrdqeddtru5cuXj7vmmmsmPPPMM6MOPfTQ8iOPPNJuVmg59thjp9199935DRs2NFxih6CIoAqNheTXFZJg82ZnUXFbrolutRkrtazQ0uyIoAqNxYYNestVkW5kwYsjjnAu0+a2XJOoq83EVaGl2RFBFRqLOPLrSjey4Md11/0FI0cOr4gwcmQZ110XSfk2INpqM3FUaBESrDYTBKk2I/hiip+12zeXC5cSsKPDEFE7hYKRHUmoeyKpNrNkyVgsWjQRmze34Ygj9uO66/6C+fMjK98mpIO0VpsRhOiJI7+uXzeydAcLADB//nb89a8volxejb/+9UUR0+ZDBFVoPKLOr+vVjRx1d3CjiHOjnIcgaCCCKgh+eJVpizKquFHGahvlPARBExFUQfDDqxs5yqjiRpny0yjnAZTL5TIl7YSQHirfh7Lb5yKoQnOi2yXp1o0cZVRxXFN+QhCo5zaF5xGQl7Zu3XqwiKoAGGK6devWgwG85LZOzRIuC0JqsEcCm12SgP546+LFzlHFixfr+zV5snM0sao4d3cbrcANG4xtFi8ONX4c+DKFPY+UMDg4+LnNmzffunnz5ndBGh+C0TJ9aXBw8HOuazBz3dj06dNZaFKKReZCgZnIeC0Wg++rUGA2RveGW6GQrG/FInMuN9ynXE5tf2G2dSHwZQrqS5T3WBMAqzgFzzix+rbEHdAxEdQmJWqxIGJHpSCK1u8gBBUVVfXT2H+oy6R7HjH8INBBBFUsCkvcAR0TQW1S8nmOtEUZdQs1IkI10FTUT1O0anqZEr4nIqhiUZiMC9QzzTDXr7sb6O11/swvyMXt+nhNg0mI0DNNVIKjNKNva3qZGieQSWhmklZ0HZMWqoWEu8hqhlvLxa/14nd9Ehyvc0K7gWb3v6vL//sQoA+3ZpdJWqhiDWCJO6BjIqgWUtptGTluIgB4P93r7PpoaZ3bj4WuLm/1S/M1kTFUsQYw6fKtV5qli8ytKzOf9567UWfXxzzN2ejGOnSghAzWoQNfGOvQ5+vWdbtihXfKxRR2dR8gjhzMglBjRFDrlTjKlKWN7m6gz6HEYy4H3Hij97Z1dn0WLwYube3GjzEPHehBBowO9OB7uxwGUoP+WNAQrUSG56POwSwItSbpJrKOSZevhUYfQ3U6P8CI+E1oXmbc7MoXqs/XqUs25q7bOrx0oYF0+YpFYNJCrVcavYvMqVsTAEaPVjvHOrw+o7crtjxj7rptnFS8glBbpMC4kE4yGaNxZIfI6BKsJRGn9HNFp5B5jD6l6dLXCqcC44KgS2ItVCI6iohWEtGrRPQyEV2ZlC9CCknLGKjbBNErroh+kPH8852XH3109bFiHG9My6UXhHojyS7fQQDXMvNxAE4D8E9ENC1Bf4Q0kZaIVLf+zyVLoq/3uWKF8/KHH65pbdG0XHpBqDcSE1Rm3sTMz1b+3gXgVQATk/JHSBlpGQN1i5y194lGMchYy2N5kJZLLwj1RiqCkoioA8BJAJ52+GweEa0iolVbt26ttWtCkpjdmnfeabyfMyf+ORz2+SL2ppoXYee46vSpxjyfVmawCII+iQsqEY0G8BMAVzHzTvvnzLyUmWcw84zx48fX3kEhWUInuVU8RkeH0RybM2f4sXbvVt/P2LHh/HDqayWX2tYyoCkIqSNRQSWiVhhi2s3M9yXpi5BS4p7DYRVswDm8Ncy+dQKXnPpa58+XAU1BqBMSmzZDRARgGYDtzHyVyjYybaYJiXsOh9tUlaAUCkZ37NixwM6dwMDA0Ge5XLDByFpN22liZNqMEAVJtlDPADAHwNlE9HzFXOYNCE1L3HM4gohpNuu9P2aj5JxVTIHgLeuoBzRVW87NUB5QECIkySjf3zIzMfN7mPnEirnMGxCaljjmcFiFQpdczugidhvb9CPB5Pzd3cA/j+vG7kt8xqS7u4Fx44BLLqnN2LUIttAoJJ37UMckl2+KibNwZpT7dssRrGLWPMJBtq9FqTSXa2We9joUvP3yuz5W/8Pcl5QlDIbk8hWLwBJ3QMdEUFNKyh6OTpjPfldB0RVDr8LnLjaYbXW+JlH9YOjqqi6sWrkPprsl+BRe9Tsvc72w9zxltVlFUMWisMQd0DER1JRS64ejpgBZn/2ugqJi1mrfAVq6vZm8o3MDbcP3M9AW4MdIsehepbxQOPCRbwvVq6C7db2w91yronr8iKCKRWGJO6BjIqgpReXhGFUrLEDLyPrsj6yF6nROXV3MhQKXXbYvgaq22TM677jurrztWH54tSyJDnw8G0Xug8f189qPdb2wgigtVLEGtMQd0DER1JTi93B0EsHWVmNMUldgAzyIrc9+R0FRMTLEUOV3wcass4/7kK1a5im+Jl1dzNnKttms8d7EdMjL92yWyyDuoQLPRpFno8jrUOASyBBu60mo1qENK4gpGyYQQRWLwhJ3QMdEUFOK38NRZbxR9WEaoGVkP7wpKI5i1tZmiL19311dyhrweFe1aA+AXMXTydahYOysq8t5na6uQN3OuynHF6PIC/JFQ0ydfhmo/GqIQhDjDGTTRARVLApL3AEdE0FNMV4PR79xObfWjdM+3cQ5m3V9IDs9+y9trR67NIXT7Vx0GmWPdxV5Y9ZoBW7MuncDO7VS+5DjBfnKuWSrW7UHzjdAYNSB1mYUrcMUCWJYRFDForDEHdAxEdQ6RfXB7xf0k8sZgufWKvMQhWKReUF+qKuzlHERKsWuYze3XfE59wFkuQTidSjwpa3FodPwu15BBFX1B00TIYIqFoUlnhxfaAKckjM4Yc1+5JbDd8UKI32fU1IGj0xEnejG/90zDx3oQQaMTLnk7EMl8cJvr+jGGy0dKFMGb7R04LdXdMeatCmDMlqojLMK63HO7Z1DyZDcsjJls9EnyE8w6YQgNAIiqEL82JO+5/NAW9vwdezZj9we7uZytzy+bts5CbQTkyfjt1d0470/ugyTSob4Tir14L0/ugzXHd1d9bvg0tZuvNTX4Z/tZ+ZMz8NmCpOrMwt2dwOjRjlvMG+e+g8VK7mccf2dkAo2ghCOpJvIOiZdvnWMyxQT1/G3vPN0Ei4UvLuQ3botVbpHK13Kg8g4ft6byQ87jQV5l3FYc5zSHsU8c6b7ce3n7xZwZI7zOl3XfL46oMopmjqqCFsZQxUTG2aJO6BjIqh1isoD3C4MTsE4bW3eCQwA94hUt+AeqxB7jc+iEjxkRTcoyJx6UiwO/8Fgno9VlIJOS1EVubBimLJpL2ERQRWLwhJ3QMdEUDVJSwsiyDxVN0Hy2p9dlFT37Zf9xyqoQaKX7S1GL+H226duJqG4vgMpS8wQFhFUsSgscQd0TARVgzS1IPzCY3WjgP1EUmcOrNnqZVbzQXd+bdSmIljW6UUuuX2HrRdEbFOWOjAsIqhiUVjiDuiYCKoGaWpB+PkSZJ6qX4Yg1X2b81f9upKd9h2mck0QU/lBpNoib7Dk9mERQRWLwhJ3QMdEUDXwEgfdVkmAZPTW1R/v8kk96De+6fWw92spuQU3WS2f12ptlkBDrqik/ovC3FIO2u+Jii/mNmEEUVeQ0zL84IIIqlgUlrgDOiaCqoHbA9OrC9AJzQen2+qPd9mCjtranP1zElyvB7CfMKgIqtN18bB1KAw/J83tA5t53b3uiYof5n1wuw6q6ARApWX4wQURVLEoLHEHdEwEVQOnh5hHeS9XNFsynqv7teayWf0WjN/DWqcbV0Fo+5A7kGB+N9Wwu9fqp5uvKi1t89rUssu2DrqHRVDForDEHdAxEVRN7C0It4esNdjH3uLwejg74KZfF0NxvDHIVA+rQJjdx+Y0GJXuZHM6i9Mczq6uA+kK18Go1gKELANnNTMoqlj0b7U7CHyVOUUQ26fl2Kft2MU2auoggEkEVSwKS9wBHRNBDYlXS8GtpZdxTnLA2azWIdxKmnm2okxUBCBMgJCZEN9J0Nrbq8QUYC5FIaammFvP0/zB4PZDwOwGd9uftYiAWyUZlfJsUSItVLEmscQd0DER1JB4dY8GCazROEQZmmOM5sO2q8tbQMwo3TCBQbmc0lhrGeAtyPNsFHnAobZpIHNrpbldSD8//Vp9SYibjKGKNYlJLt9mwp5Tt1Aw3gNAT4/evgoFrUNQQTNP7IYNRi7bJUuMR7AbpZKR11bXfyv9/UBvr+9qBGA8evFjzEMGLsn1dWEGWlqAc84xcgGbOYGfeGJ4Ht983riQ27d7788vH69fjuQwdHcPPwczr7Hbl+JA0mJBaBCSVnQdkxaqIjpTFPy6SsPWzvRKMkDE3N7ufFy/nL1OLdUoWoyKplMsPBJT7UmwTq1xQifLlA5JdCVHCKSFKhaBJXtw4DYAWwC8pLK+CKoCut1rXg9Y6zSNIHMIVcY1W1urxy51poAkZDUXVKvgeV1TlVy/qlmmdPALevMT+jBEMMdVBFUsCkv24MDfAjhZBDVCdMfIdBPNR+GLUysmaJIC09yCp2KyMGOogcXYGo2tIrxu+I1LBxlPVfE9jpZqROOzIqhiUVjyDgAdIqgRojtFIc4gFcUWZgnk3Ljo6nI/F+t7lekmdjPnvAYVt/b26mk2HgI6COISjKQQbuXhfM16T/y6uIP2Snh9V7xQ6XJP8RxXEVSxKCz1QUlENI+IVhHRqq1btybtTvpxC0pxW+5UpNpe7DtqX2xswGQwG3FF8+ZZanSvWOG8wdixwwNcxozR961cNsyt2LYfu3cbj24FCMBGTEYWjH/BYuzGKKhtacF6T7q7jWAsL/r7jaLqTvgFIAUpNO7nj8pxgxBnkJUg6JK0okNaqNESpAssrjyrCmOofcjxTRiePGFBXiHLkdXnIK09c/6namrCkEFPJRDPRpH74HA9VLqrg863dbonXucSxxiqtFDFmsSSd0AENXrCCGTU4mrfX1fXgffrUOAHMZNLtjmqfQgxN1bVVIqVR2gbs4Xg2ZWs4qBzTezjlioR3VFH+YYV6iDHlTFUsYQseQdEUMMRpQDWeAL+gnyxSkytIvJ4VzHeaFqv3LdRBjlFIdrmvdXdl1WM3VrjZnKMIFi/f/n8UCYn69/PiuZ2AAAgAElEQVRxV5eRKF+xlFiyBweWA9gEYADAGwD+0Wt9EVQbfgKo+6Bxe+DGlEVnV77gfLyKCBUKHP/0FKfct4qZk2ompmH9Mr8LXj4GoQ4yIKkigioWhSXugI6JoNoIkpvXK/F8mAdukFaCz9QNIuZB3ZSFuuaS+1Y7VaLTfuPostYVVLPb1y+hQxDqIEevKiKoYlFY4g7omAiqDa8pMroPuzAP3KAtFa+SacUiFwrM/Rjp7leUomr9IVAMmavXTGQQt9+65+f2edAWZR1UkVFFBFUsCiNmrl1IcUhmzJjBq1atStqN9NDR4ZzDtlAwpg043VsiY7qInUzGeX0AKBa98666+WH6snhx9fbd3cCVV7rn0G1rA+/fb7jsfuTwEA0/77Y24/3AQJxHDU426zpFheFyrYiMqTBO9yifB7ZtC+aL1/dv/fpg+0wIIlrNzDOS9kOob1I/D1XwwGsOqe58VLfl+byzGFqToHslpu/pAS67zDK5tLL9vHneCen37wchZjEFqn9E7N/vKKZcsUTJ5TzFdBtc5tROnuz+XbnxxuD+xDmHWRDqkaSbyDrWUF2+ASMT7Zs93uVRdFt3DFVl/aB1R611P+OcDhOzRRIkFeT6Wcd6HT43y8pVzXO15mO2jr9GlbQ+rjnMNQbS5SsWgXl/CGQB3JC0k6Y1jKAGHHPU3kz3YaeyfhgxDJOIQcEGkNUTvBpXqGHAOP+ZM/W3sd4jh1SLe9DKs1Hk2ShyDxWMoCrLmHCjROPGhQiqWBTmvwLwMGCMtSZtDSOoAaMjUxFUmdIKMGbGJWVBbWvjV2d2OWcuitt057jaiwe4lLxbh4Lz76CkiorXUctVBFUsClMZQ30OwM+JaA4RfcK0mHqgm4OA+UdTkbY0SJ7XmCiDUAYwiCxGoR/zsVR9zJUZNz9/Bm7H3NqPjToFhbnR2grs2mWMRTMDPT3g3bsdV+2gDVi/HuiE4hh32C+OW0Fxc4zc4vPwJM2C0JioCOpYAL0AzgbwkYp9OE6nGh7dwKBwm4XD9tBcc/T56Kec72Y6BBE0BnAz5mMPcmhBCRkALVBI0G4yMID/3XslunBL/IFPAWEAOOggI1DKgqu/kyc7ixm5bBHmi+MlmgsXGsn5rXgl6xeERiHpJrKONUyXb63GUGPwU6VrtQz94B3XFIQex9iKcNmMlHzs6ooua5JpiuXmSoBrgglH39vb3X21d9XrfHGcum+9upFV5qemrEsY0uUrFoH5rwBMAvBTAFsAvAngJwAmJeFswwgqc2RRvrE+hzwiSkMlPnARiB1o1xLi2NMSmgJhBvZojB97+bZndJ73wr+W6joUeGPW+R4EsiBRvm6/4tyOoZJUJIVBUiKoYlGY/wrArwF8FkBLxS4F8OsknG0oQa0HXAQkDiHbldcXj5oIKmC0KDWKmPv5VQZ4NryzMfUhx7NR5ItRLT6BzjufDyZiXgn13UTTTzBTEV03HBFUsShMZQx1PDPfzsyDFbsDwPhI+52FdOIyxhb5mCMR2nt7MLHkkSCiFn64sX9/1TimF35+lZHBcnQiA+fgJAZwO+ZiOTqN+uejRh1ILLEVefcEDm7kcsDevfrjmt3d7sk33AqKn3++kQhk6dLhReCXLh1KEJKK6DpBiB4VQd1GRJcQUbZil8AIUhIaHYdMOKy5C6X1mbWzIun6kSYyKGMdOtCLsY6fE4DPYhmWZK7A93YZGaXM69NOe/AcTvQ+/3x+uJjNnQu4RAbbRcwag/bGXA+xzWadl69YYbx2dhrpB8tl49WabSuR6DpBiB8VQb0MwD8A2Ayj1NqnYHQBC42K+VSdMwcYNcp4QFcezvvaXVpH+XyV+O5GrubCxwAGUxu3a0AAOtCDQ/A29qLVcZ129ONyLEXL/uGtyhz349zsI+5naKYTtIqZKXJOWETMHrg7oeTRYnRroaq0MiVlodCgqAjqUcz8UWYez8yHMfMFAI6K2zEhJtzmDlo/tz5Ve3uBPXuAO+8E1q/HyFtudM8JW+nmYxDeyBYwD0vx12whltNwExQCUEJrXbRgW1HCfrS5+popu4iWm5gBxg+gOXOG31svkbOImH22ywZ45HcuuNxXlVamX5ewid93VRDSht8gK4BnVZbVwiQoKQDWsOB8nrnVFl1qD0xRidDUiRYNmvs3pEUZsBRn8FMZ4PVwuea6qRHdpsa43VNrfmWu3twzN7Bbebqurui+tzWMBIYEJYlFYO4fAKcDuBbARgDXWOxrAF5IwlkRVE1UxcwaXek1h7Cry3s+o9ucHr8C1ym3EujA3FrDoku/aEb87iaH+9Terh5d7HbfNIrNO92i2Sga0df2exp3pG6NI4FFUMWiMPcPgA8AuB7GuOn1FrsGwJQknBVB1URVxKwT7r1aM34PbXvrFxjeYvGYx1mzKTAhbbBFffqMiu1DC69Dwfv8R4/23o9X4gnz3ipMYNZqFMZdXLzGxctFUMWiMP8VgELSTpomgqqJaiIC669+t6eqS0L2Aw85v2xChYLWXM5mMeUfEm4J9Z3ml7rdWwWUE4dIC1VMrMpUgpJuJaJDzDdEdCgRPRRu5FaoCSoBIvboSqeAkdNPd592gcqPMq9i4YAR5KQxl7PWcNQ7dJtWYkM5HrlcrvJxsK0SHGafX2qiEzlbCQDqvISw/o0WlJmwHh1Gon0n4o7UlUhgoR7xU1wAz6ksq4VJC1UTp9ZmW9tQ961qjdSUlmxLqw2CjMLvMey7BGNMdx0KfGlr0Xs8VydXr1srt7XV/fsSdx7MGubZhLRQxSIw/xWA1QAmW94XIFG+4QnzsNDZ1mldne2jTgzfBFYGKmIXz75vQhevQ4FLIPf0heZ9VYnI1gkYq0XO3QQS54ugikVh/isA5wHYAODOivUA+FASzjaMoIaZEhB2OoHO9sV4WlnNYAPIxhZo5btfIuaZM52DxNraqu+1bg9E3IXJE0icL4IqFoWprQSMg1ED9SMAxiXlbMMIapiAC7/WhF8rVOfYEU91qUUkb71EC3uaWwCSjvmJpMp3wmvfcZFQ4nwRVLEojJjZc4yViAhAJ4B3MvMiIpoM4Ahmfibs+C0RnQfgRgBZALcy87e91p8xYwavWrUq7GHjxSywvGGDERS0eHF1BphMxnhM2CEy0sV54batlbY2Y52BgeH79trO6dhuhalTDKOGSfPjIJ8HRo82grjiJpczAtAAIzuWW3CTnULBSGkYB2H+N0JARKuZeUZsBxCaApUo35thJHmYXXm/C8D/C3tgIspW9jMLwDQAs4loWtj9Joo9bV9Pj/HenjItTHJwlXX27x8upoC/CNv3W6dp3sKIKVfMb1lstLUBO3fWRkyBoWoz1shuYChCOZ83fLISd6StJM4X6hgVQT2Vmf8JwF4AYOa3ALR5b6LEKQBeY+Y/M/N+AHcD+FgE+00OezJUwLlEVpgpAU7bhsXp2F5lvRIiTmEzhdMuyLpVcLTI54cVHsCYMdU/hOLGzPNrVodhBgYHAWZ037gN/zzmNqxHAWUQ+vIF55y7USLTZYR6xq9PGMDTMLpkn628H48Ips3AqFpzq+X9HAA/dFhvHoBVAFZNnjyZU41OdhevSEa/KMeogoW8oihTPFWm7sdJ3fLdRnnNcznjOCoJNxzQjg2KMjJXonzF6tT8VzDGT+8H8AaAxQD+CODC0AcGLnQQ1Ju8tkl9UFIUARWqT7KwD1zzQeX24AoZkGTmvU1cvFLkxwEzhdNMfm+9F17re5nf/GJNhdT6KicUmRslIqhiUZjaSsCxAP4JwBcAHBfJgY1x2Ycs778K4Kte26ReUKN4sKg+ycI80M3Wi5evCVWJicNSJ6i696SrK9xcYuv3U3EbrVS6CUXmRokIqlgU5v4B8N+V1ml7LAcGWgD8GcA7YIzJvgDgeK9tUi+ozOG7q1SfZEETLpiT+90egtnskO/2B7lbyS4Eb5HWQux2o60+RNWv16CGaGlkjRPZx4EIqlgU5hWUtBTG3NP1RPSfRHQBEUURjAQAYObBSov3IQCvAriHmV+Oav+JYQZ3lMvGq24Ah2qU4403Aq2t+v7t2WO8ukWSlkrG47CnB1i2zAgGMc/ljDNcp9IEDd5R2YYD7NfKKOyPPLAolgkcGzaE//5EhFZskETmCoKBn+ICGAXg0wB+CmAzgNsA/F0S6l8XLdSw6GYysrZmZs5UG28rFNSLV1ubJHVc0zRqK4Oivx4p6yJVbizLGKqYGJjZX1CHrQy8B8BzAEpJONsUgsocfHxMdcxTN5q0QpSFtdNoOt3CPVQwEuB7XHOtbuY6E6AqUtJVHRQRVLEozH8F4HAACwA8AWPM8zsATkzC2aYR1CDotpZUW6hEBx6OvRlJlM8A70Ubz0bRaFB6TGEqw6gOU/WZWVvWHuXrR52LVpoRQRWLwlzHUInociJ6GMCzAKYC+DIzv5OZv8LMz8fR/SyEwJygr0qppLYeMzB3LpDJ4ODyW/p+pRCumCplyzYlZPBj/COWo3PoknuMK5eQrT4WM1AsHkigUDVWWqlNikzGeO3uVs/CJQhCYrjm8iWi2wEsB/AbZo4viaYGdZHLNyk6OpwDjUaPNoqDu9xnZLPq4togmFdCNVCJbevuRg6XYyl+V+jE+r5xgF9xdSfc8uGawmnNuJXLAaNGOR8nzry6TYTk8hWiwLWFysyfZeZfpUVMG57ubmDcOKO1Q2T8rdP6cAvLHDHCXUwBQ0wzKhkoGwfdiGT7uu3ox7dpIYrndwcTU8C9R8EtfaXbcXp6qluzgiAkQnM9SdNKdzfw2c8Of2j29gKXXTbU3ef30LQmODdzwy5dCmzf7n/8GKt41JpyjWrNHMUbcOaKEPmOmY37ZL2f3d36ifGJpBtYENKC2+AqgBUAOpIe5LVawwYleQUU5fP+UxJiTCGYSsvnXSNoSwBzV1f8iRzM6x3V/trbnQuCe5nb8d2m30hQkyuQoCSxCMyrhXoHgF8R0UIiCpBBQFDGK6Cot9e7go1TsMollwx1Hff1VZfgqnd6e/GXbMHxo7coD5xxBkpoie/4ZoYDl8QFDCOQaRBZ9X3u3q1XaaZQMO63E07fJwlqEoTY8SwwTkTtAK4DcB6AO2FJEMPM34vdOxsNG5TkFlDkhVlwWWXb1lbgoIOM7t+xY4OP+6UFIqw5ez7e+T+3oM2Ws4gBkF8x9TBkMkNd5O3thhA6MIgsPoNluB2XYQT2R+uD3713ClTSWbcJkaAkIQr8xlAHAOwGMALAGJsJUbF4sX4aQbN1pDJdZmDAiPa9886h1IP1DDOOXXkLWh0SAFLl89iwjje7iCkAZFHCcnSij2L4VzHvvU5+QLfviQQ1CUJkeM1DPQ/A8wByAE5m5uuZ+eum1czDRsQeZAQAt9/uOp+xanlbm9GVm8moR+hu2OAcQVqvlGsVfhSMErLI5YCxrBAUpoNVMN0C0Zzy/7rl1ZWgJkGIDK+n8UIYdU//FzM3yFM4BbiNZXnBPPTQzOeN9729xqvqHNLJk/WTPzQQA8hiJ9pDJ9pXgQF0t8/D0qUAFTQSxLe1Gd3IbuTz1YJpT6YPOLc4nVqzTl3j1vF5QRD0SDoqSsdSGeWrGjnpVTLNjMxUqZkVJGrXjAqu14jfCKJp96GF+1Cj+q5dXcPvu1u+X3tRcLNcntd3xO+76Ffj1vpd9breTQYkylcsAkvcAR1LnaCqVtlQSVxv5sz125+uuFhFvqsr2qketTCzwHbI/ShPo9GduqIiRtYfM275e1W/I17oFvpugMLgUSGCKhaFJe6AjqVOUFUfSCotQ7Owdz4/vNViF2e3feXz3i1lnWo0Tr4lIabm9ajVjwBrgW+AOZMJtg8/nHo1VL4jfvvWLfTdAGXXokIEVSwKk0xJYXAbk7QvVxm7NAt79/Yakbh33ulcYNotsvPGG6vH0qypDOfMCR6QlFSuX/N6MNfmeH19xqt5je0ZpPJ5I6k9s/HqNCZ5/vnex3AbQ/eb+uRa3duCaqFvMyhuzhwjR3A+7x/UJAiCP0kruo6lroWadylnptNCdWv9ebVG/MZti0VjfC6qlptXCzVIKy7Nlsu53tdd+cLw6++2vVcLz207r+tIZHR7q9x3laxa0iqtAtJCFYvAEndAx1IlqMWi83hbW5veg86rOzPoQy5o8FFLS/U5+XUTu/2oaEArA7ynPW9cJ691vX4MBe2+VklBaX7XvERXxk0dEUEVi8ISd0DHQglq1HlMvcYynY4LOAekeImfX8vB7ZzCPLSt+zTHcz3WLyPZIKfYc/YGMa/goagjrXWFUHectUkQQRWLwhJ3QMcCC2oU3VxBphwE7YJTeWA6RexGMT3GOoXDr3Xa3s670B78WJpWM/HM58NNsbEGGtkDzfL5aLvjdYVQWqiOiKCKRWGJO6BjgQU17ENEJ0JWZc6oGdFrPniLRff92QXaTyzNfYZ9aCu2cpNoIcZ+zGKRF+SLvAXuVW1czZzm4/V9aW0dHsnt123uMa6rLYQyhuqICKpYFJa4AzoWSFBVxcoL1RafffxURZT8WpXmA1NV1M1zKhabanwzMps588Dl6yHF+269V0GmwDjdW/O7Y/3RFZUQShm3KkRQxaKwxB3QMW1BDdqdakd1TNI+fqoqxOZDzR4Q1Nrqnz3H75zqLZFDja1csQFk+Y72rmHaoj0+rHPN7T/m3ETOury9fSgaOJsdnpFJCIUIqlgUlsxBgQsBvAyjHNwM1e20BTVMwI/qfuymm/3GfLhG1U2rGtWpuj9FUYpL7OISUtO2Is/rUOASiNehwJe2FocuYdAfMlEkaTC/P17fCemqjQwRVLEoLJmDAscBOAbAI7EKalRTUnTGUJ2CjswWhtec07DRn+Zcxa6uoeNks0YXptP0nmx2eKCM03QZ675itJLL8h1o58EYo4gHQFWivQetvCBvSdUY9J57fV9UhVCly77Jg4miQgRVLApL9uBxC2qUEY32qE2vnK9u+w86H9VLRM3jFYvuAjBz5vCHszk9xn5O7e3V60TRZeyyj7LFnIWWuBSBoLrt3235FuS9vz9+aR7Nez16tPN3Q/XHnOq1FUIjgioWhSV7cAVBBTAPwCoAqyZPnsxaxBnRGDTYyW2sTLeF6vRg9mpNBknG7hVdCqi3Xh2SEqh0565DgddB87pEYGXAuEZh5my6/bjRGfdU/R4IoRFBFYvC4tsx8BsALznYxyzrxNtCZVaKaAwc9Bh1C1ilWzlIOS6nbVUF3EtQVY8LqHV920TNrwWrZAEKAhwQ1DD31+0cs1nPr4D1du5pV5hOI2OokSCCKhaFJXvwWgiqD6EasVG3gN2muti7dt2OrdOi0enKdcszqzrn1R4sVevqMbrTh8xo7TD312v/Lrf+0tbisACpJZkuHsy6DC3IdJdIEUEVi8KSPXgKBDV0IzOOOX0q+wwaxGR2V4YNgrIKi4JgrUNh6FS8LnpUqfls8zztwlSijPsPhcpc1FD3V7OFuiBfrMrO1Icc39HeJXNGa4AIqlgUlsxBgY8DeAPAPgBvAnhIZbs4BLVuU5t6tfL8xlKZg7Vw7RmeVHwxBQx0QIcf74o4OMtL7Nm99eca8OQ0/UgXzTFUt7HidSiE80NQQgRVLApL3AEdS2ULNSmCZFbymtJj5u/1y1Ps1GJTaFWuQ2G4i2GCs/y6mG1iaN/lbFS3BiP7AgRMxOAm7iWk/ZddYyCCKhaFJe6AjqVyDDWp7rggghk2kYVbCTGf3LV9yPFsFIfpsud5eQmm35Sl0aOrzpnIEFGzhToAhejkIF0UIb5Mu/LO1/xADVZz/9L9GwsiqGJRWOIO6Fhc9VADPafSkGQ8rgesakIDa2vOJfinDPAOjB4mqJ4tVPO87PvK5/0TTbjUc72jvUu/ekyQFmqY7o5ikQfahvs40GaL6E76+9bAiKCKRWGJO6BjqSownua+4iBCqzmtxbE159Fda7ZSXcdQ7RVYVMrHObVeHZaXMgGyPVl9URWtsAPyXvctzd+3BkAEVSwKS9wBHUuVoKY1mkm3JRNkWonTQ90r0UXFNmYLhpiqCLZucJIpgGHOwzR79K9qSzBO0Uvr961BEEEVi8IyEIIxebLe8rjp7gY6OoBLLgH6+4d/1t8PLFzovM28eUBvb/Dj5nLA+ecb+/FhUqkHZy6bB5RK/vtl1vdF99pns8NfCwUgnwfK5eHr9fcDc+ca18uLxYuN62EllzOWh2XsWOflSX3fBEGoQgQ1KHE+PHXo7gbGjTOEtKfHfb0NG4bW7+gAMhlDJOziq0OhACxdCqxYobafTCbc8bzYvt0QdiK19XM5YNkyQ7gHB43X9euN/ThRKhk/GpxE1bymc+YAo0YZokw0dH06O4df944Of3G273/XLufP+vr09iUIQnwk3UTWsVR1+TIPnzJidmOqjLlFFUykM5fUPE6Q7Ep2M7tAFafM1MScIpD9roUTfudjnZZkrmvvjlWpPhNl+UAJTgoNpMtXLAJL3AEdS52gMqs/LHUewCrH1BEyc/9RiZ8pplGIc1TmlvXIbn5jjn7nZc7F9Tt3lfqoqmOrKmPDEpwUChFUsSgscQd0LJWCqvKw1H0Ae6ErZNbWWFT5e73OO4TVoqC46hQW12tllm7TEe6wAUW6xxO0EUEVi8JkDDUs5tik1/KFC/3HDt32Y0dlX4AxRlgsGuOCnZ3GMtUAllwO+PznvceIVf3VQHH0MziqY9ydne5BQIDauVuvddgANqfx+qD7EgQhNppPUMMEhzih8rDUfQB74RV4ZJLPDwXDWHEJpFozswtvZAsog/BGtoDfzl0K3HyzsY9CoTrARsffJGltdQ4QUsEtOGn7dv9ztwt32AC2zs6hewFUB14lEQwnCEI1STeRdSx0l28c2WZU9qkbVOIWtOSXPD5AQNTjXcVgl0SlbFuSls3qJ7RQySnsFtzlVGJP5ThBkBSEkQPp8hWLwBJ3QMdCC2pcE+/9HnAqD2CVoCU3/0NURwl1ScImhIjLnLIuOUVjO2VjskYwe/3SEFFrKERQxaKwxB3QsdCCmmS2Gb/ctWEjZgMS6pLoBDnZ121pUdsun9dLhdjert5ydvPfPjXGes9ESBsSEVSxKKy5xlCTzG7U2WkECJXLxnjXwoVD47hXXhk+wUJAQl0SnevGPHw89vLLjfFNP7Zvr85c5EV/P7B/v7pPTphj3tZ7tn69sWzePGMcm9l4dUv2IAhC09FcgpqG7EZmuj/rQzmK1H8BA62ULolTIFd3t5Glx4ar9BUKw39QLFumdt6TJ+sLd1jcjucUYe2W1lEQhOYj6SayjkUyDzXpLrso52+aRatDBlp5XhKn7ujW1qpu1TLAW5Dnm+BQKk03SKtiuynHF6PIC/LVpc0iM50kG5KgvmGBdPmKRWCJO6BjqUzsoEtUFVHMB7lqYomgY4EaPwDWocDA8GLe6+Cwb69rkM9zGcQ9VBhWQ/XS1qJRbFvl+qleY7M4uuoPLCmh1rCIoIpFYYk7oGOpF1QVkYqyhWoey6vV5BbwpFqiTOMHQAmkpjVe16BQ8Nctr+2dRNItyle3dyKKaVdJ95AIjoigikVhiTugY3EJaiTPOJ2cvj4RvfYUfCWHZWZrznXqSpAUgU7qp7H9ALIHWqVmMXHHa+lVO5XIv2fV7Rrm8/ELVJgvSxzzoIVIEEEVi8ISd0DH4hDUyJ5xOt2BPonqy8CwLtPZKPLFKBpTQuzrt7UZY5puJ6A7tUXlAjmModptN+WMYuJuOJ1LRRSVLmU9tvSkyzi1iKCKRWGJO6BjcQhqZM+4IAErLq3LLchXLV6QV0jY7iQuYVuozP5jsG7zRL0uolvLOp9v3IacBDWlFhFUsSgscQd0LA5BjewZF0SZHdL3Dba08aWtxSox2ZV32b+fs37pCqNQrCAX0csnrs8GqC/SQk0tIqhiUVgi81CJ6AYiWkNEfyCinxLRIUn4AUSY6yHIHNfOTuC224YlPMjecRvOub2zKif96O0eCfa9nO3sBObPr06o3tYWPHG86vG9/HL7jAjo7q7KqdDZiWgLG0RdJEGFNMyDFgQhPpJQcQDnAmip/P0dAN9R2S7VY6jmzuJqVrl1kfrl8bWO1+pEuOqcS5CL6Fdz1Mn/sIXZw/gbFQ3Z9K5/IC1UsQgseQeAjwPoVlk31VG+cVIsVgcemdbVVb2ueTL5fHXwkIpwBBVI63GtyendtvPqgnZLUB9Fd6l0vQo2RFDFojBi5oTaxgZE9AsA/8nMRb91Z8yYwatWraqBVymjo8O5Dmo+D2zbNvTeTGvolxfYTANop7vbSKPnVnPVbTv7Puw+5HLOXcpu52UeC/Cv/0qkl+sXMLp5nb73QfYlNAREtJqZZyTth1DfxDaGSkS/IaKXHOxjlnUWAhgE4DqARUTziGgVEa3aunVrXO4mi994nluBcnsRbKdcs0447c+aY1hnOzs6+W69xg43bIi2MLvKNvVQNF0QhPSSVNMYwFwATwLIqW6T+kxJQQhToNzeRak65zRoAgeVLlHdiF+vxBQ+PvnOdXWjYeflCEGBdPmKRWBJRfmeB+ArAD7KzCHqljUAKi061ehQ1RbW+edXL/NrDapGo+q2/m680f3cHM67DEIZwHoU8Dleig8t69QP0O3sNLqg7aHUQaOcBUEQgMSifF8DsBHA8xVborJdQ7ZQVVt0KpFTqoXKnRJBeLUGdVL6hQ1ociq+XvlsY3Z4wnyJJRKiAtJCFYvAEndAxxpSUN2EzCv7kaIAKXX/moLnVAYuqCDqVHDRQBINCXEhgioWhSXugI41pKA6tei88vPqtAA1S68tyBe5lNFMI1jD8UiZ7SLEhQiqWBSW+LQZHRp22ow5XWXDBmOssa8P6O2tXs9rKonTlBbVaTQwxiazKKOEDDJw+E64TSlxm/qiMsVGE50ZOYKgg0ybEaIgkaAkwYY9z559OoyJ11QSp+Vm8E0+P7Qs43zLN4Xz6lsAAAkbSURBVGDysNcq3IKKdPwJicQSCYKQZkRQ04hXpGyQOZR79gz97dDK3I0c/gVGBO8vcT7KsOX99YrwrfGcTsccv4IgCClABDWNeE2T8frMKUGEW7KHbBZlENajgMuxFMvRidnoxmexbHiXLxEwd667cknCd0EQBIOkB3F1rCGDktxQjeS11id1Cg5yC0QiqtpkHQrO6/pF/aQ+GbIgeAMJShKLwCQoKc3Yg5UWL3ZvKboFB2WzQKlUvbwSNGQ9xCBrBiQJQoMgQUlCFEiXb1qx5tZlNl7nzXOv2+kWBFQqeXbJWsckMwXJcSsIghAUEdS0opNkHnAXPTMUViU0No7x0CQKeQuCICSACGpa0Z2O4iWGqqGxUc9L0W1lC4Ig1DEyhppWgiRM0BlzrQU1TPogCGGQMVQhCqSFmlaCdL+mbZJmDZM+CIIgJI0IalpphLRAUshbEIQmQgQ1zaStxamLJH0QBKGJEEEV4qMRWtmCIAiKtCTtgNDgdHaKgAqC0BRIC1UQBEEQIqC5BFWSDAiCIAgx0Txdvvbq1GaSAUC6JAVBEITQNE8LVTeVnyAIgiBo0DyC2oxJBqSLWxAEoWY0j6A2W5IByaMrCIJQU5pHUJstyYB0cQuCINSU5hHUZksy0Ixd3IIgCAmSSJQvEX0DwMcAlAFsAXApM/819gM3U5KByZOdK700ahe3IAhCwiTVQr2Bmd/DzCcC+CWA6xLyo3Fpti5uQRCEhElEUJl5p+VtO4D6KcpaLzRbF7cgCELCJFZgnIgWA/gMgB0APsjMW13WmwdgHgBMnjx5eo9TN6YgCEIIpMC4EAWxCSoR/QbAEQ4fLWTmn1vW+yqAkcx8vd8+Z8yYwatWrYrQS0EQBBFUIRpiC0pi5nMUV70LwH8D8BVUQRAEQUgriYyhEtEUy9uPAliThB+CIAiCEBVJJcf/NhEdA2PaTA+A+Qn5IQiCIAiRkIigMvMnkziuIAiCIMRF82RKEgRBEIQYEUEVBEEQhAhIbB5qEIhoK4wx16CMA7AtInfiQnyMjnrwsx58BOrDzzA+Fph5fJTOCM1HXQlqWIhoVdrnmomP0VEPftaDj0B9+FkPPgqNjXT5CoIgCEIEiKAKgiAIQgQ0m6AuTdoBBcTH6KgHP+vBR6A+/KwHH4UGpqnGUAVBEAQhLpqthSoIgiAIsSCCKgiCIAgR0FSCSkTfIKI/ENHzRPQrIpqQtE9OENENRLSm4utPieiQpH2yQ0QXEtHLRFQmolRNVSCi84joj0T0GhH9r6T9cYKIbiOiLUT0UtK+uEFERxHRSiJ6tXKvr0zaJyeIaCQRPUNEL1T8/HrSPgnNSVONoRLRQcy8s/L3PwOYxsypS8xPROcCeJiZB4noOwDAzF9J2K1hENFxMIob3ALgi8ycikK1RJQFsBbA3wF4A8DvAcxm5lcSdcwGEf0tgD4A/8HM70raHyeI6EgARzLzs0Q0BsBqABek8FoSgHZm7iOiVgC/BXAlMz+VsGtCk9FULVRTTCu0A0jlrwlm/hUzD1bePgVgUpL+OMHMrzLzH5P2w4FTALzGzH9m5v0A7gbwsYR9qoKZHwOwPWk/vGDmTcz8bOXvXQBeBTAxWa+qYYO+ytvWiqXyf1tobJpKUAGAiBYT0UYAnQCuS9ofBS4D8EDSTtQREwFstLx/AykUgXqDiDoAnATg6WQ9cYaIskT0PIAtAH7NzKn0U2hsGk5Qieg3RPSSg30MAJh5ITMfBaAbwBfS6mdlnYUABiu+ptLHFEIOy6S1EgIiGg3gJwCusvXypAZmLjHziTB6c04holR2owuNTVIFxmODmc9RXPUuAP8N4PoY3XHFz08imgvgwwBmckID3RrXMk28AeAoy/tJAP6akC91T2VM8icAupn5vqT98YOZ3yaiRwCcByC1AV9CY9JwLVQviGiK5e1HAaxJyhcviOg8AF8B8FFm7k/anzrj9wCmENE7iKgNwEUA7k/Yp7qkEuzz7wBeZebvJe2PG0Q03oyEJ6JRAM5BSv+3hcam2aJ8fwLgGBjRqT0A5jPzX5L1qhoieg3ACAC9lUVPpS0amYg+DuAmAOMBvA3geWb+ULJeGRDR+QB+ACAL4DZmXpywS1UQ0XIAZ8EoOfYmgOuZ+d8TdcoGEZ0J4HEAL8L4nwGAf2HmFcl5VQ0RvQfAMhj3OwPgHmZelKxXQjPSVIIqCIIgCHHRVF2+giAIghAXIqiCIAiCEAEiqIIgCIIQASKogiAIghABIqiCIAiCEAEiqELiVKqarCOisZX3h1beF2zrPUJEH7Itu4qIbg5wzAuIaFo4zwVBEIYQQRUSh5k3AvgRgG9XFn0bwFJm7rGtuhxGogYrF1WW63IBAC1BJaKGyywmCEJ0yDxUIRVUUtytBnAbgMsBnFSpFmNdJw8jA84kZt5XSdj+GIACMzMRfQnAP8BIivFTZr6+st1nAHwRRk7fP8AQ718C2FGxTwIYA2AJgByA1wFcxsxvVdLY/Q7AGQDuZ+Z/i+saCIJQ38gvbiEVMPNARRAfBHCuXUwr6/QS0TMw8rT+HEbr9D8rYnougCkwyrcRgPsrNUd7ASwEcAYzbyOiscy8nYjuB/BLZr4XAIjoDwAWMPOjRLQIRo7nqyqHPoSZPxDn+QuCUP9Il6+QJmYB2ATAq1KItdvX2t17bsWeA/AsgGNhCOzZAO5l5m0AwMxVNUiJ6GAYovloZdEyAH9rWeU/g5yMIAjNhQiqkAqI6EQAfwfgNABXE9GRLqv+DMBMIjoZwCizADaMVun/YeYTK3Z0JTcuIXz5tt0htxcEoQkQQRUSp1LV5Ecw6m1uAHADgO86rcvMfQAegTHWag1GegjAZZXanSCiiUR0GID/AfAPlfFXmJHEAHbBGDcFM+8A8BYRvb/y2RwAj0IQBEEDEVQhDVwOYAMz/7ry/mYAxxKR27jlcgAnALjbXMDMv4JR4/ZJInoRwL0AxjDzywAWA3iUiF4AYJYhuxvAl4joOSL6GwBzAdxQGUs9EYBUKxEEQQuJ8hUEQRCECJAWqiAIgiBEgAiqIAiCIESACKogCIIgRIAIqiAIgiBEgAiqIAiCIESACKogCIIgRIAIqiAIgiBEwP8PKJEMyivd7AIAAAAASUVORK5CYII=\n", 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" ] @@ -233,7 +280,20 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Step Simulation" + "## Step Function Simulation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Step Function $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n", + "\n", + "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n", + "\n", + "$$Y=\\textbf{I}(w^{T}X>0)+\\epsilon$$\n", + "\n", + "where $\\textbf{I}$ is the indicator function, that is $\\textbf{I}(z)$ is unity whenever $z$ is true, and $0$ otherwise." ] }, { @@ -253,7 +313,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -283,6 +343,17 @@ "## Quadratic Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Quadratic $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n", + "\n", + "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n", + "\n", + "$$Y=(w^{T}X)^{2}+0.5\\kappa \\epsilon$$" + ] + }, { "cell_type": "code", "execution_count": 13, @@ -300,7 +371,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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tAeDQoUM5H3zwQfP5fPrpp22HDh3aKu/RMKASkWP9+sW3PFtMnoy9Dz2ETb1744QI0Ls3Tjz0EDZNnoy9bh2jqqpqx/79+5vrcWfNmrV53rx53QcMGFA6f/78bo8++uiWRPfdvXv3kxUVFXWlpaWDx48ff9aQIUOOxNrm8ssvP7BkyZJO1vPRo0cf3rNnT97o0aMPA0BpaenRgQMHHrVKnnY33HDD7vHjx/e3d0pK1EUXXVR/3XXX7Rk2bNjZZWVlZ19//fV19upeAHj11Vc7lZaWDj777LNLX3zxxa4//elPdxYVFTXOmTNn44QJE84cMGBAaVlZ2aAPP/ywHQBs2bIlt23btlpcXBxXr6RATd82fPhw5Vi+RN4JbUMFgIICYO7cYLehishyVR1uX/b+++9vHDJkyG6v8hQEZWVlA1999dX13bt3P+l1Xtx0zz33nN65c+emqVOntnr/33///e5DhgwpCbcdS6hE5FhFhRE8i4sBEeMx6MGUEvfAAw9s3bBhQ9Idr/ymS5cuJ3/4wx/G/WOKvXyJKC4VFQygZBgzZkzMquEguu222/Yksh1LqERERC5gQCUiInIBAyoREZELGFCJiHzKi9lmEp2hhRhQiYh8K9nZZhKR6AwtxIBKROSO2bMLUVR0LnJyylBUdC5mz056+rZEZpuxS+cMLcSASkSUvNmzCzF1ajG2b8+HMX9bPqZOLXYjqCYy24xdumZoIQZUIqLkzZjRB6GDyR87loMZM5Kevs0+24x9+cqVKztMmjRpL2DMNrN8+fKO4ba3Zmjp3bt32BlaTjvttCZrhhb7dhdccMGR+fPnd582bVrRu+++275r165Nixcv7mDN0DJo0KDSZ555ptvmzZszbmCHRHFgByKiZO3YET6oRFoepzvvvHPnsGHDSidMmBD36D3JztDy/PPPn3bjjTee8aMf/WhnYWFh40UXXXTwpZde+jTefGQDllCJKDB8O7l5r17hp2mLtDxObs82k6oZWrIdAyoRBYI1MP+mTYDqqcnNfRFUp0/fhnbtWs6d2a5dE6ZPd2X6NsDd2WZSMUMLcbYZopSrqTEm4N682ZjmbOZMjoWbiJISI4iGKi4GNm5Mbt+uzDYze3YhZszogx078tGr1wlMn74Nkye7Nn0b+UO02WbYhkqUQqHTnVmlKoBBNV6+n9x88uS9DKDZjVW+lBDftmX5TFVVy7lDAeN5VZU3+QkyTm5OfseASnHzdVuWz/i+VBUgM2cak5nbFRQYy4n8gAGV4sZSl3MsVbnHg8nNm5qamiRle6fAMT8PTZFeZ0CluLHU5RxLVe6qqDA6IDU1GY8pbodeVVdXdxqDKgFGMK2rqzsNwKpI63jWKUlEPgfgKQC9YET8uar6sFf5Ief69Qvf25KlrtasL3z28g2exsbGW3bs2PHYjh07zgELH2TEqVWNjY23RFrBs9tmRKQ3gN6qukJEOgFYDuBKVV0TaRveNuMPoT1XAaPUleLqN6KUCXfbDFG8PPvVparbVXWF+fchAGsBJD3uJaWeB21ZRES+54uBHUSkBMBSAOeo6sGQ1yYBmAQA/fr1K9sUrq6RiCgJLKGSGzxvFxCRjgCeB3B7aDAFAFWdq6rDVXV4jx490p9BIiIiBzwNqCKSByOY1qjqC17mhYiIKBmeBVQREQB/ALBWVR/0Kh9ERERu8LKEOgrA9QDGiMh7ZrrUw/xExaH2iIgoGs/uQ1XVfwAIxA3THOCciIhi8bxTUhBwqD0iIoqFAdUBDrVHfsMmCCL/YUB1gAOck59wth8if2JAdcCLAc5ZAqFI2ARB5E8MqA6ke6g9lkAoGjZBEPkTA6pDqZg2KlIplCUQioZNEET+xIDqkWilUJZAKJp4myDYfECUHgyoKZZIKZQlEIomniYINh8QpQ8DagolUgrdtAk4fLj18lidoFgKyS5OmyDYfECUPr6Yvs2poE0wXlJiBMhQxcXGY7jXRIzga9etG/Dww5G/NDnhN0WSk9P68wQYn7OmpvTnx684fRu5gSXUFIrWFhquHSxcMAWAjh2jB0aWQigSPzcfsFaFMg0DagpF+zIL1w4WqbIgVmckdmKiSLy4h9oJtu1SJmJATaFYX2ah7WBWVXCoWKUJP5dCyFvpvofaqURqVcKVaFnKJV9R1cCksrIyDZrqatXiYlUR47G6Ovq6BQWqxm92IxUURN8m2naVlc6PTZROIi0/r1YSCb9+uM94Xp5qfn78/y/hAFimPviOYwp2Yqckn6mpMX6lb95slDBnznRWmgjd7tJLgSefZEcl8qdoHfY2bnS+fjiR9hENOyWRGxhQM1S8X1hE6RRvz/RIvZXDSaQHMwMquYFtqEnwc/tNJndU8vN1J2dite2GvseFhc73zb4D5JVcrzMQVKG/sK1eioA/qlT79QtfQg36l43frzs5V1ERfXQn+3uclwfk5wMnTpxaLy/PCMb2ZX7owUzZiyXUBPn93k+vbpdIdenRyXVnCTbYwr3HDQ1Ap04tS7RPPAE8/rj/ejBTFvO6V1Q8yU+9fOPtpeiFeHoYu3W8RHopxyPWdU9HHkKl+zr7PR/J8uJ/C+zly+RC8jwD8SQ/BdTiYg37T19c7HXOvJOOaxLrGOl+X7wI4H7Ohxu8+N9iQGVyI7HKN0F+HYHGS+noCBXruqe7M5Zfqv79ko9kWFX1mzYZVbh22f6/RcHAgJogv45A46V0jNgU67qne9Qov/Sm9ks+EmUfihAwyqRWUOX/FgUF70Ml1/hh1pt058Ev9/v6JR+J8jr/vA+V3MASagTsKRo/P5Ta481Dsu+zX6r+/ZKPRAW9hE0EgJ2SwsmkDh6ZIhU9WN16n73sXWs/drduRgpiL1+vO/mBnZKYXEieZyCelK6A6vU/N7WUqh84QX+fM+mHn9fnwoDK5EZiG2oYkcYNTWSMUEpeqtrXgv4+e93u6LZEJ4ZwA9tQyQ1sQw2D84v6S6ra14L+PmdCu6O9Dbuqygii1vzA7NVLQcOAGkbQO3hkmlQFvqC/z0H/QWC/VUb11LjM7ABIQcWAGoYfeqvSKakKfEF/n4P+gyATBqMgasHLBlwAjwPYBWCVk/UT7pSUKYOcZjG+heEF+bq4MmavSxcA7JTE5ELytFOSiHwZwGEAT6nqObHWT6hTUk0NcNNNLed4AoDSUmD16vj2RUSuSbpT1ZQpwKxZLZfl5ABPPRV3NQM7JZEbPK3yVdWlAPam9CC33dY6mALAmjVGPd/YsSk9PBGFl3CVdU0N0LFj62AKGD2abrnFtTwSxcP3bagiMklElonIsrq6uvh3sGdP9Nf//negT58WizhKUubge+lfCbVhjx0LTJwIHDkSeZ1jx1zPK5ETnt+HKiIlAP43ZVW+odNWRFNejprvvu75eLTkDj+MLUwuGTvW+PHrVJzfa6zyJTdkfkDt3j12KdXmMNqjE+pbLQ/qzfLZLNMGPshKNTVGiTReDKjkAd9X+Sbt4YfjWr0DjqIJgiPIb7E8SDfLkyETBj7IBAlXu1vVu/EqL49/GyIXeBpQRWQ+gLcBDBSRrSJys+sHqagAKiud58lM7dGAkxBcC+O/Pyg3y/uJ1+2XQR/4wAmvr3EsCQ3eMGWK0VQTTxWvpagIeP31hPNLlBSv79uJJyU1OH51deQb36KkJjNtLS1P/NgZxsmtf14Pdu6XPKRSEM4vrgkIKivj/v9skSorE84neB8qkwvJ8wzEk9yYbebNymptgGhTIv+weXlJHz/onH6J+2UmlyAPfBCLX65xNI4Hbygtjf//0UqlpUnnkwGVyY3keaekeCQ724y91+d7GIwvYA3i6AN8ShYPCuG0o0/QZ3IJgiBc45ifl8GDjXvCEyECzJvnSpdtdkoiN2R+pyQb+9ih52E1KlCNRgBx/6SwBoUYPNjlHPqf044+2dB+6bUgXOOogzfk5yceTKurjV8NvP+JfCSrAmrol/58VCAPir+hPP6gCkDXrMFe6ZqSjiB+7Wzi9Es86AO3B4Gfr7H1+b3+eqB9e6BbN+M36Jo2g3G4XlAxUYCGhvh3nJdnFMsZSMmPvK5zjicl24Yaqc0JUL0W1XoAHeJuW7U6LR3Pa59U3uz83NkknrxFar/M5HbNdPPjtYz0GWnIyYvrf6tVo2sKTw5sQ2VyIXmegXhSsgE13D96uMB6MoF/+BaBOMl/fL93NknmS9zPPxbIHaGf31dQ3vzDM6FgmkTvXacYUJncSFnVKQkwqqKqqozq35wc4OTJ1usUFwMbG/oAn32W1LFQXZ1Q1VQQOpskiqMXZb6cHOA3OgVTMKu501/cnf/atAGefDJtVbvslERuyKo2VMD4/9y40QhMTz4ZpQ1q2zYjqpWWJn6wiRONjhdx8lNnE7fbct0evcivbc3Z7IQKfoBZyMGpgVLiUloKNDaynZQCJ2pAFZE2IvJAujKTbo5mu1i92gisRUUAEugR3NBg7FzE8be9XzqbJDTKTZh92ANeYWH49eL9sVBTYwzTPHFicvkjl9TUNH/O2yCBIGqprs7aW9IoA8SqEwbwBsxB9L1ObgzskLTS0sTbggDVcmcjLvmhs0mybbnh2kvz843xMZJpQ43VFu6XtuasUF2t2qFD4v8PVopjcIZU/G+AbahMLqSYbagi8j8A+gP4M4DmSQhV9YXUhfnw3GhDdcWUKeEnN46Hizelp0qybbmR2ku7dTPmh9682SiZzpwZ32WItN9480dJ6pN4PwPrYyXl5XGNvZuqKfnYhkpucBJQnwizWFX1ptRkKTLfBFRLMqO82Pl05KVkOxClqnNVpP1a2MEphaZMAWbPjv4GRGFttRlFKC3YFncgTFWnNgZUckPMTkmq+t0wKe3B1Jes9tXq6uT249ORl5y05UbrFJSqzlXRtvfLwAYZx5oBZtashIKpmulvKEcOFCXYhvp6o8d9PDglH/larDphAH0B/AXALgA7ATwPoK8X9dNet6HGbLtJdraMBNqTUi3aOce6pzRV95xGakPt1o33s7oumUHrbekRVIZ9qdUg+TGk6h5tsA2VyYUUewXgNQDfBZBrphsBvOZFZr0MqHEFB5e+hLRLl7SfZzycfLmlqnOVHzptZSzbD8OkOuABzYMyuBUIU/UjjQGVyY0UewXgPSfL0pG8DKgJfSG4FVh9GlwdT81FweBWDQvQaqpDNwMhe/ky+TU5Gdhht4hMNO9JbSMiEwHsca/SORgSarux2liTGRzCsn+/0YaVl+ebGy39NAAFORO2zXvs2FPto8kqLzc+8ydOtFjs6J5vh+yDs2zc6OuO8pRtYkVcAP0ALABQB6Md9a8A+nkR/QNXQg3lZokVUC0qcuXcEv3Fn0ipg1W13rG/XxtR1Dy+btLVum3bBv6NBEuoTC6k2CsAo5wsS0cKTBuqE+3ba1JfYqEpwYwke17xBEgOjO+tP3aodC+IJvm58xsGVCY3UuwVgBVOlqUj+b6Xb7wqKyM3RKap1JrOmW38PotOxjLbRpMNolYgbmiTnzGB1MKAyuRGyo1UFSwiIwFcCKCHiEyzvdQZQBt3K56DwWqrsWarse6hS7gN59FHjQS4N0jEZ58ZjVSWyspTxwgjnff18R7CNKmpMWb2Vm2xONHxda29fCZFWDxvG9ssiSKI1ikpH0BHGLfKdLKlgwCuTn3W/MeNweIjsg8SIQkPLd7arFnG/nJzw2Y0nR2L2IkphWpqjJ5GIsaMASHBNGFt2kCqqyGq6NPEYEoUVawiLIBir4vRVvK6yjdSlaVVbelqLVh1tWq7dpEPmESV3UmIri2vbD5Muto12YbqMjdvc0n5B9rfwCpfJhdS7BWMgR262J53BfCqF5n1OqDGau5MWXCorna9rbW5Y0qbNvpmZXXaet6yl2+Systd/Ry0Sg5nQ8o0DKhMbiQng+OvVNWhsZalg9eD48ea5QRI08DsbdqkdjoVnw7Wn5XcmNnIiRht7cmqqTnV9yCRGYZSjYPjkxucDOzQJCLNrVwiUgzEP892Jgg3WHyotHSwOXnSuIE+VazB+kWMdjmfDCSRNQYPPnX9UxlMrUEYVFMeTFPW94DIR5wE1CoA/xCReSIyD8BSAHemNlv+ZB/tJZK0dbB5/fXWFXZFRe4fR9Xo5GIPsFP2m4M/AAAUc0lEQVSmuH+cBEWb7Sbaa75ijVRkJTd6e9sobL+Ai4pOfV7imIc0GVVVLecvBZDQTDNEvuekXhhAdwBfB3AZgO5e1U973YZq59sONtXVqh06hIba1CaP2t2ivQe+fX/cHi0rRht5E6AH0N7T8ZWDMOYz2IbK5EKKvYJx+9pEANPN5/0AjPAis34KqKoB6GBj68zk2sg4Pgq00QaK8HwQiVT2wI0RSI8gX69Ftevnnejn3fP3wgEGVCY3UuwVgFkAfgdgrfm8K4B/e5FZvwXUVHM1YKe6d2g8yaUxiKOVfNJWKvLTdS0tTesctE7369vaAhsGVCY3UuwVzGEGAay0LXvfi8x6EVC9KoWm/EvI6y//aMlhyTYtJVQ/BczQJNI836hdIp/ZWNskez39XpvDgMrkRoq9AvAvGEMNWoG1hz24JnVw4BIAHwFYD+DnsdZPd0D18pd1WqvJ/Bw0oqSmBJPX+U4qpeDD5+RzHoR20GQwoDK5kZzch1oB4NsAhgF4Esawg3ep6p8T7Qhl7rcNgFoAXwWwFcC/AVyrqhG7OKb7PtRI952m417TnBzjKyuUSGpvQQVg9OKdPTt8Bii9ioqAbdtSeggnn3Mv/xfSgfehkhti3jajqjUAfgrgFwC2A7gy2WBqGgFgvap+oqonADwD4AoX9usaLwdz93Tc20cfNaK2mgWRVNyOQ+GVlrYsBKY4mALOPufh7sEuKDCWE5EhYkAVkf8TkQoR6aCq61T1d6r6iKqudenYfQBssT3fai4LzcckEVkmIsvq6upcOrQzXgY1X32BbdvWurYvlQNLZIsuXVpfVw9GqHLyObffgy1iPM6d66/Rjoi8Fq2EOhfGvacbReRPInKliOS7eOxwU6q0qmNU1bmqOlxVh/fo0cPFw8fmZVDz/RdYuIElKiu9zpV/VVe3vl779qXt8NEGuXD6Oa+oMKp3m5qMR998Fon8IlYjK4D2MNpQ/wJgB4DHAXw12cZbACNhG2QfxuhLd0bbJpt6+WaUFAzu72WK2uGpfXuvr3YrTjodZfvnHOyUxORCim9l4AsAVgI4mfSBjXlWPwFwBoy5V98HMDjaNtl2H2qyAvMlmabRgxIJkC2Cpe3+WT9e20h5CsLACl5jQGVyI8VeAegJ4FYAb5kB8JcAznPl4MClMHr6bgBQFWv9bAmobnxZB+Fmej+xX/Nu3Yzkp2AZS7T3O9NveXEDAyqTGynyC8D3ALwBYBuA3wIY5XVmsyGguhUIM6FU4sdSYCi/5NHXwzAGAAMqkxsp8gvAEwDGAcjxOpNWyoaA6taXX9BLJUEoYfspj9Hebz/l068YUJncSBF7+arqd1X1b6qa6mEEfMEvU325de+rp/exuiAIU375KY/R3m/f9xgnyhBO5kPNeH6aANmtQOir+1gTEOkHxKZN/pnX1MuBP0LFer95ywtR6kUb2OFlESlJX1a846eShluBMEilknC1A9F+QHj1YyeUn2oBgvR+E2WsSHXBAL4FowduFYA8r+umVVPXhuq39ka/dHRJh0jte5WVrZf7rUMN2yYzB9iGyuRCitaG+iyAoQA6A1gmIneIyDQrpSHWp42fShqAv6rnUt22HKl24OWXjRJWJF5Uq4bK5lKhX/ocEPlJbozXGwAcAdAWQCcAGdlBaeZMoxrR/sUepPbGVLHalq3rYrUtA+4FjWhtpVVVQLduwJ49rV/3S+eqiorsCKB26fhcEAVRxOnbROQSAA8CWABghqrWh10xjVI5fVtNjfEFvnmz8WU9cya/HNIxZVekY1jy8ozS34kTp5YVFGRPSdCPMnEqN07fRm6IFlDfBDBZVdM//UUE6Z4PNdulY07W0NJOON26AR07Gj92CguNZXv38oePVzydqzdFGFDJDdHaUL/kp2BKqRfaLmYFr1BuVrfa2yEj2bvXKPnMmwccPWpUAavHtzdlM7/1OSDyC96HSgDC34t76JBR5WqXirZlqxNWpKBqfVH76fambBb0e5yJUoUBlQCED1YnTgCdO6evF2usL+pkBlKwSt8iQG6u8cjeqYnJ5t7NRNFEbEP1I7ahpo5f2sWidQ5LtDNMtHZadnAigG2o5A6WUAmAf9rFot2Dm2hVY7jSt4VVxkTkFgZUAhCMdrFEqxpjVQn7YZAIIgo+BlQCEJx2sURGkYpVymbvVCJyAwMqNfPTkIduClf6tvitFE5EwcWAShkv9F7XNm2MR7+WwpPFcXaJvMGASmmXyBd+skHCKn2rAo2NxmMmlcItfprblyjb8LYZSqtwt7DEunUlkW2yVSaOs5sOvG2G3MASKqVVIqMdcYQk55IZ/CIRrF4mOoUBldIqkS/8dAeJIEvn/cSsXiZqiQGV0iqRL3y/DDoRBDNnAvn5LZfl56emJzNrDohaYkCNgVVa7kpkAIkgDDqRDk4/i6HdIlLVTYI1B0QhVDUwqaysTNOpulq1oEDV+EoyUkGBsZwSV12tWlysKmI8OrmeiWyTSZx+FouLW65jpeJi9/OUzmOlGoBl6oPvOKZgJ/byjYI9JskvnH4W0znJQSb1vmYvX3IDq3yjYJUW+YXTz2I625uDMlwlUbowoEbBzjDeYvv1KU4/i+lub87U4SqJEsGAGgU7w3iHt2S05PSzyFIjkXfYhhpDtAmvKXXYft0aP4upwzZUcgMDKvlSOjvXEDGgkhtY5UuucbPN04/t12zTJaJoPAmoInKNiKwWkSYR4a/CDOB2m6ff2q/ZpktEsXhVQl0F4CoASz06PrnM7WHo/Na5hsPsEVEsuV4cVFXXAoCIeHF4SoFU3LNbUeGfTje8J5mIYvF9G6qITBKRZSKyrK6uzuvsUAR+bPN0U6afHxElL2UBVUReF5FVYdIV8exHVeeq6nBVHd6jR49UZZeS5Lc2T7e5cX7s1ESU2VJW5auqY1O1b/Ifq2o2U++TTPb8Qse9tTo12fdNRMHm6X2oIrIYwB2q6ujmUt6HSkHFgSr8jfehkhu8um3mGyKyFcBIAP8nIq96kQ+idGGnJqLM50lAVdW/qGpfVW2rqj1V9Wte5IMoXdipiSjz+b6XL1EmyPROW0TEgEqUFn4bqIKI3OfJwA5E2chPA1UQkftYQiUiInIBAyoREZELGFCJiIhcwIBKRETkAgZUIiIiFzCgEkXBAe2JyCneNkMUAQe0J6J4sIRKFEFV1algaqmvN5YTEYViQCWKgAPaE1E8GFCJIuCA9kQUDwZUogg4oD0RxSOrAyp7cKZfkK45B7QnoniIqnqdB8eGDx+uy5Ytc2VfoT04AaP0wS/M1OE1J78SkeWqOtzrfFCwZW1ALSkxboMIVVwMbNzoyiEoBK85+RUDKrkha6t82YMz/XjNiSiTZW1AZQ/O9OM1J6JMlrUBlT0404/XnIgyWdYGVPbgTD9ecyLKZFnbKYmIyMJOSeSGrC2hEhERuYkBlcingjQIBhExoBIB8F/wsgbB2LQJUD01dZzX+SKiyBhQKev5MXhx6jii4GFApaznx+DFQTCIgocBlbKeH4MXB8EgCh4GVMp6fgxeHASDKHgYUCnr+TF4cRAMouDJ9ToDRF6zglRVlVHN26+fEUy9Dl4VFd7ngYic8ySgisgDAC4DcALABgDfVdX9XuSFCGDwIqLkeVXl+xqAc1T1CwBqAdzpUT6IiIhc4UlAVdW/qWqj+fQdAH29yAcREZFb/NAp6SYACyO9KCKTRGSZiCyrq6tLY7aIiIicS1kbqoi8DqBXmJeqVPVFc50qAI0AIo5Jo6pzAcwFjNlmUpBVIiKipKUsoKrq2Givi8gNAL4OoFyDNIccERFRGF718r0EwM8AXKyq9bHWJyIi8juv2lAfAdAJwGsi8p6IzPYoH0RERK7wpISqqmd5cVwiIqJU8UMvXyIiosBjQKUW/DbRNhFRUHAsX2pmTbRtzQ1qTbQNcFg+IqJYWEKlZn6caJuIKCgYUKmZHyfaJiIKCgZUaubHibaJiIKCAZWa+XGibSKioGBApWYVFcDcuUBxMSBiPM6dyw5JREROsJcvtcCJtomIEsMSKhERkQsYUImIiFzAgEpEROQCBlQiIiIXMKASERG5gAGViIjIBaKqXufBMRGpA7Apwc27A9jtYnZ4bP8fn8fmsZ0qVtUebmaGsk+gAmoyRGSZqg7nsbPn+Dw2j02UTqzyJSIicgEDKhERkQuyKaDO5bGz7vg8No9NlDZZ04ZKRESUStlUQiUiIkoZBlQiIiIXZFRAFZFrRGS1iDSJSMTu8yJyiYh8JCLrReTntuVniMi/RORjEfmTiOTHcexCEXnN3PY1EekaZp2viMh7tnRMRK40X/ujiHxqe+08N49trnfStv8FaTzv80TkbfO9+UBEvm17Le7zjvT+2V5va57HevO8Smyv3Wku/0hEvub0POM49jQRWWOe599FpNj2Wtjr7+KxbxSROtsxbrG9doP5Hn0sIjek4NgP2Y5bKyL7ba8le96Pi8guEVkV4XURkd+YeftARIbZXkvqvInioqoZkwCcDWAggMUAhkdYpw2ADQDOBJAP4H0ApeZrzwKYYP49G0BlHMf+fwB+bv79cwC/jLF+IYC9AArM538EcHWC5+3o2AAOR1ie0vMGMABAf/PvIgDbAXRJ5LyjvX+2daYAmG3+PQHAn8y/S8312wI4w9xPG5eP/RXbe1ppHTva9Xfx2DcCeCTCZ+0T87Gr+XdXN48dsv6tAB5347zN7b8MYBiAVRFevxTAQgAC4AIA/3LjvJmY4k0ZVUJV1bWq+lGM1UYAWK+qn6jqCQDPALhCRATAGADPmes9CeDKOA5/hbmN022vBrBQVevjOIZbx26WjvNW1VpV/dj8+zMAuwAkOipN2PcvSp6eA1BunucVAJ5R1eOq+imA9eb+XDu2qi6yvafvAOgbx/6TOnYUXwPwmqruVdV9AF4DcEkKj30tgPlx7D8qVV0K48dnJFcAeEoN7wDoIiK9kfx5E8UlowKqQ30AbLE932ou6wZgv6o2hix3qqeqbgcA8/H0GOtPQOsvnZlmldVDItI2BcduJyLLROQdq6oZaT5vERkBo5SzwbY4nvOO9P6FXcc8rwMwztPJtske2+5mGCUnS7jr7/axv2ley+dE5HMJ5jvRY8Os4j4DwBu2xcmcdzL5S/a8ieKS63UG4iUirwPoFealKlV90ckuwizTKMsdHdvBce376Q3gXACv2hbfCWAHjGAzF8DPAMxw+dj9VPUzETkTwBsi8iGAg2HWS+V5zwNwg6o2mYujnne43cTKb5R1nGwbjePtRWQigOEALrYtbnX9VXVDuO0TPPZLAOar6nERmQyjlD4mnnwncWzLBADPqepJ27JkzjuZ/CV73kRxCVxAVdWxSe5iK4DP2Z73BfAZjEG1u4hIrlmqsZY7OraI7BSR3qq63Qwcu6Lk4VsA/qKqDbZ9bzf/PC4iTwC4w+1jm9WtUNVPRGQxgKEAnkcazltEOgP4PwB3mdVyjs47jEjvX7h1topILoDTYFQZOtk22WNDRMbC+LFxsaoet5ZHuP5OA0vMY6vqHtvT3wP4pW3b0SHbLnZ4XEfHtpkA4Ach+UrmvJPJX7LnTRSXbKzy/TeA/mL0bM2H8QWwQFUVwCIYbZsAcAMAJyVeywJzGyfbtmpjMoOR1aZ5JYCwPRoTPbaIdLWqU0WkO4BRANak47zN6/wXGO1cfw55Ld7zDvv+RcnT1QDeMM9zAYAJYvQCPgNAfwDvOjpLh8cWkaEA5gC4XFV32ZaHvf4uH7u37enlANaaf78KYJyZh64AxqFl7UjSxzaPPxBG55+3bcuSPW8nFgD4jtnb9wIAB8wfasmeN1F8vO4V5WYC8A0Yv0qPA9gJ4FVzeRGAl23rXQqgFsav5Crb8jNhfMGuB/BnAG3jOHY3AH8H8LH5WGguHw7gMdt6JQC2AcgJ2f4NAB/CCCjVADq6eWwAF5r7f998vDld5w1gIoAGAO/Z0nmJnne49w9GNfHl5t/tzPNYb57XmbZtq8ztPgIwPoHPWKxjv25+9qzzXBDr+rt47F8AWG0eYxGAQbZtbzKvx3oA33X72ObzuwHcH7KdG+c9H0bP8AYY/983A5gMYLL5ugD4nZm3D2Hr4Z/seTMxxZM49CAREZELsrHKl4iIyHUMqERERC5gQCUiInIBAyoREZELGFCJiIhcwIBKnhORz4kx40yh+byr+bw4ZL3FEjJDjIjcLiKPJnDMK0WkNLmcExGdwoBKnlPVLQBmAbjfXHQ/gLmquilk1fkwBhWwCzcmshNXwph9xjFz1CUiorB4Hyr5gojkAVgO4HEA3wMwVI2ZTezrdAOwDkBfNcarLQGwFECxqqqI/ATGsI5tYQzt+F/mdt+BMaShAvgARvD+XxiD5h8A8E0AnWBMXVcAY4CAm1R1nzlU3j9hjPCzQFX/J1XXgIiCjb+4yRdUtcEMiK8AGBcaTM119ojIuzCm4HoRp+Y6VREZB2MowREwRs5ZICJfBrAHxuhIo1R1t4gUqupeMSa6/l9VfQ4AROQDALeq6hIRmQHgvwDcbh66i6raB7knImqFVb7kJ+NhDDF3TpR17NW+9urecWZaCWAFgEEwAuwYGLOf7AYAVW01r6aInAYjaC4xFz0JY1Jry58SORkiyi4MqOQLInIegK8CuADA1JCB3u3+CmPC8GEA2qvqCmsXAH6hqueZ6SxV/YO5PNl2jSNJbk9EWYABlTxnzjQzC8DtqroZwAMAfhVuXVU9DGMKrsfRsjPSqwBuEpGO5j77iMjpMAbs/5bZ/gqrJzGAQzDaTaGqBwDsE5Evma9dD2AJiIjiwIBKfvA9AJtV9TXz+aMABolIpHbL+QCGAHjGWqCqfwPwNIC3zYnTnwPQSVVXA5gJYImIvA/gQXOTZwD8RERWisjnYUz39oDZlnoeok9yTkTUCnv5EhERuYAlVCIiIhcwoBIREbmAAZWIiMgFDKhEREQuYEAlIiJyAQMqERGRCxhQiYiIXPD/AQeyxBgaAevJAAAAAElFTkSuQmCC\n", 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" ] @@ -330,6 +401,17 @@ "## W-Shaped Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "W-Shape $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U \\sim \\mathcal{U}(-1,1)^{p}$,\n", + "\n", + "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n", + "\n", + "$$Y=4\\left[\\left((w^{T}X)^{2}-\\frac{1}{2}\\right)^{2}+w^{T}U/500\\right]+0.5\\kappa\\epsilon$$" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -347,7 +429,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -377,6 +459,20 @@ "## Spiral Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Spiral $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U \\sim \\mathcal{U}(0,5)$, $\\epsilon\\sim\\mathcal{N}(0,1)$,\n", + "

\n", + "

\n", + "
$X_{|d|}=U\\sin(\\pi U)\\cos^{d}(\\pi U)$ for $d=1,...,p-1$
\n", + "\n", + "$$X_{|p|}=U\\cos^{p}(\\pi U)$$\n", + "\n", + "$$Y=U\\sin(\\pi U)+0.4p\\epsilon$$" + ] + }, { "cell_type": "code", "execution_count": 17, @@ -394,7 +490,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -424,6 +520,17 @@ "## Uncorrelated Bernoulli Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Uncorrelated Bernoulli $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U \\sim \\mathcal{B}(0.5)$, $\\epsilon_{1}\\sim \\mathcal{N}(0,I_{p})$, $\\epsilon_{2}\\sim \\mathcal{N}(0,1)$,\n", + "\n", + "$$X \\sim \\mathcal{B}(0.5)^{p}+0.5\\epsilon_{1}$$\n", + "\n", + "$$Y=(2U-1)w^{T}X+0.5\\epsilon_{2}$$" + ] + }, { "cell_type": "code", "execution_count": 19, @@ -441,7 +548,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -471,6 +578,17 @@ "## Logarithmic Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Logarithmic $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $\\epsilon\\sim\\mathcal{N}(0,I_{p})$,\n", + "\n", + "$$X \\sim \\mathcal{N}(0,I_{p})$$\n", + "

\n", + "
$Y_{|d|}=2\\log _{2}{(|X_{|d|}|)}+3\\kappa\\epsilon_{|d|}$ for $d=1,...,p$
" + ] + }, { "cell_type": "code", "execution_count": 21, @@ -488,7 +606,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -518,6 +636,17 @@ "## Fourth-Root Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fourth-Root $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$:\n", + "\n", + "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n", + "\n", + "$$Y=|w^{T}X|^{\\frac{1}{4}}+\\frac{\\kappa}{4}\\epsilon$$" + ] + }, { "cell_type": "code", "execution_count": 23, @@ -535,7 +664,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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mz58/rK2tLVCHoWS2bdtWA3DooYf2bNmypeaee+5J2ts33tFHH71j6dKle3rITpo0aev8+fMP/uAHP7i1sbGxZ9OmTf1ef/31ARMnTtyR+NpBgwb1xu5f5uuMM87Yeu+99w557733at59992ae++9d+hHP/rR9+L3Wbp0aX1TU9Pur3zlK29Pmzbt7WeeeaZh0qRJ7y9evHjwiy++2B/gvffeq3n++ef3nM8bb7zRf8KECfuVPR0FVREpWStXZre+mGbM4J3rr6f7sMPYZQaHHcau66+ne8aMjBOLBDZ79ux1mzdv3tPCeOONN6687bbbRowdO7b1jjvuGD537tyMNcJURowY0dve3r6htbV1/NSpU486/vjj38/0mnPOOWfLo48+uqeZddKkSVs3btxYN2nSpK0Ara2t248++ujtsRpovEsuueTtqVOnjonvqJSr008/fduFF1648cQTTzxm4sSJx1x00UUbTjvttO3x+9x///0HtLa2jj/mmGNaf/e73w39p3/6p7caGxt75s+fv+L8888/cuzYsa0TJ04c98ILLwwAePPNN/v179/fNTc3Z9VTKVC1uZRo7F+Rwuvq8mqHK1fC6NFw3XWFaX5tafGafBM1N8OKFeHmZWZPO+fa4tc999xzK44//vhAza3VauLEiUfff//9y0aMGNFb7LKE6V/+5V8OPvDAA/uuuuqq/T7/5557bsTxxx/fkux1qqmKSFqx+5rd3eDc3vuamToMhdHB6LrroCGh72VDg7deSsMPfvCDVcuXL8+7M1apGTJkSO+XvvSlrL9QKaiKSFq53NfMNRAnam+HBQu8mqmZ93PBgtLrpFTNzjjjjPdPPvnk7Zn3LC9XXnnlxrq6rDr+AgqqIpJBLvc1w+xg1N7uNfX29Xk/FVCllFV9UC2XZ+BEimX06OzWQ3l1MBIJU1UH1bCaqEQqWS73NXMJxCKVoKqDajk9AydSLLnc11QHo/AUY5aaXGd2kSoPqmqiEgkm2/ua6mAUnnxnqclFrjO7SJUHVTVRiUSnKjsYzZs3jMbGY6mpmUhj47HMm5f31G+5zFITr5Azu0iVB1U1UYlIaObNG8ZVVzWzdm093txv9Vx1VXMYgTWXWWriFWpmF6nyoKomKhEJzZw5TSQOQL9jRw1z5uQ99Vsus9TEK+TMLtWuqoMqVGkTlUjI9GgasG5d8sCSan2Wrr766rduv/32Ee+//37W1+18Z3Zpamrademllx7x4x//eLhzjtNPP/3dV155Zckrr7yyZPny5S/dddddSQaTrE5VH1RFJD96NM136KHJp3hLtT5LYc9SE9XMLtVOQVVE8qJH03zXXLOaAQP2nXtzwIA+rrkmlKnfINxZaqKY2UU0S42I5KmmxquhJjLzbquUi1BmqZk3bxhz5jSxbl09hx66i2uuWc2MGaFN/SalId0sNQV77klEKtPo0cmnZ6vKR9NmzHhHQbS6Rdb8a2Y3m9l6M3sxxfZ2M3veT0+Y2fFRlUVEoqNH00T2ivKe6q3AWWm2vwF8xDl3HPAtYEGEZRGRiOjRNJG9Imv+dc4tMrOWNNufiFt8EhiVal8RKW3t7RUbRPv6+vqspqamvDqfSGT6+voMSNlboFR6/34BuC/VRjObbmaLzWzxhg0bClgsEalyL27YsOEg/0IqVa6vr882bNhwEJD0tiaUQEclM/soXlA9PdU+zrkF+M3DbW1t+sYoIgXR09Nz+bp1625at27dByidSogUTx/wYk9Pz+WpdihqUDWz44CbgKnOuY3FLIuISKKJEyeuB84pdjmkfBTtm5eZjQZ+DVzknFtarHKISPnQcIhS6iKrqZrZHcAkYISZrQK+CdQBOOfmAdcAw4G5ZgbQk/jgtYhITGw4xNjoTbHhEKFiO0lJGdKISiJSFlpakg8y0dzsTYaRr2QjKolkSzfeRaQsrFyZ3XqRYlBQFZGykGrYw6ocDlFKloKqiARWzI5CGg5RyoGCqogEUux5UzUcopQDdVQSkUCi7ihUbOqoJGFQTVVEAlFHIZHMFFRFJBB1FBLJTEFVRAJRRyGRzBRUE2gYtPzpPaxM6igkklnVBdV0F/xi926sBHoPK1t7u9cpqa/P+6mAKrKvqgqqmS74s2fvHVc0Zts2b70Eo/ew/BSqZUEtGFINquqRmkyPBNTUeME2kZn3zVwy03tYXhIHqQfvPmnYzbqFyicfeqRGwlBVNdVMjwSod2P+9B6Wl6hbFmK102nT1IIh1aGqguqwYcnXxy746t2YP72H5SVZy0269dmIv92Sip5xlUpTNUG1qwvefXf/9fX1ey/4xezdWCn3m9RDtLzU1ma3PhvJasGJ1IIhlaZq7qmmup86fDi8/Xb+5cpHOdxvkspklnpbvpeGVPfXY0rtb1z3VCUMVVNTTdXM9M47hS1HMuoxK8XS3Jzd+mykq4UOH15aAVUkLFUTVEu5A43GVJViifIe+HXXpa4JDx6sgCqVqWqCail3oCnlgC+VLcp74O3tqZt/9YVRKlXVBNVS7kBTygFfKl+UoySlakbWF0apVFUTVKF0h1gr5YAvko+ovzBWSq95qRz9il0A8bS3K4hK5Yn9Tc+e7TX5jh7tBdQw/tYTe83Hhh2Nz1ek0KqqpioSJdWakouqhUi95qUURRZUzexmM1tvZi+m2G5m9h9mtszMnjezE6MqCwBDh3ptq/EpsV0qR7qYimbnKbyVK2EFTfRh+6Sl3XV646Vooqyp3gqclWb7VGCMn6YDN0ZWkqFDYfPm/ddv375vkJ0yJetD62IqoFpTQc2cCWb0OmM0azDYJ9XT4w02rH9CKYLIgqpzbhGQbmiFTwC/cJ4ngSFmdlgkhUkWUJN58MGsAmxXF1xyiS6momeNoxDfArS6pgkX+9+80fv+HQuiKemfUIqgmPdUm4A345ZX+ev2Y2bTzWyxmS3esGFDQQq3T4AdP36/zbEaam9v8pfrYlpd9KxxuLq64Lhp43mj26uRNro16QNoMvonlCIoZlBN9j+S9FFx59wC51ybc65t5MiRERcriSVLvOA6cOCeJqVMg4XrYlpd9KxxSKZMATMunGZ8gCX7NOtmTf+EUgTFDKqrgMPjlkcBayLJaciQcI6zY4d3r8aMxd1DU+6mi2n10bPGeWhq2tsq9OCDQB6BNJ7+CaUIihlUFwIX+72ATwG2OOfWRpLTpk3hBVbfcDbv6W24nhFcgFeDra3VxbRalergIkEUvAd7VxcMGOAF0jUhf5c2g87O8voApGJE+UjNHcD/Akeb2Soz+4KZzTCzGf4u9wKvA8uAnwIzoyoL4AVW56CjI5TDxTdLjWQjXUyjD6P76Ckl9b+sx30qU5ifa0F7sI8f7wW9adNg587wj9/Z6X2rKaV/QqkuzrmyShMnTnSh6ehwzruORJNaW8Mraw46O51raNi3SA0N3nopX2F/rs3Nyf98m5tDLPTkySX/PwYsdiVwjVMq71TdIyrNnbvvv2hItdg9Yh2ccnj+NQxRPzupWnBxhP25RvI4kP8saeK90lA0Nu79n33ppfCOKxKC6g6qiWJBdvLkcI+b5fOvYYny2UkNelE8YX+uoT4OFAumN4Y8lsuQIXsD6erV4R5bJEQKqsk88EB0tddYgG1K+kjufvKpDUb57GS62pJqsNEK+3PN+3Gg2H3SsINpa+ve/8NNm8I7rkiUit3+nG0K9Z5qtlpbXWj3ggLcF8r33lmU91TNUp+O7uNGK4rPtbPTu4dq5v1MdqzEfVa1RnCftF8/91hHZ8ayRAHdU1UKIRW9ANmmogbVeFEE2MbGfbIIowNJkItlLlKVrbY2/zJXmig+g6g+13T5NTQ4dwGd7n36uz5wfRH87Rezc52CqlIYqegFyDYVOqgGung1NrpQg2ttrXOdnSlrg2YFfQuSSnXxS3VKpVDmYqiUHti3DuoIP5AmaaEpSE/kFBRUlcJIRS9AtqmQQTWnC2KINdg+cCtozPkCE3VtJtnxi3lRLEVl/374f8+hBdP+/dP+IRbzi6SCqlIYqegFyDYVMqjmdUEM6bm8WO1gN+YuoDNwLadYNaRKqZmFpZRbG1Lq7HSuvj6Uv989JxvwD0A1VaVyT0UvQLapkEE11AvikCHJD5ZlgN1ZNzBQdsW8OBX6fl+U8j2XsqqphtlPoK4upyLonqpSuaeiFyDbVDY11WQ6O73mrzAuWh0dabMqyxpSiQnjAl8WNfewO93lOcpRsb6UKagqhZGKXoBsUyncU+3oCOGfvrPTRXkRK6saUokK6z0s2Zp7WMF0yJBQilPs90lBVSmMVPQCZJuK3fu3oyPkmkeYtYS4QpRFDanEVWxtP8ze6pMnh1KkUvh7VVBVCiMVvQDZpmI/pxpZDTDMziH+ha7Y3/zLXcXV9sMa1H7QoND/mErhvVZQVQojaZjCLEU2nm57uzcVlnPe8Gz58IdCbH98ZtnO71kK8h6+r1TEhhHMd1D72DylW7eG/scU5TjVIoWkoJqlKMfT3eOll7zgmu/A/jfe6F0Ihw4Np1xVpr3dm3C+udl7G5uby2wC+ilTvIIvWZLfcWKzwkQ4T2lB/q9ECkBBNUsFrb3EBvYfMiSvw7jNm+kz0wD3OWhvp/xq+7GZYvKpmQ4cuLcVtgCzwlRMq4BUPQXVLBWl9rJpk3dxGzgwp5ebn3qd8Xq3sfXimVUVWKtm1pxYM28+M8UMHuw18SZOQRSxsm8VEPGZc67YZchKW1ubW7x4cbGLUXxTpuRcE3HAGmukqa/y56WMzfsaHyMaGirsgt3VBRdd5H3xylW/fnDrrRX0pmTPzJ52zrUVuxxS3lRTLXEpa1kPPODVKGprsz6mAY1uDdTXh1jS0pRu3teKMHQoTJuWe0CNzVm6e3dVB1SRsCiolrBYLau727vudXd7y3sCa3s79PTkdEE18C6kscmlA06aXm4qtldprBPS5s25H6Oz0+sUJyKhSRtUzazWzH5QqMJUgjDv32VVy8q3t/CaNd5Fevz43I9RgiquV2lXV/6dkDo7vb8X1UxFQpc2qDrneoGJZmYFKk9JyTZAZqxZZinrWlast3BnZ24Zgvf4RWI3zDJWMb1KYz16p03L7fX+M6ZdnY6W2e2V32lLpFgyjQ4B/DuwELgI+FQsBRlZAjgLeBVYBnwjyfbRwMPAs8DzwNmZjlmoEZVyGTYt7FFh8j5evqM0hTSma7JiFXKkp2KMLBVqnvkMKxj3GZbCUIClDI2opBRCyrwD3JIk3RzgdbXAcuBIoB54DmhN2GcB0OH/3gqsyHTcQgXVXAJa2GPFhnoRrKtLXrgshj0MQ6Vd2JMFz9DOMd9JFxJmMiqFoQBLmYKqUhgpugPDqcD9cctXA1cn7DMf+Hrc/k9kOm6hgmouATKKi1bJ1HjynM4rppIu7KmC5/DhIZxjPvPvppgWsGInCAiJgqpSGClj718zG2VmvzGz9Wb2lpn9ysxGBWhZbgLejFte5a+Ldy0wzcxWAfcCV6Qow3QzW2xmizds2BAg6/zl0sEl2f07M+/eaq73r0Id0Wf1au86WpNDp+8lS0IZ7rCSeuOm6ki2cWPy/QOdY+zeaS69emOPx8ydm3RzxXXaEilBQa6ut+DdU23EC4r3+OsySda5ySUsXwDc6pwbBZwN3GZm+5XJObfAOdfmnGsbOXJkgKzzl0sHl/hRYcC7Njr/jPPttBSq3l7o6Mj+dZs3eyc1ZUrOWVfShT3bLwIZz3HmzNxHQwrweEzFdNoSKWWZqrLAX4OsS7JPkObfl4DD45ZfBw5Od9xCT1Kea9Nr2TRz5jqfa46dmCrpnmqqz3j48NTnmPRvKp85dVM09aai6QBTQ82/SiGkzDvAA8A0vI5Htf7vDwZ4XT8/SB7B3o5K4xP2uQ+41P/9GGAN/tCJqVKx51MNqlj3r3K+aOZ6YW9sLFwZS0y6LwhBOzA9T6vrK+CXGklNQVUpjJR5B++xl4XABmA98FtgdKCDe026S/F6Ac/2180BzvF/bwUe9wPuX4EzMx2zXIJqMWqqedcCOzqSFzpIqlLZfEGI/5u4gE63G8stoBZYpXwJykRBVSmMlHkHOC3IukKlcgmqxWjmDC2Q5xJca2pCOYdKvoDHWi9W0JhbMA3x0aa7+uaAAAAa20lEQVSgKqm5PhMFVaUwUuYd4Jkg6wqVyiWoOlf4ABF6k3O2j+BkeX8vUaVfwJubnXufuuwDahGCaXyZC93iUiwKqkphpJRTv5nZqcCHgC8D18dtOhD4pHPu+DT9nyKjqd9Sa2nxehknam72HsfJSS49UltbcxqoPZLyl5Beq6WGvqTd4pOaPNkberKIamq8MJrIzHvMq5Jo6jcJQ7pHauqBwXgdjg6IS+8C50VfNMlWJI9MzJ2b/eM3S5bQU1uf9cQClfQM637MqM0moDY2Fj2gQmU9AiVSEJmqskBzsavT8amcmn+LIdIm5yx6CPeB24W5C+gM3IxbkU2NkycHfs9Kobk3UaU3ycdDzb9KIaTMO8CfgCFxy0OJe/600ElBtQTU1LhsgusKGgMFx4q7gA8cGPh92pNK8GQrufNYPAVVpTBSvwCV2RHOuT1jpjnnNpnZwaFXmaV89PYGvtdqwGjW8D71DF65K+2+sSEYZ8/2mnxHj/aarsty2s/6em8S+Gy45P0biq29vUw/A5EiCDJMYZ+Z7bmDYmbNsN9wg1Jt5s4NPCm6AQPZzTZXn3HfUMc6LpZsA+rkySUbUEUkO0GC6mzgf8zsNjO7DViEN+SgVLsHHgjcicmA/uyuqAnQk2poyC6gdnaWRIckEQlHxqDqnPsDcCLwS+AuYKJz7v6oCyZlYu5cr5bV2JhxVwPYvh3Gj4+8WLnq6iLrXst7NDV55xdE7FmVsqyKi0gqQaZ+M+As4ETn3D1Ag5mdFHnJpLysXh0osAK4JUvYZbW5Ba4IdXV5Mwl1d3vxLquZhcxgzZpgGdXVefelRaTiBGn+nYs348wF/vJ7wE8iK5GUnMC1t9WrvYCRgQF19LHTWUlNiZdqftTZs9O8qKvLC6hBDRwIu9J32BKR8hUkqJ7snPsHYAd4vX/xBoaQKpB17W3XLhgyJONxDW9Ukb8yPnPgKpCsB5+YOROmTQueweTJ+0XtvJqbRaTkBAmqu82sFr/Hr5mNBCpsgLLyF9XFOafa26ZNgTowGXAcS1hBU0mMmpTV6EFdXcGHbxw40PtGktAhKa/m5gqgLxRSkTI9yAq04039tgq4DngV+EyxHqyt5sEfUj2EH+WgCXkP0h9gFKY+cKss+3lZw5bV+xh0MIc0881W5AhSAZXiQB9o8AelEFLKAfXjmdk4YDJe5eJB59zLUQX5TKp1QP1YrSa+1tjQAAsWeLXGqAaiD2WQ+9rajKOvO8CGDPFquUXU1RVg8ImmpuCdktL8f1XTYPWJSnHyBA2oL2FI2fxrZv9tZu1mNsg594pz7ifOuR8XM6CWmzCbt9I1w0Y5EH0og/QH6OlqAJs3ewMnFFHGwSdCCqhQ3YPVV/TkCVLV0t1TXQB8DFhhZr80s3PNTB2UAsr3flliQE72rR721qiSCePi3N7u1Yabm70aVHOzt5z145XOeVPCZbJ7txe4SlHQgNraGmiEpEhmFSoT1fyFQipcpvZhYCDwOeA3wDrgZuD/FKu9ulTuqWYaZDyf+2XJ7jelurcZy7vU7k+lFHTi8zwnPA9d0NlmBg7M6rDVMlh9olL8m0X3VJVCSNntDMcBzwK9xSpwKQTVIBeEfDr4pArIiceMzzNdJ6aSu2jX1iY/wVKesSVoxyQJrNT+NhVUlcJImXeAQ4ArgMeB14HvAScUq8ClEFSD1ELzqammCsix1we9CJVibWBPwYIEqH79ilK0/d7j1lbXV25fAiRrCqpKYaTUG+CLwEPAauA/gdOKXVjnSiOoBqmF5hPQwnrUoqQf2Zg8OVigSvNIStiSfWZbGBisnEVori61ml65U1BVCiOl3gC3AGcCNcUuZHwqhaAaNFhlc9GL33f4cOfq6/c9di41zLyfMY1QZ6dzfyJgYM3yPmWuEj/X9Qwp6YBakq0QZUxBVSmMVPQCZJuKEVQTg2NHR7gXtGQXyLo6L7jmUwsp5ZpqrGx/JWDTagFqrPFfQv4QIOD3gdeBqQhK+bMtVwqqSmGkaA/uzW7zKrAM+EaKfT4LLAFeAm7PdMxCB9VUNYKOjvCa3qKo+aYre6rX5VqzzuX84wNY4MCap6A9ti+gM1BAfbS+OAHVudJuhXCuPJumFVSVwkipN8C9QEvOB4ZaYDlwJN4A/M8BrQn7jPF7Ew/1lw/OdNxCB9VC1AiivEcb9OKWzfHDaHpMfF8DBdY8aoVByhzbpzdAQH2e1qIGilKuqZZr07SCqlIYKfUGrwa5FJgN1GV9YG+6uPvjlq8Grk7Y5/vA5dkct9BBtRA1gqh7E4dVhjDLkuzC201j5sCa45U5aJlXtWZu9u0BN3x4TsUITSkHrlIO+OkoqCqFkVKOqOScuwuYABwILDazr5rZrFhKN6CErwl4M255lb8u3lhgrJk9bmZPmtlZyQ5kZtPNbLGZLd6wYUOArMNTiJFfgoysE/WwbtkcP4yytLfDJZfsOxVpM6u9qZDSueyy4JnECVrmpiUPkm52VAdcRCfvvJNTMUIT2khXEdAQhFLNMk39tht4H+gPHJCQMkl2bUq8ZvbDawKehDcJ+k1mtt9knM65Bc65Nudc28iRIwNkHZ5CDCUX5AIZdXDP5vhhleXee706TLy5dKQPrLt25TSIcqAy19amPYYDfkIHd9BeEsPpZRynuEg0BKFUtVRVWLxORkuA7wIN2VaBCdb8Ow+4NG75QeCD6Y5bCr1/i9HEFnVzX6HvqTqXuml9BxlGXMqh7T1jmTs60ucJrhdKqpm1VJVy03Q6qPlXKYSUegM8BozP+cBeLfR14Aj2dlQan7DPWcDP/d9H4DUXD0933FJ4TrVYog7uhez961zqe29XDA8w4lIOz66mLXOG/PrAXUhn2fRkLbZS+CKaLQVVpTBStAeHs/E6Oy0HZvvr5gDn+L8b8EO/RvwCcH6mY1ZzUK00aWs0QQawTzLoQk4X8wATqRdyZCcpDgVVpTBSoEnKS0m1TlJeqdJOCm7pugz54v5+003knvZ+Y5b5SGXSJOUShkwdlUQilbazTUdH5gPEdVpKN5F7XoKUQ0QEVFOVEtfQANu3p95u5kVkvAndk/05x+2yv9raNBvxAurcucHLK2VLNVUJg2qqUtoSq56JnIOZM4EcHuUYPz59QAUFVBHJioKqlL8bbwRyeKZ4yZL0x508Of+yiUhVUVCV0hfknubMmVmNMvRO0/jMozc98EAupRWRKqZ7qlIemppgzZrU29PeON1XVxdcOM3SDkdIYyOsXp1VEaW86Z6qhEE1VSkPmQJcFl8On7oywDCHCqgikgMFVSkfmZ4nDTgm8Hc3Xpa+lqpHaEQkRwqqUj5mzEi//corAx1mILvS76AevyKSIwVVKR9z56bvkbtxY+Zj+I/fiIhEQUFVykumHrmZguaCBembfvUYjYjkQUFVctLVBS0t3ihGLS05TXEajfnz02/v7U29CWhZ9kDpnIuIlB0FVclabOD67m6v0213t7dcsGA0fHjqbX19qQuSphbrgIvoLPy5iEhFUVCVrGUzcH0kNdobbki/PVWHpXnzkq52wB+ZzB14o0SEMgi/iFQlBVVKuCmzRK1cGWx9ZDXa9vbcOiyleZb1LPa9V5vqHEVE0qn6oFr0pswyFHTg+simYoPIhxBMOQh/xPQFT6S8VX1QjfTCX6GCDlwftEZbEFOmpNyUWH9taICzzy58cNMXPJHyV/VBtaQu/GUi6MD1WU/FFqUHH0y5aenkjn3O5ZJL4Oc/L3xw0xc8kfJX9QPqt7R4F81Ezc2wYkVo2VSlWM0rPlA0NKSeOSZrI0akvn/a2blvJumGOEz4HyjW30ROk6xLaDSgvoSh6muqWc/BKYFlMxVbTtL1Ao7vAZxlFbNYrRclVbMXkZxUfVCN/MJf5drbvdpdX5/3M9T3Nd3BNm7cG0yzbD8tVnDTFzyR8lf1QRUivvBLtJqbU2+LBdN0VcwkM9IUK7jpC55I+av6e6pS5rq6YNq01NudS32TdNAg2Lo15WFnz/bi8ejRXkBVcKtsuqcqYYi0pmpmZ5nZq2a2zMy+kWa/88zMmZn+oCU77e3phy3s6vKej0nsqNTQkHacYLVeiEguIguqZlYL/ASYCrQCF5hZa5L9DgD+EXgqqrJIhUvXYWnGDPjZz/bvVnvJJYqUIhK6KGuqJwHLnHOvO+d2AXcCn0iy37eA7wM7IiyLVLL29v0GcNhj61bYlWRS8rvuirJEIlKlogyqTcCbccur/HV7mNkE4HDn3O/THcjMppvZYjNbvGHDhvBLKmUtp0EZgkxoLiKSpSiDarKn7fdUKMysBrge+EqmAznnFjjn2pxzbSNHjgyxiFIJNOKQiJSKKIPqKuDwuOVRwJq45QOADwCPmNkK4BRgoTorlZ9iDwKf06AM6To3iYjkKMqg+hdgjJkdYWb1wPnAwthG59wW59wI51yLc64FeBI4xzmn52XKSCkMAp/1oAw1NZnnZI1T7C8NIlI+Iguqzrke4EvA/cDLwF3OuZfMbI6ZnRNVvlJYpTAI/HXXwXsMCv6CoUMD9/wthS8NpUpfNkT2p8EfJC+pBoEH79HQQg2c8D8zu/jQjdOCfUvMYoR6TbiQXOSTJRSBBn+QMGiYQslLuqbXQtbsTp/bHvyPOYv24mIMrl8ONcBSaKEQKUUKqpKXZOPkJiqpi219fVaD+BZ6cP1yaW7WPMQiySmoSl4SB4FPpWQutn5bddDaYKEH1y+XGqCmqRNJTkFV8hY/Tm6qSWNK5mK7ezdbr5wduDZY6JljyqUGqGnqRJJTUJVQlcPFtmHjyqxqg4UcXL9caoCapk4kOQVVCVVRL7bp5laNs5LkESrq2mCQJudy+FISo5l8RPanoCqhS7zYQoF6s153XeqB9eP8cHjyCBVlbTBoByTVAEXKm4KqRKqgvVnTzVYT5+Qb2kOvDWaqhWbTAUk1QJHypaAqkSp0b9aMf9C1taHXBoN8cSiXDkgikh+NqCSRSjXiUhaDGmUn3XM9MSH/zQcZdUkjM5U+jagkYVBNVSJVcr1ZA3ZmykaQWmg5dUASkdwpqEqkSimYOICjjgr9uEG+OKgDkkh1UFCVSJVSMDGARx4J/bhBvzioA5JI5etX7AJI5WtvL6EA0tsb+iFj5zZ7ttfkW6iZeUSk9CioSkVx+DXSVGprI8m3pL44iEjRqPlXKkagZ1+nT4+8HCJSvRRUpWLMng1vMzz1DoMGwdy5hSuQiFQdBVWpGCtXwpXckHpUpcRRKEREQqagKhVj9Gi4g/bUtdVSm+pFRCqOgqpUjNijLVdyA+9TIg/HikhVUVCVnASZxqzQYs/EPtHcznQWsKq2GYdGWhCRwtHYv5K12ADy8bcoGxoUt6S8aexfCUOkNVUzO8vMXjWzZWb2jSTbZ5nZEjN73sweNLPwB2aV0BV65hkRkXIRWVA1s1rgJ8BUoBW4wMxaE3Z7Fmhzzh0H3A18P6rySHiKNY1ZKTY5i4jEi7KmehKwzDn3unNuF3An8In4HZxzDzvnYnWeJ4FREZZHQlKMmWeynuxcEVhEiiDKoNoEvBm3vMpfl8oXgPuSbTCz6Wa22MwWb9iwIcQiSi6KMfNMVk3OXV3w+c/vG4E//3kFVhGJXJRBNdkQrEl7RZnZNKAN+EGy7c65Bc65Nudc28iRI0MsouSiGDPPZNXkfOWVsHv3vut27/bWi4hEKMoB9VcBh8ctjwLWJO5kZlOA2cBHnHM7IyyPhKjQA8iPHu1VOJOt38/GjckPkmq9iEhIoqyp/gUYY2ZHmFk9cD6wMH4HM5sAzAfOcc6tj7AsUuZKabJzEZFUIguqzrke4EvA/cDLwF3OuZfMbI6ZnePv9gNgMPBfZvZXM1uY4nBS5UppsnMRkVQ0+INUnhEjkjf1Dh8Ob79d+PJIWdDgDxIGDVMoleeGG6Cubt91dXXeehGRCCmoSuVpb4dbbtm3rfiWW9RWLCKRU1CVsqdxHkSkVET5SI1I5BIH9+/uhgc+38XnbDr9dsWtnD7d+121VRGJkDoqSVlradn/+dU3aKGFJA+1NjfDihWFKJaUIXVUkjCo+VfKWrIRlUZTpBH/RaTqKahKWUs2otJKijDiv4gICqpS5pKNtPQvddexs9++K3vqNfySiERPQVXKWrKRlgZe3s4MW8AKmunDWEEzX3QL6EKdlEQkWuqoJBUnWeclUD8lSU8dlSQMqqlKxclqmjgRkRApqErFSdUfSf2URCRqCqpScTRNnIgUi4KqVBxNEycixaJhCqUitbcriIpI4ammKiIiEhIFVRERkZAoqIqIiIREQVVERCQkCqoiIiIhUVAVEREJiYKqiIhISMpuQH0z2wAkGS49sBHA2yEVR3krb+VdOXk3O+dGhlkYqT5lF1TzZWaLizUThfJW3sq7cvMWATX/ioiIhEZBVUREJCTVGFQXKG/lrbyVt0gUqu6eqoiISFSqsaYqIiISCQVVERGRkFRkUDWzz5jZS2bWZ2Ypu9eb2Vlm9qqZLTOzb8StP8LMnjKz18zsl2ZWn0Xew8zsT/5r/2RmQ5Ps81Ez+2tc2mFm5/rbbjWzN+K2nRBm3v5+vXHHX1jA8z7BzP7X/2yeN7PPxW3L+rxTfX5x2/v757HMP6+WuG1X++tfNbO/C3qeWeQ9y8yW+Of5oJk1x21L+v6HmPelZrYhLo/L47Zd4n9Gr5nZJRHkfX1cvkvNbHPctpzP28xuNrP1ZvZiiu1mZv/hl+t5Mzsxblte5yySFedcxSXgGOBo4BGgLcU+tcBy4EigHngOaPW33QWc7/8+D+jIIu/vA9/wf/8G8L0M+w8D3gEa/OVbgfNyPO9AeQNbU6yP9LyBscAY//dGYC0wJJfzTvf5xe0zE5jn/34+8Ev/91Z///7AEf5xakPO+6Nxn2lHLO9073+IeV8K/DjF39rr/s+h/u9Dw8w7Yf8rgJtDOu+/BU4EXkyx/WzgPsCAU4CnwjhnJaVsU0XWVJ1zLzvnXs2w20nAMufc6865XcCdwCfMzIAzgLv9/X4OnJtF9p/wXxP0tecB9znntmWRR1h571GI83bOLXXOveb/vgZYD+Q6gk3Szy9Nme4GJvvn+QngTufcTufcG8Ay/3ih5e2cezjuM30SGJXF8fPKO42/A/7knHvHObcJ+BNwVoR5XwDckcXxU3LOLcL78pnKJ4BfOM+TwBAzO4z8z1kkKxUZVANqAt6MW17lrxsObHbO9SSsD+oQ59xaAP/nwRn2P5/9LzzX+U1Y15tZ/wjyHmBmi83syVizMwU+bzM7Ca+2szxudTbnnerzS7qPf15b8M4zyGvzzTveF/BqUTHJ3v+w8/60/17ebWaH51juXPPGb+4+AngobnU+551r2fI9Z5Gs9Ct2AXJlZg8AhybZNNs597sgh0iyzqVZHyjvAPnGH+cw4Fjg/rjVVwPr8ALOAuDrwJyQ8x7tnFtjZkcCD5nZC8C7SfaL8rxvAy5xzvX5q9Oed7LDZCpvmn2CvDadwK83s2lAG/CRuNX7vf/OueXJXp9j3vcAdzjndprZDLza+hnZlDuPvGPOB+52zvXGrcvnvHMtW77nLJKVsg2qzrkpeR5iFXB43PIoYA3eYNxDzKyfX7uJrQ+Ut5m9ZWaHOefW+sFjfZoyfBb4jXNud9yx1/q/7jSzW4Cvhp233/SKc+51M3sEmAD8igKct5kdCPw38M9+M12g804i1eeXbJ9VZtYPOAivCTHIa/PNGzObgveF4yPOuZ2x9Sne/6DBJWPezrmNcYs/Bb4X99pJCa99JGC+gfKOcz7wDwnlyue8cy1bvucskpVqbv79CzDGvB6v9XgXgYXOOQc8jHevE+ASIEjNN2ah/5ogr93vnpMfkGL3OM8FkvZ2zDVvMxsaa1o1sxHAacCSQpy3/z7/Bu/e138lbMv2vJN+fmnKdB7wkH+eC4HzzesdfAQwBvhzoLMMmLeZTQDmA+c459bHrU/6/oec92Fxi+cAL/u/3w+c6ZdhKHAm+7aS5J23n//ReJ2C/jduXb7nnclC4GK/F/ApwBb/i1q+5yySnWL3lIoiAZ/E+4a6E3gLuN9f3wjcG7ff2cBSvG/Ls+PWH4l3kV0G/BfQP4u8hwMPAq/5P4f569uAm+L2awFWAzUJr38IeAEvqHQCg8PMG/iQf/zn/J9fKNR5A9OA3cBf49IJuZ53ss8Pr8n4HP/3Af55LPPP68i41872X/cqMDWHv7FMeT/g/+3FznNhpvc/xLz/FXjJz+NhYFzcay/z349lwOfDzttfvhb4bsLr8jpvvC+fa/2/n1V496lnADP87Qb8xC/XC8T1+s/3nJWUskkaplBERCQk1dz8KyIiEioFVRERkZAoqIqIiIREQVVERCQkCqoiIiIhUVCVkmBmh5s3S80wf3mov9ycsN8jljCrjJl92czm5pDnuWbWml/JRUT2UlCVkuCcexO4Efiuv+q7wALnXHfCrnfgDToQL9n4yUGcizdjTWD+yEwiIknpOVUpGWZWBzwN3Ax8EZjgvNlQ4vcZDrwCjHLe2LYtwCKg2TnnzOxreMM/9scbAvKb/usuxhv60AHP4wXw3+MNsr8F+DRwAN6Udw14gwhc5pzb5A+p9wTeKEALnXP/HtV7ICLlTd+6pWQ453b7QfEPwJmJAdXfZ6OZ/Rlv+q7fsXeeVGdmZ+INOXgS3gg7C83sb4GNeCMoneace9vMhjnn3jFvouzfO+fuBjCz54ErnHOPmtkc4JvAl/2shzjn4gfFFxHZj5p/pdRMxRuO7gNp9olvAo5v+j3TT88CzwDj8ILsGXgzprwN4Jzbb15OMzsIL3A+6q/6Od7E2DG/zOVkRKS6KKhKyTCzE4D/A5wCXJUwMHy83+JNOH4iMNA590zsEMC/OudO8NNRzrmf+evzvc/xfp6vF5EqoKAqJcGfneZG4MvOuZXAD4B/S7avc24r3vRdN7NvB6X7gcvMbLB/zCYzOxhvgP/P+vdjifUwBt7Du4+Kc24LsMnMPuxvuwh4FBGRLCioSqn4IrDSOfcnf3kuMM7MUt3HvAM4HrgztsI590fgduB//YnX7wYOcM69BFwHPGpmzwE/9F9yJ/A1M3vWzP4Gb5q4H/j3Vk8g/STpIiL7Ue9fERGRkKimKiIiEhIFVRERkZAoqIqIiIREQVVERCQkCqoiIiIhUVAVEREJiYKqiIhISP4/MxH+Dp39LFYAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] @@ -565,6 +694,18 @@ "## Sinusoidal (4$\\pi$) Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sine Period 4$\\pi$ $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $U\\sim\\mathcal{U}(-1,1)$, $V\\sim\\mathcal{N}(0,1)^{p}$, $\\theta=4\\pi$,\n", + "

\n", + "

\n", + "
$X_{|d|}=U+0.02pV_{|d|}$ for $d=1,...,p$
\n", + "\n", + "$$Y=\\sin(\\theta X)+\\kappa \\epsilon$$" + ] + }, { "cell_type": "code", "execution_count": 25, @@ -582,7 +723,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -612,6 +753,13 @@ "## Sinusoidal (16$\\pi$) Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sine Period 16$\\pi$ $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Same as above except $\\theta=16\\pi$ and the noise on $Y$ is changed to $0.5\\kappa \\epsilon$." + ] + }, { "cell_type": "code", "execution_count": 27, @@ -629,7 +777,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -659,6 +807,17 @@ "## Square Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Square $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $U\\sim\\mathcal{U}(-1,1)$, $V\\sim\\mathcal{U}(-1,1)$, $\\epsilon\\sim\\mathcal{N}(0,1)^{p}$, $\\theta=-\\frac{\\pi}{8}$,\n", + "\n", + "$$X_{|d|}=U\\cos(\\theta)+V\\sin(\\theta)+0.05p\\epsilon_{|d|}$$\n", + "\n", + "$$Y_{|d|}=-U\\sin(\\theta)+V\\cos(\\theta)$$" + ] + }, { "cell_type": "code", "execution_count": 29, @@ -676,7 +835,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -706,6 +865,13 @@ "## Diamond Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Diamond $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Same as above except $\\theta=-\\frac{\\pi}{4}$." + ] + }, { "cell_type": "code", "execution_count": 31, @@ -723,7 +889,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -753,6 +919,17 @@ "## Two Parabolas Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Two Parabolas $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $\\epsilon\\sim\\mathcal{U}(0,1)$, $U\\sim\\mathcal{B}(0.5)$,\n", + "\n", + "$$X \\sim \\mathcal{U}(-1,1)^{p}$$\n", + "\n", + "$$Y=\\left((w^{T}X)^{2}+2\\kappa\\epsilon\\right)\\cdot\\left(U-\\frac{1}{2}\\right)$$" + ] + }, { "cell_type": "code", "execution_count": 33, @@ -770,7 +947,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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Y2Ji9jj2Fgq6IVLxiqoeXLctvealcdRVv9e/PLifo/v3puuoq3opi+/vss8+OU045Zd3tt98+PLHssMMO23jjjTcOAbj++uuHTpw4MacOTels2rSpDmDfffftXL9+fd29996btrdysoMOOmjLokWLdvbwPf744zdcf/31e3/sYx/bMHLkyM5169Y1vPbaa/1bWlq2pL534MCBOxLtp8U64YQTNtx3332DP/jgg7r333+/7r777hvyyU9+cpdAv2jRor6jRo3a/rWvfW3N1KlT1zzzzDONxx9//Mb58+cPevHFF/sBfPDBB3XPP//8zuN5/fXX+x122GG75T0bBV0RqWiJ6uGlS8G9u3o418A7Zkx+y0tl2jTe/fGPWbrffmwzg/32Y9uPf8zSadN4N6p9XHnllSvfe++9nXXGs2fPXnbbbbcNP/DAA5vvuOOOYbNmzXqz0G0PHz58R2tr6+rm5uYJJ5988ocPOeSQjT2959RTT13/6KOP7pF4fvzxx29Yu3Ztn+OPP34DQHNz8+aDDjpoc6IEm+y8885bc/LJJ49L7khVqOOOO27T2Wefvfbwww8/uKWl5eBzzjlndXLVMsADDzywR3Nz84SDDz64+Te/+c2Qf/7nf35n5MiRnddff/0bU6ZMOeDAAw9sbmlpGf/CCy/0B3jzzTcb+vXr501NTXn1pMqp2F1NJk6c6Bp7WaR2jB0bBNpUTU3wxhs9vz+1TRegsRFuuCG/Nl0ze9rdJyYve+6559445JBD1uS+ld6npaXloAceeGDx8OHDd8SdlyhdffXVe++5555dl1122W7f/3PPPTf8kEMOGZvufSrpikjJxVk93NoaBNimJjALHvMNuFK4H/zgB8uXLFlSdGexSjN48OAdF198cd4XXAq6WVTCbQYi1a4SqodbW4NScVdX8KiAWz4nnHDCxiOPPHJzz2tWl0svvXRtnz55dVwGFHQzKvZEIVJtSnWRWWzv4Zkzg+rgZI2NwXKRaqOgm0Gl3GYgUg6lvMhU9bBINwXdDCrlNgORcijlRaaqh0W6KehmUCm3GYiUQykvMlU9XFpxzDJU6Mw8oqCbkU4U0puU8iJT1cOlVewsQ4UodGYeUdDNqNgThXo+SzUp9UWmqodDc+YMZeTIj1JX18LIkR9lzpyip/YrZJahZOWcmUcUdLMq9EShns9SbVQaLYM5c4Zy2WVNrFjRl2Buv75cdllTFIG3kFmGkpVrZh5R0C0J9XyWaqTSaInNmDGK1AkCtmypY8aMoqf2S55lKHn5s88+O/Ciiy56F4JZhp5++ulB6d6fmJlnv/32Szszz1577dWVmJkn+X1HHXXUxjvuuGP45ZdfPvIvf/nLgCFDhnQ98sgjAxMz84wfP775zjvvHLZs2bKaGxyjUJrarwTU81lEdrNyZfrAk2l5nq644op3Dj/88OYpU6bkPUpSsTPz/OpXv9rr/PPP3/8rX/nKO0OHDu087rjj3r/33ntfzzcfvYFKuiVQqk4paicWqWL77pt+Cr9My/MU9SxDpZqZp7dT0C2BUnRKUTuxSJW76qq36N9/17lX+/fv4qqrIpnaD6KdZagUM/NIzLMMmdlNwGeAVe7+kTSvG/AT4NPAJuB8d38m2zYrZZahjo6gDXfZsqCEO3NmcW1kxc60IiLFiWSWoTlzhjJjxihWruzLvvtu46qr3mLatMim9pPKUMmzDP0cOCnL6ycD48J0ETC7DHmKRLGdUlKrktMFXFA7sfROVdvUMm3au7z99gt0dT3N22+/oIDb+8QadN39Mcg6gfNpwK0eeBIYbGb7lSd38UlXlWyWfl2NkFUeVXuSr0FqapFqFndJtyejgOQ2iOXhsl2Y2UVmNt/M5q9evbpsmSuVdLccue8eeDVCVnnoJF9ZdEueVLNKD7rpyne7NUK7+w3uPtHdJ44YMaLkmSp1qSdTlbG7Bi+Ig07ylaXCbsnr6urqylAPJb1R+HvoyvR6pd+nuxxIHkFlNPB2THkBuks9iZNwotQD0QXAMWPUaaqSVNhJvtfL9P8RU1PLi6tXr24eMWLE+rq6uvh6pUpF6OrqstWrV+8FvJhpnUoPunOBi83sTuBIYL27r4gzQ9lKPVEF3Zkzdw3soKrkOFXYSb7Xq6T/j87OzgtXrlx548qVKz9C5dccSul1AS92dnZemGmFWIOumd0BHA8MN7PlwLeBPgDuPge4j+B2ocUEtwx9IZ6cditHqScRvKO85UgKV0kneams/4+WlpZVwKnl37NUq1jv0y2FUt+nq/tle6eo77uW6pPuPl2RfKk6JE+aZ7d3ynbfdSk71ulWJZHaUultuhWnkqq2JH6l7FhXjk57IlJeql4WKUIpmxvUlFFZVL0sUVD1skgRStmxTrcqidQeBV2RIpRqGsdSb1tE4qGgK1KEUnasU6c9kdqjoCs1I46evq2twXCcpRies5TbFpF4qCOV1ITUnr4QlAoVpCQq6kglUVBJV2qCJiUQkWqgoCs1QT19RaQaKOhKTVBPXxGpBgq6UhPU07d303CZUi0UdDPQP3F1UU/f3ivRiW7pUnDvHi5T/7NSidR7OQ31hBWpHuUaLlO9lyUKKummoZ6wItVDneikmijopqF/4tqlZoPak6mzXF2dvmepPAq6aagnbCCXAFVNQUxtf9Ujn99Vuk50ADt26HuWCuTuNZVaWlq8WO3t7o2N7sG/bJAaG4PlvUUun0G1fU5NTbvmNZGamuLOmSQr5HfV3h58j2bu9fWl+Z6B+V4B5zil6k7qSJVBR0flT1Rfyjzm0jml2uZ7rasLTr+pzKCrq/z5kfSK/V2V6ntWRyqJgoJulSp1D+tcTlzVFsSq7SKhtyr0d5W4CE33HUPx37OCrkRBbbpVqtQ9rHNp1662tm8NoFEdCvldJbfXp6PvWSqFgm6VKnUP61wCVLUFMQ2gUR0K+V2luwhN0PcsFSXuRuWoUxQdqapBOToFJXdOaWpK35Ell3VE8pXv78os/f+DWXR5Qh2plCJIatOtUho1S6RbOdrr1aYrUVD1cpVSValIt2pr6pDeqyHuDEjhWlsVZEWg+/+g0m/zE1HQFZGaoItQqQaqXhaRmlVNw5RK76CSrojUpNTOhokxmEElYolPrCVdMzvJzF4xs8Vm9s00r59vZqvN7K9hurBkmZk+PbgcNgvSHnvosriGqQRU+xL37p5FB6sYThfGhk3GyecO1xcusYmtpGtm9cBPgU8By4GnzGyuuy9MWfUX7n5xSTMzfTrMnr3rsg0bYOrU4G9dFtcUlYB6h2XLgoD7c86lL93jRw7tWgsXXBA80RcuZRZnSfcIYLG7v+bu24A7gdNiyckNN2R+bepUXRXXmFIPoSkVYPp0Ot3oYOouAXenbdv0hUss4gy6o4A3k54vD5el+pyZPW9md5vZh9JtyMwuMrP5ZjZ/9erV+edkx47sr59zTlAalppQ6iE0JWYTJsDs2dQBlm09feESgziDbrr/h9Thse4Fxrr7/wHmAbek25C73+DuE9194ogRI/LPSX199tfdg+pnMxgwoCJLvmqjzF21TdQgOejogEGDgv/RhaktVBnoC5cYxBl0lwPJJdfRwNvJK7j7WnffGj79GdBSkpwkGvRysWVLUOU8YUJJslKI5BlW3LvbKBV409PoRTVmwoTgf3Ljxvzepy9cYhBn0H0KGGdm+5tZX2AKMDd5BTPbL+npqcBLJcnJrFkwcmR+71m4MLiqbmiIvepZbZT50RCaNWLy5PxKtsna2vSFSyxiC7ru3glcDDxAEEzvcvcFZjbDzE4NV/uKmS0ws+eArwDnlyxDb70Fkybl/74dO4Kq5xirndVGmb/W1mAg/K6u4FHn3yrS0QH9+sGDD+b/3oEDob09uNAWiUGs9+m6+33ufqC7/427zwyXXeXuc8O/r3D3Ce5+iLt/0t1fLmmG5s0L6mfb2oIr6Hxs2QLnnhtL4FUbZeXpbW3sZTveyZODquRt2/J/b1tbcCugrrAkTnHPLRh1imw+3fZ29/79Pe0knbmkSZOiyUeOWW1s3HX3jY2a2zYupf4+Km0O47L9/pqbC/tfbGuLZPdoPl2lCFLsGYg6RT6J/aRJXnDghbKdESvtRNybNTWl/yk0NRW/7Uq8wCrZ8ba3uw8bVvj/3siRERxdNwVdpSiSJrHP1eTJhbUhQdCOdP31qtbqJerqgrN+KrOgDbkY5ZisPV8lOd6OjmDUqEKqkSHonzFvXoE7T0+T2EsUNMtQrhLtve75d7jauDFoh6qri72ns5RelG3sqW2l6QIuxNtpLtI+BYkeyYW029bVBZ2k3CMPuCJRUdAtxLx5hfV09nCQjX79ar9nTS8W1X3A6e6/ztS/L85Oc5Ec7/TpwcEVWps0aBDceqtqk6TyxV2/HXWKvE03m7Y2L7i9CYKOWmp8rUlRtLFnais12/V53G267gUeb7GdFSPuKNUT1KarFEGKPQNRp7IG3YSRI72ok0bEHT6qjTqBpZcaXFM7KUX1eUX9+ee0vUJ7IidfeZQp2CYo6CpFkWLPQNQplqCbUGxPZ3AfOLBXRZ1K7I1bKUrZCzoh6s+/x+21t7vX1xf+/xFDsE1Q0FWKIsWegahTrEE3odhq5zJWmcWtHIGlWpXjgiTqzz/d9q6lzTupK/x/oa6uIq7CFHSVokjqSFUKs2YFvSiHDSt8G4lZjRoaarrTVTFDWNb6qE/lGCM66iFEk993Fh1so45/Yjb16ea0zYWZOkhJTVHQLZXWVlizJrhWb2srfDs7dgS3T5gFt1PUmEJvN+ktMyuVeozoqIcQvXhoB+vZgy6CCeT74NnntM1m0qTgwBVwpYYo6JZDouTbv39x23nwwSD49u9fM9Gl0NtNMs2sdN55tVvyzaSYEn+k0xxOn85P1k5lTzZg9DCBfCZ9++peW6ltcddvR50qok03m2I7ktRg228hvWez9eztTR2yomj3Lar3chT9FyDozVzhUJuuUgQp9gxEnSo+6KYq9najDMG31m/DydQBqLd1yIqlI1p7e25XPbmkYcOq5sepoKsURVL1ctwKncc3VaLj1fTpJWvvrKSOS+mqRdOp9TmFyzqX8vTpUF8f9DFwL3w7Zt1VyGvWqM1Wepe4o37UqepKuskiqqrrCtMqhvlZtOdU+umpZFyJ99Mm5zlTjb1Kut0Krv2IqgoZyjrlZdRQSVcpgpT9RagHfhB3JvNJVR10UxU7ak9SAH6dJj+b9GfZXAJqpd9PG8dFQSVU4ed63AV9PlEG2yqpQs5GQVcpitTzCvAQBFMAVkOqqaDrHpys+vb1qErA6UobuQTUTE14ZmX9NLIqZxCspJJ/Lsed00VTBBd5u6Uq6CCVKwVdpShSj/Ppmtn/A8YBvwQ2JlVL31OS+u4ilWw+3UpQzJy+qQYPhnXrgNzmQ63EeVzjVG2fR7rv+Cw6uJnz6MeO6HfY1hbcKldDNJ+uRCGXjlRDgbXACcApYfpMKTMlGcybV9xAG8neey8Y7cqMHW50YaxiOGfR3TsqeYCESO/nrAFl7cAUgcR3eRYdbKTfzsErIg24kyZ1l3FrLOCKRCbuonbUqeaql7MpQXVgog14B/hLk3rXbUj5qMQ27ozfT1ub77C6nd9tZL+XPn3iO9gYoOplpQhSjyVdMxttZv9tZqvM7B0z+5WZjS7D9YD0ZMGC7lNgW1vmGc7zkBhJqA4Y/2B4G1I4BGWphySsJpVW8k++TWyKd7BwaT/Onmq4GcyeTZ13FT5KVDqDB8O2bVFtTaTXyKV6+WZgLjASGAXcGy6TSjJrVhANEwG4LuJbsBNDUCbSqFHRbr/KlGMygnz8+dIOFmwau7PauJFt0QbZ+vrgd5W4yAv7A4hIfnLpSPVXdz+0p2WVoqY7UuWrowMuvRTWri39vszgttt6d/G3nKZPDwZECTkRBtiE+nq45RZ9pyF1pJIo5FIcWmNmU82sPkxTCTpWSaVLnukoilGvsnHvng0pMSXh9Oml3WdvMWHCrrUMYZVxskgDbnNz8H12dirgikQsl6B7AfCPwEpgBXAG8IVSZkpKYN68XbvBFDvfb0927OgemtIMhg/vPdP+FCMx1GJygF24sDz7TlQfL1hQnv2J9EK5BN0Puft0HokaAAAcG0lEQVSp7j7C3fd299OBD5U6Y1Ji5SwFQ1DFnVwSTk719b2vVNzREVyIpCvBdhU44Xu+EiXaRNJtPiIll0vQvTbHZVKtEqXg9nYYNKj8++/q2rVUnJomTCh/noqVKagm5kOeOrU8be2pRo7sDrIq0YqUXcaga2ZHm9nXgBFmdnlS+g7BmMxSa1pb4YMPdr0NqRIsXJg5ICenfv1KWoXd0QGP9ZuMm+1MGfOSLahu3VqyPO6iqal7Np9Eeuut8uxbRNLKVtLtCwwCGoA9ktL7BO26RTOzk8zsFTNbbGbfTPN6PzP7Rfj6n81sbBT7lRzNmrXrCbsc1dDF2LYtcxV2kcnNOHuq8fFtD+68FSfy3sJRSA60vf1mapEK1JDpBXd/FHjUzH7u7mlGmS2OmdUDPwU+BSwHnjKzue6e3Gvki8A6d/+wmU0B/g34fNR5kRzNm7fr8+nT4frry9cGGaOKDLD19cGIGGqLFakaubTp3mhmgxNPzGyImT0Qwb6PABa7+2vuvg24EzgtZZ3TgFvCv+8GJplFMOySRGPWrKCXcmqv6IED485Zbamr23VgikTq7FTAFakyuQTd4e7+XuKJu68D9o5g36OAN5OeLw+XpV3H3TuB9cBu97mY2UVmNt/M5q9evTqCrEnBWlthw4Zdg3BDxgoVyWbYsODz27FDwVWkRuQSdLvMbOd8M2bWRDAATrHSlVhTt5vLOrj7De4+0d0njhgxIoKsSUGmTw9KZakdijo7485ZdVq7Fp86NeiwpfucRWpCLkH3SuCPZnabmd0GPAZcEcG+l7Pr/b6jgbczrWNmDcBewLsR7FuikBpkZ89OPzGvFGxnh61M9zkrGItUlR6Drrv/Djgc+AVwF9Di7lG06T4FjDOz/c2sLzCFYGKFZHOB88K/zwAe8p4Gi5bSSR2OsIKDrGdJNSVdMO5tA42IVJFcpvYz4CTgcHe/F2g0syOK3XHYRnsx8ADwEnCXuy8wsxlmdmq42n8Bw8xsMXA5sNttRVJCo0bFMxxhIZInUHfn9nZnUKNTR3ca1Bgs361DUr6pUu5fzmT2rlMyikjlyGWWodlAF3CCux9sZkOA/3X3j5Ujg/nSLEMRSJnBJlZNTcEktQXcb9rRAVdeCcuWwZgxBW+mcJMnB1MiVormZo1CVQTNMiRRyCXoPuPuh5vZs+5+WLjsOXc/pCw5zJOCbp46OuCCC+KdkHzAANi0Kb79x2H6dJgzZ7fq+cSzst0X19amntE5UtCVKOTSkWp7OJCFA5jZCIKSr1Sr5GrjqVNLEnDTXsr177/7sITuOwNuRweMHRv0zRo7tnT9g8q1n6xmzQoGFUn5LMydVya1sYO68rRDqypapKxyCbr/Cfw3sLeZzQT+CHy/pLmS6CUPwP92aifx4qV2Vlo3snn34Lp5c8b63Y6OYHClpUuDVZcuDZ5HHRDLtZ9ijJ83i3rfgYVt0zfUtdFFGTqDPfhgdwAelXrLvIhEIZfeyx3APwP/SjCf7unu/stSZ0wi0NEBe+zR8wD8RdoyaBiXDmun3pz9m4JAcf+/L8irNHnllbvXMG/aFCyPUrn2E5XWVhh06ywOaPKdn+/jbe1BW3cpvf128LsZNKiyrkhEqlzGNl0z+x/gduDX7r6xrLkqQq9v0+3ogC9/GTaW8Cvr3x9uvLHHUmtycGtshBtuyNyRqa4u/d1HZtEO7Vyu/ZRdhjbiSPXtCzfd1GsnUVCbrkQhW0n3BuAzwBvhTD+nh/fTSqVJNFImSrRRB9yBA3dti81STQyFlSbHjMlveaHKtZ+yS24jLtW8yMmzOGlQDpGCZAy67v4bdz8LGAPcQzBIxTIzu8nMPlWuDEoWkyd3B9qlEU8ElTzZ+YYNeZVuli3LbzkEt/M0Nu66rLExWB6lcu0nVqnzIre3B+M4RykxKMeAAQq+InnIpU13s7v/wt3/ATgROAz4XclzJpkleh9HfQ9oYoD9AiY7T+4RXJfhV5WtNNnaGlQ/NzUFh9bUlL06OtO+e2o/LmY/Vau1FdasKU0A3rIlCL4TJkS3TZFa5u5ZE7APcAnwOPAawZy2h/b0vrhSS0uL16S2tmLHUdo9DRvm3t6edbft7e5NTe5mwWO61dvb3Rsbs++qsbHHXRUk3b5Lta+a09YWfLEx/K6qETDfK+Acp1TdKfML8CXgIeAt4Frg2Lgzm0uqqaBbikBrFmw3B7kGtKam9Luqr88erKOQad9NTaXZXyXK5cIoJ6X4vUHOv7dKp6CrFEXK1nv5ZuAOYJ67V02/zprovdzREVTZRcAJRzcqYOShsWPTNxU3NcEbb3Q/j7NHcM32Rs5RIT3Fc97w+edHNy3j4MGwbl0024qJei9LFLJ1pPqCu/9vNQXcqjd9enfHqCJ4mLowXpnUFkSlAob6y7VDVJw9gmu2N3KOSnbfcWsrbN8etAFbBINSvvdesJ36es2CJL1aLiNSSSkl3+5T5CQDDiyvb2Iq7ezf5NzR3sX4eZmDbU8dkHINaHH2CK6G3silHHaykJ7ieWlt3fVWpL5F3jXY1RX8zhsa1OtZeqdM9c7AfcDYuOu/801V06YbdfvZpEl57T6X9tp8OilF1q5YgDj33ZNSd/SKpU27vd29X79ofrf19ZX1hWWB2nSVIkiZX4B/BBYBVwJ94s5orqkqgm5zs0dywurXr+ATVq4n60oOaNWg1EEx9t7bUfaArvBezwq6SlGk7C/CQIJbhJ4Dvk4wkfzlwOVxZzxTqtigm4heFdIbNNN50ix79hV885Pv51yIivlu2tvd+/eP5jdegT8wBV2lKFJPbbrbgY1AP2CPlCS56OgIxiqOYtSotsI7RaXKpwNSNczMU6nK0dGrtTXoTd7VFTyWY6CPtO3Ura3BEKHt7UGHqWJMnaqZjqQ2ZYrGwEnAQuAaoDHuq4NcU8WUdNvbg/aqYq/4m5tLlr1cqyV1L2zhYq/+LYFcj6m93f3nA9t891mD80x9+1bEB4ZKukoRpMwvwB+ACXFnMN9UEUE3ijbbMgwokGu1ZDmqSGtZxVT/RiSXi7DkwHwW7b6VhuKDb4kuQHOloKsURco4OEa1im1wjKimVitgEItSy3WQDOkdchmQJN1v5lqmM53Zxd+n2N4ey2DZGhxDoqD7dKMwfXpw72ExATfC9tqoVcO9sFI+ubRTp7tP+BJm0WBhubWtrfAMJKYX1CQLUoUUdIsxZEhxg1o0NXXP6lOBwTYhipl5SjlAhJRXLhdhPQbmWbOC3/2kSYVnZOHC4AelH5NUk7jrt6NOZWvTHTzYq7VtqtxqsTNRb9dTO3Xe33mxg8XkOThMIVCbrlIESSXdfHR0BMPXmQVjyRairQ0WLIg2XxWuZOMDS2x6uk0p79qRRMm30GrnBx8MdmSmsZ2loqkjVS46OuC882DHjsLe37cv3HRTjc+UnllvnwlICpDoJ1GoAQN2v9IrkjpSSRRU0u3JhAlBx41CAu6kSUG02bo1r4Bba+2fvX0mIClAsW2+mzcHV3WTJ0ebL5EiKehmkphmb+HC/N87bFjQQWrevLzfGsXoT5UWtNX7WQo2b17x1c6pPz6ROMXdqBx1iqQjVaGdOsyK7h1U7OhPldRpKbmzzbBhQaqVASIkJsV0uCpywBnUkUopgqQ23WSTJwdXxvlqbo6sc1Sx7Z+VMpBFosSe3KzW2Jj/rUYiaRXa5msGt91W0I9QbboShViql81sqJn93sxeDR+HZFhvh5n9NUxzS5qpUaMKC7gjR0baG7nY9s+ST2qeI/VYlpIqtM3XPeijoR7OEpO42nS/CTzo7uOAB8Pn6Wx290PDdGrJcjN9Orz9dn7vqa8P2m3feivSrBTb/lkpnZYqJfhLjUu0+dbleSqbPTv+zg7SK8UVdE8Dbgn/vgU4PaZ8BG64Ifd1E8G2s7OgKqqeOjkVO/pTpXRaqpTgL73Ejh1BM08+VO0icYijIRl4L+X5ugzrdQLzgSeB07Ns76JwvfljxozxvJVp1JtydXKqhFltKqlDl/QyI0fm9v+c5zRZqCOVUgSpZB2pzGwesG+al64EbnH3wUnrrnP33dp1zWyku79tZgcADwGT3H1Jtv0W1JGqoaHn+3AjmP2nUjo5lUtHR1CYWLYsKOHOnKlOVFImHR1B2202ef7jqSOVRCGW3stm9gpwvLuvMLP9gEfc/aAe3vNz4Lfufne29QoKutl6QlZQz2QRydOQIemHbC1glDgFXYlCXG26c4Hzwr/PA36TuoKZDTGzfuHfw4FjgQJGqsjBrFlBSba+PnheX9891V4F9UyuNZU2iIfUoHXrgj4Yw4Z1Lxs2rFcPyyrxiivoXgN8ysxeBT4VPsfMJprZjeE6BwPzzew54GHgGncvTdCFIPB2dgaBtrOzJFPtVUonp0oQxchboguXnLS2wpo13a25a9Yo4EpsNDhGmamdM9Db2rdLQQOQlJeqlyUKCroSC7VvF08XLuWloCtR0IQHEgu1bxdPA5CIVB8FXYmF2reLpwsXkeqjoCuxKHbkLdGFi0g1UtCV2LS2Bm2PXV3BowJufqrpwkW9rEUCCrpSFr3hpBvHMVbDhYtuDxPppqBbYWoxOMV90i3HZxr3MVYyTfMokiTuwZ+jTi0tLV6tanWSgKamXY8pkZqaSr/vcn2mcR5jqUQ1cYZZ+s8mz/kGYocmPFCKIKmkW0FqtUQQ560tPX2mUZWCa+32nShL7uplLdJNQbeC1NqJOyGOk24imKYbPAKCz1SBJbMoLwDVy1qkm4JuBam1E3dCuU+6ycE0kzFjFFiyifICsJp6WYuUmoJuBam1E3dCuU+66YJpssRnqsCSWdQXgNXQy1qkHDT2coXRhAjFyzSuMwTBMPGZauzizDSZwu409rJEQSXdCqMSQfEylcYSwTTxmdZqzUIUaq3kLlIpFHSl5uQaTGs9sBTbM1sXgCLRU9DNQ7kHrqjFgTLKIZ9gWquBRYN1iFQmtenmqNxtXGpTk2KovTp6atOVKCjo5qjcJzGdNKUYmTqTmQWlesmfgq5EQdXLOSr3wBW1OlCGlEet3vMtUu0UdHNU7pOYTppSDPXMFqlMCro5KvdJTCdNKUat98wWqVYKujkq90lMJ00pVq32zBapZgq6OUjcunPOOcHz224rz0lMJ02RbrqFTmpBQ9wZqHSpt+4k7ncEBUGRctH/odQKlXR7UKtz3IrkK86Spv4PpVYo6PZAt+6IxDPCVXKQzzYvskg1UdDtQS3duqM2MSlUuUuaqUE+k2r8P5TeTUG3B5V0604xQVNj8Uoxyl3j09OcyKBb6KQ6Kej2oFJu3Sk2aKpNTHqS7aKu3DU+2YJ54v/wvPOC369qbqSquHvZE3AmsADoAiZmWe8k4BVgMfDNXLbd0tLi1aS93b2pyd0seGxvT79eU5N7EG53TU1Nue3HLP37zaI5Dqlu7e3ujY27/jYaG7t/jz29HrWefu/lzo+7OzDfYzhfKtVWimencDBwEPBIpqAL1ANLgAOAvsBzQHNP266moJvPiaPYoFls0JbalsvvI9cLxCj09L8Rx+9ZQVcpihRL9bK7v+Tur/Sw2hHAYnd/zd23AXcCp5U+d+WTT5VvsdV7+bZNq9NV75JLm23qYC1Qut9IT806uqtAqlacEZ/sJd0zgBuTnp8DXJdh3YuA+cD8MWPGeLXIp/QaRXVariWVYvZVztKQRCffkmMc1bvF5DcKqKSrFEEq3YZhHvBimnRa0jrZgu6ZaYLutT3tt5qqlws50ZUjoBV6Qov7RCyFy/e7i7u5Qm26StWa4t159qB7NPBA0vMrgCt62mY1Bd1KDVKFth/HfSKW4uRzUVcJHfPKXauioKsURarkW4aeAsaZ2f5m1heYAsyNOU+RqpTbkVIV2n6sdrbqkKm9Pp8JNiph0BhNCCLVKJaga2b/YGbLCUqz/2NmD4TLR5rZfQDu3glcDDwAvATc5e4L4shvKVXiiaPQAUEq4UQs2UU1SEolDRojUlXiLmpHnaqperkYpa5aK2T7lVpdLt2ibALobZ3mUPWyUgTJ3D3uuB+piRMn+vz58+PORkmlTnMGQSmjEqqmOzqCW56WLQtKuDNnxp8n6VZXF4TZVGZBbYtkZmZPu/vEuPMh1a2S23SrSjnva63kIR0rsbpcuqkJQCReCroRKPdkAuqwJIVSW6xIvBR085CpNJup5HnppaUp/aq0IoWqhB7zGu1MerOGuDNQLVLbUROlWchcwly7Nkip6xd7gps5M32brkorkovW1viq/bP9H6kpQnoDlXRzlK0dNdcSZrp210Ku+iuhtCK9W6Gl1UrujyBSDuq9nKNsvT5vu233kmcmyb1EK7kXskgmxfxuq7n3tHovSxRU0s1RtnbUdCXPYcN63o6u+qUaFfO7VX8E6e0UdHPUU6/P1FtlfvKTnnuJqheyVKNifrfqPS29nYJujvJtR81lfV31SzUq5ner/gjS26lNN0Zq05Vq1Ft/t2rTlSiopBsjXfVLNdLvVqRwKumKiORAJV2Jgkq6IiIiZaKgKyIiUiYKuhHTuLIiIpKJgm6E0s02NHUqDB+u4CsiIgq6kUo3Ug8Ekx6Ucqo/ERGpDgq6Eco2Io+GdxQREQXdCPU0Io+GdxQR6d0UdCOUblzZZBreUUSkd1PQjVBipJ50MwxpUHcREVHQjVhrK6xZA+3tGiZPRER21RB3BmpVa6uCrIiI7EolXRERkTJR0BURESkTBV0REZEyUdAVEREpEwVdERGRMlHQFRERKRNz97jzECkzWw0sLWITw4E1EWVH+9a+te/a2XeTu4+IMjPS+9Rc0C2Wmc1394nat/atfWvfIlFT9bKIiEiZKOiKiIiUiYLu7m7QvrVv7Vv7FikFtemKiIiUiUq6IiIiZaKgKyIiUia9Muia2ZlmtsDMusws4+0DZnaSmb1iZovN7JtJy/c3sz+b2atm9gsz65vHvoea2e/D9/7ezIakWeeTZvbXpLTFzE4PX/u5mb2e9NqhUe47XG9H0vbnlvG4DzWzJ8Lv5nkz+3zSa3kdd6bvLun1fuExLA6PaWzSa1eEy18xs7/L9Rjz2PflZrYwPMYHzawp6bW0n32E+z7fzFYn7ePCpNfOC7+fV83svBLs+8dJ+11kZu8lvVbscd9kZqvM7MUMr5uZ/WeYt+fN7PCk14o6bpG8uHuvS8DBwEHAI8DEDOvUA0uAA4C+wHNAc/jaXcCU8O85QFse+/534Jvh398E/q2H9YcC7wKN4fOfA2cUeNw57RvYkGF5SY8bOBAYF/49ElgBDM73uLN9d0nrTAfmhH9PAX4R/t0crt8P2D/cTn0ex5nLvj+Z9H22Jfad7bOPcN/nA9dl+J29Fj4OCf8eEuW+U9a/BLgpiuMO3/+3wOHAixle/zRwP2DAUcCfozhuJaV8U68s6br7S+7+Sg+rHQEsdvfX3H0bcCdwmpkZcAJwd7jeLcDpeez+tPA9ub73DOB+d9+Uxz6i2vdO5Thud1/k7q+Gf78NrAIKGQEo7XeXJT93A5PCYzwNuNPdt7r768DicHuR7dvdH076Pp8ERuex/aL2ncXfAb9393fdfR3we+CkEu77LOCOPLaflbs/RnBxmslpwK0eeBIYbGb7Ufxxi+SlVwbdHI0C3kx6vjxcNgx4z907U5bnah93XwEQPu7dw/pT2P3kNDOsIvuxmfUrwb77m9l8M3syUa1NmY/bzI4gKDEtSVqc63Fn+u7SrhMe03qCY8zlvdnk+/4vEpTAEtJ99lHv+3Ph53i3mX2owHwXum/C6vT9gYeSFhdz3MXkr9jjFslLQ9wZKBUzmwfsm+alK939N7lsIs0yz7I8p33nsN/k7ewHfBR4IGnxFcBKgoB0A/B/gRkR73uMu79tZgcAD5nZC8D7adYr5XHfBpzn7l3h4qzHnbqJnvKaZZ1c3ptNzu83s6nAROATSYt3++zdfUm69xe473uBO9x9q5lNIyjtn5BPvovYd8IU4G5335G0rJjjLiZ/xR63SF5qNui6++QiN7Ec+FDS89HA2wSDpQ82s4awhJRYntO+zewdM9vP3VeEwWVVljz8I/Df7r49adsrwj+3mtnNwNej3ndYtYu7v2ZmjwCHAb+iDMdtZnsC/wN8K6wGzOm4U2T67tKts9zMGoC9CKonc3lvNjm938wmE1yMfMLdtyaWZ/jscw0+Pe7b3dcmPf0Z8G9J7z0+5b2P5LjfnPadZArwTyn5Kua4i8lfscctkhdVL2f2FDDOgh67fQlOFHPd3YGHCdpaAc4Dcik5J8wN35PLe3dr9woDVqKN9XQgbW/NQvdtZkMSVbdmNhw4FlhYjuMOP+f/Jmh7+2XKa/kcd9rvLkt+zgAeCo9xLjDFgt7N+wPjgL/kfJQ57NvMDgOuB05191VJy9N+9hHve7+kp6cCL4V/PwCcGOZhCHAiu9awFL3vcP8HEXRYeiJpWbHHnYu5wLlhL+ajgPXhhVyxxy2Sn7h7csWRgH8guMLdCrwDPBAuHwncl7Tep4FFBFfcVyYtP4DgRLwY+CXQL499DwMeBF4NH4eGyycCNyatNxZ4C6hLef9DwAsEQacdGBTlvoFjwu0/Fz5+sVzHDUwFtgN/TUqHFnLc6b47guroU8O/+4fHsDg8pgOS3ntl+L5XgJML+H31tO954e8ucYxze/rsI9z3vwILwn08DIxPeu8F4eexGPhC1PsOn38HuCblfVEc9x0Evd23E/xvfxGYBkwLXzfgp2HeXiDproVij1tJKZ+kYSBFRETKRNXLIiIiZaKgKyIiUiYKuiIiImWioCsiIlImCroiIiJloqArVcPMPmTBTENDw+dDwudNKes9YimzA5nZV81sVgH7PN3MmovLuYhIQEFXqoa7vwnMBq4JF10D3ODuS1NWvYNgcIZk6cawzsXpBDMP5Swc4UpEZDe6T1eqipn1AZ4GbgK+BBzmwaw2yesMA14GRnswxvBY4DGgyd3dzL5BMMRmP4JhNr8dvu9cguElHXieIMD/lmAyhPXA54A9CKY1bCQYaOECd18XDl34J4LRlOa6+/8r1WcgItVLV+RSVdx9exg0fwecmBpww3XWmtlfCKZo+w3d8+W6mZ1IMLTjEQSjFM01s78F1hKMRHWsu68xs6Hu/q4FE6r/1t3vBjCz54FL3P1RM5sBfBv4arjrwe6ePHmBiMguVL0s1ehkgiH/PpJlneQq5uSq5RPD9CzwDDCeIAifQDDzzRoAd99tblYz24sgsD4aLrqFYPL0hF8UcjAi0nso6EpVMbNDgU8BRwGXpQzgn+zXBBPTHw4McPdnEpsA/tXdDw3Th939v8Llxba1bCzy/SJS4xR0pWqEMwzNBr7q7suAHwA/TLeuu28gmKLtJnbtQPUAcIGZDQq3OcrM9iaYhOEfw/ZgEj2kgQ8I2nFx9/XAOjP7ePjaOcCjiIjkSEFXqsmXgGXu/vvw+SxgvJllake9AzgEuDOxwN3/F7gdeMLMXgDuBvZw9wXATOBRM3sO+FH4ljuBb5jZs2b2NwTTAf4gbNs9lGAWHRGRnKj3soiISJmopCsiIlImCroiIiJloqArIiJSJgq6IiIiZaKgKyIiUiYKuiIiImWioCsiIlIm/x/pC4cPV59kKAAAAABJRU5ErkJggg==\n", 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" ] @@ -800,6 +977,20 @@ "## Circle Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Circle $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U\\sim\\mathcal{U}(-1,1)^{p}$, $\\epsilon\\sim\\mathcal{N}(0,I_{p})$, $r=1$,\n", + "

\n", + "

\n", + "
$X_{|d|}=r\\left(\\sin(\\pi U_{|d+1|})\\prod\\limits_{j=1}^d \\cos(\\pi U_{|j|})+0.4\\epsilon_{|d|}\\right)$ for $d=1,...,p-1$
\n", + "\n", + "$$X_{|d|}=r\\left(\\prod\\limits_{j=1}^p \\cos(\\pi U_{|j|})+0.4\\epsilon_{|p|}\\right)$$\n", + "\n", + "$$Y_{|d|}=\\sin(\\pi U_{|1|})$$" + ] + }, { "cell_type": "code", "execution_count": 35, @@ -817,7 +1008,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -847,6 +1038,13 @@ "## Ellipse Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ellipse $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: Same as above except $r=5$." + ] + }, { "cell_type": "code", "execution_count": 37, @@ -864,7 +1062,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -895,6 +1093,17 @@ "## Multiplicative Noise Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Multiplicative Noise $(x,y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}^{p}$: $u\\sim\\mathcal{N}(0,I_{p})$,\n", + "\n", + "$$x \\sim \\mathcal{N}(0,I_{p})$$\n", + "

\n", + "
$y_{|d|}=u_{|d|}x_{|d|}$ for $d=1,...,p$
" + ] + }, { "cell_type": "code", "execution_count": 39, @@ -912,7 +1121,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -941,6 +1150,17 @@ "## Multimodal Independence Simulation" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Multimodal Independence $(X,Y) \\in \\mathbb{R}^{p} \\times \\mathbb{R}$: $U\\sim\\mathcal{N}(0,I_{p})$, $V\\sim\\mathcal{N}(0,I_{p})$, $U'\\sim\\mathcal{B}(0.5)^{p}$, $V'\\sim\\mathcal{B}(0.5)^{p}$\n", + "\n", + "$$X=U/3+2U'-1$$\n", + "\n", + "$$Y=V/3+2V'-1$$" + ] + }, { "cell_type": "code", "execution_count": 41, @@ -958,7 +1178,7 @@ "outputs": [ { "data": { - "image/png": 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\n"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\n", 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