def testSorting(self):
"""components should be sorted by decreasing variance
"""
x = generate_covsig(np.diag([1, 9, 2, 6, 3, 8, 4, 5, 7]), 500)
w, v = pca(x, sort_components=True)
c = np.cov(np.dot(w.T, x))
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5, 4, 3, 2, 1]), rtol=1e-1, atol=1e-2))
w, v = pca(x, sort_components=True)
c = np.cov(np.dot(w.T, x))
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5, 4, 3, 2, 1]), rtol=1e-1, atol=1e-2))
def testSorting(self):
"""components should be sorted by decreasing variance
"""
x = generate_covsig(np.diag([1, 9, 2, 6, 3, 8, 4, 5, 7]), 500)
w, v = pca(x, reducedim=5)
c = np.cov(x.dot(w).T)
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5]), rtol=1e-1, atol=1e-2))
def testDecorrelation(self):
"""components should be decorrelated after PCA
"""
x = generate_covsig([[3, 2, 1], [2, 3, 2], [1, 2, 3]], 500)
w, v = pca(x)
c = np.cov(np.dot(w.T, x))
c -= np.diag(c.diagonal())
self.assertTrue(np.allclose(c, np.zeros((3, 3)), rtol=1e-2, atol=1e-3))
def testInverse(self):
i = np.abs(self.v.dot(self.w))
self.assertTrue(np.abs(np.mean(i.diagonal())) - 1 < epsilon)
self.assertTrue(np.abs(np.sum(i) - i.trace()) < epsilon)
w, v = pca(self.x, subtract_mean=True, normalize=True)
i = np.abs(v.dot(w))
self.assertTrue(np.abs(np.mean(i.diagonal())) - 1 < epsilon)
self.assertTrue(np.abs(np.sum(i) - i.trace()) < epsilon)
def testIdentity(self):
"""identity covariance in -> identity covariance out
test for up to 50 dimensions
"""
for i in range(1, 50):
x = generate_covsig(np.eye(i), 500)
w, v = pca(x)
c = np.cov(np.dot(w.T, x))
self.assertTrue(np.allclose(c, np.eye(i)))
def setUp(self):
self.x = np.random.rand(10, 100)
self.y = self.x.copy()
self.m, self.n = self.x.shape
self.w1, self.v1 = pca(self.x, reducedim=0.9)
self.w2, self.v2 = pca(self.x, reducedim=5)
def testInputSafety(self):
self.assertTrue((self.x == self.y).all())
pca(self.x, subtract_mean=True, normalize=True)
self.assertTrue((self.x == self.y).all())
def setUp(self):
self.x = np.random.rand(10, 100)
self.y = self.x.copy()
self.m, self.n = self.x.shape
self.w, self.v = pca(self.x)
import numpy as np
from scot.pca import pca
from scot.var import VAR
# Set random seed for repeatable results
np.random.seed(42)
# Generate data from a VAR(1) process
model0 = VAR(1)
model0.coef = np.array([[0.3, -0.6], [0, -0.9]])
x = model0.simulate(10000).squeeze()
# Transform data with PCA
w, v = pca(x)
y = np.dot(w.T, x)
# Verify that transformed data y is decorrelated
print("Covariance of x:\n", np.cov(x.squeeze()))
print("\nCovariance of y:\n", np.cov(y.squeeze()))
model1, model2 = VAR(1), VAR(1)
# Fit model1 to the original data
model1.fit(x)
# Fit model2 to the PCA transformed data
model2.fit(y)
# The coefficients estimated on x (2) are exactly equal to the back-transformed
import numpy as np
from scot.pca import pca
from scot.var import VAR
# Set random seed for repeatable results
np.random.seed(42)
# Generate data from a VAR(1) process
model0 = VAR(1)
model0.coef = np.array([[0.3, -0.6], [0, -0.9]])
x = model0.simulate(10000).squeeze()
# Transform data with PCA
w, v = pca(x)
y = np.dot(w.T, x)
# Verify that transformed data y is decorrelated
print('Covariance of x:\n', np.cov(x.squeeze()))
print('\nCovariance of y:\n', np.cov(y.squeeze()))
model1, model2 = VAR(1), VAR(1)
# Fit model1 to the original data
model1.fit(x)
# Fit model2 to the PCA transformed data
model2.fit(y)
# The coefficients estimated on x (2) are exactly equal to the back-transformed