def test_matrix_sqrt_eigs(self):
import spectral as spy
from spectral.algorithms.spymath import matrix_sqrt
stats = spy.calc_stats(self.data)
(evals, evecs) = np.linalg.eig(stats.cov)
S = matrix_sqrt(eigs=(evals, evecs))
assert_allclose(S.dot(S), self.C, atol=1e-8)
def set_background(self, stats):
'''Sets background statistics to be used when applying the detector.'''
from spectral.algorithms.spymath import matrix_sqrt
self.background = stats
self.u_b = stats.mean
# Matrix square root of inverse of cov: C**(-1/2)
self.C_1_2 = matrix_sqrt(np.linalg.inv(stats.cov))
def whiten(self, X):
'''Transforms data to the whitened space of the background.
Arguments:
`X` (ndarray):
Size (M,N,K) or (M*N,K) array of length K vectors to transform.
Returns an array of same size as `X` but linearly transformed to the
whitened space of the filter.
'''
import math
from spectral.algorithms.transforms import LinearTransform
from spectral.algorithms.spymath import matrix_sqrt
if self._whitening_transform is None:
A = math.sqrt(self.coef) * matrix_sqrt(self.C_1, True)
self._whitening_transform = LinearTransform(A, pre=-self.u_b)
return self._whitening_transform(X)
def get_whitening_transform(self):
'''Returns transform that centers and whitens data for these stats.'''
from spectral.algorithms.transforms import LinearTransform
from spectral.algorithms.spymath import matrix_sqrt
C_1 = np.linalg.inv(self.cov)
return LinearTransform(matrix_sqrt(C_1, True), pre=-self.mean)
def test_matrix_sqrt_eigs(self):
stats = spy.calc_stats(self.data)
(evals, evecs) = np.linalg.eig(stats.cov)
S = matrix_sqrt(eigs=(evals, evecs))
assert_allclose(S.dot(S), self.C, atol=1e-8)
def test_matrix_sqrt_sym_inv(self):
S = matrix_sqrt(self.C, symmetric=True, inverse=True)
assert_allclose(S.dot(S), np.linalg.inv(self.C), atol=1e-8)
def test_matrix_sqrt_sym(self):
S = matrix_sqrt(self.C, symmetric=True)
assert_allclose(S.dot(S), self.C, atol=1e-8)
def test_matrix_sqrt_inv(self):
S = matrix_sqrt(self.X, inverse=True)
assert_allclose(S.dot(S), np.linalg.inv(self.X))
def test_matrix_sqrt(self):
S = matrix_sqrt(self.X)
assert_allclose(S.dot(S), self.X)
def test_matrix_sqrt_sym_inv(self):
from spectral.algorithms.spymath import matrix_sqrt
S = matrix_sqrt(self.C, symmetric=True, inverse=True)
assert_allclose(S.dot(S), np.linalg.inv(self.C), atol=1e-8)
def test_matrix_sqrt_sym(self):
from spectral.algorithms.spymath import matrix_sqrt
S = matrix_sqrt(self.C, symmetric=True)
assert_allclose(S.dot(S), self.C, atol=1e-8)
def test_matrix_sqrt_inv(self):
from spectral.algorithms.spymath import matrix_sqrt
S = matrix_sqrt(self.X, inverse=True)
assert_allclose(S.dot(S), np.linalg.inv(self.X))
def test_matrix_sqrt(self):
from spectral.algorithms.spymath import matrix_sqrt
S = matrix_sqrt(self.X)
assert_allclose(S.dot(S), self.X)