def test_mixture_of_kernels():
for xx2d in [
np.array(
np.meshgrid(np.arange(-100, 100, 5), np.arange(-100, 100, 5))),
np.array(
np.meshgrid(np.arange(-100, 100, 5),
np.arange(-100, 100, 5))).reshape(2, -1)
]:
# Make a 2D mixture of 2 Gaussians:
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
kernel1 = ebp.gaussian_kernel(xx2d, params1)
mean2 = [30, 40]
sigma2 = [10, 50]
params2 = np.hstack([mean2, sigma2])
kernel2 = ebp.gaussian_kernel(xx2d, params2)
betas = [0.3, 0.7]
signal1 = betas[0] * kernel1 + betas[1] * kernel2
signal2 = ebp.mixture_of_kernels(xx2d, betas, [params1, params2],
ebp.gaussian_kernel)
npt.assert_almost_equal(signal1, signal2)
def test_elastic_basis_pursuit():
"""
"""
xx2d = np.array(np.meshgrid(np.arange(0,50,1),
np.arange(0,50,1)))
bounds = [[0,50], [0,50], [0, None], [0, None]]
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
kernel1 = ebp.gaussian_kernel(xx2d, params1)
mean2 = [30, 40]
sigma2 = [10, 50]
params2 = np.hstack([mean2, sigma2])
kernel2 = ebp.gaussian_kernel(xx2d, params2)
beta = [0.3, 0.7]
signal = (beta[0] * kernel1 + beta[1] * kernel2).ravel()
initial_theta = np.hstack([np.mean(xx2d, axis=(-1, -2)), 1, 1])
theta, err, r = ebp.elastic_basis_pursuit(xx2d.reshape(-1, signal.shape[0]),
signal,
ebp.leastsq_oracle,
ebp.gaussian_kernel,
initial_theta=initial_theta,
bounds=bounds,
max_iter=1000,
beta_tol=10e-6)
def test_elastic_basis_pursuit():
"""
"""
xx2d = np.array(np.meshgrid(np.arange(0, 50, 1), np.arange(0, 50, 1)))
bounds = [[0, 50], [0, 50], [0, None], [0, None]]
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
kernel1 = ebp.gaussian_kernel(xx2d, params1)
mean2 = [30, 40]
sigma2 = [10, 50]
params2 = np.hstack([mean2, sigma2])
kernel2 = ebp.gaussian_kernel(xx2d, params2)
beta = [0.3, 0.7]
signal = (beta[0] * kernel1 + beta[1] * kernel2).ravel()
initial_theta = np.hstack([np.mean(xx2d, axis=(-1, -2)), 1, 1])
theta, err, r = ebp.elastic_basis_pursuit(xx2d.reshape(
-1, signal.shape[0]),
signal,
ebp.leastsq_oracle,
ebp.gaussian_kernel,
initial_theta=initial_theta,
bounds=bounds,
max_iter=1000,
beta_tol=10e-6)
def test_mixture_of_kernels():
for xx2d in [np.array(np.meshgrid(np.arange(-100, 100, 5),
np.arange(-100, 100, 5))),
np.array(np.meshgrid(np.arange(-100, 100, 5),
np.arange(-100, 100, 5))).reshape(2, -1)]:
# Make a 2D mixture of 2 Gaussians:
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
kernel1 = ebp.gaussian_kernel(xx2d, params1)
mean2 = [30, 40]
sigma2 = [10, 50]
params2 = np.hstack([mean2, sigma2])
kernel2 = ebp.gaussian_kernel(xx2d, params2)
betas = [0.3, 0.7]
signal1 = betas[0] * kernel1 + betas[1] * kernel2
signal2 = ebp.mixture_of_kernels(xx2d, betas, [params1, params2],
ebp.gaussian_kernel)
npt.assert_almost_equal(signal1, signal2)
def test_gaussian_oracle():
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
xx2d = np.array(np.meshgrid(np.arange(-100, 100, 5),
np.arange(-100, 100, 5))).reshape(2, -1)
gauss2d = ebp.gaussian_kernel(xx2d, params1)
# Oh, we're totally stuffing this ballot box:
initial = params1
theta_est = ebp.leastsq_oracle(xx2d, gauss2d, ebp.gaussian_kernel, initial,
bounds=[[None, None], [None, None], [0, None],
[0, None]]) # Variance can't be negative!
npt.assert_almost_equal(theta_est, params1)
def test_parameters_to_regressors():
"""
"""
xx2d = np.array(np.meshgrid(np.arange(-100, 100, 5),
np.arange(-100, 100, 5)))
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
mean2 = [30, 40]
sigma2 = [10, 50]
params2 = np.hstack([mean2, sigma2])
params = [params1, params2]
reference = np.array([ebp.gaussian_kernel(xx2d.reshape(2, -1), p)
for p in params]).T
regressors = ebp.parameters_to_regressors(xx2d, ebp.gaussian_kernel, params)
npt.assert_almost_equal(reference, regressors)
def test_gaussian_oracle():
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
xx2d = np.array(
np.meshgrid(np.arange(-100, 100, 5), np.arange(-100, 100,
5))).reshape(2, -1)
gauss2d = ebp.gaussian_kernel(xx2d, params1)
# Oh, we're totally stuffing this ballot box:
initial = params1
theta_est = ebp.leastsq_oracle(xx2d,
gauss2d,
ebp.gaussian_kernel,
initial,
bounds=[[None, None], [None,
None], [0, None],
[0, None]
]) # Variance can't be negative!
npt.assert_almost_equal(theta_est, params1)
def test_parameters_to_regressors():
"""
"""
xx2d = np.array(
np.meshgrid(np.arange(-100, 100, 5), np.arange(-100, 100, 5)))
mean1 = [20, 20]
sigma1 = [10, 10]
params1 = np.hstack([mean1, sigma1])
mean2 = [30, 40]
sigma2 = [10, 50]
params2 = np.hstack([mean2, sigma2])
params = [params1, params2]
reference = np.array(
[ebp.gaussian_kernel(xx2d.reshape(2, -1), p) for p in params]).T
regressors = ebp.parameters_to_regressors(xx2d, ebp.gaussian_kernel,
params)
npt.assert_almost_equal(reference, regressors)
def test_gaussian_kernel():
xx3d = np.array(np.meshgrid(np.arange(-10,10,1),
np.arange(-10,10,1),
np.arange(-10,10,1)))
# Means are identical:
mean3d = [0, 0, 0]
# Variance/covariance matrix:
sigma3d = np.array([[10, 10, 0], [0,10, 10], [10,10,10]])
gauss3d = ebp.gaussian_kernel(xx3d, np.hstack([mean3d, sigma3d.ravel()]))
# Verify against a 1D case:
x = xx3d[0,0,:,0]
gauss1d = ( 1/(sigma3d[0,0] * np.sqrt(np.pi))
* np.exp(-0.5 * (x - mean3d[0]) **2 / sigma3d[0,0]))
# should be identical up to a scaling factor:
ratio = gauss3d[10, 10]/gauss1d
should_be_ones = ratio / np.mean(ratio)
npt.assert_almost_equal(should_be_ones, np.ones(should_be_ones.shape))
# Test that the inputs are being checked:
npt.assert_raises(ValueError, ebp.gaussian_kernel, xx3d, mean3d)
def test_gaussian_kernel():
xx3d = np.array(
np.meshgrid(np.arange(-10, 10, 1), np.arange(-10, 10, 1),
np.arange(-10, 10, 1)))
# Means are identical:
mean3d = [0, 0, 0]
# Variance/covariance matrix:
sigma3d = np.array([[10, 10, 0], [0, 10, 10], [10, 10, 10]])
gauss3d = ebp.gaussian_kernel(xx3d, np.hstack([mean3d, sigma3d.ravel()]))
# Verify against a 1D case:
x = xx3d[0, 0, :, 0]
gauss1d = (1 / (sigma3d[0, 0] * np.sqrt(np.pi)) *
np.exp(-0.5 * (x - mean3d[0])**2 / sigma3d[0, 0]))
# should be identical up to a scaling factor:
ratio = gauss3d[10, 10] / gauss1d
should_be_ones = ratio / np.mean(ratio)
npt.assert_almost_equal(should_be_ones, np.ones(should_be_ones.shape))
# Test that the inputs are being checked:
npt.assert_raises(ValueError, ebp.gaussian_kernel, xx3d, mean3d)