def plot_covariances(X, Theta, Y=None):
if Y is None:
eigvals, eigvecs = scipy.linalg.eigh(Theta)
Y = eigvecs.dot(np.diag(1 / np.sqrt(eigvals))).dot(eigvecs.T)
plt.figure()
plt.subplot(221)
plt.matshow(Theta, cmap=plt.cm.RdBu_r, fignum=False)
plt.clim((-1, 1))
plt.title('population precision matrix')
plt.colorbar()
plt.subplot(222)
sample_prec = scipy.linalg.inv(cov2corr(X.T.dot(X)))
plt.matshow(sample_prec, cmap=plt.cm.RdBu_r,
fignum=False)
max_plot = np.max(np.abs(sample_prec)) / 5.
plt.clim((-max_plot, max_plot))
plt.title('sample (n={}) precision matrix'.format(X.shape[0]))
plt.colorbar()
plt.subplot(223)
plt.matshow(cov2corr(Y.T.dot(Y)), cmap=plt.cm.RdBu_r, fignum=False)
plt.clim((-1, 1))
plt.title('population correlation matrix')
plt.colorbar()
plt.subplot(224)
plt.matshow(cov2corr(X.T.dot(X)), cmap=plt.cm.RdBu_r, fignum=False)
plt.clim((-1, 1))
plt.title('sample correlation matrix')
plt.colorbar()
plt.show()
def plot_covariance(cov, scaled=True, aux=None, diag=True, grid=True):
cov_ = cov.copy()
if scaled:
from covariance_learn import _cov_2_corr as cov2corr
cov_ = cov2corr(cov_)
if not diag:
cov_.flat[::cov_.shape[0] + 1] = 0.
plt.figure()
ax = plt.gca()
if aux is None:
aux = np.ones(cov_.shape)
im = plt.matshow(np.ma.masked_equal(aux, 0) * cov_, cmap=plt.cm.RdBu_r,
fignum=False)
ax.set_axis_bgcolor('.4')
ax.set_xticklabels([])
ax.set_yticklabels([])
divider = make_axes_locatable(ax)
if cov_.shape[0] == 16 and grid:
for k in np.arange(4 - 1):
plt.plot([-.5, 15.5], [4 * (k + 1) - .5, 4 * (k + 1) - .5],
linewidth=2, color='black')
plt.plot([4 * (k + 1) - .5, 4 * (k + 1) - .5], [-.5, 15.5],
linewidth=2, color='black')
plt.xlim((-.5, 15.5))
plt.ylim((15.5, -.5))
elif cov_.shape[0] == 512 and grid:
for k in np.arange(64 - 1):
plt.plot([-.5, 512.5], [8 * (k + 1) - .5, 8 * (k + 1) - .5],
linewidth=1 + int(not((k + 1) % 8)), color='black')
plt.plot([8 * (k + 1) - .5, 8 * (k + 1) - .5], [-.5, 512.5],
linewidth=1 + int(not((k + 1) % 8)), color='black')
plt.xlim((-.5, 512.5))
plt.ylim((512.5, -.5))
m = np.max(np.abs(cov_))
plt.clim((-m, m))
cax = divider.append_axes('right', size='5%', pad=.05)
cb = plt.colorbar(im, cax=cax)
cb.ax.tick_params(labelsize=18)