def test_pca():
p = np.array([[4., 2., 0.6],
[4.2, 2.1, 0.59],
[3.9, 2.0, 0.58],
[4.3, 2.1, 0.62],
[4.1, 2.2, 0.63]])
RES_COV = np.array([[0.025, 0.0075, 0.00175],
[0.0075, 0.0070, 0.00135],
[0.00175, 0.00135, 0.00043]])
RES_EIGV = np.array([[ 0.93676841, 0.34958469, -0.0159843 ],
[ 0.34148069, -0.92313136, -0.1766902 ],
[ 0.0765238 , -0.16005947, 0.98413672]])
RES_EIGS = np.array([0.0278769, 0.00439387, 0.0001592])
eigs, eigv = pca(p)
nt.assert_true(np.allclose(eigs, RES_EIGS))
nt.assert_true(np.allclose(eigv[:,0], RES_EIGV[:,0]) or np.allclose(eigv[:, 0], -1. * RES_EIGV[:, 0]))
nt.assert_true(np.allclose(eigv[:,1], RES_EIGV[:,1]) or np.allclose(eigv[:, 1], -1. * RES_EIGV[:, 1]))
nt.assert_true(np.allclose(eigv[:,2], RES_EIGV[:,2]) or np.allclose(eigv[:, 2], -1. * RES_EIGV[:, 2]))
def principal_direction_extent(tree):
'''Calculate the extent of a tree, that is the maximum distance between
the projections on the principal directions of the covariance matrix
of the x,y,z points of the nodes of the tree.
Input
tree : a tree object
Returns
extents : the extents for each of the eigenvectors of the cov matrix
eigs : eigenvalues of the covariance matrix
eigv : respective eigenvectors of the covariance matrix
'''
# extract the x,y,z coordinates of all the points in the tree
points = np.array([value[COLS.X: COLS.R]for value in val_iter(ipreorder(tree))])
# center the points around 0.0
points -= np.mean(points, axis=0)
# principal components
_, eigv = pca(points)
extent = np.zeros(3)
for i in range(eigv.shape[1]):
# orthogonal projection onto the direction of the v component
scalar_projs = np.sort(np.array([np.dot(p, eigv[:, i]) for p in points]))
extent[i] = scalar_projs[-1]
if scalar_projs[0] < 0.:
extent -= scalar_projs[0]
return extent
