def calc_gaunt_tensor(filename, lmax=4):
jmax = myutil.maxl2maxj(lmax)
G = np.zeros((jmax, jmax, jmax))
for index, g in np.ndenumerate(G):
print(index)
l1, m1 = myutil.j2lm(index[0])
l2, m2 = myutil.j2lm(index[1])
l3, m3 = myutil.j2lm(index[2])
G[index] = Rgaunt(l1, l2, l3, m1, m2, m3)
np.save(filename, G)
return G
def multiply_sh_coefficients(a, b, evaluate=True):
maxl, m = myutil.j2lm(len(a) - 1)
c = [0] * (myutil.maxl2maxj(maxl + 2))
for i, ai in enumerate(a):
l1, m1 = myutil.j2lm(i)
for j, bi in enumerate(b):
l2, m2 = myutil.j2lm(j)
for k, ci in enumerate(c):
l3, m3 = myutil.j2lm(k)
if ai != 0 and bi != 0:
c[k] += ai * bi * Rgaunt(
l1, l2, l3, m1, m2, m3, evaluate=evaluate)
return c
def __init__(self,
f=np.zeros((3, 3, 3, 15), dtype=np.float32),
vox_dim=(1, 1, 1),
sphere=get_sphere('symmetric724')):
self.X = f.shape[0]
self.Y = f.shape[1]
self.Z = f.shape[2]
# Calculate band dimensions
self.lmax, mm = util.j2lm(f.shape[-1] - 1)
self.J = util.maxl2maxj(self.lmax)
# Fill the rest of the last l band with zeros
if f.shape[-1] != self.J:
temp = np.zeros((self.X, self.Y, self.Z, self.J))
temp[..., :f.shape[-1]] = f
self.f = temp
else:
self.f = f
self.vox_dim = vox_dim
self.sphere = sphere
self.sphere = sphere.subdivide()
self.N = len(self.sphere.theta)
self.calc_B()
def calc_B(self):
# Calculate odf to sh matrix
B = np.zeros((self.N, self.J))
for (n, j), x in np.ndenumerate(B):
l, m = util.j2lm(j)
B[n, j] = util.spZnm(l, m, self.sphere.theta[n],
self.sphere.phi[n])
self.B = B
self.Binv = np.linalg.pinv(self.B, rcond=1e-15)
def plot_spectrum(self, filename='spectrum.pdf'):
print('Plotting: ' + filename)
f, ax = plt.subplots(1, 1, figsize=(4, 4))
# Create image of spherical harmonic coefficients
image = np.zeros((self.rmax, self.mmax))
for j, c in enumerate(self.coeffs):
l, m = util.j2lm(j)
image[int(l / 2), self.lmax + m] = c
# Label rows and columns
for l in range(self.lmax + 1):
if l == 0:
prepend = 'l='
else:
prepend = ''
if l % 2 == 0:
ax.annotate(r'$' + prepend + str(l) + '$',
xy=(1, 1),
xytext=(-0.75, int(l / 2)),
textcoords='data',
ha='right',
va='center')
ax.annotate(r'$m=$',
xy=(1, 1),
xytext=(-0.75, -0.75),
textcoords='data',
ha='right',
va='center')
for m in range(2 * self.lmax + 1):
ax.annotate('$' + str(m - self.lmax) + '$',
xy=(1, 1),
xytext=(int(m), -0.75),
textcoords='data',
ha='center',
va='center')
# Label each pixel
for (y, x), value in np.ndenumerate(image):
if value != 0:
ax.annotate("{0:.2f}".format(value),
xy=(1, 1),
xytext=(x, y),
textcoords='data',
ha='center',
va='center')
ax.imshow(image,
cmap='bwr',
interpolation='nearest',
vmin=-np.max(self.coeffs),
vmax=np.max(self.coeffs))
ax.axis('off')
f.savefig(filename, bbox_inches='tight')
def __init__(self, coeffs):
self.lmax, mm = util.j2lm(len(coeffs) - 1)
self.jmax = int(0.5 * (self.lmax + 1) * (self.lmax + 2))
self.mmax = 2 * self.lmax + 1
self.rmax = int(self.lmax / 2) + 1
# Fill the rest of the last band with zeros
temp = np.zeros(self.jmax)
temp[:len(coeffs)] = coeffs
self.coeffs = temp
def H(self, pol=None):
if pol is None: # For normalization
cc = sh.SHCoeffs([1, 0, 0, -1 / np.sqrt(5), 0, 0]) / np.sqrt(
4 * np.pi)
if self.optical_axis == [1, 0, 0]: # x-illumination
cc = cc.rotate()
return cc
out = []
for j in range(6):
l, m = util.j2lm(j)
theta, phi = util.xyz2tp(*pol)
if l == 0:
cc = 1.0
else:
cc = 0.4
out.append(cc * util.spZnm(l, m, theta, phi))
return sh.SHCoeffs(out)
def calc_sh2tensor(filename, lmax=2):
jmax = myutil.maxl2maxj(lmax)
H = np.zeros((6, jmax))
theta = Symbol('theta', real=True)
phi = Symbol('phi', real=True)
elems = [(cos(phi) * sin(theta))**2, (sin(phi) * sin(theta))**2,
cos(theta)**2,
cos(phi) * sin(phi) * (sin(theta)**2),
sin(phi) * sin(theta) * cos(theta),
cos(phi) * sin(theta) * cos(theta)]
for i, elem in enumerate(elems):
for j in range(jmax):
l, m = myutil.j2lm(j)
Znm = sh.Znm(l, m, theta, phi).expand(func=True)
theta_int = integrate(sin(theta) * Znm * elem, (theta, 0, pi / 2))
final_int = integrate(expand_trig(theta_int.rewrite(cos)),
(phi, 0, 2 * pi))
H[i, j] = final_int.evalf()
print(i, l, m, final_int)
import pdb
pdb.set_trace()
np.save(filename, H)
def plot_dist(self,
filename='dist.png',
n_pts=2500,
r=1,
mag=1,
show=False,
force_positive=True):
from mayavi import mlab
print('Plotting: ' + filename)
# Flip sign if [1,1,1] direction is negative
coeffs = self.coeffs
if force_positive:
test_radii = 0
for i, c in enumerate(coeffs):
l, m = util.j2lm(i)
test_radii += c * util.spZnm(l, m, np.pi / 4, np.pi / 4)
if test_radii < 0:
coeffs = -coeffs
# Calculate radii
tp = util.fibonacci_sphere(n_pts)
xyz = util.fibonacci_sphere(n_pts, xyz=True)
radii = np.zeros(tp.shape[0])
for i, c in enumerate(coeffs):
l, m = util.j2lm(i)
radii += c * util.spZnm(l, m, tp[:, 0], tp[:, 1])
# radii = radii/np.max(np.abs(radii)) # Handle edge cases below
radii = np.nan_to_num(radii / np.max(np.abs(radii)))
# Split into positive and negatives
n = r * radii.clip(max=0)
p = r * radii.clip(min=0)
# Triangulation
from scipy.spatial import ConvexHull
ch = ConvexHull(xyz)
triangles = ch.simplices
# Create figure
mlab.figure(1, bgcolor=(1, 1, 1), fgcolor=(0, 0, 0), size=(400, 400))
mlab.clf()
# Plot
mlab.triangular_mesh(p * xyz[:, 0],
p * xyz[:, 1],
p * xyz[:, 2],
triangles,
color=(1, 0, 0))
s = mlab.triangular_mesh(n * xyz[:, 0],
n * xyz[:, 1],
n * xyz[:, 2],
triangles,
color=(0, 0, 1))
s.scene.light_manager.light_mode = "vtk"
# View and save
mlab.view(azimuth=45,
elevation=45,
distance=5,
focalpoint=None,
roll=None,
reset_roll=True,
figure=None)
mlab.savefig(filename, magnification=mag)
subprocess.call(
['convert', filename, '-transparent', 'white', filename])
if show:
mlab.show()