"""
======================
MultiTensor Simulation
======================

In this example we show how someone can simulate the signal and the ODF of a
single voxel using a MultiTensor.
"""

import matplotlib.pyplot as plt
import numpy as np

from dipy.core.sphere import disperse_charges, HemiSphere
from dipy.core.gradients import gradient_table
from dipy.data import get_sphere
from dipy.sims.voxel import multi_tensor, multi_tensor_odf
from dipy.viz import window, actor

###############################################################################
# For the simulation we will need a GradientTable with the b-values and
# b-vectors. To create one, we can first create some random points on a
# ``HemiSphere`` using spherical polar coordinates.


n_pts = 64
theta = np.pi * np.random.rand(n_pts)
phi = 2 * np.pi * np.random.rand(n_pts)
hsph_initial = HemiSphere(theta=theta, phi=phi)

###############################################################################
# Next, we call ``disperse_charges`` which will iteratively move the points so
# that the electrostatic potential energy is minimized.


hsph_updated, potential = disperse_charges(hsph_initial, 5000)

###############################################################################
# We need two stacks of ``vertices``, one for every shell, and we need two sets
# of b-values, one at 1000 $s/mm^2$, and one at 2500 $s/mm^2$, as we discussed
# previously.


vertices = hsph_updated.vertices
values = np.ones(vertices.shape[0])

bvecs = np.vstack((vertices, vertices))
bvals = np.hstack((1000 * values, 2500 * values))

###############################################################################
# We can also add some b0s. Let's add one at the beginning and one at the end.


bvecs = np.insert(bvecs, (0, bvecs.shape[0]), np.array([0, 0, 0]), axis=0)
bvals = np.insert(bvals, (0, bvals.shape[0]), 0)

###############################################################################
# Let's now create the ``GradientTable``.


gtab = gradient_table(bvals, bvecs)

###############################################################################
# In ``mevals`` we save the eigenvalues of each tensor.


mevals = np.array([[0.0015, 0.0003, 0.0003],
                   [0.0015, 0.0003, 0.0003]])

###############################################################################
# In ``angles`` we save in polar coordinates (:math:`\theta, \phi`) the principal
# axis of each tensor.


angles = [(0, 0), (60, 0)]

###############################################################################
# In ``fractions`` we save the percentage of the contribution of each tensor.


fractions = [50, 50]

###############################################################################
# The function ``multi_tensor`` will return the simulated signal and an array
# with the principal axes of the tensors in cartesian coordinates.


signal, sticks = multi_tensor(gtab, mevals, S0=100, angles=angles,
                              fractions=fractions, snr=None)

###############################################################################
# We can also add Rician noise with a specific SNR.


signal_noisy, sticks = multi_tensor(gtab, mevals, S0=100, angles=angles,
                                    fractions=fractions, snr=20)

plt.plot(signal, label='noiseless')

plt.plot(signal_noisy, label='with noise')
plt.legend()
# plt.show()
plt.savefig('simulated_signal.png')

###############################################################################
# .. figure:: simulated_signal.png
#    :align: center
# 
#    **Simulated MultiTensor signal**


###############################################################################
# For the ODF simulation we will need a sphere. Because we are interested in a
# simulation of only a single voxel, we can use a sphere with very high
# resolution. We generate that by subdividing the triangles of one of DIPY_'s
# cached spheres, which we can read in the following way.


sphere = get_sphere('repulsion724')
sphere = sphere.subdivide(2)

odf = multi_tensor_odf(sphere.vertices, mevals, angles, fractions)

# Enables/disables interactive visualization
interactive = False

scene = window.Scene()

odf_actor = actor.odf_slicer(odf[None, None, None, :], sphere=sphere,
                             colormap='plasma')
odf_actor.RotateX(90)

scene.add(odf_actor)

print('Saving illustration as multi_tensor_simulation')
window.record(scene, out_path='multi_tensor_simulation.png', size=(300, 300))
if interactive:
    window.show(scene)


###############################################################################
# .. figure:: multi_tensor_simulation.png
#    :align: center
# 
#    Simulating a MultiTensor ODF.
# 
# .. include:: ../links_names.inc
#