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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 For the testing we will use a standard DSI acqusition scheme with 514 gradient directions and 1 S0. There's also the alternative of having a scheme with 4195 directions. In the case of the simulated multi-tensor signal is doesn't seem to make a big difference.
Step1:  Let’s create a multi tensor with 2 fiber directions at 60 degrees.
Step2:  Perform the reconstructions with standard DSI. To get sharp results, having a large r_end seems to have the biggest impact but increasing the qgrid_size also has some effect. Also, you can effectively disable the Hanning filter by setting the filter_width to infinity.
Step3:  Predict the test data values using GP. To save time the hyperparameters are set to the values that the training would otherwise yield.
Step4:  Visualize the ground truth ODF together with the DSI.
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Python Code:
btable = np.loadtxt(get_data('dsi515btable'))
#btable = np.loadtxt(get_data('dsi4169btable'))
gtab['test'] = gradient_table(btable[:, 0], btable[:, 1:],
                              big_delta=gtab['train'].big_delta, small_delta=gtab['train'].small_delta)
gtab['test'].info
Explanation: For the testing we will use a standard DSI acqusition scheme with 514 gradient directions and 1 S0. There's also the alternative of having a scheme with 4195 directions. In the case of the simulated multi-tensor signal is doesn't seem to make a big difference.
End of explanation
evals = np.array([[0.0015, 0.0003, 0.0003],
                  [0.0015, 0.0003, 0.0003]])
directions = [(-30, 0), (30, 0)]
fractions = [50, 50]
for key, _gtab in gtab.items():
    data[key] = multi_tensor(_gtab, evals, 100, angles=directions,
                             fractions=fractions, snr=None)[0][None, None, None, :]
sphere = get_sphere('symmetric724').subdivide(1)
odf['gt'] = multi_tensor_odf(sphere.vertices, evals, angles=directions,
                             fractions=fractions)[None, None, None, :]
Explanation: Let’s create a multi tensor with 2 fiber directions at 60 degrees.
End of explanation
dsi_model = DiffusionSpectrumModel(gtab['test'], qgrid_size=25, r_end=50, filter_width=np.inf)
dsi_fit = dsi_model.fit(data['test'])
odf['dsi'] = dsi_fit.odf(sphere)
#dsi_model.filter
#plt.plot(gtab['train'].qvals)
plt.plot(data['test'].flatten())
#plt.plot(data['pred'].flatten())
plt.plot(dsi_fit.data.flatten() * dsi_model.filter)
dsi_fit.rtop_pdf(normalized=False)/dsi_fit.rtop_signal(filtering=True)
#/dsi_model.fit(data['pred']).rtop_signal(filtering=True)
Explanation: Perform the reconstructions with standard DSI. To get sharp results, having a large r_end seems to have the biggest impact but increasing the qgrid_size also has some effect. Also, you can effectively disable the Hanning filter by setting the filter_width to infinity.
End of explanation
if dataset == 'HCP':
    kernel = get_default_independent_kernel(3, n_max=6, q_lengthscale=1.16, coefficients=(1778, 31.4, 3.63, 0.56))
    gp_model = GaussianProcessModel(gtab['train'], kernel=kernel)
    gp_fit = gp_model.fit(data['train'], retrain=False)
elif dataset == 'SPARC':
    kernel = get_default_independent_kernel(3, n_max=6, q_lengthscale=0.57, coefficients=(2578, 52, 5.0, 0.94))
    gp_model = GaussianProcessModel(gtab['train'], kernel=kernel, verbose=False)
    gp_fit = gp_model.fit(data['train'], retrain=False)
odf['gp'] = gp_fit.odf(sphere)
Explanation: Predict the test data values using GP. To save time the hyperparameters are set to the values that the training would otherwise yield.
End of explanation
ren = fvtk.ren()
odfs = np.vstack((odf['gt'], odf['dsi'], odf['gp']))
odf_actor = fvtk.sphere_funcs(odfs, sphere)
odf_actor.RotateX(90)
fvtk.add(ren, odf_actor)
fvtk.record(ren, out_path='dsi_sim.png', size=(300, 300))
Explanation: Visualize the ground truth ODF together with the DSI.
End of explanation
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