def test_imshow_heatmap():
from scipy.interpolate import griddata
from matplotlib import pyplot as plt
mesh3D = mesh(200)
mesh2D = proj_to_2D(mesh3D)
data = np.zeros((3,3))
data[0,1] += 2
vals = np.exp(log_dirichlet_density(mesh3D,2.,data=data.sum(0)))
temp = log_censored_dirichlet_density(mesh3D,2.,data=data)
censored_vals = np.exp(temp - temp.max())
xi = np.linspace(-1,1,1000)
yi = np.linspace(-0.5,1,1000)
plt.figure()
plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),vals,(xi[None,:],yi[:,None]),method='cubic'))
plt.axis('off')
plt.title('uncensored likelihood')
plt.figure()
plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),censored_vals,(xi[None,:],yi[:,None]),method='cubic'))
plt.axis('off')
plt.title('censored likelihood')
def prior_posterior_2D(meshsize=250,alpha=2.,data=np.array([[0,2,0],[0,0,0],[0,0,0]])):
assert data.shape == (3,3)
mesh3D = simplex.mesh(meshsize)
mesh2D = simplex.proj_to_2D(mesh3D) # use specialized b/c it plays nicer with triangulation algorithm
priorvals = np.exp(dirichlet.log_dirichlet_density(mesh3D,alpha))
posteriorvals_uncensored = np.exp(dirichlet.log_dirichlet_density(mesh3D,alpha,data=data.sum(0)))
temp = dirichlet.log_censored_dirichlet_density(mesh3D,alpha,data=data)
temp = np.exp(temp - temp.max())
posteriorvals_censored = temp/temp.sum() # direct discretized integration!
# used for grid interpolation
xi = np.linspace(mesh2D[:,0].min(), mesh2D[:,0].max(), 2000, endpoint=True)
yi = np.linspace(mesh2D[:,1].min(), mesh2D[:,1].max(), 2000, endpoint=True)
plt.figure(figsize=(8,8))
# use exactly one of the next two code lines!
# this one performs interpolation to get a rectangular-pixel grid, but
# produces a blurred image
plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),priorvals,(xi[na,:],yi[:,na]),method='cubic'))
# this one exactly represents the data by performing a DeLaunay
# triangulation, but it must draw each triangular pixel individually,
# resulting in large files and slow draw times
# plt.tripcolor(mesh2D[:,0],mesh2D[:,1],priorvals) # exact triangles, no blurring
plt.axis('off')
save('../writeup/figures/dirichlet_prior_2D.pdf')
plt.figure(figsize=(8,8))
plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),posteriorvals_uncensored,(xi[na,:],yi[:,na]),method='cubic'))
# plt.tripcolor(mesh2D[:,0],mesh2D[:,1],posteriorvals_uncensored)
plt.axis('off')
save('../writeup/figures/dirichlet_uncensored_posterior_2D.pdf')
plt.figure(figsize=(8,8))
plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),posteriorvals_censored,(xi[na,:],yi[:,na]),method='cubic'))
# plt.tripcolor(mesh2D[:,0],mesh2D[:,1],posteriorvals_censored)
plt.axis('off')
save('../writeup/figures/dirichlet_censored_posterior_2D.pdf')
def test_pcolor_heatmap():
# import matplotlib.tri as tri
from matplotlib import pyplot as plt
mesh3D = mesh(100,edges=True)
mesh2D = proj_to_2D(mesh3D)
# triangulation = tri.Triangulation(mesh2D) # this is called in tripcolor
data = np.zeros((3,3))
data[0,1] += 1
vals = np.exp(log_dirichlet_density(mesh3D,2.,data=data.sum(0)))
temp = log_censored_dirichlet_density(mesh3D,2.,data=data)
censored_vals = np.exp(temp - temp.max())
plt.figure()
plt.tripcolor(mesh2D[:,0],mesh2D[:,1],vals)
plt.title('uncensored')
plt.figure()
plt.tripcolor(mesh2D[:,0],mesh2D[:,1],censored_vals)
plt.title('censored')
def aux_posterior_2D(meshsize=250,alpha=2.,data=np.array([[0,2,0],[0,0,0],[0,0,0]])):
assert data.shape == (3,3)
mesh3D = simplex.mesh(meshsize)
mesh2D = simplex.proj_to_2D(mesh3D) # use specialized b/c it plays nicer with triangulation algorithm
# get samples
auxsamples = sampling.generate_pi_samples_withauxvars(alpha,10000,data)
# evaluate a kde based on the samples
aux_kde = density.kde(0.005,auxsamples[len(auxsamples)//20:])
aux_kde_vals = aux_kde(mesh3D)
### plot
# used for grid interpolation
xi = np.linspace(mesh2D[:,0].min(), mesh2D[:,0].max(), 2000, endpoint=True)
yi = np.linspace(mesh2D[:,1].min(), mesh2D[:,1].max(), 2000, endpoint=True)
plt.figure(figsize=(8,8))
plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),aux_kde_vals,(xi[na,:],yi[:,na]),method='cubic'))
plt.axis('off')
save('../writeup/figures/dirichlet_censored_auxvar_posterior_2D.pdf')