def plot_heatmap_at_iteration(self, iteration, **options):
'''I line up the actual grid with interpolating grid so there is no interpolation, actually.
Options:
min_max_scale: [min, max] of the scale
colorbar_decimals: number of decimals used in the colorbar
'''
ax = plt.subplot()
ternary.plot_heatmap(lambda x: self.interp_histogram_at_iteration(iteration, x),
steps = self.num_individuals, boundary=True, **options)
scale = self.num_individuals
ternary.draw_boundary(scale=scale, ax=ax)
plt.gca().set_aspect('equal', adjustable='box')
plt.xlim([-.1*scale,1.1*scale])
plt.ylim([-0.13*scale, scale])
plt.text(1.01 * scale, -.05*scale, r'$f_1$', fontsize=35 )
plt.text(-.08 * scale, -.05*scale, r'$f_3$', fontsize=35 )
plt.text(.46*scale, .9*scale, r'$f_2$', fontsize=35)
plt.gca().yaxis.set_visible(False)
plt.gca().xaxis.set_visible(False)
plt.grid(False)
# Plot the fractional generation
generation_formatted = '%.2f' % self.frac_gen[iteration]
textbox = r'$N=' + str(self.num_individuals) + r'$' '\n'
textbox += 'Num Simulations: ' + r'$10^' + str(int(np.log10(self.num_simulations))) + r'$' + '\n'
textbox += 'Generation: ' + generation_formatted
plt.text(.71*scale, .85*scale, textbox, fontsize=15, linespacing=1.75)
def plot_shell(steps=10, fill_color="black"):
"""Plot an empty heatmap shell for illustration."""
for i in range(steps + 1):
for j in range(steps - i):
vertices = ternary.triangle_coordinates(i, j, alt=False)
x, y = ternary.unzip(vertices)
pyplot.fill(x, y, facecolor=fill_color, edgecolor="black")
for i in range(steps + 1):
for j in range(steps - i - 1):
vertices = ternary.triangle_coordinates(i, j, alt=True)
x, y = ternary.unzip(vertices)
pyplot.fill(x, y, facecolor="w", edgecolor="black")
ternary.draw_boundary(scale=steps, linewidth=1)
def basic_example():
# Projection dynamic.
initial_state = normalize(numpy.array([1,1,4]))
m = rock_scissors_paper(a=1., b=-2.)
fitness = linear_fitness(m)
incentive = replicator_incentive_power(fitness, 0)
mu = uniform_mutation_matrix(3, ep=0.2)
t = compute_trajectory(initial_state, incentive, escort=power_escort(0), iterations=10000, verbose=True, mu=mu)
ternary.plot(t, linewidth=2)
ternary.draw_boundary()
## Lyapunov Quantities
pyplot.figure()
# Replicator Lyapunov
e = normalize(numpy.array([1,1,1]))
v = [kl_divergence(e, x) for x in t]
pyplot.plot(range(len(t)), v, color='b')
d = q_divergence(0)
v = [d(e, x) for x in t]
pyplot.plot(range(len(t)), v, color='r')
pyplot.show()
def plot_heatmap_at_iteration(self, iteration, **options):
'''I line up the actual grid with interpolating grid so there is no interpolation, actually.
Options:
min_max_scale: [min, max] of the scale
colorbar_decimals: number of decimals used in the colorbar
'''
ax = plt.subplot()
ternary.plot_heatmap(
lambda x: self.interp_histogram_at_iteration(iteration, x),
steps=self.num_individuals,
boundary=True,
**options)
scale = self.num_individuals
ternary.draw_boundary(scale=scale, ax=ax)
plt.gca().set_aspect('equal', adjustable='box')
plt.xlim([-.1 * scale, 1.1 * scale])
plt.ylim([-0.13 * scale, scale])
plt.text(1.01 * scale, -.05 * scale, r'$f_1$', fontsize=35)
plt.text(-.08 * scale, -.05 * scale, r'$f_3$', fontsize=35)
plt.text(.46 * scale, .9 * scale, r'$f_2$', fontsize=35)
plt.gca().yaxis.set_visible(False)
plt.gca().xaxis.set_visible(False)
plt.grid(False)
# Plot the fractional generation
generation_formatted = '%.2f' % self.frac_gen[iteration]
textbox = r'$N=' + str(self.num_individuals) + r'$' '\n'
textbox += 'Num Simulations: ' + r'$10^' + str(
int(np.log10(self.num_simulations))) + r'$' + '\n'
textbox += 'Generation: ' + generation_formatted
plt.text(.71 * scale,
.85 * scale,
textbox,
fontsize=15,
linespacing=1.75)
lines = terntransform(a, b, c, d)
step = 0.2
plt.figure()
for line,color,label in zip(lines,colors,datalabels):
tern.plot(line, color = color, linewidth=2.0, label = label)
ip = baryIntersect(lines)
tern.plotIntersect(ip)
tern.gridlines(step, '0.7')
tern.draw_boundary()
tern.addlabels(endmembers)
plt.legend()
#pyplot.box(on='off')
h = plt.gca()
#plt.axis('off')
xmin = -0.1
xmax = 1.1
ymin = -0.1
ymax = 1
v = [xmin, xmax, ymin, ymax]
plt.axis(v)
h.axes.get_xaxis().set_visible(False)
h.axes.get_yaxis().set_visible(False)
def heatmap_example(func, steps=100, boundary=True):
ternary.plot_heatmap(func, steps=steps, boundary=boundary)
ternary.draw_boundary(scale=steps)
"""Plot an empty heatmap shell for illustration."""
for i in range(steps + 1):
for j in range(steps - i):
vertices = ternary.triangle_coordinates(i, j, alt=False)
x, y = ternary.unzip(vertices)
pyplot.fill(x, y, facecolor=fill_color, edgecolor="black")
for i in range(steps + 1):
for j in range(steps - i - 1):
vertices = ternary.triangle_coordinates(i, j, alt=True)
x, y = ternary.unzip(vertices)
pyplot.fill(x, y, facecolor="w", edgecolor="black")
ternary.draw_boundary(scale=steps, linewidth=1)
if __name__ == "__main__":
pyplot.figure()
plot_shell(16)
pyplot.figure()
heatmap_example(shannon_entropy, steps=100, boundary=True)
pyplot.figure()
func = dirichlet([6, 10, 13])
heatmap_example(func, steps=100, boundary=False)
pyplot.figure()
points = []
with open("curve.txt") as handle:
for line in handle:
points.append(map(float, line.split(" ")))
ternary.plot(points, linewidth=2.0)
ternary.draw_boundary()
pyplot.show()
"""Computes the Shannon Entropy at a distribution in the simplex."""
s = 0.
for i in range(len(p)):
try:
s += p[i] * math.log(p[i])
except ValueError:
continue
return -1.*s
if __name__ == '__main__':
## Boundary and Gridlines
pyplot.figure()
steps = 30
gs = gridspec.GridSpec(1,2)
ax = pyplot.subplot(gs[0,0])
ax = ternary.draw_boundary(steps, color='black', ax=ax)
ternary.draw_gridlines(steps, ax=ax, color='black')
ax.set_title("Simplex Boundary and Gridlines")
## Various lines
ax = pyplot.subplot(gs[0,1])
ternary.draw_boundary(steps, linewidth=2., color='black', ax=ax)
ternary.draw_horizontal_line(ax, steps, 16)
ternary.draw_left_parallel_line(ax, steps, 10, linewidth=2., color='red', linestyle="--")
ternary.draw_right_parallel_line(ax, steps, 20, linewidth=3., color='blue')
p1 = ternary.project_point((12,8,10))
p2 = ternary.project_point((2, 26, 2))
ternary.draw_line(ax, p1, p2, linewidth=3., marker='s', color='green', linestyle=":")
ax.set_title("Various Lines")
## Heatmap roundup
colors = ['b', 'g', 'c', 'm', 'r', 'y']
lines = terntransform(*data)
for line, color, label in zip(lines, colors, datalabels):
tern.plot(line,
color=color,
linewidth=2.0,
label=label if (ind == 0) else None)
ip = baryIntersect(lines)
tern.plotIntersect(ip, marker='o' + colors[ind], label=region[0])
step = 0.2
tern.gridlines(step, '0.7')
tern.draw_boundary()
tern.addlabels(endmembers)
plt.legend()
#pyplot.box(on='off')
h = plt.gca()
#plt.axis('off')
xmin = -0.1
xmax = 1.1
ymin = -0.1
ymax = 1
v = [xmin, xmax, ymin, ymax]
plt.axis(v)
h.axes.get_xaxis().set_visible(False)
h.axes.get_yaxis().set_visible(False)
