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simplex_opt.py
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import math
import numpy as np
import argparse
import sys
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.animation as animation
plt.rcParams['savefig.dpi'] = 200
plt.rcParams['figure.dpi'] = 100
plt.rcParams['axes.axisbelow'] = True
from matplotlib import cm
import seaborn as sns
sns.set_style('white')
parser = argparse.ArgumentParser(description=u'SimpleOpt Method')
args = parser.parse_args()
num_divs = 50
x_min = -5
x_max = 5
y_min = -5
y_max = 5
scope_x = [float(x_min), float(x_max)]
scope_y = [float(y_min), float(y_max)]
def get_symmetry_point(points, index):
A = points[index]
B = points[(index + 1) % 3]
C = points[(index + 2) % 3]
D = B + C - A
return D
def get_symmetry_triangle(points, index):
D = get_symmetry_point(points, index)
new_points = np.copy(points)
new_points[index] = D
return new_points
def check_range_valid(x_min, x_max, y_min, y_max, x, y):
if (x >= x_min and x <= x_max and y >= y_min and y <= y_max):
return True
return False
def is_triangle(points):
if(len(points) != 3):
print("len:", len(points))
return False
for i in range(3):
A = points[i]
B = points[(i + 1) % 3]
C = points[(i + 2) % 3]
AB = np.linalg.norm(A - B)
AC = np.linalg.norm(A - C)
BC = np.linalg.norm(B - C)
# print("A:", A, "B:", B, "C:", C, "AB:", AB, "AC:", AC, "BC:", BC)
if (AB + AC <= BC):
return False
return True
def func_sin(points):
return np.sin(np.sqrt(np.square(points[:, 0]) + np.square(points[:, 1])))
def func_square(points):
return -(np.square(points[:, 0]) + np.square(points[:, 1]))
def func_exp(points):
n_points = np.shape(points)[0]
values = np.mat(np.zeros((n_points, 1)))
for i in range(n_points):
x = points[i, 0]
y = points[i, 1]
value = (1 - x / 2 + x**5 + y**3) * np.exp(-x**2 -y**2)
values[i, 0] = value
return values
def simplex_opt(x_min, x_max, y_min, y_max, x, y, a, obj_func, tol):
triangle_list = []
value_list = []
error = np.inf
while (error >= tol):
p = a * (np.sqrt(3) + 1) / (2 * np.sqrt(2))
q = a * (np.sqrt(3) - 1) / (2 * np.sqrt(2))
triangle = np.mat([[x, y], [x + p, y + q], [x + q, y + p]])
is_valid_triangle = is_triangle(triangle)
if (is_valid_triangle == False):
print("invalid triangle:", triangle)
return
optimal_point = np.mat([-np.inf, -np.inf])
optimal_idx = -1;
symmetry_point = np.mat([-np.inf + 1, -np.inf + 1])
worst_point = np.mat([-np.inf, -np.inf])
optimal_repeat_times = 0
iter = 0;
while (optimal_repeat_times < 3):
iter += 1
triangle_list.append(np.mat(np.copy(triangle)))
fxy = obj_func(triangle)
value_list.append(np.mat(np.copy(fxy).reshape(-1, 1)))
min_idx = np.argmin(fxy)
current_worst_point = triangle[min_idx]
max_idx = np.argmax(fxy)
current_optimal_point = np.mat(triangle[max_idx, :])
worst_point = np.mat(triangle[min_idx, :])
if ((current_optimal_point == optimal_point).all() == True):
optimal_repeat_times += 1
else:
optimal_repeat_times = 1
optimal_point = current_optimal_point
optimal_idx = max_idx
second_worst = 0;
for i in range(3):
if (i != min_idx and i != max_idx):
second_worst = i
break
if ((symmetry_point == current_worst_point).all() == True):
triangle = get_symmetry_triangle(triangle, second_worst)
symmetry_point = triangle[second_worst]
else:
triangle = get_symmetry_triangle(triangle, min_idx)
symmetry_point = triangle[min_idx]
is_valid = check_range_valid(x_min, x_max, y_min, y_max, symmetry_point[0],
symmetry_point[1])
if (is_valid == False):
triangle = get_symmetry_triangle(triangle, min_idx)
triangle = get_symmetry_triangle(triangle, second_worst)
symmetry_point = triangle[second_worst]
optimal_value = obj_func(optimal_point)
worst_value = obj_func(worst_point)
error = np.abs((optimal_value - worst_value) / optimal_value)
print("optimal_point:", optimal_point, "optimal value:", optimal_value, "worst_value:", worst_value, "error:",
error)
optimal_repeat_times = 0
if error >= tol:
x = optimal_point[0, 0]
y = optimal_point[0, 1]
a = a / 2.0
triangle_and_value_list = []
for i in range(len(triangle_list)):
triangle_and_value = np.copy(np.hstack((triangle_list[i], value_list[i])))
triangle_and_value_list.append(triangle_and_value)
optimal = np.copy(np.hstack((optimal_point, optimal_value)))
return triangle_and_value_list, optimal
def func(x, y):
return -(np.square(x) + np.square(y))
# return np.sin(np.sqrt(np.square(x) + np.square(y)))
#return (1 - x / 2 + x ** 5 + y ** 3) * np.exp(-x ** 2 - y ** 2)
def snapshot2D(ax):
a = np.linspace(scope_x[0] - 0.2, scope_x[1] + 0.2, num_divs)
b = np.linspace(scope_y[0] - 0.2, scope_y[1] + 0.2, num_divs)
x, y = np.meshgrid(a, b)
# z=func(x,y)
# ax.contour(x, y,z, levels=np.logspace(-3,3,25), cmap='jet')
ax.contourf(x, y, func(x, y), 50, cmap=cm.hot, alpha=0.7)
CS = ax.contour(x, y, func(x, y), 15, colors='k')
ax.clabel(CS, inline=True, fontsize=13)
ax.set_xlabel(r'x', fontdict={'fontsize': 18, 'fontweight': 'medium'})
ax.set_ylabel(r'y', fontdict={'fontsize': 18, 'fontweight': 'medium'})
ax.set_title(r'Simple_opt $f(x,y)$', fontdict={'fontsize': 12, 'fontweight': 'medium'})
ax.xaxis.set_tick_params(labelsize=18)
ax.yaxis.set_tick_params(labelsize=18)
# ax.plot(final_x, final_y, marker='*', c='r', markersize=15)
# ax.scatter(final_x, final_y, marker='*', c='r', s=50, label='Final Result')
return ax
def snapshot3D(ax):
a = np.linspace(scope_x[0] - 0.2, scope_x[1] + 0.2, num_divs)
b = np.linspace(scope_y[0] - 0.2, scope_y[1] + 0.2, num_divs)
X, Y = np.meshgrid(a, b)
Z = func(X, Y)
# ax.plot_surface(X, Y, Z, rstride=1, cstride=1, edgecolor='none', cmap='jet')
ax.plot_wireframe(X, Y, Z, rstride=1, cstride=1, cmap='jet')
cset = ax.contourf(X, Y, Z, zdir='z', offset=-0.5, cmap='jet', alpha=0.2)
cset = ax.contourf(X, Y, Z, zdir='x', offset=scope_x[0] - 0.3, cmap='jet', alpha=0.2)
cset = ax.contourf(X, Y, Z, zdir='y', offset=scope_y[1] + 0.3, cmap='jet', alpha=0.2)
# CS = ax.contour(x, y, func(x, y), colors='k')
# ax.clabel(CS, inline=True, fontsize=13)
ax.set_xlabel(r'X', fontdict={'fontsize': 18, 'fontweight': 'medium'})
ax.set_ylabel(r'Y', fontdict={'fontsize': 18, 'fontweight': 'medium'})
ax.set_ylabel(r'Z', fontdict={'fontsize': 18, 'fontweight': 'medium'})
ax.set_title(r'Simple opt $f(x,y)$ 3D', fontdict={'fontsize': 15, 'fontweight': 'medium'})
ax.xaxis.set_tick_params(labelsize=18)
ax.yaxis.set_tick_params(labelsize=18)
# ax.plot([final_x], [final_y], [final_z], marker='*', c='r', markersize=20, label='Final result')
# ax.scatter([final_x], [final_y], [final_z], marker='*', c='r', s=80, label='Final result')
# ax.plot(track_x[0], track_y[0], c='b', marker='o')
return ax
def init3D():
line.set_data([], [])
line.set_3d_properties([])
point.set_data([], [])
point.set_3d_properties([])
# point1.set_data([], [])
# point1.set_3d_properties([])
# point2.set_data([], [])
# point2.set_3d_properties([])
#
# point3.set_data([], [])
# point3.set_3d_properties([])
display_value.set_text('')
return line, point, display_value
# return line, point, point1, point2, point3, display_value
def animate3D(i):
# ti = 5
a_tri = triangle_and_value_list[i]
line.set_data(a_tri[:, 0], a_tri[:, 1])
line.set_3d_properties(a_tri[:,2])
point.set_data(a_tri[:, 0], a_tri[:, 1])
point.set_3d_properties(a_tri[:,2])
# point1.set_data(track_x[i], track_y[i])
# point1.set_3d_properties([-0.5] * len(track_x[i]))
# line.set_data(track_x[i], track_y[i])
# line.set_3d_properties(track_z[i])
#
# point.set_data(track_x[i], track_y[i])
# point.set_3d_properties(track_z[i])
#
# point1.set_data(track_x[i], track_y[i])
# point1.set_3d_properties([-0.5] * len(track_x[i]))
# point2.set_data(scope_x[0]* len(track_x[i]), track_y[i]) # a bug here
# point2.set_3d_properties(track_z[i])
# point2.set_data([scope_x[0] - 0.3] * len(track_x[i]), track_y[i])
# point2.set_3d_properties(track_z[i])
#
# point3.set_data(track_x[i], [scope_y[1] + 0.3] * len(track_x[i]))
# point3.set_3d_properties(track_z[i])
display_value.set_text('Iteration: ' + str(i + 1) +
'\n'
# r'$x(\alpha_1)= $' '{0:.4f}'.format(track_x[i][1]) + r' $x(\alpha_2)= $' '{0:.4f}'.format(
# track_x[i][2]) +
# '\n'
# r'$y(\alpha_1)= $' '{0:.4f}'.format(track_y[i][1]) + r' $y(\alpha_2)= $' '{0:.4f}'.format(
# track_y[i][2]) +
# '\n'
# r'$z(\alpha_1)= $' '{0:.4f}'.format(track_z[i][1]) + r' $z(\alpha_2)= $' '{0:.4f}'.format(
# track_z[i][2])
)
return line, point, display_value
# return line, point, point1, point2, point3, display_value
if __name__ == '__main__':
print("----test func_sin---")
triangle_and_value_list, optimal = simplex_opt(-5, 5, -5, 5, 3, 2, 1.0, func_sin, 0.01)
print(triangle_and_value_list, optimal)
print("----test func_square---")
triangle_and_value_list, optimal = simplex_opt(-5, 5, -5, 5, 3, 2, 1.0, func_square, 0.5)
print(triangle_and_value_list, optimal)
print("----test func_exp---")
triangle_and_value_list, optimal = simplex_opt(-5, 5, -5, 5, 3, 2, 1.0, func_exp, 0.01)
# print(triangle_and_value_list, optimal)
# fig = plt.figure(figsize=(6, 6))
# ax = fig.add_subplot(111)
# ax=snapshot2D(ax)
# plt.show()
fig1 = plt.figure(figsize=(8, 8))
ax2 = Axes3D(fig1)
ax2 = snapshot3D(ax2)
# ti = 5
# a_tri=triangle_and_value_list[ti]
#ax2.scatter([a_tri[:, 0]], [a_tri[:, 1]], [a_tri[:, 2]], marker='*', c='r', s=80, label='Triangle')
# ax2.scatter([a_tri[:, 0]], [a_tri[:, 1]], [a_tri[:, 2]], marker='o', c='r', s=80, label='Triangle')
line, = ax2.plot([], [], [], 'r', lw=1.5)
point, = ax2.plot([], [], [], 'ro', markersize=10, label='Experiments') # on the surface
# point1, = ax2.plot([], [], [], 'ro', markersize=10, alpha=0.2) # projection to z
# point2, = ax2.plot([], [], [], 'ro', markersize=10, alpha=0.2) # projection to x
# point3, = ax2.plot([], [], [], 'ro', markersize=10, alpha=0.2) # projection to y
display_value = ax2.text(scope_x[1], scope_y[1], 0.5, '', transform=ax2.transAxes)
ax2.grid(False)
ax2.legend(loc=1)
anim = animation.FuncAnimation(fig1, animate3D, init_func=init3D,
frames=len(triangle_and_value_list),
interval=1000,
repeat_delay=80, blit=True)
Writer = animation.writers['ffmpeg']
writer = Writer(fps=2, metadata=dict(artist='L'), bitrate=1800)
anim.save('simpleopt-001.mp4', writer=writer)
anim.save('simpleopt-001.mp4', writer='imagemagick')
anim.save('simpleopt-001.gif', writer='imagemagick', fps=2)
plt.savefig('simpleopt-001.pdf')
plt.savefig('simpleopt-001.png')
plt.show()