import csv
import numpy as np
from numpy import sin, cos, tan, pi, exp
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
from matplotlib import cm
import time
import sys
# optimization parameters
x0 = [0.0, 0.0]
if __name__ == "__main__":
if len(sys.argv) >= 2:
x0[0] = float(sys.argv[1])
if len(sys.argv) >= 3:
x0[1] = float(sys.argv[2])
# target function
functype = 'ellipsoid'
if functype == 'ellipsoid':
alpha = 0.03
else:
alpha = 0.01
eps = 1.0e-5
nmaxiter = 200
iprintiterval = 1
# differentiation x mesh
h = 0.01
# graph plot parameters
fplot = 1
ngdata = 51
xgmin = -4.0
xgmax = 4.0
ygmin = -4.0
ygmax = 4.0
tsleep = 0.3
# first derivative of func(x)
[ドキュメント]
def ediff1(i, x):
if i == 0:
return 2.0 * x[0]
if i == 1:
return 18.0 * x[1]
[ドキュメント]
def gdiff1(i, x):
if i == 0:
return - 10.0 - 60.0 * x[0] + 4.5 * x[0]*x[0] + 12.0 * x[0]*x[0]*x[0] \
+ 3.0 * x[1] * x[1]
if i == 1:
return 30.0 - 60.0 * x[1] + 12.0 * x[1]*x[1]*x[1] \
+ 6.0 * x[0] * x[1]
[ドキュメント]
def efunc(x):
return x[0]*x[0] + 9.0*x[1]*x[1]
[ドキュメント]
def gfunc(x):
return -3.0 - 10.0 * x[0] - 30.0 * x[0]*x[0] + 1.5 * x[0]*x[0]*x[0] + 3.0 * x[0]*x[0]*x[0]*x[0] \
+ 30.0 * x[1] - 30.0 * x[1]*x[1] + 3.0 * x[1]*x[1]*x[1]*x[1] \
+ 3.0 * x[0] * x[1] * x[1]
# global function variables
if functype == 'ellipsoid':
diff1 = ediff1
func = efunc
else:
diff1 = gdiff1
func = gfunc
[ドキュメント]
def main():
global plt, ngdata, xgmin, xgmax
global x0, dump, eps, nmaxiter, iprintinterval
global func, diff1
print("Find minimum / maximum point by Newton-Raphson method")
print("")
# plot surface graph
if fplot == 1:
xgstep = (xgmax - xgmin) / (ngdata - 1)
ygstep = (ygmax - ygmin) / (ngdata - 1)
xg = np.empty([ngdata, ngdata])
yg = np.empty([ngdata, ngdata])
zg = np.empty([ngdata, ngdata])
for ix in range(ngdata):
for iy in range(ngdata):
xg[ix, iy] = xgmin + ix * xgstep
yg[ix, iy] = ygmin + iy * ygstep
zg[ix, iy] = func([xg[ix][iy], yg[ix][iy]])
fig = plt.figure(figsize = (10, 5))
ax = fig.add_subplot(1, 2, 1)
ax2 = fig.add_subplot(1, 2, 2, projection='3d')
# ax = fig.add_subplot(111, projection='3d')
# surf = ax.plot_surface(xg, yg, zg, cmap=cm.coolwarm)
surf = ax2.plot_wireframe(xg, yg, zg, rstride=2, cstride=2)
# ax.set_zlim3d(-3.01, 3.01)
# plt.colorbar(surf, shrink=0.5, aspect=10)
ax.set_title('contour')
contour = ax.contourf(xg, yg, zg, levels = 51, cmap = 'Spectral')
# contour = ax.contour(xg, yg, zg, levels = 51, cmap = 'Spectral')
solve, = ax.plot([], color = 'blue', marker = 'o', linestyle = '-')
# solve, = ax.plot([], color = 'blue', marker = 'o', linestyle = '')
plt.pause(0.1)
# plt.show()
n = len(x0)
Si = np.empty(n)
# calculate initial parameters
f = func(x0)
print("x0 = ({}, {}): f = {}".format(x0[0], x0[1], f))
xt = []
yt = []
xt.append(x0[0])
yt.append(x0[1])
# optimization start
for iter in range(nmaxiter):
for i in range(0, n):
Si[i] = diff1(i, x0)
dx = -alpha * Si
print(" dx=", dx)
x0 = x0 + dx
f = func(x0)
dxmax = max(abs(dx))
print("{:4d}: x = ({:12.6g}, {:12.6g}) dx = {:12.6g}: f = {:12.6g}".format(iter, x0[0], x0[1], dxmax, f))
if fplot == 1:
xt.append(x0[0])
yt.append(x0[1])
solve.set_data(xt, yt)
plt.pause(0.1)
time.sleep(tsleep)
if dxmax < eps:
print("Converged at x = ", x0, " dx = {} f = {}".format(dxmax, f))
break;
else:
print("Not converged")
if fplot == 1:
print("Press enter to terminate:", end = '')
ret = input()
if __name__ == "__main__":
main()