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SP4EHW_IM/HW1/Exercise1.py
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Exercise1.py
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# =============================================================================
# Mahmoud and Igor HW #1 - EX. #1 - SP4E Course
# =============================================================================
# Import Packages
import numpy as np
import scipy
import scipy.optimize
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# Defined Functions
def objective(x):
return (2*x[0]**2+1.5*x[1]**2+x[0]*x[1]-x[0]-2*x[1]+6)
def objective1(x,y):
return 2*x**2+1.5*y**2+x*y-x-2*y+6
global xmatrix
global counter
global zz
global xx
global yy
initial=[3,3] # Initial Guesses
counter=0
xmatrix=[[initial[0],initial[1]]] # The found parameters x,y, .. etc. per iteration
xx=[initial[0]]
yy=[initial[1]]
zz=[objective1(initial[0],initial[1])]
def getIterationSteps(x):
global counter
global xx
global yy
global zz
xmatrix.append([x[0],x[1]])
zz.append(objective1(x[0],x[1]))
counter+=1
xx.append(x[0])
yy.append(x[1])
ret=scipy.optimize.minimize(objective, initial, tol=1e-9, callback=getIterationSteps)
#print (ret)
# Plot Results and Objective Function
X, Y = np.meshgrid(np.linspace(-3.0, 3.0, 30), np.linspace(-3.0, 3.0, 30))
Z = objective1(X,Y)
fig = plt.figure()
ax = plt.axes(projection='3d')
#Surface plot or wireframe plot !
#ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='viridis', edgecolor='none')
ax.plot_wireframe(X, Y, Z, color=[0.7,0.7,0.7])
ax.set_title('Objective Function');
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
#Plotting iterations
np.transpose(zz)
ax.plot3D(xx,yy,zz, c='red', marker='o', markersize=15, linewidth=5)
plt.show()
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