Make a python3 file called, "Peaks Optimization.py"

Question

Make a python3 file called, "Peaks Optimization.py"

Plot a surface plot of the "peaks" function from "Peaks plotting.py"

Find the peaks and valleys from peaks function using scipy minimize, using Nelder-mead method

Print the (x, y) coordinates of minimums and maximums of the function, using the following starting guesses:

Find minimums using 2 guesses:

· (0, -2) and (-2, 0)

Find maximums using 2 guesses:

· (0, 2) and (-1, 1)

Peaks Optimization.py:

from scipy.optimize import minimize
import numpy as np
import matplotlib.pyplot as plt

# Find minimums using two different guesses:
# (0, -2) and (-2, 0)

# Find maximums using two different guesses:
# (0, 2) and (-1, 1)

def main():


main()

Peaks plotting.py:

from mpl_toolkits import mplot3d
import numpy as np
import matplotlib.pyplot as plt


def peaks(x, y):
    return 3*(1-x)**2.*np.exp(-(x**2) - (y+1)**2) 
   - 10*(x/5 - x**3 - y**5) * np.exp(-x**2-y**2) 
   - 1/3*np.exp(-(x+1)**2 - y**2)

def surfacePlot():
    x = np.outer(np.linspace(-3, 3, 30), np.ones(30))
    y = x.copy().T  # transpose

    z = np.zeros((30, 30))
    for i in range(len(x)):
        for j in range(len(y)):
            z[i, j] = peaks(x[i, j], y[i, j])

    fig = plt.figure()
    ax = plt.axes(projection='3d')
    ax.plot_surface(x, y, z, cmap='PuBu', edgecolor='none')
    ax.set_title('Surface plot')
    plt.show()


surfacePlot()

Key (code we need to write in main() is hidden):

Screenshot 2020-11-12 192802.jpg

Answer 1

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