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79 lines
1.8 KiB
Python
79 lines
1.8 KiB
Python
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch17_01.py
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import sympy
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import numpy as np
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from sympy.functions import exp
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#define symbolic vars, function
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x1,x2 = sympy.symbols('x1 x2')
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f_x = x1*exp(-(x1**2 + x2**2))
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print(f_x)
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#take the gradient symbolically
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grad_f = [sympy.diff(f_x,var) for var in (x1,x2)]
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print(grad_f)
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f_x_fcn = sympy.lambdify([x1,x2],f_x)
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#turn into a bivariate lambda for numpy
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grad_fcn = sympy.lambdify([x1,x2],grad_f)
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import matplotlib.pyplot as plt
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xx1, xx2 = np.meshgrid(np.linspace(-2,2,40),np.linspace(-2,2,40))
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# coarse mesh
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xx1_, xx2_ = np.meshgrid(np.linspace(-2,2,20),np.linspace(-2,2,20))
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V = grad_fcn(xx1_,xx2_)
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ff_x = f_x_fcn(xx1,xx2)
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color_array = np.sqrt(V[0]**2 + V[1]**2)
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# 3D visualization
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ax = plt.figure().add_subplot(projection='3d')
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ax.plot_wireframe(xx1, xx2, ff_x, rstride=1,
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cstride=1, color = [0.5,0.5,0.5],
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linewidth = 0.2)
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ax.contour3D(xx1, xx2, ff_x, 20, cmap = 'RdBu_r')
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ax.xaxis.set_ticks([])
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ax.yaxis.set_ticks([])
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ax.zaxis.set_ticks([])
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plt.xlim(-2,2)
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plt.ylim(-2,2)
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ax.view_init(30, -125)
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ax.set_xlabel('$x_1$')
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ax.set_ylabel('$x_2$')
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ax.set_zlabel('$f(x_1,x_2)$')
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plt.tight_layout()
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# 2D visualization
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fig, ax = plt.subplots()
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plt.contourf(xx1, xx2, ff_x,20, cmap = 'RdBu_r')
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plt.quiver (xx1_, xx2_, V[0], V[1],
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angles='xy', scale_units='xy',
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edgecolor='none', facecolor= 'k')
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plt.show()
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ax.set_aspect('equal')
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ax.xaxis.set_ticks([])
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ax.yaxis.set_ticks([])
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ax.set_xlabel('$x_1$')
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ax.set_ylabel('$x_2$')
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plt.tight_layout()
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