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[code language="python"] import os import numpy as np import matplotlib.pyplot as plt import matplotlib as mpl mpl.rcParams['text.usetex'] = True import sympy os.chdir(r'D:\projects\wordpress\ex32') os.getcwd() def plot_direction_field(x, y_x, f_xy, x_lim=(-5, 5), y_lim=(-5, 5), ax=None): f_np = sympy.lambdify((x, y_x), f_xy, 'numpy') x_vec = np.linspace(x_lim[0], x_lim[1], 20) y_vec = np.linspace(y_lim[0], y_lim[1], 20) if ax is None: _, ax = plt.subplots(figsize=(4, 4)) dx = x_vec[1] - x_vec[0] dy = y_vec[1] - y_vec[0] for m, xx in enumerate(x_vec): for n, yy in enumerate(y_vec): Dy = f_np(xx, yy) * dx Dx = 0.8 * dx**2 / np.sqrt(dx**2 + Dy**2) Dy = 0.8 * Dy*dy / np.sqrt(dx**2 + Dy**2) ax.plot([xx - Dx/2, xx + Dx/2], [yy - Dy/2, yy + Dy/2], 'b', lw=0.5) ax.axis('tight') ax.set_title(r"$%s$" % (sympy.latex(sympy.Eq(y(x).diff(x), f_xy))),fontsize=18) return ax x = sympy.symbols("x") y = sympy.Function("y") fig, axes = plt.subplots(1, 3, figsize=(12, 4)) plot_direction_field(x, y(x), y(x)**2 + x, ax=axes[0]) plot_direction_field(x, y(x), -x / y(x), ax=axes[1]) plot_direction_field(x, y(x), y(x)**2 / x, ax=axes[2]) fig.tight_layout() plt.savefig("example32.png", dpi=100) plt.show() plt.close() [/code] |
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