import numpy as np import matplotlib.pyplot as plt import matplotlib.ticker as mt from plotstyle import * def create_data(): # wikipedia: # Generally, males vary in total length from 250 to 390 cm and # weigh between 90 and 306 kg c = 6 x = np.arange(2.2, 3.9, 0.05) y = c * x**3.0 rng = np.random.RandomState(32281) noise = rng.randn(len(x))*50 y += noise return x, y, c def plot_mse(ax, x, y, c): ccs = np.linspace(0.5, 10.0, 200) mses = np.zeros(len(ccs)) for i, cc in enumerate(ccs): mses[i] = np.mean((y-(cc*x**3.0))**2.0) imin = np.argmin(mses) ax.plot(ccs, mses, **lsAm) ax.plot(c, 500.0, **psB) ax.plot(ccs[imin], mses[imin], **psC) ax.annotate('Minimum of\ncost\nfunction', xy=(ccs[imin], mses[imin]*1.2), xycoords='data', xytext=(4, 7000), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.2,0.0), connectionstyle="angle3,angleA=10,angleB=90") ) ax.text(2.2, 500, 'True\nparameter\nvalue') ax.annotate('', xy=(c-0.2, 500), xycoords='data', xytext=(4.1, 700), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(1.0,0.0), connectionstyle="angle3,angleA=-10,angleB=0") ) ax.set_xlabel('c') ax.set_ylabel('Mean squared error') ax.set_xlim(2, 8.2) ax.set_ylim(0, 10000) ax.set_xticks(np.arange(2.0, 8.1, 2.0)) ax.set_yticks(np.arange(0, 10001, 5000)) def plot_mse_min(ax, x, y, c): ccs = np.arange(0.5, 10.0, 0.05) mses = np.zeros(len(ccs)) for i, cc in enumerate(ccs): mses[i] = np.mean((y-(cc*x**3.0))**2.0) imin = np.argmin(mses) di = 25 i0 = 16 dimin = np.argmin(mses[i0::di])*di + i0 ax.plot(c, 500.0, **psB) ax.plot(ccs, mses, **lsAm) ax.plot(ccs[i0::di], mses[i0::di], **psAm) ax.plot(ccs[dimin], mses[dimin], **psD) #ax.plot(ccs[imin], mses[imin], **psCm) ax.annotate('Estimated\nminimum of\ncost\nfunction', xy=(ccs[dimin], mses[dimin]*1.2), xycoords='data', xytext=(4, 6700), textcoords='data', ha='left', arrowprops=dict(arrowstyle="->", relpos=(0.8,0.0), connectionstyle="angle3,angleA=0,angleB=85") ) ax.set_xlabel('c') ax.set_xlim(2, 8.2) ax.set_ylim(0, 10000) ax.set_xticks(np.arange(2.0, 8.1, 2.0)) ax.set_yticks(np.arange(0, 10001, 5000)) ax.yaxis.set_major_formatter(mt.NullFormatter()) if __name__ == "__main__": x, y, c = create_data() fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 1.1*figure_height)) fig.subplots_adjust(**adjust_fs(left=8.0, right=1.2)) plot_mse(ax1, x, y, c) plot_mse_min(ax2, x, y, c) fig.savefig("cubiccost.pdf") plt.close()