import numpy as np import matplotlib.pyplot as plt from matplotlib.ticker import MultipleLocator def load_data(): num_pts=21; a0=3.0*50; a1=0.5*50; mu=0; sigma=1; ae=0.5*50; seed=1234; np.random.seed(seed) xmin = 0 xmax = 10 x1 = np.linspace(xmin, xmax, num_pts) e1 = np.array([np.random.normal(mu, sigma) for n in range(num_pts)]) x2 = np.linspace(xmax + 0.5, xmax + (xmax-xmin), num_pts-1) e2 = np.array([np.random.normal(mu, sigma) for n in range(num_pts-1)]) x0 = np.linspace(xmin - np.abs(xmax-xmin), xmin - 0.5, num_pts-1) e0 = np.array([np.random.normal(mu, sigma) for n in range(num_pts-1)]) y1 = a0 + (a1*x1) + ae*e1 y2 = (y1[-1] +a1*x1[-1] ) + -1.0*a1*(x2) + ae*e2 y0 = a0 + 0.25*a1*x0 + ae*e0 x = np.concatenate((x0, x1, x2)) y = np.concatenate((y0, y1, y2)) return x, y def plot_data(x, y): font_options = {'family': 'Arial', 'size': 16} plt.rc('font', **font_options) fig, axis = plt.subplots(figsize=(8,6)) axis.plot(x[(x>=0) & (x<=10)], y[(x>=0) & (x<=10)], color="black", linestyle=" ", marker="o") axis.plot(x[x>10], y[x>10], color="blue", linestyle=" ", marker="o") axis.plot(x[x<0], y[x<0], color="blue", linestyle=" ", marker="o") axis.grid(True, which="both") axis.axhline(0, color="black") axis.axvline(0, color="black") axis.set_ylim([-5*50, 15*50]) axis.set_xlim([-15, 25]) axis.xaxis.set_major_locator(MultipleLocator(5.0)) axis.xaxis.set_minor_locator(MultipleLocator(1.0)) axis.yaxis.set_major_locator(MultipleLocator(5.0*50)) axis.yaxis.set_minor_locator(MultipleLocator(1.0*50)) axis.set_ylabel('Altitude (meters)') axis.set_xlabel('Step Distance (kilometers)') axis.set_title("Hiking Trip") return fig def model(x, a0=150, a1=25): ym = a0 + (a1*x) return ym def plot_data_model_tolerance(x_data, y_data, y_model, tolerance=100): """ Purpose: Plot data (x_data, y_data) and overplot model (x_data, y_model) Args: x_data (np.array): numpy array of values of independent variable y_data (np.array): numpy array of values of dependent variable y_model (np.array): numpy array of values of the modeled dependent variable tolerance (float): for plotting when np.abs(y_model - y_data) < tolerance Returns: fig (matplotlib.figure): matplotlib figure object """ residuals = np.abs(y_model - y_data) x_good = x_data[residuals < tolerance] y_good = y_model[residuals < tolerance] x_min = np.min( x_good ) x_max = np.max( x_good ) font_options = {'family': 'Arial', 'size': 16} plt.rc('font', **font_options) fig, axis = plt.subplots(figsize=(8,6)) x = x_data y = y_data axis.plot(x[(x>=0) & (x<=10)], y[(x>=0) & (x<=10)], color="black", linestyle=" ", marker="o") axis.plot(x[x>10], y[x>10], color="blue", linestyle=" ", marker="o") axis.plot(x[x<0], y[x<0], color="blue", linestyle=" ", marker="o") axis.plot(x_data, y_model, color="red") axis.grid(True, which="both") axis.axhline(0, color="black") axis.axvline(0, color="black") axis.set_ylim([-5*50, 15*50]) axis.set_xlim([-15, 25]) axis.xaxis.set_major_locator(MultipleLocator(5.0)) axis.xaxis.set_minor_locator(MultipleLocator(1.0)) axis.yaxis.set_major_locator(MultipleLocator(5.0*50)) axis.yaxis.set_minor_locator(MultipleLocator(1.0*50)) axis.set_ylabel('Altitude (meters)') axis.set_xlabel('Step Distance (Kilometers)') axis.set_title("Hiking Trip") style_options = dict(color="green", alpha=0.35, linewidth=8) line = axis.plot(x_good, y_good, **style_options) plt.show() return fig x_data, y_data = load_data() y_model = model(x_data, a0=150, a1=25)

적합도(Goodness-of-Fit)

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