# coding: utf-8 # # Choice of Nodes for Polynomial Interpolation # In[5]: get_ipython().magic(u'matplotlib qt4') # In[6]: import numpy as np import numpy.linalg as la from matplotlib.pyplot import ( clf, plot, show, xlim, ylim, get_current_fig_manager, gca, draw, connect) # Choose a function below: # In[9]: func = "runge" if func == "sin": def f(x): return np.sin(5*x) elif func == "jump": def f(x): result = 0*x result.fill(-1) result[x > 0] = 1 return result elif func == "runge": def f(x): return 1/(1+25*x**2) else: raise RuntimeError("unknown function '%s'" % func) # Run this cell to play with the node placement toy: # In[10]: x_points = [] y_points = [] deg = [1] def update_plot(): clf() xlim([-1, 1]) ylim([-1.5, 1.5]) gca().set_autoscale_on(False) plot(x_points, y_points, 'o') x = np.linspace(-1, 1, 500) plot(x, f(x), "--") if len(x_points) >= deg[0]+1: eval_points = np.linspace(-1, 1, 500) poly = np.poly1d(np.polyfit( np.array(x_points), np.array(y_points), deg[0])) plot(eval_points, poly(eval_points), "-") def click(event): """If the left mouse button is pressed: draw a little square. """ tb = get_current_fig_manager().toolbar if event.button == 1 and event.inaxes and tb.mode == '': x_points.append(event.xdata) x_ary = np.array([event.xdata]) y_ary = f(x_ary) y_points.append(y_ary[0]) if event.button == 2 and event.inaxes and tb.mode == '': if len(x_points) >= deg[0]+2: deg[0] += 1 update_plot() draw() update_plot() connect('button_press_event', click) show() # In[ ]: