jupytersketcher/examples/integral.py

"""Comic strip for illustrating numerical integration."""

from pysketcher import *
xdcd = True

def f(x):
    return 3*np.exp(-x**4)

xmin = -2
drawing_tool.set_coordinate_system(xmin=xmin, xmax=4,
                                   ymin=0, ymax=4,
                                   axis=True, xkcd=xkcd)
drawing_tool.set_linecolor('blue')

import numpy as np
x = np.linspace(xmin, 3, 201)
y = f(x)
curve = Curve(x, y)

x2 = np.linspace(xmin, 0.2, 201)
y2 = f(x2)
x2 = x2.tolist()
y2 = y2.tolist()
x2.append(x2[-1])
y2.append(0)
x2.append(xmin)
y2.append(0)
#x2 = np.array(x2)
#y2 = np.array(y2)
filled = Curve(x2, y2).set_filled_curves(pattern='/')

text1 = Text_wArrow('The integral $\int_{-\infty}^{0.2} 3e^{-x^4}dx$\nis impossible to calculate\nby hand but so easy with\na program!', (1.5, 3.5), (-0.2, 1), alignment='left')

fig = Composition(dict(curve=curve, integral=filled, comment=text1))
fig.draw()
drawing_tool.display()
drawing_tool.savefig('tmp1')

#input()

# Draw piecewise curve for midpoint rule
def piecewise_curve_for_midpoint_rule(N):
    dx = (0.2 - xmin)/float(N)
    x3_double = []
    y3_double = []
    y_prev = 0
    for i in range(N):
        x = xmin + i*dx
        x3_double.append(x)
        y3_double.append(y_prev)
        x3_double.append(x)
        y_next = 0.5*(f(x) + f(xmin+(i+1)*dx))
        y3_double.append(y_next)
        y_prev = y_next
    x = xmin + (i+1)*dx
    x3_double.append(x)
    y3_double.append(y_prev)
    x3_double.append(x)
    y3_double.append(0)
    # Back to start
    x3_double.append(xmin)
    y3_double.append(0)
    midpoint_curve = Curve(x3_double, y3_double).set_filled_curves(pattern='/').set_linecolor('red')
    return midpoint_curve

text2 = Text_wArrow('We just draw some rectangles\nto approximate the area\nunder the curve and sum up\nthe rectangular areas!', (1.2, 3.5), (-0.2, 1), alignment='left')

drawing_tool.erase()
fig = Composition(dict(curve=curve, integral=piecewise_curve_for_midpoint_rule(N=4), comment=text2))
fig.draw()
drawing_tool.display()
drawing_tool.savefig('tmp2')

text3 = Text_wArrow('Just add more rectangles\ngo get the integral\nmore accurate!', (1.5, 3.5), (-0.2, 1), alignment='left')

drawing_tool.erase()
fig = Composition(dict(curve=curve, integral=piecewise_curve_for_midpoint_rule(N=10), comment=text3))
fig.draw()
drawing_tool.display()
drawing_tool.savefig('tmp3')

import os
comic = 'comic' if xkcd else 'non_comic'
os.system('doconce combine_images pdf -3 tmp1 tmp2 tmp3 integral_%s_strip' % comic)
os.system('doconce combine_images png -3 tmp1 tmp2 tmp3 integral_%s_strip' % comic)

input()