eic-opticks/ana/trapz.py

0001 #!/usr/bin/env python
0002 """
0003 https://en.wikipedia.org/wiki/Trapezoidal_rule
0004
0005 Integral ( f(x) ) dx   ~    (b - a) 0.5(f(a) + f(b))
0006   a->b
0007
0008
0009 https://numpy.org/doc/stable/reference/generated/numpy.trapz.html
0010
0011 """
0012 import numpy as np
0013 import matplotlib.pyplot as plt
0014
0015 if __name__ == '__main__':
0016
0017      x = np.arange(10, dtype=np.float64)
0018      y = x*x
0019      i_ = lambda _:np.power(_, 3)/3.
0020
0021      area_approx = np.trapz( y, x )
0022      area = i_( x[-1] ) - i_(x[0])
0023
0024      fig, ax = plt.subplots()
0025      fig.suptitle( " np.trapz(y,x)  area_approx : %10.4f  area : %10.4f  " % (area_approx, area) )
0026      ax.plot( x, y )
0027      ax.scatter( x, y )
0028
0029      fig.show()
0030
0031
0032