Effect of h for numerial differentiation
Download script from .\diff_h.py
import csv
import numpy as np
"""
Effect of h for numerial differentiation
"""
# define function to be differentiated
def func(x):
return x**3
# define analytical deviation of f(x)
def dfdx(x):
return 3.0 * x * x
# numerical differentiation by two-point forward difference method
def diff2forward(func, x, h):
return (func(x+h) - func(x)) / h;
#===================
# parameters
#===================
outfile = 'diff_h.csv'
h = [1.0, 0.1, 0.01, 0.001, 1.0e-6]
x0 = 0.0
xstep = 0.1
nx = 21
#===================
# main routine
#===================
print("Numerical differentiation using two-point forward difference method")
print("Write to [{}]".format(outfile))
# open outfile to write a csv file
f = open(outfile, 'w')
fout = csv.writer(f, lineterminator='\n')
fout.writerow([
'x', 'f(x)', 'df/dx',
'Df/Dx(h={})'.format(h[0]),
'Df/Dx(h={})'.format(h[1]),
'Df/Dx(h={})'.format(h[2]),
'Df/Dx(h={})'.format(h[3]),
'Df/Dx(h={})'.format(h[4])
])
print("")
print("{:^5}:\t{:^12}\t{:^12}\t"
"{:^12}\t{:^12}\t{:^12}\t{:^12}\t{:^12}"
.format(
'x', 'f(x)', 'df/dx',
'h={}'.format(h[0]),
'h={}'.format(h[1]),
'h={}'.format(h[2]),
'h={}'.format(h[3]),
'h={}'.format(h[4]))
)
for ix in range(nx):
x = x0 + ix * xstep
fx = func(x)
f1x = dfdx(x)
print("{:^5.3f}:\t{:^10.6f}\t{:^10.6f}\t".format(x, fx, f1x), end = '')
diff = []
for i in range(len(h)):
diff.append(diff2forward(func, x, h[i]))
print("{:^12.8f}\t".format(diff[i]), end = '')
fout.writerow([x, fx, f1x] + diff)
print("")
f.close()
