Difference between revisions of "Numerical differentiation and integration"
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| Line 49: | Line 49: | ||
In = In + 2. * f(x); | In = In + 2. * f(x); | ||
end | end | ||
In = ( In + f(b) ) * h * 0.5; | In = (In + f(b)) * h * 0.5; | ||
% end of function | % end of function | ||
</syntaxhighlight> | </syntaxhighlight> | ||
| Line 85: | Line 85: | ||
In += 2*f(x) | In += 2*f(x) | ||
return ( In + f(b) )*h*0.5 | return (In + f(b))*h*0.5 | ||
if __name__ == '__main__': | if __name__ == '__main__': | ||
Revision as of 13:22, 10 November 2010
Part A: Numerical differentiation
<pdfreflow> class_date = 01 to 04 November button_label = Create my course notes! show_page_layout = 1 show_frame_option = 1 pdf_file = E-Numerical-differentiation-01-Nov-2010.pdf </pdfreflow>
Part B: Numerical integration
<pdfreflow> class_date = 08 to 15 November button_label = Create my course notes! show_page_layout = 1 show_frame_option = 1 pdf_file = E-Numerical-integration-08-Nov-2010.pdf </pdfreflow>
Source code used in slides
| MATLAB | Python |
|---|---|
function In = trapezcomp(f, a, b, n)
% Composite trapezoidal function integration
%
% INPUTS:
% f: the function to integrate
% a: lower bound of integration
% b: upper bound
% n: number of panels to create between ``a`` and ``b``
% Initialization
h = (b-a)/n;
x = a;
% Composite rule
In =f(a);
for k=2:n
x = x + h;
In = In + 2. * f(x);
end
In = (In + f(b)) * h * 0.5;
% end of function
Then use this function as follows: >> f = @(x)sin(x);
>> I1 = trapezcomp( f, 0, pi/2, 1 ) % 0.7854
>> I2 = trapezcomp( f, 0, pi/2, 2 ) % 0.9481
|
import numpy as np
def trapezcomp(f, a, b, n):
"""
Composite trapezoidal function integration
INPUTS:
f: the function to integrate
a: lower bound of integration
b: upper bound
n: number of panels to create between ``a`` and ``b``
"""
# Initialization
h = (b - a) / n
x = a
# Composite rule
In = f(a)
for k in range(2, n+1):
x = x + h
In += 2*f(x)
return (In + f(b))*h*0.5
if __name__ == '__main__':
def func(x):
return np.sin(x)
print(trapezcomp(func, 0, np.pi/2, 1)) # 0.785398163397
print(trapezcomp(func, 0, np.pi/2, 2)) # 0.948059448969
|