simps

Simpson's numerical integration

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Syntax
Description
Examples
Information
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About the author

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simps.m

Syntax

   z = simps(y)
   z = simps(x,y)
   z = simps(...,dim)

Description

z = simps(y) computes an approximation of the integral of y via the Simpson's method (with unit spacing). To compute the integral for spacing other than one, multiply z by the spacing increment. Input y can be complex.

If y is a vector, simps(y) is the integral of y. If y is a matrix, simps(y) is a row vector with the integral over each column. If y is a multidimensional array, simps(y) works across the first nonsingleton dimension.

z = simps(x,y) computes the integral of y with respect to x using the Simpson's rule. Inputs x and y can be complex. If x is a column vector and y an array whose first nonsingleton dimension is length(x), simps(x,y) operates across this dimension.

z = simps(...,dim) integrates across the dimension of y specified by scalar dim. The length of x, if given, must be the same as size(y,dim).

Examples

Let us define by I the following integral:

Its exact value is 2. To approximate I numerically on a uniformly spaced grid, use

x = 0:pi/100:pi;
y = sin(x);

Then both

I = simps(x,y);

and

I = pi/100*simps(y);

produce I = 2.000. In comparison, I = trapz(x,y) produces I = 1.9998.

This example uses complex inputs:

z = exp(1i*pi*(0:100)/100);
simps(z,1./z)

ans =

   0.0000 + 3.1416i

Information

Simpson's rule on Wolfram MathWorld.

About the author

Damien Garcia, Eng., Ph.D.
Assistant professor, Department of radiology
CRCHUM, University of Montreal Hospital
Montreal, QC, Canada
Damien.Garcia.REMOVE-THIS@BiomeCardio.com