# MATLAB Matlab Numerical Integration - Syntax/Style Query

#### pete j

Hi,

Pretext: I have no formal background in matlab or maths in general, so apologies if any of the following doesn't make sense. I am also new to this forum, so apologies if this post is incorrect in any way. [n.b. I also posted this thread on mathhelpforum.com]

Context: Ok, so I wanted to find the response value for various parameter values, using the following equation:

http://www.nitric.net/~pete/pictures/pj.integral.GIF [Broken]

[If you can't see the image, it is an integration with infinite bounds over an equation consisting of a Gaussian probability density function multiplied by the the square of a Gaussian cumulative density function plus one minus the square of another Gaussian cumulative density function]

I wasn't sure whether it was possible to do this using the matlab symbolic toolkit (syms), so I thought I'd take a crack at it using numerical integration, using the quad command. After much effort and confusion, I ended up with the following code.

Code:
mu=0;
sigma=1;
s=0;
alpha=0.4;

mu=sprintf('%f', mu);
sigma=sprintf('%f', sigma);
s=sprintf('%f', s);
alpha=sprintf('%f', alpha);

f=strcat('normpdf(x+',s,',',mu,',sqrt(2)*',sigma,').*(normcdf(x,',mu,',sqrt(2)*',alpha,'*',sigma,').^2 + (1 - normcdf(x,',mu,',sqrt(2)*',alpha,'*',sigma,')).^2)');

quad(f,-1000,1000)
This code *DOES* appear to work (i.e. yields the expected answers). But it strikes me as being more than a little crude. My questions therefore are as follows:

1. From a mathematical point of view, was using numerical integration with suitably wide bounds the right way to go about this problem?
2. From a programming point of view, is there a more elegant way to execute the above numerical integration? (i.e. a better approach than wrapping everything up as one big string which is then passed to the quad function)

Best,
pete

Last edited by a moderator:
Related Math Software Workshop News on Phys.org

"Matlab Numerical Integration - Syntax/Style Query"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving