Calling result data from another function issues?

Hi,

I am trying to implement Romberg's integration process in MAT LAB (i.e. recursive-trapezoidal to simpson's 1/3 rule(or Richardsons's extrapolation) to finally Boole's rule. After computing my answers for the trapezoidal rule, I then call on the results from my trapezoidal code to then apply Romberg intergration for Simpson's 1/3 rule. And then call on the results from the Rom berg simpson code to finally apply Romberg integration using Boole's rule.

My question is simply around the inability to call the results effectively. My code for Romberg Simpson's 1/3 is able to call on the trapezoidal results correctly, but for some reason my Romberg boole code keeps calling the trapzoidal data instead of the newly extrapolated Romberg Simpson's 1/3 data and applies the equation. And I dont understand why?

TRAPEZOIDAL

n=1;
%first value of area (i.e. trapezoidal rule)
result(n)=((b-a)./2*(func(b)-func(a)))
%start error 
error_result=1;
%while loop that creates error bounds. Will cycle until error is larger
%than toler
while error_result(n)>toler;
 it=2.^(n-1);
 tnm=it; 
 h=(b-a)./tnm; 
 %first x values is from startig from a +0.5 h interval due to split
 x=a+0.5.*h; 
 %first sum=0
 sum=0.0; 
 for j=1:it 
 %sum is sum of 
 sum=sum+feval(func,x); 
 %finding next x value
 x=x+h; 
 end
%Answer/Result of integration at given interval split  
result(n+1)=0.5.*(result(n)+h.*sum);
%error analysis for each interval split
error_result(n+1)=abs((result(n+1)-result(n)));
%counter
n=n+1;
end

ROMBERG SIMPSON

function[result]=Rombergsimp(func,a,b,toler)
%starting counter
n=1;
%error starter
error_result=1;
while error_result(n)>toler;
%calling result values from trapezoidal code
 result = trapz(func,a,b,toler);
 %defining new result values by applying simpsons 1/3 romberg integration.
 result_romsim(n+1)=result(n+1)+1/3.*(result(n+1)-result(n));
 %error analysis of each step
 error_result(n+1)=abs(((result_romsim(n+1)-result_romsim(n))));
 %counter+1
 n=n+1;
%printing results
end

ROMBERG BOOLE

function[result]=Rombergboole(func,a,b,toler)
%counter
n=1;
%error starter
error_result=1;
%while lopp defining error analysis
while error_result(n)>toler;
%calling result values from Rombergsimp m-function
 result = Rombergsimp(func,a,b,toler)
 %Applying Boole's rule to the already extrapolated simpson data
 result_romboole(n+1)=result(n)+16/15.*(result(n+1)-result(n));
 %displaying results
 disp(result_romboole);
 %error check between each new Romber_boole value.
 error_result(n+1)=abs(((result_romboole(n+1)-result_romboole(n))));
 %counter+1
 n=n+1;
end

I am sorry for the lengthiness of the code and question but I didn't know how else to ask it.

thanks

Answer 1

[Star Strider]

I don’t completely understand how you’re calling your routines, but it seems if you call ‘Rombergboole’ alone, it calls all the others, first ‘Rombergsimp’ that itself calls ‘trapz’ and returns the eventual result.

I don’t understand what ‘func’ is. The trapz function takes a vector (or array) argument — not a function argument — and produces a scalar (or vector) result. There would seem to me to be nothing left to integrate. In other places, it seems that you are calling ‘func’ as a function handle. If you want to integrate a function, the integral (or in earlier versions, quad) function would be appropriate.

[Tim]

'func' is the specified function that we were asked to integrate. My lecturer explained it to me that;

result=trapz(func,a,b,toler)

simply calls all previous answers that trapz came up with into a vector, in which the Rombergsimp code is now able to apply its formula to. The exact same process should be done for Rombergboole, this time calling Rombergsimp values.

I forgot to add the function part for trapz at the very top it is;

function [result]=trapz(func,a,b,toler) 
%Start counter
n=1;
%first value of area (i.e. trapezoidal rule)

and ill add the first trapezoidal m-file with the data;

%ID:25118900 DATE:26/8/2014
%RECURSIVE TRAPEZOIDAL RULE FOR INTERGRATION-DATA FILE
%====================================================
%Function handle of current equation where x=t
func=@(x) (10.*exp((-2.5.*x)./1).*sin((3.5.*pi.*x))./1).^2
%starting intergrad bound
a=0;
%end bound
b=0.5;
%tolerance
toler=10^-4;
%Linkage to m-function.
[result]=trapz(func,a,b,toler);

and unfortunately we can just use quad to integrate as they don't let us.

[Star Strider]

The problem is that:

result=trapz(func,a,b,toler)

isn’t going to work. See the documentation on trapz.

Creating your own function and calling it trapz is quite definitely bad MATLAB programming practice. This is called ‘overshadowing’ because it creates a second function to the core MATLAB function of the same name. If that’s what you’re doing, it part of the problem I’m having with your code.

The added script lines do help me understand your code.

Still, your description of how you want your code to work doesn’t match what it appears to me to do. (I couldn’t run it without the code you just now added.) Your (unfortunately named) ‘trapz’ function doesn’t seem to me to call any other functions. However your ‘Rombergboole’ function calls all of them.

I’ll work with your code in the morning. It’s GMT-6 here, and the end of my day.