Make Matlab show number of intervals used to perform action?

Hi everybody,

I am fairly new to Matlab, and I am currently struggling with it. I am trying to make a Simpson-integral with Matlab and making Matlab show an output with the number of intervals, n, it has used to perform the action, I made it.

Here is my script:

clear all
syms x
a=input('lowest x-value: ');
b=input('highest x-value: ');
n=input('number of intervals: '); %remember n has to be an equal number
f=input('function: ');
fx=inline(f);
m=n/2;
h=(b-a)/(2*m);
xtal=[a:h:b];
ytal=fx(xtal);
J=0;
for i=1:m
    J=J+1/3*ytal(2*i-1)+4/3*ytal(2*i)+1/3*ytal(2*i+1);
end
format long
J=J*h

while abs(J-4.67077427)>0.000000001;
    disp('How large a number n do you need for J to be exact with 8 decimals?')
    n=2:2:100;
    i=1:m;
    J=0;
    J=J+1/3*ytal(2*i-1)+4/3*ytal(2*i)+1/3*ytal(2*i+1);
    J=J*h
    if J==abs(J-4.67077427)<=0.000000001;
    disp('J is exact to 8 decimals')
    break
    end
end

%while J<4.67077427;
    %n=n+1
%end
%elseif J>4.67077427;
    %disp('J is exact to more than 8 decimals')
    %break
%else J<4.67077427;
    %break
%end

I am currently only working with the first two sections, i.e. not with the last one after the last space. I haven't yet come to the part where I tell Matlab how to show me the number of intervals n used to let J=4.67077427+-0.000000001, because I can't make the program give me another number of J than the one given after the first section. The first section works perfectly fine, though, but the second one is a problem, because it is there I am trying to make Matlab show me the number of intervals used by the program to both give me the value of J, I showed you four lines ago and give me the lowest number of n used by the program to give me that value of J.

I hope this is sufficient. If not, please ask for more information.

Best regards, Mads

Answer 1

[Walter Roberson]

Look again at your code. You have

J==abs(J-4.67077427)<=0.000000001

That is going to be interpreted as

((J==abs(J-4.67077427)) <= 0.000000001)

the first one is going to test whether J is exactly equal to abs(J-4.67077427) . That test can only be true if J is exactly equal to (4.67077427 / 2). In that one (unlikely) case, the comparison will return 1 (true), and in all other cases the comparison will return 0 (false). You then compare that 0 or 1 to 0.000000001; that is going to result in true only if the first comparison returned 0 (false).

Answer 2

[Mads]

Thanks for your post.

Yes, I am aware of that abs returns the result exact and positive. Though, I also tried out the J==absTol(J-4.67077427)<=0.000000001, but it returns the answer "Undefined function 'absTol' for input arguments of type 'double'."

Now, I tried to change the section, where it now says: if (J-4.67077427)>0.000000001; disp('How large a number n do you need for J to be exact with 8 decimals?') n=2:2:100; i=1:m; J=0; J=J+1/3*ytal(2*i-1)+4/3*ytal(2*i)+1/3*ytal(2*i+1); J=J*h elseif J==((J-4.67077427)<=0.000000001); disp('J is exact to 8 decimals') break end

In the command window, I type in the following commands and it returns what is afterwards:

lowest x-value: 1 highest x-value: 2 number of intervals: 10 function: exp(x)

J =

   4.670776862260303

How large a number n do you need for J to be exact with 8 decimals?

J =

Columns 1 through 3

   0.601835428232711   0.735083452001940   0.897832955753068

Columns 4 through 5

   1.096615648523895   1.339409377748689

It can't seem to change the values for J, nor summarize them, nevertheless if I change the while-loop to a if-loop. I don't know why.