MATLAB Trapezium Rule - Input Error

Hi there,

I have written a mathematical code to calculate the trapezium rule for a set function. For my entire program, I have attempted to make it as 'user-friendly' as possible; whereby all variables are set upon running the code. This way, the script does not need to be editted in any way - see my code if you're confused in any way.

The issue I have is that when I input the actual mathematical 'function' into the program, it keeps being called multiple times, when I only want it to be called once. For example, if the function I needed evaluating was: 2x^2, I would input ' 2*x.^2 ', but would have to do this several times instead of once.

I think that the number of times the program calls upon this input is related to the number of strips to calculate - try this and see if you think I'm right? Therefore, I believe the loop inside the script keeps calling the mathematical 'function' user input continuously - I don't know how to stop this from happening?

I am a beginner to MATLAB and whilst it appears that I'm overcomplicating everything, I'm only trying to make everything as 'user-friendly' as possible...

My script: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>.

        disp('Trapezium Rule Calculator');
        disp('Truth and Absolute Values');
        disp('-------------------------');
        disp(' ');

        % F. Variables
        a = input('Enter the value of the lower bound:');
        b = input('Enter the value of the upper bound:');
        n = input('Enter the number of strips required:');
        disp(' ');

        h = ((b - a)/ (n));

        % Summation of First and Last Tra.
        sum = 0.5*( f(a) + f(b) );

        % Loop for Middle Tra.s
        for i = 1 : n-1;
            sum = sum + f(a+i*h);
        end

        % Truth - Integral Calculation
        g = @f;
        truth = integral(g,a,b);
        disp(' ');
        disp('Actual Value of Integral:');
        disp(truth);

        % Final Value of Tra.
        Answer = h*sum;
        ModAnswer = abs(Answer);

        disp('Value of Trapezium Area Calculated:');
        disp(ModAnswer);

        % Difference (Accuracy)
        ModTruth = abs(truth);
        diff = abs( ModTruth - ModAnswer);
        disp('Difference in Calculation:');
        disp(diff);

        % Percentage Accuracy
        format short
        PInaccuracy = ( (diff) / (ModTruth) )*100;
        PA = 100 - PInaccuracy;
        disp('Percentage Accuracy (%):');
        disp(PA);

        % Functions Formulae
        function y = f(x)
        y = input('Enter function for processing:');
        end

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Please help me on how to solve this issue please?

Thank you!

Answer 1

[M P]

Solved it!

The best way is to NOT use the function script at the bottom of the file...

Instead, assign a variable and use an input function along with it - see code below!

Here, adding >> @(x) << before whatever you input stores it as a function, and the following code will do its job as normal!

Thanks for your help anyways!

      disp('Trapezium Rule Calculator');
      disp('Truth and Absolute Values');
      disp('-------------------------');
      disp(' ');

      % F. Variables
      a = input('Enter the value of the lower bound: ');
      b = input('Enter the value of the upper bound: ');
      n = input('Enter the number of strips required: ');
      f = input('Enter function: [@(x)...]: ');
      disp(' ');

      h = ((b - a)/ (n));

      % Summation of First and Last Tra.
      sum = 0.5*( f(a) + f(b) );

      % Loop for Middle Tra.s
      for i = 1 : n-1;
          sum = sum + f(a+i*h);
      end

      % Final Value of Tra.
      Answer = h*sum;
      ModAnswer = abs(Answer);
      disp('Value of Trapezium Area Calculated:');
      disp(ModAnswer);

      % Truth - Integral Calculation
      truth = integral(f,a,b);
      disp('Actual Value of Integral:');
      disp(truth);

      % Difference (Accuracy)
      ModTruth = abs(truth);
      diff = abs( ModTruth - ModAnswer);
      disp('Difference in Calculation:');
      disp(diff);

      % Percentage Accuracy
      format short
      PInaccuracy = ( (diff) / (ModTruth) )*100;
      PA = 100 - PInaccuracy;
      disp('Percentage Accuracy (%):');
      disp(PA);

For example:

      Trapezium Rule Calculator
      Truth and Absolute Values
      -------------------------

      Enter the value of the lower bound: 1
      Enter the value of the upper bound: 2
      Enter the number of strips required: 16
      Enter function: [@(x)...]: @(x) 1./x

      Value of Trapezium Area Calculated:
          0.6934

      Actual Value of Integral:
          0.6931

      Difference in Calculation:
         2.4402e-04

      Percentage Accuracy (%):
         99.9648

Answer 2

[Jan]

The problem is that "f" is called n times, such that the input command appears so often.

Use a function instead of a script. Then provide the function as anonymous function as usual in Matlab (see ode45 or fzero).

Avoid "sum" as name of a variable, because this is an important Matlab function and shadowing it causes unexpected behavior frequently.

[M P]

Hi Jan,

Thank you for your prompt reply!

I somewhat undrestand where you're coming from in terms of 'n' times the input is called.

I'm using R2016b and so I've placed the function within the script at the bottom - is this any different from creating a 'm' (function) file, since I'll still want the function to be 'user-friendly' and be open to the user's choice?

Is there by any chance a way to set a mathematical function once, then call upon the 'function' function and then let that run through the program?

I am a beginner but I've heard of prompts and strings - could this be a solution, i.e. string in some user prompt and set that as a function? If you understand what Im trying to say?

I only used 'sum' because my engineering computation book told me to do so in such a code - I will change the name of this variable, so thank you!

Thank you for your help!

Answer 3

[Sanaz Kb]

Hello,

I have a question about the accepted code. When I've implemented your code, in the line which is related to the "truth = integral(f,a,b);", I've faced with this error:

Error using integral Too many input arguments.

Error in Untitled12 (line 24) truth = integral(f,a,b);

and also I have another questioin, How can I solve the integral if the upper limit be the vector not scalar? Could you please help me?

Thanks