How do I plot my own coded function?

Hi all, my code creates a function that finds the natural log of the input.

function [answer, n] = mylog(x)
 fprintf("calculating the log:\n");
 tolerance     = 1e-10;
 maxIterations = 300;
 answer = 0;
 
 for n=0:maxIterations
     answer = answer + (2/(2*n+1)) * ((x-1)/(x+1))^(2*n+1);
     error = (2/(2*n+3)) * ((x-1)/(x+1))^(2*n+3);
     relError = abs(error);
     if (relError < tolerance)
     	break;
     end
 end
 
 if (relError > tolerance)
     fprintf("The log(x) could not be found\n");
 else
     fprintf("mylog(x) = %4e and n(x) = %i\n", answer, n);
 end 

To the best of my knowledge, the code works perfectly fine but I don't understand how to plot the graph (x, mylog(x)). I use x=linspace(0.001, 1), and I see that for a native function you can just do y=sin(x) and then its easily plotted. But when I try to do y=mylog(x), y is just a single value and not an array. What am I doing wrong and how do I fix it?

Answer 1

[Walter Roberson]

function [answer, n] = mylog(x)
 fprintf("calculating the log:\n");
 tolerance     = 1e-10;
 maxIterations = 300;
 answer = 0;
 
 for n=0:maxIterations
     answer = answer + (2/(2*n+1)) * ((x-1)./(x+1)).^(2*n+1);
     error = (2/(2*n+3)) * ((x-1)./(x+1)).^(2*n+3);
     relError = abs(error);
     if all(relError < tolerance)
     	break;
     end
 end
 
 if any(relError > tolerance)
     fprintf("The log(x) could not be found\n");
 else
     fprintf("mylog(x) = %4e and n(x) = %i\n", [answer(:), n(:)].');
 end 

[Wilson Zheng]

Thank you! Are you sure that this is correct tho? The loop breaks (via the first if statement) at different number of iterations for each input. And the n is printed and returned to show how many loops the function needed.

[Walter Roberson]

The function is nearly correct, and in particular is correct with regards to the point you are discussing.

The number of iterations used would be the worst-case over all of the x: it will not stop until you are out of iterations or all of the logs are found to the required accuracy. This is reasonable behaviour for a function whose operation on vectors has not been otherwise defined.

The error in the function is that the line

     fprintf("mylog(x) = %4e and n(x) = %i\n", [answer(:), n(:)].');

should be

     fprintf("mylog(x) = %4e and n(x) = %i\n", [answer(:), repmat(n,length(answer),1)].');