How do I plot my own coded function?

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Wilson Zheng
Wilson Zheng 2020-1-27
评论： Walter Roberson 2020-1-27
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?

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Walter Roberson
Walter Roberson 2020-1-27
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
  2 个评论
Wilson Zheng
Wilson Zheng 2020-1-27
编辑：Wilson Zheng 2020-1-27
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
Walter Roberson 2020-1-27
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)].');

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