Write a function file, $[$y$,$ Err, n$]=$ ARCTANA$($x$),$ that takes input argument x as an array of any size and returns the values of the arctan y calculated from an equation, the absolute differences Err of the value from an equation and the built$-$in atan function, and the number of iterations used to perform the summation n as arrays of the same size as the input. Your function must perform the following: $1.$ Iterate through all the elements in the input array and individually calculate the outputs for each element. $2.$ Pre$-$allocate the output parameters.