Need help writing matlab code with given pseudocode

Hello,

Given Problem:

Exercise 2: Loss of Significance

• Suppose that you define b = a(1+epsilon). Write a function that calculates magnitude of relative and absolute errors in epsilone when 'a' and epsilon are introduced. The loss of significance is defined by first calculating 'b', and then back‐ calculating for known values of 'a' and 'b' .

• If a = pi and epsilon = 10^-j, then use this function to create plots of the magnitude of relative and absolute errors for varying j.

Given pseudo-code:

Exercise 2: Loss of Significance

1. Main function
a. Define a 1x10 array for the magnitude of relative error
b. Create a loop for ݆ j = 1: 10
    i. Define epsilon
    ii. Call the subfunction that determines the magnitude of absolute and relative
errors for a = pi and epsilon
c. Create plots of the magnitude of absolute and relative errors vs. ݆

2. Subfunction
a. Inputs: a and epsilon
b. Outputs: magnitudes of absolute and relative error
c. Calculate b = a(1+epsilon)
d. Calculate epsilon based on a and b.   Call this parameter epsilon prime.
.
e. Determine the magnitudes of absolute and relative error by comparing the calculated epsilon Prime
to the “true” value of epsilon.

My attempt:

function LossOfSignificance()

clc; 
clear;  
RelError = zeros(1,10)  
for j = 1:10  
    MyFun(pi, 3e-5)  
    epsilon = epsilon*10^(-j)  
end

end

function MyFun(a,epsilon)  
a;   
epsilon  
b = a*(1+epsilon);  
epsilonPrime = (b-a)/a;  
bPrime = a*(1+epsilonPrime);  
AbsErrorPrime = abs(bPrime -a);  
RelErrorPrime = abs(AbsErrorPrime/a);  
end

My output error:

??? Undefined function or variable "epsilon".
Error in ==> LossOfSignificance at 8
    epsilon = epsilon*10^(-j)

I'm not very experienced with Matlab. Please help. Thanks.

Answer 1

[Walter Roberson]

epsilon should not be 10^-j times its previous value: it should just be that calculation

Answer 2

[Steven Lord]

As written, the variable epsilon only exists in the workspace of the MyFun function. When the function finishes executing, its workspace (and all the variables the workspace contains) are destroyed. If you want variables created inside MyFun to exist outside, define them as output arguments to your function in the definition:

function AbsErrorPrime = MyFun(a,epsilon)

or

function [AbsErrorPrime, RelErrorPrime] = MyFun(a,epsilon)

and call the function with one or more outputs inside LossOfSignificance.

[AEP, REP] = MyFun(pi, 3e-5) % Assuming MyFun is defined to return two outputs