What does X(counter) do in this piece of code?

This code uses a while loop to determine which value of x can be taken to say that the value of e^-x is approximately equal to zero. In order to do this, a tolerance value has been added (1e-3) so that if the output exceeds the tolerance, the for loop terminates.

For context, this code was given to us to demonstrate how to use a "counter" within a while loop.

I am struggling to understand how the "counter" value works within this code.

1) There seems to be x(counter), yet we have not yet determined what the value of x is equal to. I understand that it is effectively saying x(1) = 0 but surely we need to assign a value to x?

2) Why do we need to rewrite result(counter)= e^-x(counter) inside the while loop, why will the code not work if we simply put result(counter)?

clear; clc;
tol = 1E-3;
counter = 1;
x(counter) = 0; %we haven't yet determined the value of x, so why can we have a value for x(counter)?
result(counter) = exp(-x(counter))

result = 1

while result(counter)>tol;
    counter = counter + 1;
    x(counter) = x(counter-1) + 1;
    result(counter) = exp(-x(counter)) %why do we need to rewrite the full equation?
end

result = 1×2

1.0000 0.3679

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result = 1×3

1.0000 0.3679 0.1353

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result = 1×4

1.0000 0.3679 0.1353 0.0498

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result = 1×5

1.0000 0.3679 0.1353 0.0498 0.0183

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result = 1×6

1.0000 0.3679 0.1353 0.0498 0.0183 0.0067

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result = 1×7

1.0000 0.3679 0.1353 0.0498 0.0183 0.0067 0.0025

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result = 1×8

1.0000 0.3679 0.1353 0.0498 0.0183 0.0067 0.0025 0.0009

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Answer 1

[akshatsood]

Hi @Asher,

I understand that you want clarification on how the "counter" functions within the while loop. Let's break down the code.

Understanding the Code

1. Initialization:

• sets the tolerance value, which is the threshold for determining when is approximately zero.
• initializes counter and keeps track of number of iterations and index for arrays "x" and "result".
• initializes the first value of "x" as 0. This is the starting point for calculating .

2. First Calculation: calculates for initial value of "x", which is 0. This result is stored in "result" array at the index "counter".

3. While Loop: The loop continues as long as . This means the loop will keep iterating until becomes less than or equal to the specified tolerance.

Addressing Your Questions

1. Why can we have a value for "x(counter)" without assigning it first? - The line explicitly assigns the value 0 to "x(1)" (since "counter" is initially 1). This initializes the first element of the "x" array. As the loop progresses, "x(counter)" is updated to new values based on the previous value, thus determining its value dynamically.

2. Why do we need to rewrite inside the while loop? - Each iteration of the while loop calculates for a new value of "x". If you only wrote "result(counter)", it would not perform any calculation. It would merely reference the current or previous value of "result(counter)", which doesn't change on its own.

To summarise, the counter keeps track of number of iterations and serves as an index for "x" and "result" arrays. This allows dynamic updates to the values of "x" and until the condition of the while loop is no longer met.

I hope this helps.