Matlab Question Error! Index dimension error.

The error occurs at the loop - while, giving me the error "Index exceeds matrix dimension"

function result = my_sqrt(x,q)

clc;

% This function uses a for loop to approximate the square root of a number

% and compare to the built in sqrt function in matlab.

% Variable declaration & Initialization

x = input('Enter a value for x: ');

q = input('Enter a value for q: ');

t = 5;

n = 1;

% Calculation

 while ((abs(x(n+1)-x(n)))<=q)    

        y(n) = (1/t).*x(n).^2

        x(n+1) = ((x(n)/8)*(15-y(n)*(10-(3*y(n)))))       

        n = n+1;    

    end

Answer 1

[Ben11]

That's because x(n+1) is undefined when you enter the while loop. From what you posted x is a single digit and not a vector, so trying to access x(2) generates the error. Also is 'x' the number you want to calculate the root of and q the precision you want?

Also t seems to be undefined is that a mistake?

[Dylan Flores]

The primary purpose of the function is to estimate the approximation to the square root of number t. x is the initial guess and q is the convergence criterion.

Answer 2

[Joseph Cheng]

So just as Ben11 did state x(n+1) is undefined when you first attempt the while loop. In the initialization of the function there is no x(2) defined. Without a x(2) defined you cannot do x(2)-x(1) and check if it is <=q. On a side note i believe that your while loop condition should be >=q as you want to probably loop while the square root approximation is greater than the convergence threshold.

to remedy this you could also initialize a x(2) which is x(1)+q+1 which would be replaced by the stated square root approximation you have there. (I did not check the legitimacy of your equation though).

[Joseph Cheng]

AND we've answered your question. I've copied your function, ran then function, debuged your function and it breaks at the condition for the loop. the error i get is at the start of the loop in the while ((abs(x(n+1)-x(n)))<=q) line.

where we've both stated x(n+1) is not defined. Also this is not a loop-while call. this is a while-loop call which means it'll check the condition before it does it.

[Dylan Flores]

so how do i prevent this error? Do i change x into a vector?

also in reply to your previous reply, it has to be <=q as stated by the question.

[Ben11]

well for this specific error yes you could use a vector, assigning it a size corresponding to the approximate number of iterations required to meet the criterion.

[Joseph Cheng]

Well thinking and playing around with it a bit more. Not entirely sure this does a sqrt approximation. However its the n+1 call that gets you into trouble. so.....

i broke it down like this such that x(n+1) is defined before you check the value. However i still have not checked your approximation equations. also check the logic for when to break out of the loop. I just copied the condition down so reverse or invert the condition.

while 1
        y(n) = (1/t).*x(n).^2
        x(n+1) = ((x(n)/8)*(15-y(n)*(10-(3*y(n)))))       

          if ((abs(x(n+1)-x(n)))<=q)    
              return
          end
          n = n+1;    
      end

Answer 3

[Patrik Ek]

There are a number of issues with this piece of code.

1) You should not have a clc inside a function. It is bad practice since the user may not want to clear the command window.

2) You have x and q as arguments already so you do not need the input. My advice would be to remove the inputs and either define x and q outside the function or assign them directly in the function call (in in the command window), like xSqrt = my_sqrt(3,0.01).

3) result is not defined. Also, you only need the current x and the previous, my advice would then be to define a new variable xNext and update it. Then either return xNext, update x and return x or define result = x (or xNext depending on when it is updated).

4) The algorithm that you use seems to be unstable. Read on wikipedia about methods for square root calculations. There they also advices in how to select the initial condition.

This should work fine:

function [result,n] = my_sqrt(x2,q)
% result = sqrt(x2)
% q - tolerance;

% Initial guess only a dummy for now. Check the article to improve the
% guess
x = 3;

% Counts the number of iterations, not necessary, but good now for testing
% effectivity
n = 1;
quitLoop = false;

while (~quitLoop)
    xNext = 0.5*(x+x2/x);
    if (abs(xNext-x)<q)
        quitLoop = true;
    else
        n = n+1;
        x = xNext;
    end
end
result = xNext;

where x2 is defined as the number that you want to calculate the root of. The algorithm uses newton-raphson and have a fast convergence.