index exceeds the number of array elements (1).

i have function to check percentage of an error. when i run, i have error message

Index exceeds the number of array elements (1).

Error in tutorial2 (line 10)

fvalue=4/(1 + midx(i)^2);

could you guys help me to solve this problem?

function err = tutorial2(nPoints)
%% Midpoint rule for integral 4/(1 + x^2) from x = 0 to x = 1
% inputs:   - nPoints    number of points in domain
% outputs:  - err        percentage error (absolute value)
x=linspace(0,1,nPoints);
dx=x(2)-x(1);
numSol=0;
    for i=1:nPoints
        midx=(x(i)+x(i+1))/2;
        fvalue=4/(1 + midx(i)^2);
        numSol=numSol+fvalue;
    end
    numSol=numSol*dx;
    analyticalSol=pi/4;
    err=abs((analyticalSol-numSol)*100/numSol);
end

Answer 1

[Geoff Hayes]

changsu - I think there are a couple of bugs with the above code. When running it, the first error is

Attempted to access midx(2); index out of bounds because numel(midx)=1.

Error in tutorial2 (line 10)
        fvalue=4/(1 + midx(i)^2);

this is because of the code

midx=(x(i)+x(i+1))/2;
fvalue=4/(1 + midx(i)^2);

In the first line, you treat midx as a scalar, but in the second line, midx is considered to be an array. If you don't need to store the mid-point from each iteration then just do

midx=(x(i)+x(i+1))/2;
fvalue=4/(1 + midx^2);

Else pre-allocate (pre-size) midx as an array outside of the loop and then update and use as such.

The second error will be with

for i=1:nPoints
    midx(i)=(x(i)+x(i+1))/2;
    % etc.
end

x is an array with nPoints elements...which is fine except on the last iteration of the for loop when i is equal to nPoints which will cause a problem with x(i+1) and throw a Index exceeds matrix dimensions. To get around this, just change the upper bound on your loop to

x=linspace(0,1,nPoints);
dx=x(2)-x(1);
midx = zeros(nPoints, 1);
numSol=0;
for k=1:nPoints-1
    midx(k)=(x(k)+x(k+1))/2;
    fvalue=4/(1 + midx(k)^2);
    numSol=numSol+fvalue;
end
numSol=numSol*dx;
analyticalSol=pi/4;
err=abs((analyticalSol-numSol)*100/numSol);

Note how I've replaced i with k to avoid confusion with the imaginary number (represented in MATLAB by i or j).

[changsu namgung]

as you suggested me to fix it, which i did. It runs on matlab but the reason why it keep saying an error message is that i get wrong answer out of this function.

below is error message that i get this time.

Undefined function or variable 'npoints'. Error in tutorial2 (line 7) midx=zeros(npoints,1); Error in Test1

i'm getting 75.0082 with this code on matlab

But the error percentage i'm supposed to have is around 0.0655

Could you see this again? thanks

function err = tutorial2(nPoints)
%% Midpoint rule for integral 4/(1 + x^2) from x = 0 to x = 1
% inputs:   - nPoints    number of points in domain
% outputs:  - err        percentage error (absolute value)
x=linspace(0,1,nPoints);
dx=x(2)-x(1);
midx=zeros(npoints,1);
numSol=0;
    for i = 0:nPoints-1
        midx(i)=(x(i)+x(i+1))/2;
        fvalue=4/(1 + midx(i)^2);
        numSol=numSol+fvalue;
    end
    numSol=numSol*dx;
    analyticalSol=pi/4;
    err=abs((analyticalSol-numSol)*100/numSol);
end

[Walter Roberson]

nPoints and npoints are different variables.