Index exceeds the number of array elements (2). Error (line 41)

I don't understand this error, I get this Index exceeds the number of array elements (2). Error (line 41) Can you please correct this problem for me?

Index exceeds the number of array elements (2).
Error in Untitled (line 35)
       B(i) = 3*(dy_v(i) - (1/h_v(i-1))*(y_v(i) - y_v(i-1)) );       

%% Enter the data for the curve-1 
clear    % Clear all the previous Variables 
syms x  % Define x as a symbolic variable 
x_v=[27.7 28 29 30];  % The corresponding x values 
y_v = [4.1 4.3 4.1 3.0];    % The corresponding y values 
dy_v= [0.33 -1.5];  % The slopes/clamps at the end. The mid values are filled with NaN values 

n=length(x_v) -1;  % Find the n for size of the matrix  
h_v = diff(x_v);  % Find the h values (step size) from x values 

%% Create Matrix A
for i=1:n+1  % Start row loop  
    for j=1:n+1  % Start column loop  
        if i==1&&j==1   % Condition for first row and first column  
            A(i,j) = 2*h_v(i);  % First Entry  
        elseif i==n+1&&j==n+1  % Condition for last row and last column  
            A(i,j) = 2*h_v(i-1);  % Last Entry  
        elseif j==i-1   % Condition for element jsut left of the diagonal  
            A(i,j) = h_v(i-1);
         elseif j==i+1   % Condition for element jsut right of the diagonal  
             A(i,j) = h_v(i);
        elseif i==j  % Condition for element in diagonal  
            A(i,j) = 2*(h_v(i-1)+h_v(i));
        else
            A(i,j) = 0;  % Condition for all other elements in matrix  
        end
    end
end
 
%% Create Vector B 
for i=1:n+1
   if i==1   % Condition for first row 
       B(i) = 3*((1/h_v(i))*(y_v(i+1) - y_v(i)) - dy_v(i));  
   elseif i==n+1   % Condition for last row 
       B(i) = 3*(dy_v(i) - (1/h_v(i-1))*(y_v(i) - y_v(i-1)) );
   else   % Condition for all other elements 
        B(i) = 3*((1/h_v(i))*(y_v(i+1) - y_v(i)) - (1/h_v(i-1))*(y_v(i) - y_v(i-1)));
   end
end
 
%% Find the Matrix C 
c = (A^-1)*B';    % Find the product of inverse of A and B 

for i=1:n  % Loop for remaining constants (bs) and (ds) 
    b(i) = (1/h_v(i))*(y_v(i+1) - y_v(i)) - (h_v(i)/3)*(2*c(i) + c(i+1));
    d(i) =  (1/(3*h_v(i)))*(c(i+1) - c(i));
end

%% Find the splines 
for i=1:n
    S{i} = num2str(y_v(i),8) + num2str(b(i),8)*(x-  num2str(x_v(i),8) ) + num2str(c(i),8)*(x- num2str(x_v(i),8)).^2 +   num2str(d(i),8)*(x- num2str(x_v(i),8)).^3;
    SS{i} =['$$' latex(S{i}) '$$'];
    SS2{i} =[ latex(S{i}) ];
    SSD{i} =[ latex(diff(S{i})) ];
end

Answer 1

[drummer]

Well, you're trying to reach n + 1 when creating the B vector.

But n is 3. Thus your for loop goes until 4.

The problem is that dy_v has only 2 elements. Your loop is going from 1 to 4 while dy_v(i) is going from 1 to 2. That's the problem.

You mentioned the middle values of dy_v are NaN.

I declared dy_v = [0.33, NaN, NaN, -1.5] and the code worked.

Not sure if the math make sense by doing this, I didn't go through it.

If that helps, please accept the answer.

Cheers.

Answer 2

[per isakson]

dy_v is a row vector with length two

dy_v= [0.33 -1.5];

The end value, n+1, of this loop is 4

%% Create Vector B 
for i=1:n+1    

in the line

    B(i) = 3*(dy_v(i) - (1/h_v(i-1))*(y_v(i) - y_v(i-1)) );

dy_v(4) throws the error