Index exceeds the number of array elements (4)

I am computing and I get an error on line 38

x_v=[1 2 5 6 7 8 10 13 17];   % The corresponding x values 
y_v = [3 3.7 3.9 4.2 5.7 6.6 7.7 6.7 4.5];   % The corresponding y values 
dy_v= [1 NaN  NaN  -0.67];   % The slopes/clamps at the end 

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

[Walter Roberson]

dy_v= [1 NaN  NaN  -0.67];   % The slopes/clamps at the end 

4 entries.

x_v=[1 2 5 6 7 8 10 13 17];   % The corresponding x values 
n=length(x_v) -1;  % Find the n for size of the matrix

So n is 9-1 = 8

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

So i can be at most 8+1 = 9

    
   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

When i reaches 5, it is not the special case i==1 or the special case i==n+1, so the else branch is used. But the else branch does not reference dy_v(i) so that is not a problem.

But when i reaches n+1 the elseif branch is taken, and dy_v(i) is referenced, which is a problem because i = 9 and dy_v(9) does not exist.

You could change the code to

   if i==1   % Condition for first row 
       B(i) = 3*((1/h_v(i))*(y_v(i+1) - y_v(i)) - dy_v(1));  
   elseif i==n+1   % Condition for last row 
       B(i) = 3*(dy_v(end) - (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

but then I would have to ask why you have more than two entries in dy_v since you only reference the first and last of them?

[camilo jose]

Thanks!

Now I have problem near line 65

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

[camilo jose]

say Unrecognized function or variable 'x'.