Use this pseudo code to write the matlab function Spline3Coe

Use this pseudo code to write the matlab function Spline3_Coef

Procedure Spline3-Coef (n, (t_i), (y_i), (z_i)) integer i, n; real array (t_i)_0:n (y_i)0:n, (Z_i)o:n allocate real array (h_i)o:n-1, (b_i)o:n-i. (u_i)1:n-1, (v_i)1:n-1 for i = 0 to n - 1 do h_i leftarrow t_i + 1 - t_i d_-i leftarrow (y_i + 1 - y_i)/hi u_1 leftarrow 2(h_0 + h_1) v_1 leftarrow 6 (b_1 - b_0) for i = 2 to n - 1 do u_i leftarrow 2(h_i + h_i -1) h^2_i - 1/u_i - 1 z_0 leftarrow 0 deallocate array (h_i), (b_i), (u_i), (v_i) end procedure Spline3-Coef

Solution

Code for the above psuedocode is below:

function [h,b,u,v] = Spline3_Coef(n,t,y,z)

h =0;b=0;u=0;v=0;

for i=1:n-1

h(i) = t(i+1) - t(1);

b(i) = (y(i+1)-y(i))/h(i);

end

u(i) = 2*(h(1)+h(2));

v(i) = 6*(b(2)-b(1));

for i = 3:n-1

u(i) = 2*(h(i)+h(i-1))-(h(i-1)^2)/u(i-1);

v(i) = 6*(b(i)-b(i-1))-(h(i-1)*v(i-1))/u(i-1);

end

z(n) = 1;

for i = n-1:-1:1

z(i) = v(i)-(h(i)*z(i+1))/u(i);

end

z(1) = 0;

Below are the sample test cases on the above code for your reference:

Test 1

n = 10;
t = 0:0.1:1;
y = 1:2:2*length(t);
z = 2:3:3*length(t);

>>disp(h);

   0.10000   0.20000   0.30000   0.40000   0.50000   0.60000   0.70000   0.80000   0.90000
>> disp(b);

   20.0000   10.0000    6.6667    5.0000    4.0000    3.3333    2.8571    2.5000    2.2222
>> disp(u);

   0.00000   0.00000      -Inf   1.40000   1.68571   2.05169   2.42454   2.79790   3.17126
>> disp(v);

     0     0   NaN   NaN   NaN   NaN   NaN   NaN   NaN

Test 2

n = 10;
t = 0:2:20;
y = 1:4:4*length(t);
z = 2:1:length(t)+1;

>> disp(h);

    2    4    6    8   10   12   14   16   18
>> disp(b);

   2.00000   1.00000   0.66667   0.50000   0.40000   0.33333   0.28571   0.25000   0.22222
>> disp(u);

    0.00000    0.00000       -Inf   28.00000   33.71429   41.03390   48.49071   55.95799   63.42514
>> disp(v);

     0     0   NaN   NaN   NaN   NaN   NaN   NaN   NaN