Hi
I took a look at the function spline.m, trying to understand the algorithm for cubic hermite interpolation.
the spline.m focuses on calculating the slope of every spline function, then using the slope to calculate the coefficients of the second and third order elements. if in every interval, Si(x)=a+b(x-xi)+c(x-xi)^2+d(x-xi)^3, then the slope is b. c and d are calculated based on b (in pwch.m) .
in spline.m, I really want to understand this part of code. is there anyone who can explain it??? Thanks a lot!!!!
b=zeros(yd,n);
b(:,2:n-1)=3*(dx(dd,2:n-1).*divdif(:,1:n-2)+dx(dd,1:n-2).*divdif(:,2:n-1));
if isempty(endslopes)
x31=x(3)-x(1);xn=x(n)-x(n-2);
b(:,1)=((dx(1)+2*x31)*dx(2)*divdif(:,1)+dx(1)^2*divdif(:,2))/x31;
b(:,n)=...
(dx(n-1)^2*divdif(:,n-2)+(2*xn+dx(n-1))*dx(n-2)*divdif(:,n-1))/xn;
else
x31 = 0; xn = 0; b(:,[1 n]) = dx(dd,[2 n-2]).*endslopes;
end
dxt = dx(
;
c = spdiags([ [x31;dxt(1:n-2);0] ...
[dxt(2);2*[dxt(2:n-1)+dxt(1:n-2)];dxt(n-2)] ...
[0;dxt(2:n-1);xn] ],[-1 0 1],n,n);
% sparse linear equation solution for the slopes
mmdflag = spparms('autommd');
spparms('autommd',0);
s=b/c;
