[Zz小猪]

分段三阶hermit
function yhat=hermint(x,f,fp,xhat)%分段三阶hermite插值
n=length(x);
if length(f)~=n,error('x and f are not compatible');
elseif length(fp)~=n,error('x and fp are not compatible');end
x=x(: );xhat=xhat(: );f=f(: );fp=fp(: );
dx=diff(x);
divdif=diff(f)./dx;
a=f(1:n-1);
b=fp(1:n-1);
c=(3*divdif-2*fp(1:n-1)-fp(2:n))./dx;
d=(fp(1:n-1)-2*divdif+fp(2:n))./dx.^2;
i=zeros(size(xhat));
for m=1:length(xhat)
i(m)=binSearch(x,xhat(m));
end
xx=xhat-x(i);
yhat=a(i)+xx.*(b(i)+xx.*(c(i)+xx.*d(i)));