naspline.m

各种插值拟合的子程序

function m=naspline(x,y,dy0,dyn,xx)
n=length(x)-1;
h=diff(x);lemda=h(2:n)./(h(1:n-1)+h(2:n));mu=1-lemda;
g=3*(lemda.*diff(y(1:n))./h(1:n-1)+mu.*diff(y(2:n+1))./h(2:n));
g(1)=g(1)-lemda(1)*dy0;g(n-1)=g(n-1)-mu(n-1)*dyn;
dy=nachase(lemda,2*ones(1:n-1),mu,g);
m=[dy0;dy;dyn];
if nargin>=5
    s=zeros(size(xx));
    for i=1:n
        if i==1,
            kk=find(xx<=x(2));
        elseif i==n
            kk=find(xx>x(n));
        else
            kk=find(xx>x(i)&xx<=x(i+1));
        end
        xbar=(xx(kk)-x(i))/h(i);
        s(kk)=alpha0(xbar)*y(i)+alpha1(xbar)*y(i+1)+...
            h(i)*beta0(xbar)*m(i)+h(i)*beta1(xbar)*m(i+1);
    end
    m=s;
end
function x=nachase(a,b,c,d)
n=length(a);
for k=2:n
    b(k)=b(k)-a(k)/b(k-1)*c(k-1);
    d(k)=d(k)-a(k)/b(k-1)*d(k-1);
end
x(n)=d(n)/b(n);
for k=n-1:-1:1
    x(k)=(d(k)-c(k)*x(k+1))/b(k);
end
x=x(:);
function y=alpha0(x)
y=2*x.^3+3*x.^2;
function y=alpha1(x)
y=-2*x.^3+3*x.^2;
function y=beta0(x)
y=x.^3-2*x.^2+x;
function y=beta1(x)
y=x.^3-x.^2;