Cubic Spline Function help

Question

Dan Smith 2018-8-2

0
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https://ww2.mathworks.cn/matlabcentral/answers/413303-cubic-spline-function-help

回答： Image Analyst 2018-8-3

I need to develop a function file [y]=Spline_Clamped(x,f,xi) that can be used to find the function value y for a given xi. I need to apply the function to a data table to generate a plot.

Data Table: Xi=[3.0,4.5,7,9] fi=[2.5,1.0,2.5,0.5] This is what I have so far:

    function[y]=Spline_Clamped(x,f,xi)
    x=A(:,1);
    f=A(:,2);
    n=length(x);
    b=zeros(n,1); c=zeros(n,1); d=zeros(n,1);
    h=zeros(n,1);
    a=f;
    for i=1:n-1
        h(i)=x(i+1)-x(i);
    end
    BB=zeros(n,n);
    rr=zeros(n,1);
    BB(1,1)=h(2);
    BB(1,2)=-(h(1)+h(2));
    BB(1,3)=h(1);
    for i=2:n-1
        BB(i,i-1)=h(i-1);
        BB(i,i)=2*(h(i-1)+h(i));
        BB(i,i+1)=h(i);
        rr(i)=3*(f(i+1)-f(i))/h(i)-3*(f(i)-f(i-1))/h(i-1);
    end
    BB(n,n-2)=h(n-1);
    BB(n,n-1)=-(h(n-2)+h(n-1));
    BB(n,n)=h(n-2);
    c=BB\rr;
    for i=1:n-1
        d(i)=(c(i+1)-c(i))/3/h(i);
        b(i)=(f(i+1)-f(i))/h(i)-h(i)/3*(2*c(i)+c(i+1));
    end
    i_knot=[1:n]'
    z=[i_knot a b c d]'
    fprintf('   interval   a_i     b_i     c_i     d_i\n', z);
    fprintf('%7d %12.4 %12.4 %12.4 %12.4 \n', z);