language.m

来自「《精通MATLAB科学计算》一书的实例源代码」· M 代码 · 共 35 行

function f = Language(x,y,x0)
syms t;
if(length(x) == length(y))
    n = length(x);    
else
    disp('x和y的维数不相等！');
    return;
end                                      %检错

f = 0.0;
for(i = 1:n)
    l = y(i); 
    for(j = 1:i-1)
        l = l*(t-x(j))/(x(i)-x(j));      
    end;
    for(j = i+1:n)
        l = l*(t-x(j))/(x(i)-x(j));      %计算拉格朗日基函数
    end;

    f = f + l;                           %计算拉格朗日插值函数      
    simplify(f);                         %化简

    if(i==n)
        if(nargin == 3)
            f = subs(f,'t',x0);          %计算插值点的函数值
        else
            f = collect(f);          %将插值多项式展开
            f = vpa(f,6);                %将插值多项式的系数化成6位精度的小数
        end
    end
end