How to define a special function with some points

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Mojtaba Mohareri 2020-10-10

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https://ww2.mathworks.cn/matlabcentral/answers/609771-how-to-define-a-special-function-with-some-points

编辑： Mojtaba Mohareri 2020-10-10

采纳的回答： Ameer Hamza

I want to define a function like this

f(0.2)=1.42007;

f(0.4)=1.88124;

f(0.5)=2.12815;

f(0.6)=2.38676;

f(0.7)=2.65797;

f(0.8)=3.94289;

f(1)=3.55975;

to use these values in a For Loop. How can I define function f?

Thanks in advance.

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采纳的回答

Ameer Hamza 2020-10-10

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编辑：Ameer Hamza 2020-10-10

在 MATLAB Online 中打开

You can use interp1()

x = [0.2 0.4 0.5 0.6 0.7 0.8 1];
y = [1.42007 1.88124 2.12815 2.38676 2.65797 3.94289 3.55975];
f = @(xq) interp1(x, y, xq);

Then you can also evaluate in for in-between points

>> f(0.2)
ans =
    1.4201
>> f(0.3)
ans =
    1.6507
>> f(0.55)
ans =
    2.2575

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Ameer Hamza 2020-10-10

在 MATLAB Online 中打开

It happens when the input xq goes beyond the range of values in x. In your case, if xq is less than 0.2 or higher than 1.0, interp1 will give NaN. To avoid this, use extrapolation.

clear all;
clc;
x = [0.2 0.4 0.5 0.6 0.7 0.8 1];
y = [1.42007 1.88124 2.12815 2.38676 2.65797 3.94289 3.55975];
f = @(xq) interp1(x, y, xq, 'linear', 'extrap');
x = 0.6;
h = 0.4;
D(1,1) = (f(x + h) -2*f(x)+ f(x - h))/(h^2)
for i=1:2
   h = h/2;
   D(i + 1,1) = (f(x + h) -2*f(x)+ f(x - h))/(h^2);
   for j=1:i
      D(i + 1,j + 1) = (4^j*D(i + 1,j) - D(i,j))/(4^j - 1)
   end
end