matlab離散數據微積分

一、一維離散數據微分、積分求解

1. 離散積分

function result = integral(x,y,c)
    result = [];
    for i=1:1:length(y)
        c=y(i)*(x(2)-x(1))+c ; 
        result(end+1) = c;
    end
end

2. 離散微分

function result = differential(x,y)
    h = x(2)-x(1);
    result = [];
    for i=1:1:length(y)
        if i <= length(y)/2
            result(end+1) = (y(i+1)-y(i))/h;
        else
            result(end+1) = (y(i)-y(i-1))/h;
        end
    end
end

3. 測試代碼

x = 0:0.001:2;
y = x;
y1 = integral(x,y,1);
plot(x,y);hold on
plot(x,y1);
figure;
y2 = differential(x,y1)
plot(x,y1);hold on
plot(x,y2)

Reference

1. matlab離散數據微積分