用trapz和MATLAB计算阈值上下曲线下的阴影面积

Question

我的代码：

%% Example 
x = 0:.01:4*pi;% x data
y = sin(x)+2;% y data
level = 2;% level
plot(x, y)
hold on
x_interest = 0:.01:x(length(y));
y_interest = sin(x_interest)+2;
xlim ([0 x(length(y))])

% Shaded area above level
area(x_interest, max(y_interest, level), level, ...
    'EdgeColor', 'none', 'FaceColor', [.6 .7 .8], ...
    'ShowBaseLine', 'off');

% Shaded area below level
area(x_interest, min(y_interest, level), level, ...
    'EdgeColor', 'none', 'FaceColor', [.5 .5 .5], ...
    'ShowBaseLine', 'off');

%%== This did not work ==%%
above = find(y_interest >= level);
below = find(y_interest <= level);
A_above = trapz(above)
A_below = trapz(below)

 %% Integrate
 plot(x, sin(x)+2)
 fun = @(x) sin(x)+2; 
 integral(fun, 0, x(length(y)))

 A = trapz(x,y)

Answer 1

在一般意义上，函数trapz(x，y)（其中x和y是相同长度的向量）估计曲线下的面积f(x)=y。这个区域被函数f(x)和x轴夹在中间。

对于a_support，需要估计曲线之间的面积F1(x_interest）=max(y_interest,level)和F2(x_interest）=level。这与曲线F1(x_interest)下移级别下的区域相同。因此可以通过以下方法进行评估：

A_above =  trapz(x_interest, max(y_interest, level)-level)

类似地，对于a_bellow:

A_below = -trapz(x_interest, min(y_interest, level)-level)