Area under and above curve

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Vera
Vera 2016-6-11
评论： Vera 2016-6-19
Dear all, if [x,y] is a matrix of values, I want to evaluate the positive and negative areas under the curve. If I use area(x,y), is the result the difference between positive and negative areas under the curves? Thanks

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回答（2 个）

Image Analyst
Image Analyst 2016-6-11
How are you defining "under" and "above"? Without any bound, the area would be infinite. What is a negative area? Do you mean the areas between the curve and the x axis? And exactly what does "Evaluate" mean to you? Do you just want the sum of the absolute value of y? Like perhaps
theArea = sum(abs(y)) * (x(2)-x(1)); % If x are uniformly spaced.
There are other options such as
theArea = cumtrapz(x, abs(y));
Maybe you can attach a diagram to illustrate what you want, if the above code doesn't work for you.
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Image Analyst
Image Analyst 2016-6-11
编辑：Image Analyst 2016-6-11
Try this:
% Compute area between positive y data and x axis:
positiveArea = sum(y(y>0))
% Compute area between negative y data and x axis:
negativeArea = sum(y(y<0))
Again, if you want the area as "triangles" instead of "bars", or have non-uniformly spaced x values, use cumtrapz().
Vera
Vera 2016-6-13
Thanks. I tried to calculate the total area with two options: sum(y)=-1.21150 e-4 trapz(y)=-1.1801 e-4 Which is the best way to calculate the area.sum and trapz are based on different hypothesys of approximation? Thanks

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Vera
Vera 2016-6-16
I have another question. Considering due curve (blu and black in the attached file). How can i Calculate and plot the area between the two curves? If y1 and y2 are the blu and dark curves respectively is: a = trapz(t,y2)-trapz(t,y1); the correct way? If yes how I can plot this area? Thanks
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Image Analyst
Image Analyst 2016-6-17
"how I can plot this area?" <== area is a single number, unless you have some other definition. You can still use plot() to plot a single number though. Or you can use bar() or stem(). Check out the MATLAB plot gallery for more options:
http://www.mathworks.com/products/matlab/plot-gallery.html
Vera
Vera 2016-6-19
With "how can I plot this area I mean how to fill area between the two curves" in order to visualize if the area is correct.

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