Area under and above curve

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

Answer 1

[Image Analyst]

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.

[Vera]

Thanks for answer.

In attach an illustration of my curve.

Positive area is between the curve (y positive) and the x axis and negative area is between curve (y negative) and x axis.

I want to calculate the positive area (sum of each sub-areas under the peak) and the and the negative area. Is the result of area(y) in matlab a numerical value that describes the difference between positive and negative area?

Thanks

[Image Analyst]

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]

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

Answer 2

[Vera]

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

[Image Analyst]

Depends on how you want to calculate the sum. What's wrong with sum(abs(y1-y2))?

[Vera]

sum(abs(y1-y2)) doesn't work as I want. I need a way to calculate and visualiza area between y2 and y1 curves

[Image Analyst]

"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]

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.