Use a custom baseline to calculate area of a graph

Hi,

I am a beginner level Matlab user. I tried searching the forum, could not find a working answer for this quesiton

I have this graph of Heat Flow vs Time. I need to calculate the mathematical area (Area above the baseline being positive and area below being negative) under the curve with a straight baseline formed between first and the last x-value (which is user defined) as shown in the figure below. At present, i am using the following code

 %this limit we defined before is passed on to the trapz function to       
 lims = (x2_values >=value_of_interest_1)&(x2_values <=value_of_interest_2);
 %perform numerical integration using the trapeoidal method
 net_heat_flow = trapz(x2_values(lims), y2_values(lims));

However, this code calculates the area based on zero baseline. So, my question is how can i define a custom baseline as a straight line formed between the two points of interest? Can this be done using Matlab?

The figure below is from custom software I am using. However, I am trying to use Matlab for this because there are over 500 data files i need to process.

Thanks. Any help or suggestion is appreciated.

Answer 1

[Star Strider]

Use trapz to calculate the area under the curve, and use trapz separately to calculate the area under the line.

Then subtract them.

Example —

x = linspace(0,10);                         % X-Vector
y = 2.5*sinc(x-5) - 0.2*x;                  % Y-Vector

sincarea = trapz(x, 2.5*sinc(x-5))          % Area Under Original Curve (Reference)

sincarea = 2.5997

yarea = trapz(x,y)                          % Area Under Displayed Curve

yarea = -7.4003

linearea = trapz(x, -0.2*x)                 % Area Under The Line

linearea = -10

curvearea = yarea - linearea                % Area Between Line And Curve

curvearea = 2.5997

figure
plot(x, y)
hold on
plot(x, -0.2*x)
hold off
grid
axis('equal')

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[Rahul Ramesh]

@Star Strider thanks for the suggestion. I did not think of this. It seems to work for mathematical area as well as absolute area. Am i correct?

[Star Strider]

My pleasure!

If I understand your comment correctly, yes.

It returns the area between the x-axis (at y=0) and the line as ‘linearea’, and the area between the x-axis and the curve as ‘yarea’ separately, then subtracts them to return ‘curvearea’. (The ‘sincarea’ calculation is not necessary for the code, other than serving as a sort of ‘proof’ tthat the code returns the correct result.)

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