how to define the curve by the area rather than area by the curve?

I used ode45 to obtain a curve using certain parameters and using trapz I find its area. Now my intention is to obtain another curve of the same equation with different parameters but the area under curve must be same as previous graph.

How do I do it?

Thank you

[Purush otham]

Is it possible to add an event or limit the second graph based on the trapz value obtained on the first graph?

[Ameer Hamza]

The only way to change area under a curve while keeping the shape same is to scale the curve by a suitable factor. All other transformation will also change the shape of the curve.

Answer 1

[Ameer Hamza]

You can do it like this,

1) Solve the equation for the first curve (say curve1). Calculate the area under curve1 and let us call it Area1.

2) Solve the equation for the second curve (say curve2) using the different set of parameters. Calculate the area under the 2nd curve and call it Area2.

3) Now change curve2 using following formula

curve2 = curve2/Area2*Area1;

The modifies curve 2 will have the same area.

[Purush otham]

Hi,

Though the logic provided by you makes sense, it did not work out in my case.

I have attached the script files used to execute the same.

Thank you

[Purush otham]

Maybe it was the way I defined the variables....using same variables confused matlab?

[Purush otham]

C1a=[1;2;3];C1b=[7;8;9]; A1=trapz(C1a,C1b) C2a=[4;5;6];C2b=[0;1;2]; A2=trapz(C2a,C2b) C3a=(C1a/A2)*A1;C3b=(C1b/A2)*A1; A3=trapz(C3a,C3b)

It also did not work for this simple code...

[Ameer Hamza]

You only need to scale the y values, not the x values. Run the following code, you will get the idea.

C1a=[1;2;3];
C1b=[7;8;9]; 
A1=trapz(C1a,C1b) 
C2a=[4;5;6];
C2b=[0;1;2]; 
A2=trapz(C2a,C2b) 

C3b=(C2b/A2)*A1;   % divide the curve you want to scale, C2b will scale to have area equal to C1b
A3=trapz(C2a,C3b)

[Purush otham]

Hi, Thanks a lot. It worked. Yet it would be nice to do the same using 'trapz' function. A loop that detects a particular trapz value and stops the ode45 from integrating further.

It does not matter if the shape of curve changes.