Integrate a 2D griddedInterpolant wrt one variable

Hello,

I would like to know how to integrate a 2D griddedInterpolant with respect to one variable.

I include an example:

[x,y] = ndgrid(-5:0.8:5);
z = x.^2 + y.^2; 
F = griddedInterpolant(x,y,z); 
integral(@(x) F(x,1),0,1)

The actual interpolant is from data and not availbe in a closed analytical form.

This produces an error. Is there a simple alternative?

[Torsten]

x = -5:0.8:5;
y = x';
z = x.^2 + y.^2;
F = griddedInterpolant({x,y},z);
integral(@(x)F(x,1),0,1,'ArrayValued',true)

[Anna Thuenen]

@Torsten

Indeed, this does not return an error message.

However, it returns:

1.6080

but it should return in this setting:

1.3333

[Torsten]

What happens if you choose a finer discretization in x-direction:

x = -5:0.01:5

e.g.

[Anna Thuenen]

As mentioned: This is an example. The actual goal is to integrate an interpolant of data.

[Torsten]

I know, but the quality of the result depends on the denseness of points (x,y) where you can supply z(x,y).

[Andrei Bobrov]

Hi friends!

>> x = -5:0.8:5;
y = x';
z = x.^2 + y.^2;
F = griddedInterpolant({x,y},z,'spline');

integral(@(x)F(x,1),0,1,'ArrayValued',true)
ans =
       1.3333
>> 

Answer 1

[Sai Bhargav Avula]

The integral function in MATLAB does Numerical Integration and is the approximate computation of an integral using numerical techniques. As mentioned by the @Torsten the quality depends on the denseness of points (x,y).