How to best perform a surface integral over 2D point data?

Question

I have a data set of 363 x- by 190 y-points with an associated functional value that I would to integrate over multiple different subregions.. I've tried to create a SciPy interp2d function to integrate; however, creating that function even with linear interpolation has taken over 2 hours (and is not yet done).

What is a better approach to perform this task?

Some snippets below...

In the convert_RT_to_XY function below, imb/jmb are the r,theta mesh boundaries that I convert to Cartesian boundaries.

Later, in my code, I convert the mesh boundaries (imb/jmb) to mesh-center values (imm,jmm), convert to vectors (iX, iY), convert my function a vector (iZ), and then attempt to make my interpolation function.

---

# Convert R, T mesh vectors to X, Y mesh arrays.                                                                       
def convert_RT_to_XY(imb, jmb):                                                                                        
    R, T = np.meshgrid(imb,jmb)                                                                                        
    X = R * np.cos(np.radians(T*360))                                                                                  
    Y = R * np.sin(np.radians(T*360))                                                                                  
    return(X, Y) 

...

imm = imb[:-1]+np.divide(np.diff(imb),2)                                                                       
jmm = jmb[:-1]+np.divide(np.diff(jmb),2) 
iX, iY =  convert_RT_to_XY(imm, jmm)   
iX = np.ndarray.flatten(iX)                                                                                    
iY = np.ndarray.flatten(iY)                                                                                    
iZ = np.ndarray.flatten(plot_function)                                                                         
f = interpolate.interp2d(iX, iY, iZ, kind='linear') 

Ultimately, I want to perform:

result = dblquad(f, 10, 30,
    lambda x: 10,
    lambda x: 30))

Answer 1

Look into SciPy's RectBivariateSpline. If you are placing your data on a Cartesian grid anyway, it performs much faster than interp2D