I need to perform this following integration for a 2D array:
That is, each point in the grid get the value RC, which is integration over 2D of the difference between the whole field and the value of the field U at certain point (x,y), multiplying the normalized kernel, that in 1D version is:
What I did so far is an inefficient iteration over indexes:
def normalized_bimodal_kernel_2D(x,y,a,x0=0.0,y0=0.0):
""" Gives a kernel that is zero in x=0, and its integral from -infty to
+infty is 1.0. The parameter a is a length scale where the peaks of the
function are."""
dist = (x-x0)**2 + (y-y0)**2
return (dist*np.exp(-(dist/a)))/(np.pi*a**2)
def RC_2D(U,a,dx):
nx,ny=U.shape
x,y = np.meshgrid(np.arange(0,nx, dx),np.arange(0,ny,dx), sparse=True)
UB = np.zeros_like(U)
for i in xrange(0,nx):
for j in xrange(0,ny):
field=(U-U[i,j])*normalized_bimodal_kernel_2D(x,y,a,x0=i*dx,y0=j*dx)
UB[i,j]=np.sum(field)*dx**2
return UB
def centerlizing_2D(U,a,dx):
nx,ny=U.shape
x,y = np.meshgrid(np.arange(0,nx, dx),np.arange(0,ny,dx), sparse=True)
UB = np.zeros((nx,ny,nx,ny))
for i in xrange(0,nx):
for j in xrange(0,ny):
UB[i,j]=normalized_bimodal_kernel_2D(x,y,a,x0=i*dx,y0=j*dx)
return UB
You can see the result of the centeralizing function here:
U=np.eye(20)
plt.imshow(centerlizing(U,10,1)[10,10])
I'm sure I have additional bugs, so any feedback will be warmly welcome, but what I am really interested is understanding how I can do this operation much faster in vectorized way.