Let's say I have an array A[i,j] and I want to compute a new quantity B[i,j] by doing something like:
for i in arange(1, n):
B[i,j+1] = a*A[i-1,j] + b*A[i,j]+ c*A[i+1,j]
What numpy functionality can I use to turn this into a pure array operation?
I was thinking of np.cumprod but it's unclear how to incorporate the coefficients into the calculation.
A.shape will be (n+1, j).
Define A_left = A[:-2, :], A_middle = A[1:-1, :] and A_right = A[2:, :]
Then B = a*A_left + b*A_middle + c*A_right
B[1:-1] = ...
n+1 as the number of rows to account for A[i+1,j].If you don't mind a bit of signal processing, you could have a generic solution (generic in the sense where you could assign more elements alongside a, b and c for scaling element from A) using signal.convolve2d.
This would be similar to this other solution where the theory of convolution as related to such cases is dealt with in a bit more detailed manner. The implementation would look like this -
from scipy import signal
B = np.zeros_like(A)
kernel = np.array([a,b,c])[::-1,None]
B[1:-1] = signal.convolve2d(A, kernel, boundary='symm', mode='valid')
