问题
I have a nested for loop that iterates over rows of the weight matrix and applies logsumexp to the upper triangular portion of the outer addition matrix from these weights rows. It is very slow so I'm trying to figure out how to speed this up by either vectorizing or taking out the loops in lieu of matrix operations.
'''
Wm: weights matrix, nxk
W: updated weights matrix, nxn
triu_inds: upper triangular indices of Wxy outer matrix
'''
for x in range(n-1):
wx = Wm[x, :]
for y in range(x+1, n):
wy = Wm[y, :]
Wxy = np.add.outer(wx, wy)
Wxy = Wxy[triu_inds]
W[x, y] = logsumexp(Wxy)
logsumexp: computes the log of the sum of exponentials of an input array
a: [1, 2, 3]
logsumexp(a) = log( exp(1) + exp(2) + exp(3) )
The input data Wm is a weights matrix of nxk dimensions. K represents a patients sensor locations and n represents all such possible sensor locations. The values in Wm are basically how close a patients sensor is to a known sensor.
example:
Wm = [1 2 3]
[4 5 6]
[7 8 9]
[10 11 12]
wx = [1 2 3]
wy = [4 5 6]
Wxy = [5 6 7]
[6 7 8]
[7 8 9]
triu_indices = ([0, 0, 1], [1, 2, 2])
Wxy[triu_inds] = [6, 7, 8]
logsumexp(Wxy[triu_inds]) = log(exp(6) + exp(7) + exp(8))
回答1:
You can perform the outer product on the full matrix Wm and then swap the axes corresponding to columns in operand 1 and rows in operand 2 in order to apply the triangle indices to the columns. The resulting matrix is filled for all combinations of rows, so you need to select the upper triangle part.
W = logsumexp(
np.add.outer(Wm, Wm).swapaxes(1, 2)[(slice(None),)*2 + triu_inds],
axis=-1 # Perform summation over last axis.
)
W = np.triu(W, k=1)
来源：https://stackoverflow.com/questions/54031980/how-to-efficiently-compute-logsumexp-of-upper-triangle-in-a-nested-loop