I don't understand the following timings:
sage: A = AlternatingSignMatrices(6)
sage: lC = [a.corner_sum_matrix() for a in A]
sage: timeit("[from_corner_sum_1(corner) for corner in lC]", number=1,
repeat=1)
1 loops, best of 1: 63 s per loop
sage: timeit("[from_corner_sum_2(corner) for corner in lC]", number=1,
repeat=1)
1 loops, best of 1: 23.3 s per loop
The first implementation, from_corner_sum_1, computes each entry of the
result matrix using just array access to four elements in the given matrix
"corner".
The second, from_corner_sum_2, computes the same, using a caching version
of a naive algorithm. (I was unaware of the first relation when I coded
it.)
Why is the second version so much faster? This looks insane to me! I hope
I have misunderstood something very basic!
Martin
def from_corner_sum_1(corner):
n = len(list(corner))-1
asm = [[corner[i+1][j+1]+corner[i][j]-corner[i][j+1]-corner[i+1][j]
for j in range(n)]
for i in range(n)]
return AlternatingSignMatrix(asm)
def from_corner_sum2(corner):
asm_list = []
n = len(list(corner)) - 1
for k in range(n):
asm_list.append([])
S = [0]*n
C = [0]*n
for i in range(n):
R = 0
for j in range(n):
y = corner[i+1][j+1] - S[j] - C[j] - R
S[j] += R
C[j] += y
R += y
asm_list[i].append(y)
return AlternatingSignMatrix(asm_list)
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