不要试图向量化不易向量化的循环。相反,使用像Numba这样的jit编译器或使用Cython。如果结果代码更易读,则向量化解决方案是好的,但就性能而言,编译解决方案通常更快,或者在最坏的情况下与向量化解决方案一样快(除了BLAS例程)。
单线程示例
import numba as nb
import numpy as np
@nb.njit()
def max_min_3(A,B,C):
max_of_min=-np.inf
for i in range(A.shape[0]):
loc_min=A[i]
if (B[i]<loc_min):
loc_min=B[i]
if (C[i]<loc_min):
loc_min=C[i]
if (max_of_min<loc_min):
max_of_min=loc_min
return max_of_min
@nb.njit()
def your_func(A):
n=A.shape[0]
save_rows=np.zeros(3,dtype=np.uint64)
global_best=np.inf
for i in range(n):
for j in range(i+1, n):
for k in range(j+1, n):
local_best = max_min_3(A[i,:], A[j,:], A[k,:])
if (local_best < global_best):
global_best = local_best
save_rows[0] = i
save_rows[1] = j
save_rows[2] = k
return global_best, save_rows
单线程版本的性能
n=100
your_version: 1.56s
compiled_version: 0.0168s (92x speedup)
n=150
your_version: 5.41s
compiled_version: 0.08122s (66x speedup)
n=500
your_version: 283s
compiled_version: 8.86s (31x speedup)
第一次调用大约需要0.3-1秒的恒定开销。为了测量计算时间本身的性能,只需调用一次,然后测量性能。
通过少量代码更改,此任务也可以并行化。
多线程示例
@nb.njit(parallel=True)
def your_func(A):
n=A.shape[0]
all_global_best=np.inf
rows=np.empty((3),dtype=np.uint64)
save_rows=np.empty((n,3),dtype=np.uint64)
global_best_Temp=np.empty((n),dtype=A.dtype)
global_best_Temp[:]=np.inf
for i in range(n):
for j in nb.prange(i+1, n):
row_1=0
row_2=0
row_3=0
global_best=np.inf
for k in range(j+1, n):
local_best = max_min_3(A[i,:], A[j,:], A[k,:])
if (local_best < global_best):
global_best = local_best
row_1 = i
row_2 = j
row_3 = k
save_rows[j,0]=row_1
save_rows[j,1]=row_2
save_rows[j,2]=row_3
global_best_Temp[j]=global_best
ind=np.argmin(global_best_Temp)
if (global_best_Temp[ind]<all_global_best):
rows[0] = save_rows[ind,0]
rows[1] = save_rows[ind,1]
rows[2] = save_rows[ind,2]
all_global_best=global_best_Temp[ind]
return all_global_best, rows
多线程版本的性能
n=100
your_version: 1.56s
compiled_version: 0.0078s (200x speedup)
n=150
your_version: 5.41s
compiled_version: 0.0282s (191x speedup)
n=500
your_version: 283s
compiled_version: 2.95s (96x speedup)
编辑
在较新的Numba版本中(通过Anaconda Python分发安装),我需要手动安装tbb
才能获得有效的并行化。
n
的大小是多少? - Brad Solomon