Numpy 双循环的向量化
如何矢量化以下双循环？
我有一个 N × A 矩阵和一个 N × B 矩阵，其中 A 和 B 可能不同，并且 N 比 A 和 B 小得多。我想按如下方式生成一个 A × B 矩阵，但理想情况下没有循环：
import numpy as np
def foo(arr):
# can be anything - just an example so that the code runs
return np.sum(arr)
num_a = 12
num_b = 8
num_dimensions = 3
a = np.random.rand(num_dimensions, num_a)
b = np.random.rand(num_dimensions, num_b)
# this is the loop I want to eliminate:
output = np.zeros( (num_a, num_b) )
for i in xrange(num_a):
for j in xrange(num_b):
output[i,j] = foo(a[:,i] - b[:,j])
任何想法？
How can I vectorize the following double-loop?
I have one N by A matrix and one N by B matrix, where A and B may differ and N is much smaller than A and B. I want to produce an A by B matrix as follows, but ideally without the loops:
import numpy as np
def foo(arr):
# can be anything - just an example so that the code runs
return np.sum(arr)
num_a = 12
num_b = 8
num_dimensions = 3
a = np.random.rand(num_dimensions, num_a)
b = np.random.rand(num_dimensions, num_b)
# this is the loop I want to eliminate:
output = np.zeros( (num_a, num_b) )
for i in xrange(num_a):
for j in xrange(num_b):
output[i,j] = foo(a[:,i] - b[:,j])
Any ideas?
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首先对
foo()进行向量化，即修改foo()使其能够正确地对形状为(N, A, B)的数组进行操作code>，返回形状为(A, B)的数组。这一步通常是最困难的一步。如何完成此操作完全取决于 foo() 的作用。对于给定的示例，这很容易做到：现在，使用 广播规则< /a> 创建一个包含所有向量差异的
(N, A, B)数组，并将其传递给foo()：First vectorise
foo(), i.e. modifyfoo()in a way that it can correctly operate on an array of shape(N, A, B), returning an array of shape(A, B). This step is usually the difficult one. How this is done entirely depends on whatfoo()does. For the given example, it's very easy to do:Now, use broadcasting rules to create a
(N, A, B)array containing all the vector differences, and pass it tofoo():