在深度学习网络中，特征层都是一个多维的数组。有时候为了把经过不同大小、形状的卷积核而得到的特征层链接在一起，就需要用到numpy的concatenate。在numpy中，concatenate的功能解释是：Join a sequence of arrays along an existing axis。下面展示相关的用法。
# 将数组a, b沿着0轴进行合并，合并之后的shape应该是(2, 5, 5)
import numpy as np
a = np.random.random((1, 5, 5))
b = np.random.random((1, 5, 5))
c = np.concatenate((a, b), axis = 0)
print "a:"
print a
print "b:"
print b
print "np.concatenate((a, b), axis = 0):"
print c
c = np.concatenate((a, b), axis = 1)
print "np.concatenate((a, b), axis = 1):"
print c
c = np.concatenate((a, b), axis = 2)
print "np.concatenate((a, b), axis = 2):"
print c
上面的输出结果如下：
a:
[[[0.84073463 0.46274429 0.08248961 0.19070404 0.9974667 ]
[0.61659658 0.37714231 0.73611954 0.1912308 0.6354842 ]
[0.12116275 0.92568538 0.24624993 0.38109115 0.49512079]
[0.3306727 0.89910473 0.13962387 0.36557941 0.5380739 ]
[0.49190266 0.21509959 0.5138292 0.29321129 0.03401961]]]
b:
[[[0.81091071 0.52620968 0.09808308 0.86436183 0.46453824]
[0.53201367 0.54038408 0.98995042 0.40034224 0.56401361]
[0.75310483 0.65040443 0.4618217 0.68053822 0.24892278]
[0.18428724 0.37016259 0.43493183 0.0686078 0.59134009]
[0.26952899 0.49031205 0.56216806 0.26634649 0.37192443]]]
np.concatenate((a, b), axis = 0):
[[[0.84073463 0.46274429 0.08248961 0.19070404 0.9974667 ]
[0.61659658 0.37714231 0.73611954 0.1912308 0.6354842 ]
[0.12116275 0.92568538 0.24624993 0.38109115 0.49512079]
[0.3306727 0.89910473 0.13962387 0.36557941 0.5380739 ]
[0.49190266 0.21509959 0.5138292 0.29321129 0.03401961]]
[[0.81091071 0.52620968 0.09808308 0.86436183 0.46453824]
[0.53201367 0.54038408 0.98995042 0.40034224 0.56401361]
[0.75310483 0.65040443 0.4618217 0.68053822 0.24892278]
[0.18428724 0.37016259 0.43493183 0.0686078 0.59134009]
[0.26952899 0.49031205 0.56216806 0.26634649 0.37192443]]]
np.concatenate((a, b), axis = 1):
[[[0.84073463 0.46274429 0.08248961 0.19070404 0.9974667 ]
[0.61659658 0.37714231 0.73611954 0.1912308 0.6354842 ]
[0.12116275 0.92568538 0.24624993 0.38109115 0.49512079]
[0.3306727 0.89910473 0.13962387 0.36557941 0.5380739 ]
[0.49190266 0.21509959 0.5138292 0.29321129 0.03401961]
[0.81091071 0.52620968 0.09808308 0.86436183 0.46453824]
[0.53201367 0.54038408 0.98995042 0.40034224 0.56401361]
[0.75310483 0.65040443 0.4618217 0.68053822 0.24892278]
[0.18428724 0.37016259 0.43493183 0.0686078 0.59134009]
[0.26952899 0.49031205 0.56216806 0.26634649 0.37192443]]]
np.concatenate((a, b), axis = 2):
[[[0.84073463 0.46274429 0.08248961 0.19070404 0.9974667 0.81091071
0.52620968 0.09808308 0.86436183 0.46453824]
[0.61659658 0.37714231 0.73611954 0.1912308 0.6354842 0.53201367
0.54038408 0.98995042 0.40034224 0.56401361]
[0.12116275 0.92568538 0.24624993 0.38109115 0.49512079 0.75310483
0.65040443 0.4618217 0.68053822 0.24892278]
[0.3306727 0.89910473 0.13962387 0.36557941 0.5380739 0.18428724
0.37016259 0.43493183 0.0686078 0.59134009]
[0.49190266 0.21509959 0.5138292 0.29321129 0.03401961 0.26952899
0.49031205 0.56216806 0.26634649 0.37192443]]]
所以如果需要把不同卷积核的输出结果接在一起时，对于numpy数组可以采用concatenate来实现。
除此之外，numpy还有一个stack的功能，stack的解释为：Join a sequence of arrays along a new axis. The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension. 翻译过来就是将沿着现有数组的一个轴来进行融合，并新建一个轴。鉴于在特征层中，前后特征层的维度基本不会改变，所以stack基本也没有什么用。
对于mxnet这个框架，可以使用mxnet.ndarray.concat来实现相同的功能。