np.array division

矩阵形式的范数归一设计到矩阵除法

举个简单的例子：
假设一个数据矩阵规模为（4，3，2），可以理解为4个样本，每个样本是一个时间长度为3的点，点是（x, y）形式的二维空间的样本。

  > A = np.random.random((4,3,2))
  array([[[0.89239403, 0.12214923],
        [0.51232698, 0.15274605],
        [0.60971146, 0.07217262]],

       [[0.19267784, 0.11648302],
        [0.09225679, 0.95131037],
        [0.25777361, 0.23847847]],

       [[0.77162583, 0.05490807],
        [0.61026345, 0.1172357 ],
        [0.9613178 , 0.56668329]],

       [[0.8195157 , 0.44777402],
        [0.77027723, 0.90067652],
        [0.48683648, 0.80049979]]])

记对每个（x, y）点求范数后的矩阵为，即相应规模为(4,3,1)

> B = np.random.random((4,3,1))
array([[[0.79237377],
        [0.17657666],
        [0.06914004]],

       [[0.76301106],
        [0.4939386 ],
        [0.64676006]],

       [[0.73634844],
        [0.78604091],
        [0.14897835]],

       [[0.2775787 ],
        [0.69762266],
        [0.42144431]]])

的结果则为（x, y）的点除以相应范数的结果。

> a/b
array([[[1.12622865, 0.15415608],
        [2.90144227, 0.86504101],
        [8.8185003 , 1.04386148]],

       [[0.25252299, 0.1526623 ],
        [0.18677785, 1.92596887],
        [0.39856143, 0.36872789]],

       [[1.04790856, 0.07456805],
        [0.77637619, 0.14914707],
        [6.45273499, 3.80379628]],

       [[2.95237238, 1.61314255],
        [1.10414594, 1.29106545],
        [1.15516206, 1.89942009]]])

验证

> 0.89239403/0.79237377
1.1262286357611258
> 0.19267784/0.76301106
0.2525229975041253
> 0.12214923/0.79237377
0.15415607460100553