Question

有没有一种有效的方法可以将许多不同的旋转矩阵乘以同一个向量？

现在我正在执行以下操作，程序极其缓慢

for i, rm in enumerate(ray_rotation_matrices):
        scan_point = rm * np.vstack([scale, 0, 0, 1])
        scan_points[i] = np.hstack(scan_point[:3])

每个rm是用于同质坐标的4x4矩阵。我可以以某种方式广播，但我如何确保它应用矩阵乘法而不是元素明智的产品？

我想摆脱for循环......

Answer 1

使用一个大的array和矩阵乘法运算符@。它是开箱即用的矢量化。例如：

# a stack of five 4x4 matrices
>>> m = np.random.random((5, 4, 4))
>>> v = np.random.random((4,))

# all five matrix vector products in one go
>>> m@v
array([[1.08929927, 0.98770373, 1.0470138 , 1.266117  ],
   [0.71691193, 0.68655178, 1.25601832, 1.22123406],
   [1.3964922 , 1.02123137, 1.03709715, 0.72414757],
   [0.9422159 , 0.84904553, 0.8506686 , 1.29374861],
   [1.02159382, 1.36399314, 1.06503775, 0.56242674]])

# doing it one-by-one gives the same answer
>>> [mi@v for mi in m]
[array([1.08929927, 0.98770373, 1.0470138 , 1.266117  ]), array([0.71691193, 0.68655178, 1.25601832, 1.22123406]), array([1.3964922 , 1.02123137, 1.03709715, 0.72414757]), array([0.9422159 , 0.84904553, 0.8506686 , 1.29374861]), array([1.02159382, 1.36399314, 1.06503775, 0.56242674])]

Numpy - 相同向量的许多矩阵

1 个答案: