<p>我认为你最初的尝试只是缺少横积应该沿着的轴的规范。你知道吗</p>
<pre><code>x, y, z = np.meshgrid(np.linspace(-2, 2, 5),np.linspace(-2, 2, 5), np.linspace(-2, 2, 5))
A = np.array([x, y, z])
cross_result = np.cross(np.array(v), A, axis=0)
</code></pre>
<p>我用下面的代码测试了这个。作为<code>np.array([x, y, z])</code>的替代方法,您还可以使用<code>np.stack(x, y, z, axis=0)</code>,它清楚地显示网格沿哪个轴堆叠以形成向量网格,向量与轴0对齐。我还每次打印形状,并使用随机输入进行测试。在测试中,公式的输出在一个随机指标下与输入向量在同一指标下与向量v的叉积进行比较</p>
<pre><code>import numpy as np
x, y, z = np.meshgrid(np.linspace(-5, 5, 10), np.linspace(-5, 5, 10), np.linspace(-5, 5, 10))
p = np.random.rand(3) # random reference point
A = np.array([x-p[0], y-p[1], z-p[2]]) # vectors from positions to reference
A_bis = np.stack((x-p[0], y-p[1], z-p[2]), axis=0)
print(f"A equals A_bis? {np.allclose(A, A_bis)}") # the two methods of stacking yield the same
v = -1 + 2*np.random.rand(3) # random vector v
B = np.cross(v, A, axis=0) # cross-product for all points along correct axis
print(f"Shape of v: {v.shape}")
print(f"Shape of A: {A.shape}")
print(f"Shape of B: {B.shape}")
print("\nComparison for random locations: ")
point = np.random.randint(0, 9, 3) # generate random multi-index
a = A[:, point[0], point[1], point[2]] # look up input-vector corresponding to index
b = B[:, point[0], point[1], point[2]] # look up output-vector corresponding to index
print(f"A[:, {point[0]}, {point[1]}, {point[2]}] = {a}")
print(f"v = {v}")
print(f"Cross-product as v x a: {np.cross(v, a)}")
print(f"Cross-product from B (= v x A): {b}")
</code></pre>
<p>结果输出如下所示:</p>
<pre><code>A equals A_bis? True
Shape of v: (3,)
Shape of A: (3, 10, 10, 10)
Shape of B: (3, 10, 10, 10)
Comparison for random locations:
A[:, 8, 1, 1] = [-4.03607312 3.72661831 -4.87453077]
v = [-0.90817859 0.10110274 -0.17848181]
Cross-product as v x a: [ 0.17230515 -3.70657882 -2.97637688]
Cross-product from B (= v x A): [ 0.17230515 -3.70657882 -2.97637688]
</code></pre>