在块矩阵中排列numpy数组 [英] Arranging numpy arrays in a block matrix

问题描述

我有3个numpy数组A，B和C.为了简单起见，让我们假设它们都是形状为[n, n]的形状.我想将它们排列成一个块矩阵

I have 3 numpy arrays A, B and C. For simplicity, let's assume that they are all of shape [n, n]. I want to arrange them as a block matrix

A    B
B^t  C

其中，B^t表示B的转置.当然，我可以通过一系列串联来做到这一点

where B^t shall denote the transpose of B. Of course, I could do this via a series of concatenations

top_row = np.concatenate([A, B], axis=1)
bottom_row = np.concatenate([B.transpose(), C], axis=1)
result = np.concatenate([top_row, bottom_row], axis=0)

有没有更简单，更易读的方式?

Is there a simpler, more readable way?

推荐答案

从NumPy 1.13开始，存在

As of NumPy 1.13, there's np.block. This builds matrices out of nested lists of blocks, but it's also more general, handling higher-dimensional arrays and certain not-quite-grid cases. It also produces an ndarray, unlike bmat.

np.block([[A, B], [B.T, C]])

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对于以前的版本，您可以使用内置的NumPy np.bmat 非常适合这样的任务，就像这样-

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For previous versions, you can use the NumPy built-in np.bmat that's perfectly suited for such a task, like so -

np.bmat([[A, B], [B.T, C]])

请在 comments by @unutbu 中提及请注意，输出将是NumPy矩阵.如果预期的输出是数组，则需要将其转换，就像这样-

As mentioned in the comments by @unutbu, please note that the output would be a NumPy matrix. If the intended output is an array instead, we need to convert it, like so -

np.asarray(np.bmat([[A, B], [B.T, C]]))

或

np.bmat([[A, B], [B.T, C]]).A

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