What it takes to transpose a matrix

That last diagram almost looks like an FFT shuffle.

Are there programming languages or optimizers that simplify this kind of plumbing?

Does it use switch in place? x = x XOR y, y = x XOR y, x = x XOR y

Is transposition a common enough operation that it might be better to avoid it by having versions of the operations/functions that take matrices that do the necessary transpositions implicitly?

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