What is the fastest way to transpose a multi dimensional (n > 2) matrix in C++?

Marek Basovník 0
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I found an answer to this question very well described for a rectangle matrix n=2 in here

What is the fastest way to transpose a matrix in C++?

But my question is how to do the same in more general case. Let have B a transpose of A as

B[i1][i2][J][i4][K][i6][i7] = A[i1][i2][K][i4][J][i6][i7]

so in this particular case of n=7 we do transpose between 3th and 5th index marked as J, K. I assume that whole data structure is within compact memory block float*. Brackets above is used just for symbolic expression of transform operation.

I am about to deal with larger dimensions (possibly n=7) with a lots of data (some dimensions has lower rank about 3-5 and some of them are realatively large about 1000).

Is there a way how to make a really fast algorithm avoid chache-misses or even better how to use advatage of SSE (or AVX) intrinsics just like in the question mentioned above?

transpose caching matrix algorithm c++
1 Answers

Have an index table to access your underlying matrix:

template <std::size_t N>
class Matrix {
  std::array<std::size_t, N> index; // init to 0, 1, 2, ..., N
  void transpose(std::size_t i, std::size_t j) {
    std::swap(index[i],index[j]);
  }
  // access M[index[i]...] instead of M[i...]
};
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