private void TransposeAndSwap(ref SubmatrixDims a, ref SubmatrixDims b)
{
Debug.Assert(a.Width == b.Height && a.Height == b.Width);
// 1. Prepare the submatrices
SubmatrixDims a11, a21, a12, a22;
SubmatrixDims b11, b21, b12, b22;
a.SplitDims(out a11, out a21, out a12, out a22);
b.SplitDims(out b11, out b21, out b12, out b22);
// 2. If the matrices are small, transpose them naively
// Check just the first one; because we have a square matrix, the other sizes should be very similar
if (a11.Width * a11.Height < NaiveThreshold)
{
TransposeAndSwapNaive(ref a11, ref b11);
TransposeAndSwapNaive(ref a21, ref b12);
TransposeAndSwapNaive(ref a12, ref b21);
TransposeAndSwapNaive(ref a22, ref b22);
return;
}
// 3. Transpose and swap them
TransposeAndSwap(ref a11, ref b11);
TransposeAndSwap(ref a21, ref b12);
TransposeAndSwap(ref a12, ref b21);
TransposeAndSwap(ref a22, ref b22);
}
// The recursion ends when the split submatrices are small enough. This saves us
// a lot of work caused by recursion. We do the recursion end check before recursing
// instead of at the start of the recursive func to reduce the recursion depth by one
// (it can further save us a lot of recursive calls -- with the tree branching
// factor of ~4 the number of leaves in the recursion tree is very high compared to
// the number of internal nodes.
private void TransposeInternal(ref SubmatrixDims dims)
{
// 1. Prepare the submatrices
SubmatrixDims a11, a21, a12, a22;
dims.SplitDims(out a11, out a21, out a12, out a22);
// 2. If the matrices are small enough, transpose them naively
if (a11.Width * a11.Height <= NaiveThreshold)
{
TransposeInternalNaive(ref a11);
TransposeInternalNaive(ref a22);
TransposeAndSwapNaive(ref a21, ref a12);
return;
}
// 3. Recurse on the submatrices
TransposeInternal(ref a11);
TransposeInternal(ref a22);
TransposeAndSwap(ref a21, ref a12);
}