# Pre-calculated cycles for 8x3 matrix transpose

### From Just in Time

When driving 8 WS2811 strips in parallel with an 8Mhz AVR we need to transpose arrays of rgb-values into groups of red-, green- and blue values (rgbrgbrgb... to rrrrrrrrggggggggbbbbbbbb). This boils down to an in-place 8*3 matrix transpose. This again boils down to going through cycles like this:

- pick up the value at position
**1** - place the saved value from the previous step at position
**8**, but first save the value at that location - place the saved value from the previous step at position
**18**, but first save the value at that location - place the saved value from the previous step at position
**6**, but first save the value at that location - etc, etc...

Obviously, when doing this, you'd need a description of the cycles, i.e. which values need to be moved where. For 24 values, finding the cycles could be done with a set of numbered cards. But of course, in about the same time, you could whip up a program that does this. The program looks like this:

<source lang="cpp">

- include <iostream>

/**

* calculate cycles along which values should be rotated in an array to perform * a 8x3 matrix transformation. See: * https://en.wikipedia.org/wiki/In-place_matrix_transposition#Non-square_matrices:_Following_the_cycles * */

void findCycles() {

// this array describes for each cell in the array // where its value should go to. // e.g. positions[2] == 16 means that the value at // position 2 needs to move to position 16 int positions[] = { 0, 8, 16, 1, 9, 17, 2, 10, 18, 3, 11, 19, 4, 12, 20, 5, 13, 21, 6, 14, 22, 7, 15, 23 };

// keep on looping until all elements are at // their destination position while (true) { // find the starting point of a cycle int seed = 0; for (;seed<24;++seed) { if (positions[seed] != seed) break; } if (seed == 24) break; // everything in place

// seed is the first element of the cycle // now walk the cycle std::cout << seed << ": "; int transfer = positions[seed]; positions[seed] = -1;

while (transfer != -1) { std::cout << transfer << " "; std::swap( positions[transfer], transfer); } std::cout << '\n'; }

}

int main() {

findCycles();

} </source>

This returns the following:

1: 8 18 6 2 16 13 12 4 9 3 1 5: 17 21 7 10 11 19 14 20 22 15 5