Fine! I believe the Hadamard transform is used in quantum computing simulation. In my brief attempt at QC, I see the Hadamard Gate involves (1% %:2) * 1 1,: 1 _1 (!)
But just before we wave bye-bye, here's a sort of unification of where I/we've got to, at least as far as the transform matrices are concerned. I think a Kronecker product is best left as defined; let's modify its inputs instead if normalisation is required. Both normalisation and ordering may be tackled with a single adverb. So, now, uHM =: (,~ cH) NB. unnormalised, Miller ordering uHW =: (, cH) NB. unnormalised, Wiki ordering nHM =: 1 & (,~ cH) NB. normalised, Miller ordering nHW =: 1 & (, cH) NB. normalised, Wiki ordering cH =: 1 : 0 0 (u cH) y : norm =. 2 ^ - -: x ones =. ,: norm * 1 _1 comma =. u n =. y h =. ones comma~ | ones n2 =. 1 while. n > n2 =. +: n2 do. h =. (h kp |ones) comma (=i. n2) kp ones end. ) (nHM; uHW) 4 NB. applying two of these 4 +-------------------------------------+----------+ |0.707107 _0.707107 0 0|1 1 1 1| | 0 0 0.707107 _0.707107|1 1 _1 _1| | 0.5 0.5 _0.5 _0.5|1 _1 0 0| | 0.5 0.5 0.5 0.5|0 0 1 _1| +-------------------------------------+----------+ Enough!? Mike On 09/01/2018 02:06, Raul Miller wrote:
Actually, I was thinking of moving on to other wavelets, Like, forinstance, the Hadamard transform, whose normalized matrix was Kp=: (%%:2) * ,/@:(,./"3)@:(*/) H1=: 1 1,:1 _1 Hm=: H1&Kp@]^:[&(,.%:2) That said, I still haven't figured out a use for these things... Thanks,
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