Categorize series of inputs into rough QR unitary matrices.

There exists support vector machine and so on to categorize vector series.
So this is another categorizer on vector series. (I didn't searched well, so might be preceding results exist.)

const auto cg(crush<double>(std::vector<SimpleVector<double> >(...),
 or we can do:crushWithOrder<double>(std::vector<double>(...),
  /* some status size (see below) */,
  /* count of blocks? (see below) */));
// cg[/* index */].first  : divided vector itself.
// cg[/* index */].second : divided vector indices.

./catg <status dimension> <count> < data.txt
# status dimension < 0 for pairwise divide left part.
# count <  - 1 for each sorted divide.
# count == - 1 for each sorted divide, divide to sqrt(num).
# count == 0 for divide to sqrt(num).
# count >= 1 for divide at most count parts.

We solve max_(n,t) min_k|A^t*n+1*t|_k / ||[n t]|| multiple times on invariant of makeProgramInvariant.

We categorize by multiple of the meaning on input stream or by complexity of input calculation. So if input stream can be described by f(x) g(x) == 0, it's not separatable by this catg program. In such case, we need to separate by multiple of p1 copy structure then, we need simple NAND gate program factorization.

We treat all input dimension as meaningful. So if it's not so, the no bias causes orthogonal to categorize.

• https://drive.google.com/drive/folders/1B71X1BMttL6yyi76REeOTNRrpopO8EAR?usp=sharing
• https://1drv.ms/u/s!AnqkwcwMjB_PaDIfXya_M3-aLXw?e=qzfKcU
• https://ja.osdn.net/users/bitsofcotton/

2023/03/13 try to real close. 2023/03/24 code clean. 2023/03/31 merge prand. 2023/04/02 fix CatG::CatG score calculation. 2023/04/03 merge. 2023/04/05 fix makeProgramInvariant scale accuracy stability. 2023/04/21 shapeup around make/revert ProgramInvariant, algorthm changed. 2023/08/02 crush to the last. 2023/10/30 copy structure reliably with randtools meaning. 2023/11/15 update readme. close.