vector basics; matrixes, serialization and half-precision floating point support

[normen662]

• contains a new package called half:
  • contains a modified version of the Half class as provided in Half4J.
• contains a new package called linear:
  • RealVector as well as three implementations HalfRealVector, FloatRealVector, DoubleRealVector in linear
  • operations on vectors
  • linear operator
  • RealMatrix as dense matrix, various implementations, operations on matrices
  • Metrics as implementation of different kinds of metrics
  • FhtKacRotator to create random orthogonal matrices as needed by rabitq
  • QRDecomposition using Householder reflections to create random orthogonal matrices
• contains a new package called rabitq:
  • rabitq implementation (extended version): quantizer and estimator, encodings
  • EncodedRealVector as implementation of RealVector as drop in for any RealVector

[alecgrieser]

I took a more detailed look at the new linear package. This combines my feedback in #3598

[hatyo]

If I am reading this correctly, each one of the Vector implementations requires the underlying byte representation to have a descriptor of the actual precision (line 106).

Is this correct? if so, why is it necessary to add this information, shouldn't the consumer of the vector array already know the type if the vector it is reading from disk?

[normen662]

Discussed offline.

[alecgrieser]

LGTM! Thanks for responding to the various suggestions I left. I think I like how the linear algebra section looks now. I've left a few things that we could probably be delayed until a follow up with the idea that we want to get the ball rolling, in particular with things like #3691

[alecgrieser]

Should this be removed? I ask because there's a discussion about using explicit calls to toRowMajor() and toColumnMajor() on a matrix prior to calling .getData() so that the user doesn't get confused about whether getData() returns data in a row-major or column-major orientation. I think that makes sense, but if RealMatrix still has a getData method on it, then the user can forget to make that call, whereas if the method is only on RowMajorRealMatrix and ColumnMajorRealMatrix, the compiler will force them to do that (or make a cast)?

[normen662]

That's a good suggestion. I think I will do that.