SciRuby/nmatrix

This is the proposed binary format for saving and loading NMatrix objects.

Order is little-endian.

List matrices should be converted to dense or yale matrices. There should be no serious need to load or save
linked-list matrices, since these exist primarily in order to construct efficient yale matrices.


First 64-bit block:
* ui16 major (version)
* ui16 minor
* ui16 release
* i16 NULL


Second 64-bit block:
* ui8 dtype
* ui8 stype
* ui8 itype # ui32 for dense
* ui8 symm
* i16 NULL
* ui16 dim    # if 1, NVector; otherwise, NMatrix


3rd - nth 64-bit block: shape

itype sets the number of bytes allocated for each shape entry. Since only yale uses itype, dense will pretty
much always be the UINT32 itype (see nmatrix.h). If the total number of bytes occupied by the shape array is
less than 8, the rest of the 64-bit block will be padded with zeros.


(n+1)th 64-bit block: depends on stype, symm

symm is designed to reduce file size by allowing us to not save certain elements in symmetric, hermitian, skew-
symmetric, and triangular matrices. These values will be defined in nmatrix.h; 0 indicates standard (no symmetry).
In later versions, additional patterns may be defined which might even have less to do with symmetry than
upper/lower do.

When storing a symmetric matrix, we will only store the upper portion. If the matrix is lower triangular, only the
lower portion will be stored.

For dense, we simply store the contents of the matrix exactly as in memory (or just the upper-triangular part if
symm is set).

For yale, we store:
* ui32 ndnz
* ui32 length (AKA size, the number of elements in A/IJA that aren't nil/undefined)

The latter will serve as the capacity when we read a Yale matrix.

Then we store the a array, again padding with zeros so it's a multiple of 8 bytes.

Then we store the ija array, padding with zeros so it's a multiple of 8 bytes.