Bill Baxter wrote:
On Sat, Jan 31, 2009 at 12:12 PM, Andrei Alexandrescu
<[email protected]> wrote:
I've updated my code and documentation to include series (as in math) in the
form of infinite ranges. Also series in closed form (given n can compute the
nth value without iterating) are supported as random-access ranges.
Also Stride is provided. The Matrix container (speaking of scientific
computing with D!) will support various representational choices, most
importantly the ones endorsed by high-performance libraries. For Matrix,
Stride is an important component as I'm sure anyone who's ever written a
matrix knows.
This sounds interesting! So you'll have diagonal, banded, upper/lower
triangular, symmetric, strided and dense matrices? How about 2D
slices?
Sparse matrices too. For dense block matrices I'm thinking of a type
like this:
alias BlockMatrix!(float, 3, [0, 2, 1]) M3;
This defines a block rectangular matrix with three dimensions laid out
in the order specified: In this case, M3 is laid out as a collection of
column-order submatrices of 2 dimensions. (I deliberately chose a
slightly odd example.) The last parameter of BlockMatrix can be any
permutation of 0, 1, and 2, thus dictating how the dimensions are laid
out. For an obvious example, here's a Fortran-compatible block matrix
with column-major layout:
alias BlockMatrix!(double, 2, [1, 0]) FortranMatrix;
So it's pretty easy to choose any layout for any matrix with any number
of dimensions. This matrix defines ranges that crawl it, called
hyperplanes. There is a "natural" hyperplane that doesn't need any
stride, and that's the cut along the dimension that varies slowest. That
cut is the most efficient because it really has the layout of a
(littler) BlockMatrix itself. Continuing on the M3 example, a "row" in
that matrix has type:
alias BlockMatrix!(float, 2, [1, 0]) M3Row;
which is obtained by chopping the first element in the array [0, 2, 1]
into [2, 1], and then decrementing what's left into [1, 2]. So if you have:
M3 m;
auto subM = m[3];
you get that smaller BlockMatrix with all amenities its larger cousin
offered. But if you want a cut along a different dimension, a strided
range will be returned.
Jagged, banded, diagonal, fixed-size, and sparse layouts come naturally
and will be hopefully supported in a mixable-and-matchable form (e.g. I
want a block matrix of 3x3 matrices). I want to focus on storage for
now, put it in the standard library, to then allow great scientific
programmers like you guys to use those storages as a common data format
on top of which cool algorithms can be implemented.
Andrei
