[pure-lang-users] ANN: Pure 0.7 released (a.k.a. Pure gets Octave-like matrix support)

[Albert G. <Dr....@t-...>]

New in this release (you guessed it): GSL (GNU Scientific Library)
matrix support.

As usual, you can grab the new release here:
http://sourceforge.net/project/showfiles.php?group_id=226193

The release notes are here:
http://sourceforge.net/project/shownotes.php?group_id=226193&release_id=628859

Note that to enjoy the full GSL matrix support, of course you need to
have GSL installed, which is available here:
http://www.gnu.org/software/gsl/

(Forgot to update the INSTALL instructions on that. Will fix that asap.)

I also updated the pure-mingw.zip file on the website, which now
includes GSL 1.11 for those of you who want to roll their own Windows
version. (Of course a ready-made msi package with a GSL-enabled version
of the interpreter is available, too.)

You can still build Pure without GSL, but then the interpreter will lack
all the numeric matrix goodness, and only symbolic matrices will work.

Backward compatibility issues: The introduction of the matrix syntax
called for some changes in the comprehension syntax as well as in the
arithmetic sequence notation:

- The pipe symbol '|' is now used to separate the template expression
and the generator and filter clauses. For consistency, this applies to
both list and matrix comprehensions. The old [x;...] syntax is still
supported in list comprehensions, but is flagged with a "deprecated"
warning by the compiler.

- Arithmetic sequences with arbitrary stepsize are now written
x:y..z instead of x,y..z. This made it possible to give the .. operator
a lower precedence than the ',' operator, which makes writing matrix
slices like x!!(i..j,k..l) much more convenient. (Actually, considering
how sequences are defined in Pure, you'll find that the new x:y..z
notation actually makes *more* sense in Pure than the old syntax.)

The matrix stuff:

You can find some matrix examples in the examples folder (linalg.pure,
gauss.pure), and in the manual. If you know Octave matrices then you
should feel right at home. Here's a brief summary of the most important
operations:

- #x
  total number of elements
- dim x
  number of rows and columns (as a pair)
- x'
  transpose of a matrix
- x!i
  ith matrix element in row-major order (zero-based)
- x!(i,j)
  jth element in ith row of the matrix (zero-based)
- x!!is, x!!(is,js)
  slicing (is and js are lists of machine ints)
- x==y, x!=y
  matrix comparisons

The curly braces construct matrices (using pretty much the same notation
as in Octave, i.e., ',' separates columns, ';' rows), e.g.:

- {1,2,3}
  a row vector consisting of machine ints
- {1.0;2.0;3.0}
  a column vector of double values
- {1.0+:0.0,0.0+:1.0}
  a complex vector (this requires math.pure, of course)
- {1,2;3,4}
  a 2x2 int matrix
- {1L,y+1;foo,bar}
  a symbolic matrix

Like in Octave, the elements in curly braces can also be submatrices,
provided that the dimensions match up. In addition, Pure also offers
non-GSL, "symbolic" matrices which can contain any combination of Pure
objects.

We also have matrix comprehensions, which work pretty much like list
comprehensions:

  > eye n = {i==j|i=1..n;j=1..n};
  > eye 3;
  {1,0,0;0,1,0;0,0,1}

(That's something which Octave doesn't have, instead you use 'for' loops
in Octave which are *much* slower than Pure's comprehensions.)

Note that only basic matrix operations are built into Pure or provided
by the prelude; Pure isn't Octave after all. The usual linear algebra
stuff can either be done using the Pure operations or by interfacing to
GSL (a simple example of that can be found in the C INTERFACE section of
the manpage). Marshalling of GSL matrices is handled transparently in
the C interface so that you can pass Pure matrices to C without much ado.

A full GSL wrapper will hopefully become available in the not so distant
future. Eddie and I will work on this together, as time permits (I have
some stuff to prepare for the upcoming semester, and Eddie is also quite
busy right now, so don't hold your breath just yet). If anyone else
wants to give a helping hand in that, please let us know so that we can
coordinate our efforts.

Well, you can probably imagine that the changes in both the interpreter
and the library were again quite substantial this time, so please report
any bugs that you find. Thanks.

Enjoy! :)
Albert

-- 
Dr. Albert Gr"af
Dept. of Music-Informatics, University of Mainz, Germany
Email:  Dr....@t-..., ag...@mu...
WWW:    http://www.musikinformatik.uni-mainz.de/ag