Hello,
lately there has been some talk about Matlab & Octave.
The Matlab language, which Octave copies, is pretty limited,
even more so that Maxima's, so I don't see much value in it as
a user language for Maxima. However it has a very convenient
syntax for matrix operations, which I think we should try to adapt.
Matlab/Octave:
a [i, :] => all elements in row i
a [:, j] => all elements in column j
a [i, [1, 3, 5, 7, 11]] => columns selected by index
a [i, [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]] => columns selected by 1's
I have tried to adapt those operations to Maxima syntax.
Matlab/Octave implements some other matrix operations,
in particular most built-in operations distribute over a matrix
argument. Also, there is no distinction between a list and
a matrix. I didn't implement either of those ideas: built-in
functions mostly do not distribute over matrices (use some
map function instead), and confounding different kinds of
arguments leads to bad surprises.
So here is what I came up with. This is the package share/contrib/amatrix.
load (amatrix);
a : random_matrix (10, 5);
a [1, all]; => all elements in row 1
a [all, 1]; => all elements in column 1
a [1, [1, 3, 5]]; => elements in row 1 selected by column index
aa : make_array (any, 5);
[aa[0], aa[2], aa[4]] : true;
b : make_matrix (1, 5, aa); => construct amatrix object from array
a [all, b]; => columns selected by true
amatrixmap (lambda ([x], 19 * x), a); => multiply each element by 10
amatrixmap (lambda ([x], is (x > 1/2)), a [all, 3]);
=> true/false according to values in column 3
a [%, all]; => select rows by preceding result
amatrix objects store data in a Lisp array, and selected rows and
columns can share that array; I attempted to implement a copy-on-write
policy, which probably has some bugs.
Anyway maybe this is of interest to someone.
Robert Dodier