speed-rational.tst

load_package sparse;

size := 500$
% Make an invertible random sparse matrix SM
% (with some fractional entries):
sm := sparse_random_matrix(size);
for i := 1:size do sm(i,i) := 1/i;
matrix_density sm;
% Make a dense matrix copy M:
m := densify sm$
% Make a sparse copy S:
s := m$ transmat s;

on time;

% Addition:
matrix msum(size,size);
for count := 1:100 do msum := msum + m; % MATRIX is slow (23515 ms)
sparse_matrix smsum(size,size);
for count := 1:100 do smsum := smsum + sm; % SPARSEMATRIX is OK (125 ms)
sparse ssum(<<size>>,<<size>>);      % doesn't accept variable size!!!
for count := 1:100 do ssum := ssum + s; % SPARSE is fastest (94 ms !!!)

% Multiplication:
m^10$                                  % MATRIX is slow (15734 ms)
sm^10$                                 % SPARSEMATRIX is fast (750 ms)
s^10$                                  % SPARSE is fastest (469 ms !!!)

% Determinant:
det m;         % MATRIX is OK (281 ms)
sparse_det sm; % SPARSEMATRIX is fastest (16 ms)
% det s;       % SPARSE crashes!
% FAILS even with size = 50: Heap exhausted (eventually)

% Inverse:
m^(-1)$                              % MATRIX is OK (469 ms)
sm^(-1)$                             % SPARSEMATRIX is fastest (62 ms)
s^(-1)$                              % SPARSE is OK (110 ms)

if m^(-1)*m = m*m^(-1) then "OK" else "***** ERROR *****"; % OK
if sm^(-1)*sm = sm*sm^(-1) then "OK" else "***** ERROR *****"; % OK
% if s^(-1)*s = s*s^(-1) then "OK" else "***** ERROR *****"; % FAILS
% Both s^(-1)*s and s*s^(-1) fail for different reasons!

;end;