sparsematrix/sparsepredicates.tst at main · fjwright/sparsematrix · GitHub

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m := mat((a,b),(c,d));
s := sparsify m;

sparse_matrix_p m;
sparse_matrix_p s;
sparse_square_matrix_p s;

% Symmetric, etc.:

sparse_symmetric_matrix_p s;
ss := s + sparse_tp s;
sparse_symmetric_matrix_p ss;
sas := s - sparse_tp s;
sparse_skew_symmetric_matrix_p sas;

m := mat((1+i,2),(3i,4+i));
s := sparsify m;
sh := s + conj sparse_tp s;
sparse_hermitian_matrix_p sh;

sah := s - conj sparse_tp s;
sparse_skew_hermitian_matrix_p sah;

m := mat((a,b),(c,d));

% Diagonal and triangular:

sd := sparsify mat((a,0,0),(0,b,0),(0,0,c));
su := sparsify mat((a,b,c),(0,d,e),(0,0,f));
sl := sparse_tp su;

sparse_diagonal_matrix_p sd;
sparse_upper_triangular_matrix_p sd;
sparse_lower_triangular_matrix_p sd;

sparse_diagonal_matrix_p su;
sparse_upper_triangular_matrix_p su;
sparse_lower_triangular_matrix_p su;

sparse_diagonal_matrix_p sl;
sparse_upper_triangular_matrix_p sl;
sparse_lower_triangular_matrix_p sl;

% Lipshutz
sparse_matrix so(3,3);
so(1,1) := so(3,2) := 1/9$
so(1,2) := so(3,1) := 8/9$
so(1,3) := so(2,2) := -4/9$
so(2,1) := so(3,3) := 4/9$
so(2,3) := -7/9$
so;
so * sparse_tp so;
sparse_identity_matrix_p ws;
sparse_orthogonal_matrix_p so;

sparse_matrix so(2,2);
so(1,1) := so(2,2) := cos theta$
so(2,1) := -(so(1,2) := sin theta)$
so;
for all th let (cos th)^2 + (sin th)^2 => 1;
so * sparse_tp so;
sparse_identity_matrix_p ws;
sparse_orthogonal_matrix_p so;

so(2,1) := -so(2,1)$
so(2,2) := -so(2,2)$
so;
sparse_orthogonal_matrix_p so;

sparse_matrix su(3,3);
su(1,1) := su(2,2) := 1$
su(1,2) := -(su(2,1) := i)$
su(1,3) := su(3,2) := -1 + i$
su(2,3) := su(3,1) := 1 + i$
su := su/2;
sparse_unitary_matrix_p su;

;end;