sparse matrix definition
sp=sparse(X)
sp=sparse(ij,v [,mn])
:X real or complex or boolean full (or sparse) matrix : :ij two columns integer matrix (indices of non-zeros entries) : :v vector : :mn integer vector with two entries (row-dimension, column-
dimension)
: :sp sparse matrix :
sparse is used to build a sparse matrix. Only non-zero entries are stored.
sp = sparse(X) converts a full matrix to sparse form by squeezing out any zero elements. (If X is already sparse sp is X).
sp=sparse(ij,v [,mn]) builds an mn(1)-by- mn(2) sparse matrix with sp(ij(k,1),ij(k,2))=v(k). ij and v must have the same column dimension. If optional mn parameter is not given the sp matrix dimensions are the max value of ij(:,1) and ij(:,2) respectively.
Operations (concatenation, addition, etc,) with sparse matrices are made using the same syntax as for full matrices.
Elementary functions are also available ( abs,maxi,sum,diag,...) for sparse matrices.
Mixed operations (full-sparse) are allowed. Results are full or sparse depending on the operations.
Note : Any operation involing dense matrices of the same size, either as argument (e.g. sp=sparse(d)) or as result (e.g. d= sp + 1.) is provided for convenience purposes but should of course be avoided. Furthermore, random access to elements ( sp(r,c)), especially for insertions, is not efficient, so any performance-constrained access should be done in batches with spget for read access and the three arguments constructor sp=sparse(ij, v, mn) for write access.
sp=sparse([1,2;4,5;3,10],[1,2,3])
`size`_(sp)
x=`rand`_(2,2);`abs`_(x)-`full`_(`abs`_(sparse(x)))
// sparse constructor taking a single dense matrix
// removes the zeros.
dense=[0., 1., 0., 0., 0.,
1., 0., 2., 0., 0.
0., 0., 0., 0., 0.
0., 0., 0., 0., -0.5];
sp=sparse(dense)
// complex matrices are also supported
sp=sparse(dense*(1+2*%i))
// for boolean matrices, the boolean sparse matrix
// only stores true values (and removes false values).
dense=[%F, %F, %T, %F, %F
%T, %F, %F, %F, %F
%F, %F, %F, %F, %F
%F, %F, %F, %F, %T];
sp=sparse(dense)