SPARSE

Build sparse matrix from nonzeros and indices.

S = SPARSE(...) is the built-in function which generates matrices

in MATLAB's sparse storage organization.  It can be called with

1, 2, 3, 5 or 6 arguments.

S = SPARSE(X) converts a sparse or full matrix to sparse form by

squeezing out any zero elements.

S = SPARSE(i,j,s,m,n,nzmax) uses the rows of [i,j,s] to generate

an m-by-n sparse matrix with space allocated for nzmax nonzeros.

The two integer index vectors, i and j, and the real or complex

entries vector, s, all have the same length, nnz, which is the

number of nonzeros in the resulting sparse matrix S .

There are several simplifications of this six argument call.

S = SPARSE(i,j,s,m,n) uses nzmax = length(s).

S = SPARSE(i,j,s) uses m = max(i) and n = max(j).

S = SPARSE(m,n) abbreviates SPARSE([],[],[],m,n,0).  This

generates the ultimate sparse matrix, an m-by-n all zero matrix.

The argument s and one of the arguments i or j may be scalars,

in which case they are expanded so that the first three arguments

all have the same length.

For example, this dissects and then reassembles a sparse matrix:

[i,j,s] = find(S);

[m,n] = size(S);

S = sparse(i,j,s,m,n);

So does this, if the last row and column have nonzero entries:

[i,j,s] = find(S);

S = sparse(i,j,s);

All of MATLAB's built-in arithmetic, logical and indexing operations

can be applied to sparse matrices, or to mixtures of sparse and

full matrices.  Operations on sparse matrices return sparse matrices

and operations on full matrices return full matrices.  In most cases,

operations on mixtures of sparse and full matrices return full

matrices.  The exceptions include situations where the result of

a mixed operation is structurally sparse, eg.  A .* S is at least

as sparse as S .  Some operations, such as S >= 0, generate

"Big Sparse", or "BS", matrices -- matrices with sparse storage

organization but few zero elements.