Random sparse symmetric matrices
R = SPRANDSYM(S) is a symmetric random matrix whose lower triangle
and diagonal have the same structure as S. The elements are
normally distributed, with mean 0 and variance 1.
R = SPRANDSYM(n,density) is a symmetric random, n-by-n, sparse
matrix with approximately density*n*n nonzeros; each entry is
the sum of one or more normally distributed random samples.
R = SPRANDSYM(n,density,rcond) also has a reciprocal condition number
equal to rcond. The distribution of entries is
nonuniform; it is roughly symmetric about 0; all are in [-1,1].
If rcond is a VECTOR of length n, then R has eigenvalues rcond.
Thus, if rcond is a positive (nonnegative) vector then R will
be positive (nonnegative) definite
In either case, R is generated by random Jacobi rotations
applied to a diagonal matrix with the given eigenvalues or
condition number. It has a great deal of topological and
R = SPRANDSYM(n, density, rcond, kind) is positive definite.
If kind = 1, R is generated by random Jacobi rotation of
a positive definite diagonal matrix.
R has the desired condition number exactly.
If kind = 2, R is a shifted sum of outer products.
R has the desired condition number only
approximately, but has less structure.
If R = SPRANDSYM(S, density, rcond, 3),
then R has the same structure as the MATRIX S and
approximate condition number 1/rcond. density is ignored.
See also SPRANDN .