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sprandsym | See Also |
Sparse symmetric random matrix
R = sprandsym(S) R = sprandsym(n,
density) R = sprandsym(n,
density,rc) R = sprandsym(n,
density,
rc,
kind)
R = sprandsym(S)
returns a symmetric random matrix whose lower triangle and diagonal have the same structure as S
. Its elements are normally distributed, with mean 0
and variance 1
.
R = sprandsym(n,density)
returns 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, and (0
density
1)
.
R = sprandsym(n,density,rc)
returns a matrix with a reciprocal condition number equal to rc
. The distribution of entries is nonuniform; it is roughly symmetric about 0; all are in .
If rc
is a vector of length n
, then R
has eigenvalues rc
. Thus, if rc
is a positive (nonnegative) vector then R
is a positive definite matrix. 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 algebraic structure.
R = sprandsym(n,density,rc,kind)
returns a positive definite matrix. Argument kind
can be:
1
to generate R
by random Jacobi rotation of a positive definite diagonal matrix. R
has the desired condition number exactly.
2
to generate an R
that is a shifted sum of outer products. R
has the desired condition number only approximately, but has less structure.
3
to generate an R
that has the same structure as the matrix S
and approximate condition number 1/rc
. density
is ignored.
sprand
Sparse uniformly distributed random matrix
sprandn
Sparse normally distributed random matrix