** 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 **

** algebraic structure. **

** **

** **

** 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 . **

** **