SPRANDSYM

 

 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 SPRANDNHNISLD.