# sprandsym

## Purpose

Random sparse symmetric matrices.

## Synopsis

    R = sprandsym(S)
    R = sprandsym(n,density)
    R = sprandsym(n,density,rc)
    R = sprandsym(n,density,rc,kind)

## Description

`R = sprandsym(S)` is 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)` 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, and `(0 <= density <= 1)`.

`R = sprandsym(n,density,rc)` has a reciprocal condition number equal to `rc`. The distribution of entries is nonuniform; it is roughly symmetric about 0; all are in [-1,1].

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)` is positive definite, where `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.

  ## See Also

      sprandn

  (c) Copyright 1994 by The MathWorks, Inc.