== MS_VRH

 MS_VRH - n phase Voigt-Reuss-Hill average of elasticity.

 // Part of MSAT - The Matlab Seismic Anisotropy Toolkit //

 Given n elasticity matricies, densities and phase volume fractions, 
     calculate the avarage of the Voigt upper and Reuss lower bound of the 
     composite material. 

  [Cave,rhave]=MS_VRH(VF, C, rh, ...)

 Usage: 
     [Cave,rhave]=MS_VRH(VF, C, rh)                    
          The volume fractions and densities (VF and rh) can be provided as
          vectors of common length n and the elasticities as a (6,6,n)
          matrix. 

     [Cave,rhave]=MS_VRH(VF, C1, rh1, C2, rh2, C3, rh3, ...)                    
          Alternitivly, VF can be a vector of volume fractions and the 
          elasticity matricies and densities given as sequence of arguments
          as (6,6) matricies and scalars. There should be a C,rho argument 
          pair for each entry in the VF vector.

     [Cave,rhave,Cvoigt,Creuss]=MS_VRH(VF, C, rh, ...)                    
          For both input argument forms, it is possible to access the upper
          and lower bound on the composite elasticity by adding output 
          arguments.

 Notes:
     The sum of the elements of VF is normalised to 1 before averaging.

 See also: MS_POLYAVERAGE
