(sw-basismat)=

# sw_basismat

## Syntax
  
`[m, asym] = sw_basismat(symop, r, tol)`
  
## Description
  
`[m, asym] = sw_basismat(symop, r, tol)` determines the allowed tensor
elements compatible with a given point group symmetry. The tensor can
describe exchange interaction or single ion anisotropy. The function
applies the symmetry invariance of the classical energy
$\mathbf{S}_i\cdot \mathcal{M}\cdot \mathbf{S}_j$. Thus this symmetry
analysis includes the transformation properties of spin operators as
well.
  
## Input Arguments
  
`symOp`
: Generators of the point group symmetry, in a matrix with dimensions of
  $[3\times 3\times n_{sym}]$ where each `symOp(:,:,ii)` matrix defines a rotation.
  
`r`
: Distance column vector between the two interacting atoms. For
  anisotropy $r=0$.
  
`tol`
: Tolerance, optional, default value is $10^{-5}$.
  
## Output Arguments
  
`M`
: Matrices, that span out the vector space of the symmetry
          allowed matrices, dimensions are $[3\times 3\times n_M]$. Any matrix is
          allowed that can be expressed as a linear combination of the
          symmetry allowed matrices.
 
`asym`
: Logical vector, for each $[3\times 3]$ matrix in $M$, tells whether it is
          antisymmetric stored in a row vector with $n_M$ elements.
  
## See Also
  
[spinw.getmatrix](#spinw-getmatrix) \| [spinw.setmatrix](#spinw-setmatrix)