degreesOfFreedomForRealMatrix

a matrix with the number of degrees-of-freedom at each entry

Declaration 

 matrix = WVGeometryDoublyPeriodic.degreesOfFreedomForFourierCoefficients(Nx,Ny,conjugateDimension);

Parameters

  • Nx grid points in the x-direction
  • Ny grid points in the y-direction
  • conjugateDimension (optional) set which dimension in the DFT grid is assumed to have the redundant conjugates (1 or 2), default is 2

Returns

  • dof matrix containing dof

Discussion

A real-valued matrix A defined on a grid of size [Nx Ny] has Nx*Ny degrees of freedom, one at each grid point. In the Fourier domain these degrees-of-freedom are more complicated, because some modes are strictly real-valued (k=l=0 and Nyquist), while others are complex, and there are redundant Hermitian conjugates.