Sparse grid utilities for IR and Chebyshev representations

Essential contents for a temperature-independent sparse grid

• stats: Bose or Fermi statistics.
• xgrid: Real space grid points in $x \in (-1, 1)$.
• ngrid: Frequency space grid points in Matsubara indices $n$, such that $\omega_n = (2n+\zeta)\pi/\beta$.
• wgrid: Frequency space grid points assuming $\beta=1$.
• uxl: Transformation matrix from the basis representation l to real space grid points x.
• ulx: Inverse of uxl.
• u1l_pos: Basis representation for $x=+1$.
• u1l_neg: Basis representation for $x=-1$.
• uwl: Transformation matrix from the basis representation l to frequency space grid points w.
• ulw: Inverse of uwl.
• metadata: Group for representation-depend information, for example:
  • For Chebyshev: ncoeff for maximum number of coefficients.
  • For IR: lambda for dimensionless cutoff $\Lambda$, ncoeff for maximum number of coefficients.

Directory structure

• python/sparse_grid/: python code for generating and parsing sparse grid data.
  • python/sparse_grid/ir/: IR-specific code.
  • python/sparse_grid/chebyshev/: Chebyshev-specific code.
  • python/sparse_grid/repn.py: Common module interface for representations.
  • python/generate.py: Script for generating HDF5 archives.
• c++/: C++ interface for loading and representing sparse grid data.
  • green/grids/: Public headers.
• data/: Pre-generated data files.
• examples: Usage examples.

Dependencies

• Python:
  • Hiroshi's sparse_ir
  • numpy, scipy, h5py, mpmath, ...
• C++:
  • Green/h5pp: for compatibility with h5py
  • Green/ndarrays: for compatibility with numpy.ndarray
  • Green/params: for comandline parameters

Acknowledgements

This work is supported by National Science Foundation under the award CSSI-2310582