first sketch of DM computation

setup.py

@@ -184,6 +184,7 @@ def run(self):
     },
     "sisl._supercell": {},
     "sisl.physics._bloch": {},
+    "sisl.physics._compute_dm": {},
     "sisl.physics._phase": {},
     "sisl.physics._matrix_utils": {},
     "sisl.physics._matrix_k": {},
@@ -219,12 +220,22 @@ def run(self):
 # List of extensions for setup(...)
 extensions = []
 for name, data in ext_cython.items():
+    file_suffix = suffix
     # Create pyx-file name
     # Default to module name + .pyx
-    pyxfile = data.get("pyxfile", f"{name}.pyx").replace(".", os.path.sep)
+    pyxfile = f"{data.get('pyxfile', name).replace('.', os.path.sep)}.pyx"
+    file_no_suffix = pyxfile[:-4]
+    # If a pyx file does not exist, look for a pure python file
+    if not os.path.isfile(pyxfile):
+        pyfile = f"{data.get('pyxfile', name).replace('.', os.path.sep)}.py"
+        if os.path.isfile(pyfile):
+            file_no_suffix = pyfile[:-3]
+            if suffix == ".pyx":
+                file_suffix = ".py"
+
     extensions.append(
         Extension(name,
-                  sources=[f"{pyxfile[:-4]}{suffix}"] + data.get("sources", []),
+                  sources=[f"{file_no_suffix}{file_suffix}"] + data.get("sources", []),
                   depends=data.get("depends", []),
                   include_dirs=data.get("include", []),
                   language=data.get("language", "c"),

sisl/physics/_compute_dm.py

@@ -0,0 +1,128 @@
+"""This file implements the cython functions that help building the DM efficiently."""
+
+
+import cython
+
+complex_or_float = cython.fused_type(cython.complex, cython.floating)
+
+@cython.boundscheck(False)
+@cython.wraparound(False)
+def add_cnc_diag_spin(state: complex_or_float[:, :], row_orbs: cython.int[:], col_orbs_uc: cython.int[:], 
+                    occs: cython.floating[:], DM_kpoint: complex_or_float[:], occtol: float = 1e-9):
+    """Adds the cnc contributions of all orbital pairs to the DM given a array of states.
+    
+    To be used for the case of diagonal spins (unpolarized or polarized spin.)
+    
+    Parameters
+    ----------
+    state:
+        The coefficients of all eigenstates for this contribution.
+        Array of shape (n_eigenstates, n_basisorbitals)
+    row_orbs:
+        The orbital row indices of the sparsity pattern. 
+        Shape (nnz, ), where nnz is the number of nonzero elements in the sparsity pattern.
+    col_orbs_uc:
+        The orbital col indices of the sparsity pattern, but converted to the unit cell.
+        Shape (nnz, ), where nnz is the number of nonzero elements in the sparsity pattern.
+    occs:
+        Array with the occupations for each eigenstate. Shape (n_eigenstates, )
+    DM_kpoint:
+        Array where contributions should be stored.
+        Shape (nnz, ), where nnz is the number of nonzero elements in the sparsity pattern.
+    occtol:
+        Threshold below which the contribution of a state is not even added to the
+        DM.
+    """
+    # The wavefunction (i) and orbital (u, v) indices
+    i: cython.int
+    u: cython.int
+    v: cython.int
+    ipair: cython.int
+
+    # Loop lengths
+    n_wfs: cython.int = state.shape[0]
+    n_opairs: cython.int = row_orbs.shape[0]
+
+    # Variable to store the occupation of each state 
+    occ: float
+
+    # Loop through all eigenstates
+    for i in range(n_wfs):
+        # Find the occupation for this eigenstate
+        occ = occs[i]
+        # If the occupation is lower than the tolerance, skip the state
+        if occ < occtol:
+            continue
+
+        # The occupation is above the tolerance threshold, loop through all overlaping orbital pairs
+        for ipair in range(n_opairs):
+            # Get the orbital indices of this pair
+            u = row_orbs[ipair]
+            v = col_orbs_uc[ipair]
+            # Add the contribution of this eigenstate to the DM_{u,v} element
+            DM_kpoint[ipair] = DM_kpoint[ipair] + state[i, u] * occ * state[i, v].conjugate()
+
+@cython.boundscheck(False)
+@cython.wraparound(False)
+def add_cnc_nc(state: cython.complex[:, :, :], row_orbs: cython.int[:], col_orbs_uc: cython.int[:], 
+                    occs: cython.floating[:], DM_kpoint: cython.complex[:, :, :], occtol: float = 1e-9):
+    """Adds the cnc contributions of all orbital pairs to the DM given a array of states.
+    
+    To be used for the case of non-diagonal spins (non-colinear or spin orbit).
+    
+    Parameters
+    ----------
+    state:
+        The coefficients of all eigenstates for this contribution.
+        Array of shape (n_eigenstates, n_basisorbitals, 2), where the last dimension is the spin
+        "up"/"down" dimension.
+    row_orbs:
+        The orbital row indices of the sparsity pattern. 
+        Shape (nnz, ), where nnz is the number of nonzero elements in the sparsity pattern.
+    col_orbs_uc:
+        The orbital col indices of the sparsity pattern, but converted to the unit cell.
+        Shape (nnz, ), where nnz is the number of nonzero elements in the sparsity pattern.
+    occs:
+        Array with the occupations for each eigenstate. Shape (n_eigenstates, )
+    DM_kpoint:
+        Array where contributions should be stored.
+        Shape (nnz, 2, 2), where nnz is the number of nonzero elements in the sparsity pattern
+        and the 2nd and 3rd dimensions account for the 2x2 spin box. 
+    occtol:
+        Threshold below which the contribution of a state is not even added to the
+        DM.
+    """
+    # The wavefunction (i) and orbital (u, v) indices
+    i: cython.int
+    u: cython.int
+    v: cython.int
+    ipair: cython.int
+    # The spin box indices.
+    Di: cython.int
+    Dj: cython.int
+
+    # Loop lengths
+    n_wfs: cython.int = state.shape[0]
+    n_opairs: cython.int = row_orbs.shape[0]
+
+    # Variable to store the occupation of each state 
+    occ: float
+
+    # Loop through all eigenstates
+    for i in range(n_wfs):
+        # Find the occupation for this eigenstate
+        occ = occs[i]
+        # If the occupation is lower than the tolerance, skip the state
+        if occ < occtol:
+            continue
+
+        # The occupation is above the tolerance threshold, loop through all overlaping orbital pairs
+        for ipair in range(n_opairs):
+            # Get the orbital indices of this pair
+            u = row_orbs[ipair]
+            v = col_orbs_uc[ipair]
+
+            # Add to spin box
+            for Di in range(2):
+                for Dj in range(2):
+                    DM_kpoint[ipair, Di, Dj] = DM_kpoint[ipair, Di, Dj] + state[i, u, Di] * occ * state[i, v, Dj].conjugate()

sisl/physics/compute_dm.py

@@ -0,0 +1,164 @@
+import numpy as np
+import tqdm
+from typing import Callable, Optional
+
+from sisl import BrillouinZone, DensityMatrix, get_distribution, unit_convert
+from ._compute_dm import add_cnc_diag_spin, add_cnc_nc
+
+def compute_dm(bz: BrillouinZone, occ_distribution: Optional[Callable] = None, 
+            occtol: float = 1e-9, fermi_dirac_T: float = 300., eta: bool = True):
+    """Computes the DM from the eigenstates of a Hamiltonian along a BZ.
+    
+    Parameters
+    ----------
+    bz: BrillouinZone
+        The brillouin zone object containing the Hamiltonian of the system
+        and the k-points to be sampled.
+    occ_distribution: function, optional
+        The distribution that will determine the occupations of states. It will
+        receive an array of energies (in eV, referenced to fermi level) and it should
+        return an array of floats.
+        If not provided, a fermi_dirac distribution will be considered, being the 
+        fermi_dirac_T parameter the electronic temperature.
+    occtol: float, optional
+        Threshold below which the contribution of a state is not even added to the
+        DM.
+    fermi_dirac_T: float, optional
+        If an occupation distribution is not provided, a fermi-dirac distribution centered
+        at the chemical potential is assumed. This argument controls the electronic temperature (in K).
+    eta: bool, optional
+        Whether a progress bar should be displayed or not.
+    """
+    # Get the hamiltonian
+    H = bz.parent
+
+    # Geometry
+    geom = H.geometry
+
+    # Sparsity pattern information
+    row_orbs, col_orbs = H.nonzero()
+    col_orbs_uc = H.osc2uc(col_orbs)
+    col_isc = col_orbs // H.no
+    sc_offsets = H.sc_off.dot(H.cell)
+
+    # Initialize the density matrix using the sparsity pattern of the Hamiltonian.
+    last_dim = H.dim 
+    S = None
+    if not H.orthogonal:
+        last_dim -= 1
+        S = H.tocsr(dim=last_dim)
+    DM = DensityMatrix.fromsp(geom, [H.tocsr(dim=idim) for idim in range(last_dim)], S=S)
+    # Keep a reference to its data array so that we can have
+    # direct access to it (instead of through orbital indexing).
+    vals = DM._csr.data
+    # And set all values to 0
+    if DM.orthogonal:
+        vals[:, :] = 0
+    else:
+        # Don't touch the overlap values
+        vals[:, :-1] = 0
+
+    # For spin polarized calculations, we need to iterate over the two spin components.
+    # If spin is unpolarized, we will multiply the contributions by 2.
+    if DM.spin.is_polarized:
+        spin_iterator = (0, 1)
+        spin_factor = 1
+    else:
+        spin_iterator = (0,)
+        spin_factor = 2
+
+    # Set the distribution that will compute occupations (or more generally, weights)
+    # for eigenstates. If not provided, use a fermi-dirac
+    if occ_distribution is None:
+        kT = unit_convert("K", "eV") * fermi_dirac_T
+        occ_distribution = get_distribution("fermi_dirac", smearing=kT, x0=0)
+
+    # Loop over spins
+    for ispin in spin_iterator:
+        # Create the eigenstates generator
+        eigenstates = bz.apply.eigenstate(spin=ispin)
+
+        # Zip it with the weights so that we can scale the contribution of each k point.
+        k_it = zip(bz.weight, eigenstates)
+        # Provide progress bar if requested
+        if eta:
+            k_it = tqdm.tqdm(k_it, total=len(bz.weight))
+
+        # Now, loop through all k points
+        for k_weight, k_eigs in k_it:
+            # Get the k point for which this state has been calculated (in fractional coordinates)
+            k = k_eigs.info['k']
+            # Convert the k points to 1/Ang
+            k = k.dot(geom.rcell)
+
+            # Ensure R gauge so that we can use supercell phases. Much faster and less memory requirements
+            # than using the r gauge, because we just have to compute the phase one time for each sc index.
+            k_eigs.change_gauge("R")
+
+            # Calculate all phases, this will be a (nnz, ) shaped array.
+            sc_phases = sc_offsets.dot(k)
+            phases = sc_phases[col_isc]
+            phases = np.exp(-1j * phases)
+
+            # Now find out the occupations for each wavefunction
+            occs = k_eigs.occupation(occ_distribution)
+
+            state = k_eigs.state
+
+            if DM.spin.is_diagonal:
+                # Calculate the matrix elements contributions for this k point.
+                DM_kpoint = np.zeros(row_orbs.shape[0], dtype=k_eigs.state.dtype)
+                add_cnc_diag_spin(state, row_orbs, col_orbs_uc, occs, DM_kpoint, occtol=occtol)
+
+                # Apply phases
+                DM_kpoint = DM_kpoint * phases
+
+                # Take only the real part, weighting the contribution
+                vals[:, ispin] += k_weight * DM_kpoint.real * spin_factor
+
+            else:
+                # Non colinear eigenstates contain an array of coefficients
+                # of shape (n_wfs, no * 2), where n_wfs is also no * 2.
+                # However, we only have "no" basis orbitals. The extra factor of 2 accounts for a hidden dimension
+                # corresponding to spin "up"/"down". We reshape the array to uncover this extra dimension.
+                state = state.reshape(-1, state.shape[1] // 2, 2)
+
+                # Calculate the matrix elements contributions for this k point. For each matrix element
+                # we allocate a 2x2 spin box.
+                DM_kpoint = np.zeros((row_orbs.shape[0], 2, 2), dtype=np.complex128)
+                add_cnc_nc(state, row_orbs, col_orbs_uc, occs, DM_kpoint, occtol=occtol)
+
+                # Apply phases
+                DM_kpoint *= phases.reshape(-1, 1, 1)
+
+                # Now, each matrix element is a 2x2 spin box of complex numbers. That is, 4 complex numbers
+                # i.e. 8 real numbers. What we do is to store these 8 real numbers separately in the DM.
+                # However, in the non-colinear case (no spin orbit), since H is spin box hermitian we can force
+                # the DM to also be spin-box hermitian. This means that DM[:, 0, 1] and DM[:, 1, 0] are complex 
+                # conjugates and we can store only 4 numbers while keeping the same information. 
+                # Here is how the spin-box can be reconstructed from the stored values:
+                # D[j, i] = 
+                # NON-COLINEAR
+                # [[ D[j, i, 0],                D[j, i, 2] -i D[j, i, 3] ],
+                #  [ D[j, i, 2] + i D[j, i, 3], D[j, i, 1]               ]]
+                # SPIN-ORBIT
+                # [[ D[j, i, 0],                D[j, i, 6] + i D[j, i, 7]],
+                #  [ D[j, i, 2] -i D[j, i, 3],  D[j, i, 1]               ]]
+
+                # Force DM spin-box to be hermitian in the non-colinear case.
+                if DM.spin.is_noncolinear:
+                    DM_kpoint[:, 1, 0] = 0.5 * (DM_kpoint[:, 1, 0] + DM_kpoint[:, 0, 1].conj())
+
+                # Add each contribution to its location
+                vals[:, 0] += DM_kpoint[:, 0, 0].real * k_weight
+                vals[:, 1] += DM_kpoint[:, 1, 1].real * k_weight
+                vals[:, 2] += DM_kpoint[:, 1, 0].real * k_weight
+                vals[:, 3] -= DM_kpoint[:, 1, 0].imag * k_weight
+
+                if DM.spin.is_spinorbit:
+                    vals[:, 4] -= DM_kpoint[:, 0, 0].imag * k_weight
+                    vals[:, 5] -= DM_kpoint[:, 1, 1].imag * k_weight
+                    vals[:, 6] += DM_kpoint[:, 0, 1].real * k_weight
+                    vals[:, 7] -= DM_kpoint[:, 0, 1].imag * k_weight
+
+    return DM