create solvers and interface modules

Co-authored-by: Johanna Zijderveld

codes/solvers.py

+import numpy as np
+from . import utils
+from .hf import updated_matrices, total_energy
+from functools import partial
+
+def optimize(mf, cost_function, optimizer, optimizer_kwargs):
+    _ = optimizer(
+        cost_function,
+        mf,
+        **optimizer_kwargs
+    )
+
+def finite_system_cost(mf, model):
+    shape = mf.shape
+    mf = utils.flat_to_matrix(utils.real_to_complex(mf), shape)
+    model.rho, model.mf_k = updated_matrices(mf_k=mf, model=model)
+    delta_mf = model.mf_k - mf
+    return utils.complex_to_real(utils.matrix_to_flat(delta_mf))
+
+def finite_system_solver(model, optimizer, cost_function, optimizer_kwargs):
+    """
+    Real-space solver for finite systems.
+
+    Parameters:
+    -----------
+    model : model.Model
+        Physical model containting interacting and non-interacting Hamiltonian.
+    optimizer : function
+        Optimization function.
+    optimizer_kwargs : dict
+        Extra arguments passed to optimizer.
+    """
+    model.mf_k = model.guess[()]
+    initial_mf = utils.complex_to_real(utils.matrix_to_flat(model.mf_k))
+    partial_cost = partial(cost_function, model=model)
+    optimize(initial_mf, partial_cost, optimizer, optimizer_kwargs)
+
+def real_space_cost(mf, model, shape):
+    mf = utils.flat_to_matrix(utils.real_to_complex(mf), shape)
+    mf_dict = {}
+    for i, key in enumerate(model.guess.keys()):
+        mf_dict[key] = mf[i]
+    mf = utils.kgrid_hamiltonian(
+        nk=model.nk,
+        hk=utils.model2hk(mf_dict),
+        dim=model.dim,
+        hermitian=False
+    )
+    model.rho, model.mf_k = updated_matrices(mf_k=mf, model=model)
+    delta_mf = model.mf_k - mf
+    delta_mf = utils.hk2tb_model(delta_mf, model.vectors, model.ks)
+    delta_mf = np.array([*delta_mf.values()])
+    return utils.complex_to_real(utils.matrix_to_flat(delta_mf))
+
+def rspace_solver(model, optimizer, cost_function, optimizer_kwargs):
+    """
+    Real-space solver for infinite systems.
+
+    Parameters:
+    -----------
+    model : model.Model
+        Physical model containting interacting and non-interacting Hamiltonian.
+    optimizer : function
+        Optimization function.
+    optimizer_kwargs : dict
+        Extra arguments passed to optimizer.
+    """
+    model.kgrid_evaluation(nk=model.nk)
+    initial_mf = np.array([*model.guess.values()])
+    shape = initial_mf.shape
+    initial_mf = utils.complex_to_real(utils.matrix_to_flat(initial_mf))
+    partial_cost = partial(cost_function, model=model, shape=shape)
+    optimize(initial_mf, partial_cost, optimizer, optimizer_kwargs)
+
+def kspace_cost(mf, model):
+    mf = utils.flat_to_matrix(utils.real_to_complex(mf), model.mf_k.shape)
+    model.rho, model.mf_k = updated_matrices(mf_k=mf, model=model)
+    delta_mf = model.mf_k - mf
+    return utils.complex_to_real(utils.matrix_to_flat(delta_mf))
+
+def kspace_totalenergy_cost(mf, model):
+    mf = utils.flat_to_matrix(utils.real_to_complex(mf), model.mf_k.shape)
+    model.rho, model.mf_k = updated_matrices(mf_k=mf, model=model)
+    return total_energy(
+        model.hamiltonians_0 + model.mf_k,
+        model.rho,
+    )
+
+def kspace_solver(model, optimizer, cost_function, optimizer_kwargs):
+    """
+    k-space solver.
+
+    Parameters:
+    -----------
+    model : model.Model
+        Physical model containting interacting and non-interacting Hamiltonian.
+    optimizer : function
+        Optimization function.
+    optimizer_kwargs : dict
+        Extra arguments passed to optimizer.
+    """
+    model.kgrid_evaluation(nk=model.nk)
+    initial_mf = model.mf_k
+    initial_mf = utils.complex_to_real(utils.matrix_to_flat(initial_mf))
+    partial_cost = partial(cost_function, model=model)
+    optimize(initial_mf, partial_cost, optimizer, optimizer_kwargs)

[Anton Akhmerov]

This is a dangerous step because we are potentially discarding nonzero contributions to a total energy, and biasing the solution. We should defined a constrained problem instead.