mirror of https://github.com/triqs/dft_tools
Corrections for new calc_dc and calc_mu
* typos and subbed check in spin polarized calculations for quantum espresso with a warning when computing the deltaN * fixed typos in comments * removed legacy mode maintaining only compatibility layer and switched to old (<3.10) python syntax * added target density output in mu finder for brent and newton, refactored tunit test for DC, changed some comments
This commit is contained in:
alberto-carta
Alexander Hampel
parent
d4f3c48784
commit
0d25aefc73
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@ -1,3 +1,2 @@
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compile_commands.json
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doc/cpp2rst_generated
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build/
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@ -38,10 +38,11 @@ from warnings import warn
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from scipy import compress
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from scipy.optimize import minimize, newton, brenth
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def compute_DC_from_density(N_tot, U, J, N_spin = None, n_orbitals=5, method='cFLL'):
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def compute_DC_from_density(N_tot, U, J, N_spin = None, n_orbitals=5, method='sFLL'):
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"""
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Computes the double counting correction in terms using various methods
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Computes the double counting correction using various methods.
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For FLL and AMF DC the notations and equations from doi.org/10.1038/s41598-018-27731-4
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are used, whereas for the Held DC the definitions from doi.org/10.1080/00018730701619647 are used.
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Parameters
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----------
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@ -69,45 +70,48 @@ def compute_DC_from_density(N_tot, U, J, N_spin = None, n_orbitals=5, method='
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List of floats:
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- DC_val: double counting potential
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- E_val: double counting energy
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todo: See whether to move this to TRIQS directly instead of dft_tools
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"""
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if N_spin is not None:
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N_spin2 = N_tot-N_spin
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Mag = N_spin - N_spin2
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L_orbit = (n_orbitals-1)/2
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match method:
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case 'cFLL':
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E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1)
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DC_val = U * (N_tot-0.5) - J *(N_tot*0.5-0.5)
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if method == 'cFLL':
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E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1)
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DC_val = U * (N_tot-0.5) - J *(N_tot*0.5-0.5)
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case 'sFLL':
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assert N_spin is not None, "Spin density not given"
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E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1) - 0.25 * J * Mag**2
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DC_val = U * (N_tot-0.5) - J *(N_spin-0.5)
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elif method == 'sFLL':
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assert N_spin is not None, "Spin density not given"
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E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1) - 0.25 * J * Mag**2
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DC_val = U * (N_tot-0.5) - J *(N_spin-0.5)
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case 'cAMF':
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E_val = +0.5 * U * N_tot **2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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DC_val = U * N_tot - 0.5*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot
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elif method == 'cAMF':
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E_val = +0.5 * U * N_tot **2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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DC_val = U * N_tot - 0.5*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot
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case 'sAMF':
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assert N_spin is not None, "Spin density not given"
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E_val = 0.5 * U * N_tot **2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*Mag**2
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DC_val = U * N_tot - (U+2*L_orbit*J)/(2*L_orbit+1)*N_spin
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elif method == 'sAMF':
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assert N_spin is not None, "Spin density not given"
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E_val = 0.5 * U * N_tot **2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*Mag**2
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DC_val = U * N_tot - (U+2*L_orbit*J)/(2*L_orbit+1)*N_spin
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case 'cHeld':
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U_mean = (U + (n_orbitals-1)*(U-2*J)+(n_orbitals-1)*(U-3*J))/(2*n_orbitals-1)
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E_val = 0.5 * U_mean * N_tot * (N_tot - 1)
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DC_val = U_mean * (N_tot-0.5)
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elif method == 'cHeld':
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# Valid for a Kanamori-type Hamiltonian where U'=U-2J
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U_mean = (U + (n_orbitals-1)*(U-2*J)+(n_orbitals-1)*(U-3*J))/(2*n_orbitals-1)
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E_val = 0.5 * U_mean * N_tot * (N_tot - 1)
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DC_val = U_mean * (N_tot-0.5)
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case 'sHeld':
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raise ValueError(f"Method sHeld not yet implemented")
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elif method == 'sHeld':
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raise ValueError(f"Method sHeld not yet implemented")
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case _:
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raise ValueError(f"DC type {method} not supported")
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else:
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raise ValueError(f"DC type {method} not supported")
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mpi.report(f"DC potential computed using the {method} method, V_DC = {DC_val:.6f} eV")
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mpi.report(f"E_DC using the {method} method, E_DC = {E_val:.6f} eV")
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@ -1735,7 +1739,7 @@ class SumkDFT(object):
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self.dc_energ = dc_energ
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def calc_dc(self, dens_mat, orb=0, U_interact=None, J_hund=None,
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use_dc_formula=0, use_dc_value=None, transform=True, legacy=True):
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use_dc_formula=0, use_dc_value=None, transform=True):
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r"""
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Calculate and set the double counting corrections.
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@ -1767,8 +1771,13 @@ class SumkDFT(object):
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Value of interaction parameter `U`.
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J_hund : float, optional
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Value of interaction parameter `J`.
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use_dc_formula : int, optional
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Type of double-counting correction (see description).
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use_dc_formula : int or string, optional
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Type of double-counting correction (see description of `compute_DC_from_density` above).
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There is an interface with the legacy implementation which allows for the old convention:
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* 0 -> 'sFLL' spin dependent fully localized limit
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* 1 -> 'cHeld' spin independent Held formula
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* 2 -> 'sAMF' spin dependent around-mean field approximation
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use_dc_value : float, optional
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Value of the double-counting correction. If specified
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`U_interact`, `J_hund` and `use_dc_formula` are ignored.
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@ -1807,68 +1816,21 @@ class SumkDFT(object):
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dim //= 2
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if use_dc_value is None:
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if legacy:
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if U_interact is None and J_hund is None:
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raise ValueError("set_dc: either provide U_interact and J_hund or set use_dc_value to dc value.")
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if use_dc_formula == 0: # FLL
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self.dc_energ[icrsh] = U_interact / \
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2.0 * Ncrtot * (Ncrtot - 1.0)
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for sp in spn:
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Uav = U_interact * (Ncrtot - 0.5) - \
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J_hund * (Ncr[sp] - 0.5)
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self.dc_imp[icrsh][sp] *= Uav
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self.dc_energ[icrsh] -= J_hund / \
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len(spn) * (Ncr[sp]) * (Ncr[sp] - 1.0)
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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elif use_dc_formula == 1: # Held's formula, with U_interact the interorbital onsite interaction
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self.dc_energ[icrsh] = (U_interact + (dim - 1) * (U_interact - 2.0 * J_hund) + (
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dim - 1) * (U_interact - 3.0 * J_hund)) / (2 * dim - 1) / 2.0 * Ncrtot * (Ncrtot - 1.0)
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for sp in spn:
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Uav = (U_interact + (dim - 1) * (U_interact - 2.0 * J_hund) + (dim - 1)
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* (U_interact - 3.0 * J_hund)) / (2 * dim - 1) * (Ncrtot - 0.5)
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self.dc_imp[icrsh][sp] *= Uav
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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elif use_dc_formula == 2: # AMF
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self.dc_energ[icrsh] = 0.5 * U_interact * Ncrtot * Ncrtot
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for sp in spn:
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Uav = U_interact * \
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(Ncrtot - Ncr[sp] / dim) - \
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J_hund * (Ncr[sp] - Ncr[sp] / dim)
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self.dc_imp[icrsh][sp] *= Uav
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self.dc_energ[
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icrsh] -= (U_interact + (dim - 1) * J_hund) / dim / len(spn) * Ncr[sp] * Ncr[sp]
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mpi.report(
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"DC for shell %(icrsh)i and block %(sp)s = %(Uav)f" % locals())
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mpi.report("DC energy for shell %s = %s" %
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(icrsh, self.dc_energ[icrsh]))
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#For legacy compatibility
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if use_dc_formula == 0:
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mpi.report(f"Detected {use_dc_formula=}, changing to sFLL")
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use_dc_formula = "sFLL"
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if use_dc_formula == 1:
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mpi.report(f"Detected {use_dc_formula=}, changing to cHeld")
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use_dc_formula = "cHeld"
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if use_dc_formula == 2:
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mpi.report(f"Detected {use_dc_formula=}, changing to sAMF")
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use_dc_formula = "sAMF"
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else:
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#For legacy compatibility
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match use_dc_formula:
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case 0:
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mpi.report(f"Detected {use_dc_formula=}, changing to sFLL")
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use_dc_formula = "sFLL"
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case 1:
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mpi.report(f"Detected {use_dc_formula=}, changing to cHeld")
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use_dc_formula = "cHeld"
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case 2:
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mpi.report(f"Detected {use_dc_formula=}, changing to sAMF")
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use_dc_formula = "sAMF"
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for sp in spn:
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DC_val, E_val = compute_DC_from_density(N_tot=Ncrtot,U=U_interact, J=J_hund, n_orbitals=dim, N_spin=Ncr[sp], method=use_dc_formula)
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self.dc_imp[icrsh][sp] *= DC_val
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self.dc_energ[icrsh] -= E_val
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for sp in spn:
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DC_val, E_val = compute_DC_from_density(N_tot=Ncrtot,U=U_interact, J=J_hund, n_orbitals=dim, N_spin=Ncr[sp], method=use_dc_formula)
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self.dc_imp[icrsh][sp] *= DC_val
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self.dc_energ[icrsh] = E_val
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@ -2048,7 +2010,6 @@ class SumkDFT(object):
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def calc_mu(self, precision=0.01, broadening=None, delta=0.5, max_loops=100, method="dichotomy"):
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r"""
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Searches for the chemical potential that gives the DFT total charge.
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A simple bisection method is used.
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Parameters
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----------
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@ -2061,7 +2022,7 @@ class SumkDFT(object):
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max_loops : int, optional
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Number of dichotomy loops maximally performed.
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max_loops : string, optional
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method : string, optional
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Type of optimization used:
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* dichotomy: usual bisection algorithm from the TRIQS library
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* newton: newton method, faster convergence but more unstable
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@ -2116,52 +2077,50 @@ class SumkDFT(object):
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mpi.report("Trying out mu = {}".format(str(mu)))
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calc_dens = self.total_density(mu=mu, broadening=broadening).real - density
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mpi.report("Delta to target density = {}".format(str(calc_dens)))
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mpi.report(f"Target density = {density}; Delta to target = {calc_dens}")
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return calc_dens
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#check for lowercase matching for the method variable
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match method.lower():
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if method.lower()=="dichotomy":
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mpi.report("\nSUMK calc_mu: Using dichtomy adjustment to find chemical potential\n")
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self.chemical_potential = dichotomy.dichotomy(function=F_bisection,
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x_init=self.chemical_potential, y_value=density,
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precision_on_y=precision, delta_x=delta, max_loops=max_loops,
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x_name="Chemical Potential", y_name="Total Density",
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verbosity=3)[0]
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elif method.lower()=="newton":
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mpi.report("\nSUMK calc_mu: Using Newton method to find chemical potential\n")
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self.chemical_potential = newton(func=F_optimize,
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x0=self.chemical_potential,
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tol=precision, maxiter=max_loops,
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)
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case "dichotomy":
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mpi.report("\nSUMK calc_mu: Using dichtomy adjustment to find chemical potential\n")
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self.chemical_potential = dichotomy.dichotomy(function=F_bisection,
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x_init=self.chemical_potential, y_value=density,
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precision_on_y=precision, delta_x=delta, max_loops=max_loops,
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x_name="Chemical Potential", y_name="Total Density",
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verbosity=3)[0]
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case 'newton':
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mpi.report("\nSUMK calc_mu: Using Newton method to find chemical potential\n")
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self.chemical_potential = newton(func=F_optimize,
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x0=self.chemical_potential,
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tol=precision, maxiter=max_loops,
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)
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case 'brent':
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mpi.report("\nSUMK calc_mu: Using Brent method to find chemical potential")
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mpi.report("SUMK calc_mu: Finding bounds \n")
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mu_guess_0, mu_guess_1 = find_bounds(function=F_optimize,
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x_init=self.chemical_potential,
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delta_x=delta, max_loops=max_loops,
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)
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mu_guess_1 += 0.01 #scrambles higher lying interval to avoid getting stuck
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mpi.report("\nSUMK calc_mu: Searching root with Brent method\n")
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self.chemical_potential = brenth(f=F_optimize,
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a=mu_guess_0,
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b=mu_guess_1,
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xtol=precision, maxiter=max_loops,
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)
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elif method.lower()=="brent":
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mpi.report("\nSUMK calc_mu: Using Brent method to find chemical potential")
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mpi.report("SUMK calc_mu: Finding bounds \n")
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case _:
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raise ValueError(
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f"SUMK calc_mu: The method selected: {method}, is not implemented\n",
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"""
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Please check for typos or select one of the following:
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* dichotomy: usual bisection algorithm from the TRIQS library
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* newton: newton method, fastest convergence but more unstable
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* brent: finds bounds and proceeds with hyperbolic brent method, a compromise between speed and ensuring convergence
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"""
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)
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mu_guess_0, mu_guess_1 = find_bounds(function=F_optimize,
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x_init=self.chemical_potential,
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delta_x=delta, max_loops=max_loops,
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)
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mu_guess_1 += 0.01 #scrambles higher lying interval to avoid getting stuck
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mpi.report("\nSUMK calc_mu: Searching root with Brent method\n")
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self.chemical_potential = brenth(f=F_optimize,
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a=mu_guess_0,
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b=mu_guess_1,
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xtol=precision, maxiter=max_loops,
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)
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else:
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raise ValueError(
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f"SUMK calc_mu: The selected method: {method}, is not implemented\n",
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"""
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Please check for typos or select one of the following:
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* dichotomy: usual bisection algorithm from the TRIQS library
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* newton: newton method, fastest convergence but more unstable
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* brent: finds bounds and proceeds with hyperbolic brent method, a compromise between speed and ensuring convergence
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"""
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)
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return self.chemical_potential
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@ -2414,7 +2373,8 @@ class SumkDFT(object):
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f.write("\n")
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elif dm_type == 'qe':
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assert self.SP == 0, "Spin-polarized density matrix is not implemented"
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if self.SP == 0:
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mpi.report("SUMK calc_density_correction: WARNING! Averaging out spin-polarized correction in the density channel")
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subgrp = 'dft_update'
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delta_N = np.zeros([self.n_k, max(self.n_orbitals[:,0]), max(self.n_orbitals[:,0])], dtype=complex)
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@ -0,0 +1,168 @@
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##########################################################################
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#
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# TRIQS: a Toolbox for Research in Interacting Quantum Systems
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#
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# Copyright (C) 2023 by A. Carta
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#
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# TRIQS is free software: you can redistribute it and/or modify it under the
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# terms of the GNU General Public License as published by the Free Software
|
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# Foundation, either version 3 of the License, or (at your option) any later
|
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# version.
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#
|
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# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
|
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# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
|
||||
# details.
|
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#
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# You should have received a copy of the GNU General Public License along with
|
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# TRIQS. If not, see <http://www.gnu.org/licenses/>.
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#
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##########################################################################
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import numpy as np
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from triqs_dft_tools.sumk_dft import *
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from triqs.gf import *
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from h5 import HDFArchive
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from triqs.operators.util import *
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import triqs.utility.mpi as mpi
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Uval = 5
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Jval = 0.3
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method_dict = {
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"FLL":{
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"numbering_convention":0,
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"new_convention":"cFLL"
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},
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"AMF":{
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"numbering_convention":2,
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"new_convention":"cAMF"
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},
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"Held":{
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"numbering_convention":1,
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"new_convention":"cHeld"
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},
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}
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def test_dc(method, method_dict, dens, Uval, Jval, filename):
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||||
|
||||
dc_no = method_dict[method]["numbering_convention"]
|
||||
dc_string = method_dict[method]["new_convention"]
|
||||
|
||||
mpi.report("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")
|
||||
mpi.report(f"\n Testing interface {method} \n")
|
||||
mpi.report("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")
|
||||
|
||||
mpi.report("\nTesting legacy compatibility layer:\n")
|
||||
SK_compat.calc_dc(dens_mat=dens[0], U_interact=Uval, J_hund=Jval, use_dc_formula=dc_no )
|
||||
mpi.report("Up DC matrix:")
|
||||
mpi.report(SK_compat.dc_imp[0]['up'])
|
||||
mpi.report(f"Double counting energy = {SK_compat.dc_energ} ")
|
||||
|
||||
mpi.report("\nTesting new dc interface:\n")
|
||||
SK_new.calc_dc(dens_mat=dens[0], U_interact=Uval, J_hund=Jval, use_dc_formula=dc_string)
|
||||
mpi.report("Up DC matrix:")
|
||||
mpi.report(SK_new.dc_imp[0]['up'])
|
||||
mpi.report(f"Double counting energy = {SK_new.dc_energ} ")
|
||||
|
||||
# Load previously computed DC values from h5 archive
|
||||
R = HDFArchive(f'./{filename}', 'r')
|
||||
dc_comp = R[f'DC_{method}_benchmark']['dc_imp']
|
||||
en_comp = R[f'DC_{method}_benchmark']['dc_energ']
|
||||
del R
|
||||
|
||||
mpi.report(f"\nAsserting comparison for method: {method}")
|
||||
assert np.allclose(SK_compat.dc_imp[0]['up'], dc_comp, atol=1e-12), f"Assertion failed comparing legacy Vdc to reference, method: {method} "
|
||||
assert np.allclose(SK_compat.dc_energ, en_comp, atol=1e-12), f"Assertion failed comparing legacy energy to reference, method {method} "
|
||||
assert np.allclose(SK_new.dc_imp[0]['up'], dc_comp, atol=1e-12), f"Assertion failed comparing Vdc to reference, method: {method} "
|
||||
assert np.allclose(SK_new.dc_energ, en_comp, atol=1e-12), f"Assertion failed comparing energy to reference, method: {method} "
|
||||
mpi.report("Comparison with stored DC values successfull!\n")
|
||||
|
||||
|
||||
|
||||
|
||||
# %% 5 orbitals testing
|
||||
|
||||
mpi.report("\n############################################")
|
||||
mpi.report("############################################")
|
||||
mpi.report(f"\n \n Starting tests for 5 orbitals \n \n")
|
||||
mpi.report("############################################")
|
||||
mpi.report("############################################")
|
||||
dft_filename = "./NiO.ref"
|
||||
use_blocks = False
|
||||
SK_compat = SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=use_blocks)
|
||||
SK_compat.set_mu(13.9)
|
||||
SK_new = SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=use_blocks)
|
||||
SK_new.set_mu(13.9)
|
||||
|
||||
|
||||
icrsh = 0
|
||||
dens = SK_compat.density_matrix()
|
||||
|
||||
with np.printoptions(precision=5):
|
||||
for key in dens[0].keys():
|
||||
mpi.report(f"{key} channel")
|
||||
mpi.report(dens[0][key].real)
|
||||
|
||||
N_up = np.trace(dens[0]['up'].real)
|
||||
N_down = np.trace(dens[0]['down'].real)
|
||||
N_tot = N_up + N_down
|
||||
|
||||
mpi.report(f"{N_up=} ,{N_down=}, {N_tot=}\n")
|
||||
|
||||
for method in ["FLL", "AMF", "Held"]:
|
||||
test_dc(method, method_dict, dens, Uval, Jval, filename = f"{dft_filename}.h5")
|
||||
|
||||
#in case implementation changes, to write new testing data into archive
|
||||
#R = HDFArchive('./NiO.ref.h5', 'a')
|
||||
#R.create_group(f'DC_{method}_benchmark')
|
||||
#R[f'DC_{method}_benchmark']['dc_imp']= SK_new.dc_imp[0]['up']
|
||||
#R[f'DC_{method}_benchmark']['dc_energ']= SK_new.dc_energ
|
||||
#del R
|
||||
|
||||
|
||||
# 3 orbital testing
|
||||
|
||||
mpi.report("############################################")
|
||||
mpi.report("############################################")
|
||||
mpi.report(f"\n \n Starting tests for 3 orbitals \n \n")
|
||||
mpi.report("############################################")
|
||||
mpi.report("############################################")
|
||||
dft_filename = "./SrVO3.ref"
|
||||
use_blocks = False
|
||||
SK_compat = SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=use_blocks)
|
||||
SK_new = SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=use_blocks)
|
||||
|
||||
icrsh = 0
|
||||
dens = SK_compat.density_matrix()
|
||||
|
||||
|
||||
with np.printoptions(precision=5):
|
||||
for key in dens[0].keys():
|
||||
mpi.report(f"{key} channel")
|
||||
mpi.report(dens[0][key].real)
|
||||
|
||||
N_up = np.trace(dens[0]['up'].real)
|
||||
N_down = np.trace(dens[0]['down'].real)
|
||||
N_tot = N_up + N_down
|
||||
|
||||
mpi.report(f"{N_up=} ,{N_down=}, {N_tot=}\n")
|
||||
|
||||
Uval = 5
|
||||
Jval = 0.3
|
||||
|
||||
for method in ["FLL", "AMF", "Held"]:
|
||||
test_dc(method, method_dict, dens, Uval, Jval, filename = f"{dft_filename}.h5" )
|
||||
|
||||
#in case implementation changes, to write new testing data into archive
|
||||
#R = HDFArchive(f'./{dft_filename}.h5', 'a')
|
||||
#R.create_group(f'DC_{method}_benchmark')
|
||||
#R[f'DC_{method}_benchmark']['dc_imp']= SK_new.dc_imp[0]['up']
|
||||
#R[f'DC_{method}_benchmark']['dc_energ']= SK_new.dc_energ
|
||||
#del R
|
||||
Loading…
Reference in New Issue