mirror of https://github.com/triqs/dft_tools
229 lines
10 KiB
Python
229 lines
10 KiB
Python
from triqs.gf import MeshImFreq, inverse, Omega
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from triqs_dft_tools.sumk_dft import SumkDFT
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from scipy.linalg import expm
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import numpy as np
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from triqs.utility.comparison_tests import assert_gfs_are_close, assert_arrays_are_close, assert_block_gfs_are_close
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from h5 import HDFArchive
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import itertools
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# The full test checks all different possible combinations of conjugated
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# blocks. This takes a few minutes. For a quick test, just checking one
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# random value suffices.
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# (this parameter affects the second test)
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full_test = False
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#######################################################################
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# First test #
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# where we check the analyse_block_structure_from_gf function #
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# for the SrIrO3_rot.h5 file #
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#######################################################################
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mesh = MeshImFreq(40, 'Fermion', 1025)
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SK = SumkDFT(hdf_file='SrIrO3_rot.h5', mesh=mesh)
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Sigma = SK.block_structure.create_gf(mesh=mesh)
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SK.put_Sigma([Sigma])
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G = SK.extract_G_loc(transform_to_solver_blocks=False)
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# the original block structure
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block_structure1 = SK.block_structure.copy()
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G_new = SK.analyse_block_structure_from_gf(G)
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# the new block structure
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block_structure2 = SK.block_structure.copy()
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with HDFArchive('analyse_block_structure_from_gf.out.h5', 'w') as ar:
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ar['bs1'] = block_structure1
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ar['bs2'] = block_structure2
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# check whether the block structure is the same as in the reference
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with HDFArchive('analyse_block_structure_from_gf.out.h5', 'r') as ar, HDFArchive('analyse_block_structure_from_gf.ref.h5', 'r') as ar2:
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assert ar['bs1'] == ar2['bs1'], 'bs1 not equal'
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a1 = ar['bs2']
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a2 = ar2['bs2']
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assert a1 == block_structure2, 'writing/reading block structure incorrect'
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# we set the deg_shells to None because the transformation matrices
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# have a phase freedom and will, therefore, not be equal in general
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a1.deg_shells = None
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a2.deg_shells = None
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assert a1 == a2, 'bs2 not equal'
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# check if deg shells are correct
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assert len(SK.deg_shells[0]) == 1, 'wrong number of equivalent groups'
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# check if the Green's functions that are found to be equal in the
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# routine are indeed equal
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for d in SK.deg_shells[0]:
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assert len(d) == 2, 'wrong number of shells in equivalent group'
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# the convention is that for every degenerate shell, the transformation
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# matrix v and the conjugate bool is saved
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# then,
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# maybe_conjugate1( v1^dagger G1 v1 ) = maybe_conjugate2( v2^dagger G2 v2 )
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# therefore, to test, we calculate
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# maybe_conjugate( v^dagger G v )
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# for all degenerate shells and check that they are all equal
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normalized_gfs = []
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for key in d:
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normalized_gf = G_new[0][key].copy()
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normalized_gf.from_L_G_R(d[key][0].conjugate().transpose(), G_new[0][key], d[key][0])
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if d[key][1]:
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normalized_gf << normalized_gf.transpose()
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normalized_gfs.append(normalized_gf)
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for i in range(len(normalized_gfs)):
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for j in range(i + 1, len(normalized_gfs)):
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assert_arrays_are_close(normalized_gfs[i].data, normalized_gfs[j].data, 1.0e-5)
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#######################################################################
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# Second test #
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# where a Green's function is constructed from a random model #
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# and the analyse_block_structure_from_gf function is tested for that #
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# model #
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#######################################################################
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# helper function to get random Hermitian matrix
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def get_random_hermitian(dim):
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herm = np.random.rand(dim, dim) + 1.0j * np.random.rand(dim, dim)
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herm = herm + herm.conjugate().transpose()
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return herm
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# helper function to get random unitary matrix
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def get_random_transformation(dim):
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herm = get_random_hermitian(dim)
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T = expm(1.0j * herm)
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return T
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# we will conjugate the Green's function blocks according to the entries
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# of conjugate_values
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# for each of the 5 blocks that will be constructed, there is an entry
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# True or False that says whether it will be conjugated
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if full_test:
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# in the full test we check all combinations
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conjugate_values = list(itertools.product([False, True], repeat=5))
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else:
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# in the quick test we check a random combination
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conjugate_values = [np.random.rand(5) > 0.5]
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for conjugate in conjugate_values:
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# construct a random block-diagonal Hloc
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Hloc = np.zeros((10, 10), dtype=complex)
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# the Hloc of the first three 2x2 blocks is equal
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Hloc0 = get_random_hermitian(2)
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Hloc[:2, :2] = Hloc0
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Hloc[2:4, 2:4] = Hloc0
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Hloc[4:6, 4:6] = Hloc0
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# the Hloc of the last two 2x2 blocks is equal
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Hloc1 = get_random_hermitian(2)
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Hloc[6:8, 6:8] = Hloc1
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Hloc[8:, 8:] = Hloc1
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# construct the hybridization delta
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# this is equal for all 2x2 blocks
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V = get_random_hermitian(2) # the hopping elements from impurity to bath
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b1 = np.random.rand() # the bath energy of the first bath level
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b2 = np.random.rand() # the bath energy of the second bath level
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delta = G[0]['ud'][:2, :2].copy()
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delta[0, 0] << (V[0, 0] * V[0, 0].conjugate() * inverse(Omega - b1) + V[0, 1] * V[0, 1].conjugate() * inverse(Omega - b2)) / 2.0
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delta[0, 1] << (V[0, 0] * V[1, 0].conjugate() * inverse(Omega - b1) + V[0, 1] * V[1, 1].conjugate() * inverse(Omega - b2)) / 2.0
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delta[1, 0] << (V[1, 0] * V[0, 0].conjugate() * inverse(Omega - b1) + V[1, 1] * V[0, 1].conjugate() * inverse(Omega - b2)) / 2.0
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delta[1, 1] << (V[1, 0] * V[1, 0].conjugate() * inverse(Omega - b1) + V[1, 1] * V[1, 1].conjugate() * inverse(Omega - b2)) / 2.0
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# construct G
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G[0].zero()
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for i in range(0, 10, 2):
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G[0]['ud'][i : i + 2, i : i + 2] << inverse(Omega - delta)
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G[0]['ud'] << inverse(inverse(G[0]['ud']) - Hloc)
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# for testing symm_deg_gf below, we need this
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# we construct it so that for every group of degenerate blocks of G[0], the
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# mean of the blocks of G_noisy is equal to G[0]
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G_noisy = G[0].copy()
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noise1 = np.random.randn(*delta.target_shape)
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G_noisy['ud'][:2, :2].data[:, :, :] += noise1
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G_noisy['ud'][2:4, 2:4].data[:, :, :] -= noise1 / 2.0
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G_noisy['ud'][4:6, 4:6].data[:, :, :] -= noise1 / 2.0
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noise2 = np.random.randn(*delta.target_shape)
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G_noisy['ud'][6:8, 6:8].data[:, :, :] += noise2
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G_noisy['ud'][8:, 8:].data[:, :, :] -= noise2
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# for testing backward-compatibility in symm_deg_gf, we need the
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# un-transformed Green's functions
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G_pre_transform = G[0].copy()
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G_noisy_pre_transform = G_noisy.copy()
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# transform each block using a random transformation matrix
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for i in range(0, 10, 2):
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T = get_random_transformation(2)
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G[0]['ud'][i : i + 2, i : i + 2].from_L_G_R(T, G[0]['ud'][i : i + 2, i : i + 2], T.conjugate().transpose())
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G_noisy['ud'][i : i + 2, i : i + 2].from_L_G_R(T, G_noisy['ud'][i : i + 2, i : i + 2], T.conjugate().transpose())
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# if that block shall be conjugated, go ahead and do it
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if conjugate[i // 2]:
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G[0]['ud'][i : i + 2, i : i + 2] << G[0]['ud'][i : i + 2, i : i + 2].transpose()
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G_noisy['ud'][i : i + 2, i : i + 2] << G_noisy['ud'][i : i + 2, i : i + 2].transpose()
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# analyse the block structure
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G_new = SK.analyse_block_structure_from_gf(G, 1.0e-7)
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# transform G_noisy etc. to the new block structure
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G_noisy = SK.block_structure.convert_gf(G_noisy, block_structure1, beta=G_noisy.mesh.beta, space_from='sumk')
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G_pre_transform = SK.block_structure.convert_gf(G_pre_transform, block_structure1, beta=G_noisy.mesh.beta, space_from='sumk')
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G_noisy_pre_transform = SK.block_structure.convert_gf(
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G_noisy_pre_transform, block_structure1, beta=G_noisy.mesh.beta, space_from='sumk'
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)
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assert len(SK.deg_shells[0]) == 2, 'wrong number of equivalent groups found'
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assert sorted([len(d) for d in SK.deg_shells[0]]) == [2, 3], 'wrong number of members in the equivalent groups found'
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for d in SK.deg_shells[0]:
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if len(d) == 2:
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assert 'ud_3' in d, 'shell ud_3 missing'
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assert 'ud_4' in d, 'shell ud_4 missing'
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if len(d) == 3:
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assert 'ud_0' in d, 'shell ud_0 missing'
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assert 'ud_1' in d, 'shell ud_1 missing'
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assert 'ud_2' in d, 'shell ud_2 missing'
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# the convention is that for every degenerate shell, the transformation
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# matrix v and the conjugate bool is saved
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# then,
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# maybe_conjugate1( v1^dagger G1 v1 ) = maybe_conjugate2( v2^dagger G2 v2 )
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# therefore, to test, we calculate
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# maybe_conjugate( v^dagger G v )
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# for all degenerate shells and check that they are all equal
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normalized_gfs = []
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for key in d:
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normalized_gf = G_new[0][key].copy()
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normalized_gf.from_L_G_R(d[key][0].conjugate().transpose(), G_new[0][key], d[key][0])
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if d[key][1]:
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normalized_gf << normalized_gf.transpose()
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normalized_gfs.append(normalized_gf)
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for i in range(len(normalized_gfs)):
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for j in range(i + 1, len(normalized_gfs)):
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# here, we use a threshold that is 1 order of magnitude less strict
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# because of numerics
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assert_gfs_are_close(normalized_gfs[i], normalized_gfs[j], 1.0e-6)
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# now we check symm_deg_gf
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# symmetrizing the GF has is has to leave it unchanged
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G_new_symm = G_new[0].copy()
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SK.symm_deg_gf(G_new_symm, 0)
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assert_block_gfs_are_close(G_new[0], G_new_symm, 1.0e-6)
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# symmetrizing the noisy GF, which was carefully constructed,
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# has to give the same result as G_new[0]
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SK.symm_deg_gf(G_noisy, 0)
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assert_block_gfs_are_close(G_new[0], G_noisy, 1.0e-6)
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# check backward compatibility of symm_deg_gf
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# first, construct the old format of the deg shells
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for ish in range(len(SK.deg_shells)):
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for gr in range(len(SK.deg_shells[ish])):
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SK.deg_shells[ish][gr] = list(SK.deg_shells[ish][gr].keys())
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# symmetrizing the GF as is has to leave it unchanged
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G_new_symm << G_pre_transform
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SK.symm_deg_gf(G_new_symm, 0)
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assert_block_gfs_are_close(G_new_symm, G_pre_transform, 1.0e-6)
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# symmetrizing the noisy GF pre transform, which was carefully constructed,
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# has to give the same result as G_pre_transform
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SK.symm_deg_gf(G_noisy_pre_transform, 0)
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assert_block_gfs_are_close(G_noisy_pre_transform, G_pre_transform, 1.0e-6)
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