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SumkDFT: analyze_block_structure_from_gf for Gf Re/Im Time/Freq
This commit is contained in:
Gernot J. Kraberger
parent
a63169e45f
commit
8d6d8b53c5
@ -883,7 +883,7 @@ class SumkDFT(object):
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the Green's function transformed into the new block structure
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"""
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# make a GfImTime from the supplied G
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# make a GfImTime from the supplied GfImFreq
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if all(isinstance(g_sh._first(), GfImFreq) for g_sh in G):
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gf = [BlockGf(name_block_generator = [(name, GfImTime(beta=block.mesh.beta,
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indices=block.indices,n_points=len(block.mesh)+1)) for name, block in g_sh])
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@ -891,9 +891,37 @@ class SumkDFT(object):
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for ish in range(len(gf)):
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for name, g in gf[ish]:
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g.set_from_inverse_fourier(G[ish][name])
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else:
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assert all(isinstance(g_sh._first(), GfImTime) for g_sh in G), "G must be a BlockGf of either GfImFreq or GfImTime"
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# keep a GfImTime from the supplied GfImTime
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elif all(isinstance(g_sh._first(), GfImTime) for g_sh in G):
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gf = G
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# make a spectral function from the supplied GfReFreq
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elif all(isinstance(g_sh._first(), GfReFreq) for g_sh in G):
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gf = [g_sh.copy() for g_sh in G]
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for ish in range(len(gf)):
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for name, g in gf[ish]:
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g << 1.0j*(g-g.conjugate().transpose())/2.0/numpy.pi
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elif all(isinstance(g_sh._first(), GfReTime) for g_sh in G):
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def get_delta_from_mesh(mesh):
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w0 = None
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for w in mesh:
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if w0 is None:
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w0 = w
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else:
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return w-w0
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gf = [BlockGf(
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name_block_generator = [(name,
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GfReFreq(
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window=(-numpy.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh)), numpy.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh))),
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n_points=len(block.mesh),
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indices=block.indices)) for name, block in g_sh])
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for g_sh in G]
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for ish in range(len(gf)):
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for name, g in gf[ish]:
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g.set_from_fourier(G[ish][name])
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g << 1.0j*(g-g.conjugate().transpose())/2.0/numpy.pi
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else:
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raise Exception("G must be a list of BlockGf of either GfImFreq, GfImTime, GfReFreq or GfReTime")
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# initialize the variables
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self.gf_struct_solver = [{} for ish in range(self.n_inequiv_shells)]
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@ -964,7 +992,8 @@ class SumkDFT(object):
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for ish in range(self.n_inequiv_shells)],None)
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G_transformed = [
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self.block_structure.convert_gf(G[ish],
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full_structure, ish, beta=G[ish].mesh.beta, show_warnings=threshold)
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full_structure, ish, mesh=G[ish].mesh.copy(), show_warnings=threshold,
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gf_function=type(G[ish]._first()))
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for ish in range(self.n_inequiv_shells)]
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if analyse_deg_shells:
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@ -1002,7 +1031,7 @@ class SumkDFT(object):
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null_space = compress(null_mask, vh, axis=0)
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return null_space.conjugate().transpose()
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# make a GfImTime from the supplied G
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# make a GfImTime from the supplied GfImFreq
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if all(isinstance(g_sh._first(), GfImFreq) for g_sh in G):
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gf = [BlockGf(name_block_generator = [(name, GfImTime(beta=block.mesh.beta,
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indices=block.indices,n_points=len(block.mesh)+1)) for name, block in g_sh])
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@ -1010,9 +1039,37 @@ class SumkDFT(object):
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for ish in range(len(gf)):
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for name, g in gf[ish]:
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g.set_from_inverse_fourier(G[ish][name])
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else:
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assert all(isinstance(g_sh._first(), GfImTime) for g_sh in G), "G must be a BlockGf of either GfImFreq or GfImTime"
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# keep a GfImTime from the supplied GfImTime
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elif all(isinstance(g_sh._first(), GfImTime) for g_sh in G):
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gf = G
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# make a spectral function from the supplied GfReFreq
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elif all(isinstance(g_sh._first(), GfReFreq) for g_sh in G):
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gf = [g_sh.copy() for g_sh in G]
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for ish in range(len(gf)):
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for name, g in gf[ish]:
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g << 1.0j*(g-g.conjugate().transpose())/2.0/numpy.pi
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elif all(isinstance(g_sh._first(), GfReTime) for g_sh in G):
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def get_delta_from_mesh(mesh):
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w0 = None
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for w in mesh:
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if w0 is None:
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w0 = w
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else:
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return w-w0
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gf = [BlockGf(
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name_block_generator = [(name,
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GfReFreq(
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window=(-numpy.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh)), numpy.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh))),
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n_points=len(block.mesh),
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indices=block.indices)) for name, block in g_sh])
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for g_sh in G]
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for ish in range(len(gf)):
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for name, g in gf[ish]:
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g.set_from_fourier(G[ish][name])
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g << 1.0j*(g-g.conjugate().transpose())/2.0/numpy.pi
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else:
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raise Exception("G must be a list of BlockGf of either GfImFreq, GfImTime, GfReFreq or GfReTime")
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if include_shells is None:
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# include all shells
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@ -1606,7 +1663,7 @@ class SumkDFT(object):
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# the helper is in the basis where the blocks are all equal
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helper.from_L_G_R(v.conjugate().transpose(), gf_to_symm[key], v)
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if C:
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conjugate_in_tau(helper, in_place=True)
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helper << helper.transpose()
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# average over all shells
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ss += helper / (1.0 * n_deg)
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# now put back the averaged gf to all shells
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@ -1618,11 +1675,7 @@ class SumkDFT(object):
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v = numpy.eye(*ss.target_shape)
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C = False
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if C:
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# we could also use
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# gf_to_symm[key].from_L_G_R(v, conjugate_in_tau(ss), v.conjugate().transpose())
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# but this is less memory-intensive:
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gf_to_symm[key].from_L_G_R(v.conjugate(), ss, v.transpose())
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conjugate_in_tau(gf_to_symm[key], in_place=True)
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gf_to_symm[key].from_L_G_R(v, ss.transpose(), v.conjugate().transpose())
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else:
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gf_to_symm[key].from_L_G_R(v, ss, v.conjugate().transpose())
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@ -2015,38 +2068,3 @@ class SumkDFT(object):
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def __set_deg_shells(self,value):
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self.block_structure.deg_shells = value
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deg_shells = property(__get_deg_shells,__set_deg_shells)
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# a helper function
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def conjugate_in_tau(gf_im_freq, in_place=False):
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""" Calculate the conjugate in tau of a GfImFreq
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Parameters
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----------
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gf_im_freq : GfImFreq of BlockGf
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the Green's function
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in_place : whether to modify the gf_im_freq object (True) or return a copy (False)
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Returns
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-------
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ret : GfImFreq of BlockGf
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the Green's function that has been FT to G(tau), conjugated, and
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FT back
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"""
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if in_place:
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ret = gf_im_freq
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else:
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ret = gf_im_freq.copy()
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if isinstance(ret, BlockGf):
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for name, gf in ret:
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conjugate_in_tau(gf, in_place=True)
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else:
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""" there is an easier way to do this, namely to make
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ret.data[:,:,:] = gf_im_freq.data[::-1,:,:].conjugate()
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ret.tail.data[:,:,:] = gf_im_freq.tail.data.conjugate()
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but this relies on symmetric Matsubara meshes and is maybe
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not safe enough"""
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G_tau = GfImTime(beta=gf_im_freq.mesh.beta,
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indices=gf_im_freq.indices,n_points=len(gf_im_freq.mesh)+1)
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G_tau.set_from_inverse_fourier(gf_im_freq)
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ret.set_from_fourier(G_tau.conjugate())
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return ret
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@ -5,7 +5,7 @@ file(COPY ${CMAKE_CURRENT_SOURCE_DIR}/${all_h5_files} DESTINATION ${CMAKE_CURREN
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FILE(COPY SrVO3.pmat SrVO3.struct SrVO3.outputs SrVO3.oubwin SrVO3.ctqmcout SrVO3.symqmc SrVO3.sympar SrVO3.parproj SrIrO3_rot.h5 hk_convert_hamiltonian.hk LaVO3-Pnma_hr.dat LaVO3-Pnma.inp DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
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# List all tests
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set(all_tests wien2k_convert hk_convert w90_convert sumkdft_basic srvo3_Gloc srvo3_transp sigma_from_file blockstructure analyze_block_structure_from_gf)
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set(all_tests wien2k_convert hk_convert w90_convert sumkdft_basic srvo3_Gloc srvo3_transp sigma_from_file blockstructure analyze_block_structure_from_gf analyze_block_structure_from_gf2)
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foreach(t ${all_tests})
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add_test(NAME ${t} COMMAND python ${CMAKE_CURRENT_SOURCE_DIR}/${t}.py)
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@ -1,5 +1,5 @@
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from pytriqs.gf import *
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from sumk_dft import SumkDFT, conjugate_in_tau
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from 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 pytriqs.utility.comparison_tests import assert_gfs_are_close, assert_arrays_are_close, assert_block_gfs_are_close
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@ -68,7 +68,7 @@ for d in SK.deg_shells[0]:
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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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conjugate_in_tau(normalized_gf, in_place=True)
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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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@ -162,8 +162,8 @@ for conjugate in conjugate_values:
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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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conjugate_in_tau(G[0]['ud'][i:i+2,i:i+2], in_place=True)
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conjugate_in_tau(G_noisy['ud'][i:i+2,i:i+2], in_place=True)
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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)
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@ -196,7 +196,7 @@ for conjugate in conjugate_values:
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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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conjugate_in_tau(normalized_gf, in_place=True)
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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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115
test/analyze_block_structure_from_gf2.py
Normal file
115
test/analyze_block_structure_from_gf2.py
Normal file
@ -0,0 +1,115 @@
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from pytriqs.gf import *
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from sumk_dft import SumkDFT
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import numpy as np
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from pytriqs.utility.comparison_tests import assert_block_gfs_are_close
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# here we test the SK.analyze_block_structure_from_gf function
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# with GfReFreq, GfReTime
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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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# construct a random block-diagonal Hloc
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Hloc = np.zeros((10,10), dtype=np.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 = GfReFreq(window=(-5,5), indices=range(2), n_points=1001)
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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+0.02j))/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+0.02j))/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+0.02j))/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+0.02j))/2.0
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# construct G
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G = BlockGf(name_block_generator=(('ud',GfReFreq(window=(-5,5), indices=range(10), n_points=1001)),))
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for i in range(0,10,2):
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G['ud'][i:i+2,i:i+2] << inverse(Omega-delta+0.02j)
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G['ud'] << inverse(inverse(G['ud']) - Hloc)
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SK = SumkDFT(hdf_file = 'SrIrO3_rot.h5', use_dft_blocks=False)
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G_new = SK.analyse_block_structure_from_gf([G])
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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)
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assert SK.gf_struct_sumk == [[('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])], [('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])]],\
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"wrong gf_struct_sumk"
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for i in range(5):
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assert 'ud_{}'.format(i) in SK.gf_struct_solver[0], "missing block"
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assert SK.gf_struct_solver[0]['ud_{}'.format(i)] == range(2), "wrong block size"
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for i in range(10):
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assert SK.sumk_to_solver[0]['ud',i] == ('ud_{}'.format(i/2), i%2), "wrong mapping"
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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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def get_delta_from_mesh(mesh):
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w0 = None
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for w in mesh:
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if w0 is None:
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w0 = w
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else:
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return w-w0
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Gt = BlockGf(name_block_generator = [(name,
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GfReTime(window=(-np.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh)), np.pi*(len(block.mesh)-1) / (len(block.mesh)*get_delta_from_mesh(block.mesh))),
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n_points=len(block.mesh),
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indices=block.indices)) for name, block in G])
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Gt['ud'].set_from_inverse_fourier(G['ud'])
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G_new = SK.analyse_block_structure_from_gf([Gt])
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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)
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assert SK.gf_struct_sumk == [[('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])], [('ud', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])]],\
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"wrong gf_struct_sumk"
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for i in range(5):
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assert 'ud_{}'.format(i) in SK.gf_struct_solver[0], "missing block"
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assert SK.gf_struct_solver[0]['ud_{}'.format(i)] == range(2), "wrong block size"
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for i in range(10):
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assert SK.sumk_to_solver[0]['ud',i] == ('ud_{}'.format(i/2), i%2), "wrong mapping"
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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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