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10
examples/06_gevp.ipynb
View file

@ -168,9 +168,9 @@
}
],
"source": [
"vec = matrix_V1V1.GEVP(t0=3, ts=6 ,state=0, sorted_list=None)\n",
"assert len(vec) == matrix_V1V1.N\n",
"print(vec)"
"vecs = matrix_V1V1.GEVP(t0=3, ts=6, sort=None)\n",
"assert len(vecs[0]) == matrix_V1V1.N\n",
"print(vecs[0])"
]
},
{
@ -202,7 +202,7 @@
}
],
"source": [
"matrix_V1V1.projected(vec).m_eff().show(comp=single_smearing.m_eff(), auto_gamma=True)"
"matrix_V1V1.projected(vecs[0]).m_eff().show(comp=single_smearing.m_eff(), auto_gamma=True)"
]
},
{
@ -266,7 +266,7 @@
"\n",
"# We then solve the GEVP to get eigenvectors corresponding to the ground state.\n",
"\n",
"vec_ground = matrix_VnVn.GEVP(t0=3, ts=6, state=0, sorted_list=None)\n",
"vec_ground = matrix_VnVn.GEVP(t0=3, ts=6, sort=None)[0]\n",
"\n",
"# Now we project the matrix-correlators to get new correlators belonging to the ground state.\n",
"\n",

109
pyerrors/correlators.py
View file

@ -241,34 +241,49 @@ class Corr:
if self.N == 1:
raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
def GEVP(self, t0, ts=None, state=0, sorted_list="Eigenvalue"):
"""Solve the general eigenvalue problem on the current correlator
def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
```python
C.GEVP(t0=2)[0] # Ground state vector(s)
C.GEVP(t0=2)[:3] # Vectors for the lowest three states
```
Parameters
----------
t0 : int
The time t0 for G(t)v= lambda G(t_0)v
The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
ts : int
fixed time G(t_s)v= lambda G(t_0)v if return_list=False
If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
If sort="Eigenvector" it gives a reference point for the sorting method.
sort : string
If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.
- "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
- "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
The reference state is identified by its eigenvalue at $t=t_s$.
Other Parameters
----------------
state : int
The state one is interested in, ordered by energy. The lowest state is zero.
sorted_list : string
if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
"Eigenvalue" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
"Eigenvector" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
The reference state is identified by its eigenvalue at t=ts
"""
Returns only the vector(s) for a specified state. The lowest state is zero.
'''
if self.N == 1:
raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
symmetric_corr = self.matrix_symmetric()
if sorted_list is None:
if (ts is None):
raise Exception("ts is required if sorted_list=None.")
if ts is not None:
if (ts <= t0):
raise Exception("ts has to be larger than t0.")
if "sorted_list" in kwargs:
warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
sort = kwargs.get("sorted_list")
symmetric_corr = self.matrix_symmetric()
if sort is None:
if (ts is None):
raise Exception("ts is required if sort=None.")
if (self.content[t0] is None) or (self.content[ts] is None):
raise Exception("Corr not defined at t0/ts.")
G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
@ -277,11 +292,10 @@ class Corr:
G0[i, j] = symmetric_corr[t0][i, j].value
Gt[i, j] = symmetric_corr[ts][i, j].value
sp_vecs = _GEVP_solver(Gt, G0)
sp_vec = sp_vecs[state]
return sp_vec
elif sorted_list in ["Eigenvalue", "Eigenvector"]:
if sorted_list == "Eigenvalue" and ts is not None:
reordered_vecs = _GEVP_solver(Gt, G0)
elif sort in ["Eigenvalue", "Eigenvector"]:
if sort == "Eigenvalue" and ts is not None:
warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
all_vecs = [None] * (t0 + 1)
for t in range(t0 + 1, self.T):
@ -292,43 +306,34 @@ class Corr:
G0[i, j] = symmetric_corr[t0][i, j].value
Gt[i, j] = symmetric_corr[t][i, j].value
sp_vecs = _GEVP_solver(Gt, G0)
if sorted_list == "Eigenvalue":
sp_vec = sp_vecs[state]
all_vecs.append(sp_vec)
else:
all_vecs.append(sp_vecs)
all_vecs.append(_GEVP_solver(Gt, G0))
except Exception:
all_vecs.append(None)
if sorted_list == "Eigenvector":
if sort == "Eigenvector":
if (ts is None):
raise Exception("ts is required for the Eigenvector sorting method.")
all_vecs = _sort_vectors(all_vecs, ts)
all_vecs = [a[state] if a is not None else None for a in all_vecs]
reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
else:
raise Exception("Unkown value for 'sorted_list'.")
raise Exception("Unkown value for 'sort'.")
return all_vecs
if "state" in kwargs:
return reordered_vecs[kwargs.get("state")]
else:
return reordered_vecs
def Eigenvalue(self, t0, ts=None, state=0, sorted_list=None):
def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
"""Determines the eigenvalue of the GEVP by solving and projecting the correlator
Parameters
----------
t0 : int
The time t0 for G(t)v= lambda G(t_0)v
ts : int
fixed time G(t_s)v= lambda G(t_0)v if return_list=False
If return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
state : int
The state one is interested in ordered by energy. The lowest state is zero.
sorted_list : string
if this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.
"Eigenvalue" - The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
"Eigenvector" - Use the method described in arXiv:2004.10472 [hep-lat] to find the set of v(t) belonging to the state.
The reference state is identified by its eigenvalue at t=ts
All other parameters are identical to the ones of Corr.GEVP.
"""
vec = self.GEVP(t0, ts=ts, state=state, sorted_list=sorted_list)
vec = self.GEVP(t0, ts=ts, sort=sort)[state]
return self.projected(vec)
def Hankel(self, N, periodic=False):
@ -1176,9 +1181,7 @@ class Corr:
if basematrix.N != self.N:
raise Exception('basematrix and targetmatrix have to be of the same size.')
evecs = []
for i in range(Ntrunc):
evecs.append(basematrix.GEVP(t0proj, tproj, state=i, sorted_list=None))
evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
rmat = []
@ -1219,8 +1222,10 @@ def _sort_vectors(vec_set, ts):
return sorted_vec_set
def _GEVP_solver(Gt, G0): # Just so normalization an sorting does not need to be repeated. Here we could later put in some checks
sp_val, sp_vecs = scipy.linalg.eigh(Gt, G0)
sp_vecs = [sp_vecs[:, np.argsort(sp_val)[-i]] for i in range(1, sp_vecs.shape[0] + 1)]
sp_vecs = [v / np.sqrt((v.T @ G0 @ v)) for v in sp_vecs]
return sp_vecs
def _GEVP_solver(Gt, G0):
"""Helper function for solving the GEVP and sorting the eigenvectors.
The helper function assumes that both provided matrices are symmetric and
only processes the lower triangular part of both matrices. In case the matrices
are not symmetric the upper triangular parts are effectively discarded."""
return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1]

7
setup.py
View file

@ -1,10 +1,13 @@
#!/usr/bin/env python
from setuptools import setup, find_packages
from pathlib import Path
this_directory = Path(__file__).parent
long_description = (this_directory / "README.md").read_text()
setup(name='pyerrors',
version='2.1.0+dev',
description='Error analysis for lattice QCD',
long_description=long_description,
long_description_content_type='text/markdown',
author='Fabian Joswig',
author_email='fabian.joswig@ed.ac.uk',
packages=find_packages(),

75
tests/correlators_test.py
View file

@ -1,5 +1,6 @@
import os
import numpy as np
import scipy
import pyerrors as pe
import pytest
@ -228,28 +229,70 @@ def test_matrix_corr():
corr_ab = 0.5 * corr_aa
corr_mat = pe.Corr(np.array([[corr_aa, corr_ab], [corr_ab, corr_aa]]))
corr_mat.gamma_method()
corr_mat.item(0, 0)
vec_0 = corr_mat.GEVP(0, 1, sorted_list=None)
vec_1 = corr_mat.GEVP(0, 1, state=1, sorted_list=None)
for (ts, sort) in zip([None, 1, 1], ["Eigenvalue", "Eigenvector", None]):
vecs = corr_mat.GEVP(0, ts=ts, sort=sort)
corr_0 = corr_mat.projected(vec_0)
corr_1 = corr_mat.projected(vec_1)
corr_0 = corr_mat.projected(vecs[0])
corr_1 = corr_mat.projected(vecs[1])
assert np.all([o == 0 for o in corr_0 - corr_aa])
assert np.all([o == 0 for o in corr_1 - corr_aa])
corr_mat.GEVP(0, sorted_list="Eigenvalue")
corr_mat.GEVP(0, 1, sorted_list="Eigenvector")
corr_mat.matrix_symmetric()
corr_mat.GEVP(0, state=0)
corr_mat.Eigenvalue(2, state=0)
def test_GEVP_warnings():
corr_aa = _gen_corr(1)
corr_ab = 0.5 * corr_aa
corr_mat = pe.Corr(np.array([[corr_aa, corr_ab], [corr_ab, corr_aa]]))
corr_mat.item(0, 0)
with pytest.warns(RuntimeWarning):
corr_mat.GEVP(0, 1, sorted_list="Eigenvalue")
corr_mat.GEVP(0, 1, sort="Eigenvalue")
with pytest.warns(DeprecationWarning):
corr_mat.GEVP(0, sorted_list="Eigenvalue")
def test_GEVP_exceptions():
corr_aa = _gen_corr(1)
corr_ab = 0.5 * corr_aa
corr_mat = pe.Corr(np.array([[corr_aa, corr_ab], [corr_ab, corr_aa]]))
corr_mat.item(0, 0)
with pytest.raises(Exception):
corr_mat.item(0, 0).projected()
with pytest.raises(Exception):
corr_mat.item(0, 0).GEVP(2)
with pytest.raises(Exception):
corr_mat.item(0, 0).matrix_symmetric()
with pytest.raises(Exception):
corr_mat.GEVP(0, 0, sort=None)
with pytest.raises(Exception):
corr_mat.GEVP(0, sort=None)
with pytest.raises(Exception):
corr_mat.GEVP(1, 0, sort="Eigenvector")
with pytest.raises(Exception):
corr_mat.GEVP(0, 1, sort="This sorting method does not exist.")
with pytest.raises(Exception):
corr_mat.plottable()
with pytest.raises(Exception):
corr_mat.spaghetti_plot()
with pytest.raises(Exception):
corr_mat.show()
@ -257,7 +300,7 @@ def test_matrix_corr():
corr_mat.m_eff()
with pytest.raises(Exception):
corr_mat.Hankel()
corr_mat.Hankel(2)
with pytest.raises(Exception):
corr_mat.plateau()
@ -290,6 +333,20 @@ def test_matrix_symmetric():
assert np.all([np.all(o == o.T) for o in sym_corr_mat])
def test_GEVP_solver():
mat1 = np.random.rand(15, 15)
mat2 = np.random.rand(15, 15)
mat1 = mat1 @ mat1.T
mat2 = mat2 @ mat2.T
sp_val, sp_vecs = scipy.linalg.eigh(mat1, mat2)
sp_vecs = [sp_vecs[:, np.argsort(sp_val)[-i]] for i in range(1, sp_vecs.shape[0] + 1)]
sp_vecs = [v / np.sqrt((v.T @ mat2 @ v)) for v in sp_vecs]
assert np.allclose(sp_vecs, pe.correlators._GEVP_solver(mat1, mat2), atol=1e-14)
def test_hankel():
corr_content = []
for t in range(8):