#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
This code aims to calculate the relaxation time based on the
PCAlipids analysis.
For details check:
[Principal Component Analysis of Lipid Molecule Conformational
Changes in Molecular Dynamics Simulations
Pavel Buslaev, Valentin Gordeliy, Sergei Grudinin, and Ivan Gushchin
Journal of Chemical Theory and Computation 2016 12 (3), 1019-1028
DOI: 10.1021/acs.jctc.5b01106 ]
and
[Principal component analysis highlights the influence of temperature,
curvature and cholesterol on conformational dynamics of lipids
Pavel Buslaev, Khalid Mustafin, and Ivan Gushchin
Biochimica et Biophysica Acta (BBA) - Biomembranes
Volume 1862, Issue 7, 1 July 2020, 183253
DOI: 10.1016/j.bbamem.2020.183253]
The main idea is to run PCA on concatenated lipid trajectory,
calculate the autocorrelation times, which are linearly related
to equilibration times of individual lipids. The parameters of linear
transform are calculated based on the trajectories from NMRlipids
databank.
The code was developed by
Dr. Pavel Buslaev, pavel.i.buslaev@jyu.fi
Dr. Samuli Olilla
Patrik Kula
Alexander Kuzmin
"""
import os
import json
import numpy as np
from scipy import signal
import MDAnalysis as mda
from deprecated import deprecated
from DatabankLib import NMLDB_SIMU_PATH
from DatabankLib.core import System
from DatabankLib.databankLibrary import lipids_set
from DatabankLib.databankio import resolve_download_file_url, download_resource_from_uri
from MDAnalysis.analysis.base import AnalysisFromFunction
import warnings
from DatabankLib.settings.molecules import Lipid
# suppress some MDAnalysis warnings issued from mda.analysis.align
warnings.filterwarnings('ignore')
from MDAnalysis.analysis import align # noqa
# TODO: now there are only regular phospholipids.
# The list should be verified by method authors.
ALLOWLIPIDS = [
"POPC", "POPG", "POPS", "POPE", "PYPC", "DMPC", "DPPC", "DPPE", "DPPG",
"DEPC", "DRPC", "DYPC", "DLPC", "DLIPC", "DOPC", "DOPE", "DDOPC", "DOPS",
"DSPC", "DAPC", "SDPE", "SOPC", "POPI", "SAPI", "SAPI24", "SAPI25",
"SLPI"
]
merge_cutoff = 2.0
trj_size_cutoff = 5000000000
TAILSN1 = "sn-1"
TAILSN2 = "sn-2"
HEADGRP = "headgroup"
# In case you want to test for a specific coordinate change the flag to yes
TEST = False
[docs]
class Parser:
"""
Class Parser is a basic class to work with the trajectory. It has basic utility
for preparing trajectories:
1. Checking if simulation has a correct name
2. Checking if trajectory is downloaded. Downloading, if not
3. Calling AmberMerger to merge head groups and tails for Amber
trajectories
4. Concatenate trajectories
"""
def __init__(
self, system: System, eq_time_fname="eq_times.json",
path=None, v=True):
"""
Constructor for Parser:
system - simulation data
eq_time_fname - name of the output file
path - name of a particular trajectory
v - verbosity for testing
"""
# Technical
self.verbose = v
self.error = 0
# Path
self.root = NMLDB_SIMU_PATH
self.eq_time_fname = eq_time_fname
# Extracting data from readme
self._path = os.path.join(self.root, system["path"])
print('Indexing path:', self._path)
if self.verbose:
print(f"Parser: Processing trajectory {self._path}")
self.doi = system["DOI"]
self.soft = system["SOFTWARE"]
if self.soft == "openMM" or self.soft == "NAMD":
try:
self.trj = system["TRJ"][0][0]
self.tpr = system["PDB"][0][0]
except Exception:
print("Parser: Did not find trajectory or pdb for openMM or NAMD")
self.error = 1
else:
try:
self.trj = system["TRJ"][0][0]
self.tpr = system["TPR"][0][0]
except Exception:
print("Parser: Did not find trajectory or tpr for GROMACS")
self.trj = ""
self.tpr = ""
self.error = 1
self.trj_name = os.path.join(self._path, self.trj)
self.tpr_name = os.path.join(self._path, self.tpr)
self.trj_len = system["TRJLENGTH"] / 1000 # ns
self.size = system["TRAJECTORY_SIZE"]
self.composition = system["COMPOSITION"]
self.lipids: dict[str, Lipid] = {
k: v for k, v in system.content.items() if k in lipids_set}
self.path = path
[docs]
@deprecated(reason="Downloading should happen somewhere else."
"Not in the analysis classes.")
def validate_path(self):
"""
Path validation. Behaviour depends on the input.
1. If ther were any errors, validation fails. Currently the only
error tested is that .xtc and .tpr files are not present. This
is the case for non-GROMACS trajectories.
2. If path is not provided, parser is iterating over all trajectories.
3. If path is provided and current path is equal to the provided one,
parser reports that it finds the trajectory for the analysis.
TODO: must be removed. Substitute path-validation part.
"""
if self.error > 0:
# This is an error message. Printing even in silent mode
print(
"Parser: Can't read TPR/PDB and TRJ from README for " +
f"{self._path}")
if self.verbose and not self.path:
print(
"Parser: Iterating over all trajectories. "
+ f"Current trajectory is {self._path}"
)
# return
# if self.path == self.indexingPath:
if os.path.isfile(os.path.join(self._path, self.eq_time_fname)):
if self.verbose:
print("Parser: Found file with equilibration data. \n"
"Not processing the trajectory")
return -1
if self.verbose:
print(f"Parser: Found trajectory {self._path}")
return 0
[docs]
@deprecated(reason="Downloading should happen somewhere else."
"Not in the analysis classes.")
def download_traj(self):
"""
TODO: must be removed. We don't download trajectory in the analysis part
Basic trajectory and TPR download.
"""
print("Downloading")
if not os.path.isfile(self.tpr_name):
self.tpr_url = resolve_download_file_url(self.doi, self.tpr)
# This is a log message. Printing even in silent mode
print("Parser: Downloading tpr ", self.doi)
# urllib.request.urlretrieve(self.tpr_url, self.tpr_name)
download_resource_from_uri(self.tpr_url, self.tpr_name)
if not os.path.isfile(self.trj_name):
self.trj_url = resolve_download_file_url(self.doi, self.trj)
# This is a log message. Printing even in silent mode
print("Parser: Downloading trj ", self.doi)
# urllib.request.urlretrieve(self.trj_url, self.trj_name)
download_resource_from_uri(self.trj_url, self.trj_name)
[docs]
def prepare_gmx_traj(self):
"""
Preparing trajectory. If centered trajectory is found, use it. If whole
trajectory is found, use it. Otherwise, call gmx trjconv to make whole
trajectory. The selected trajectory is loaded into Universe.
"""
# Look for centered.xtc
if os.path.isfile(os.path.join(self._path, "centered.xtc")):
print("Parser: Founder centered trajectory: centered.xtc")
self.trj_name = os.path.join(self._path, "centered.xtc")
# Look for whole.xtc
elif os.path.isfile(os.path.join(self._path, "whole.xtc")):
print("Parser: Founder whole trajectory: whole.xtc")
self.trj_name = os.path.join(self._path, "whole.xtc")
# Run gmx trjconv
else:
print("Parser: Making trajectory whole")
trj_out_name = os.path.join(self._path, "whole.xtc")
os.system(
f"echo System | gmx trjconv -f {self.trj_name} -s "
f"{self.tpr_name} -pbc mol -o {trj_out_name}"
)
self.trj_name = trj_out_name
# Skip frames for large trajectories
if self.size > trj_size_cutoff:
trj_out_name = os.path.join(self._path, "short.xtc")
os.system(
f"echo System | gmx trjconv -f {self.trj_name} -s "
f"{self.tpr_name} -pbc mol -o {trj_out_name} -skip 10"
)
self.trj_name = trj_out_name
# Create .gro file
self.gro_name = os.path.join(self._path, "conf.gro")
if os.path.isfile(self.gro_name):
print("Parser: Found gro file")
else:
print("Parser: Making a gro file from the first frame")
os.system(
f"echo System | gmx trjconv -s {self.tpr_name} "
f" -f {self.trj_name} -dump 0 -o {self.gro_name}"
)
# Loading trajectory
try:
self.traj = mda.Universe(self.tpr_name, self.trj_name)
except Exception:
self.traj = mda.Universe(self.gro_name, self.trj_name)
# TODO: not tested!!
[docs]
def prepare_OpenMM_traj(self): # noqa: N802
print("openMM or NAMD")
if self.size > trj_size_cutoff:
trj_out_name = os.path.join(self._path, "short.xtc")
if os.path.isfile(trj_out_name):
print("Parser: Short trajectory is found")
else:
u = mda.Universe(self.tpr_name, self.trj_name)
with mda.Writer(trj_out_name,
u.select_atoms("all").n_atoms) as mdaw:
for ts in u.trajectory[::10]:
mdaw.write(u.select_atoms("all"))
self.trj_name = trj_out_name
self.traj = mda.Universe(self.tpr_name, self.trj_name)
[docs]
def prepare_traj(self):
if self.soft == "openMM" or self.soft == "NAMD":
self.prepare_OpenMM_traj()
else:
self.prepare_gmx_traj()
[docs]
def concatenate_traj(self):
"""
Create Concatenator and corresponding concatenated trajectories for
all lipids available for the trajectory.
"""
self.concatenated_trajs = {}
for lipid_name, lipid in self.lipids.items():
if lipid_name not in ALLOWLIPIDS:
# We do not treat cholesterols
continue
topology = Topology(
self.traj,
self.composition[lipid_name]["NAME"],
lipid.mapping_dict
)
concatenator = Concatenator(topology,
self.traj,
self.composition[lipid_name]["NAME"])
self.concatenated_trajs[lipid_name] = concatenator.concatenate()
[docs]
def dump_data(self, data):
"""
Write data to json file
"""
with open(os.path.join(self._path,
self.eq_time_fname), "w") as f:
json.dump(data, f)
[docs]
class Topology:
"""
Class Topology is a class needed to extract lipid specific data and also to
merge lipids from Amber trajectories, where lipid is often represented as 3
residue types. It has the following methods:
1. Simple constructor, which sets the force field,residue names, trajectory,
and loads mapping_file
2. Mapping file loader
3. Function that outputs atomNames
4. Checker if the merge is needed. Currently defunct
5. Runner, that returns lists for head, tail1, tail2 orders for merging
Currently defunct
"""
def __init__(self, traj, lipid_resname: str, mapping_dict: dict):
"""
Constructor for Topology:
traj - MDAnalysis trajectory
lipid_resname - resname of the lipid
mapping_dict - preloaded mapping_dict
"""
self.lipid_resname = lipid_resname
self.traj = traj
self.mapping = mapping_dict
[docs]
def atom_names(self):
"""
Extract all names of heavy atoms from the mapping
"""
atoms = []
for key in self.mapping:
atom = self.mapping[key]["ATOMNAME"]
if atom[0] == "H":
continue
atoms.append(atom)
return atoms
[docs]
def is_merge_needed(self):
"""
Checker for merge. Currently it checks if the RESIDUE key is in the
mapping file.
NOTE: This has to be changed if the content of mapping file changes
"""
if "RESIDUE" not in self.mapping[list(self.mapping.keys())[0]].keys():
return False
resnames = []
for key in self.mapping:
atom = self.mapping[key]["ATOMNAME"]
anames = self.atom_names()
if atom in anames:
resnames.append(self.mapping[key]["RESIDUE"])
resnames = set(resnames)
if len(resnames) > 1:
return resnames
return False
[docs]
def get_lipid_resnames(self):
"""
Helper function that gets the residue names for lipid, if merge is needed
"""
resnames = self.is_merge_needed()
if self.is_merge_needed():
return resnames
# How can we end up here?
# Since currently we only call this function when Merge is needed,
# this is a place for checking if everything is ok and we can raise
else:
return self.lipid_resname
[docs]
def assign_resnames(self, resnames):
"""
Helper function that finds head, sn-1 and sn-2 tails
NOTE: currently there are only lipids with 2 different tails available in
databank: e.g. POPC or POPG. This leads to different names of tails. This
won't be the case for DOPC. Currently the algorithm is using that all three
groups differ
"""
if self.is_merge_needed():
resname_dict = {}
# First find headgroup
for key in self.mapping:
resname = self.mapping[key]["RESIDUE"]
if self.mapping[key]["FRAGMENT"] == HEADGRP:
resname_dict[HEADGRP] = resname
break
for key in self.mapping:
resname = self.mapping[key]["RESIDUE"]
if (
TAILSN1 not in resname_dict
and TAILSN1 == self.mapping[key]["FRAGMENT"]
and not resname_dict[HEADGRP] == resname
):
resname_dict[TAILSN1] = resname
if (
TAILSN2 not in resname_dict
and TAILSN2 == self.mapping[key]["FRAGMENT"]
and not resname_dict[HEADGRP] == resname
):
resname_dict[TAILSN2] = resname
if TAILSN1 in resname_dict and TAILSN2 in resname_dict:
break
# TODO: add check that all resnames from input are in the dict
return resname_dict
# How can we end up here?
else:
return None
[docs]
def run_merger(self):
"""
Find lipid tails that correspond to a particular head-group.
NOTE: currently there are only lipids with 2 different tails available in
databank: e.g. POPC or POPG. This leads to different names of tails. This
won't be the case for DOPC. Currently the algorithm is using that all three
groups differ
TODO: get the correspondence from structure
"""
resnames = self.get_lipid_resnames()
resname_dict = self.assign_resnames(resnames)
head_residues = [
r.atoms.select_atoms("not name H* and prop mass > 0.8")
for r in self.traj.select_atoms(
f"not name H* and resname {resname_dict[HEADGRP]}"
).residues
]
sn_1_residues = [
r.atoms.select_atoms("not name H* and prop mass > 0.8")
for r in self.traj.select_atoms(
f"not name H* and resname {resname_dict[TAILSN1]} and "
+ f"around {merge_cutoff} (resname {resname_dict[HEADGRP]} "
+ "and not name H*)"
).residues
]
sn_2_residues = [
r.atoms.select_atoms("not name H* and prop mass > 0.8")
for r in self.traj.select_atoms(
f"not name H* and resname {resname_dict[TAILSN2]} and "
+ f"around {merge_cutoff} (resname {resname_dict[HEADGRP]} "
+ "and not name H*)"
).residues
]
return head_residues, sn_1_residues, sn_2_residues
[docs]
class Concatenator:
"""
Class Concatenator is a class needed to concatenate trajectory for lipid types.
It has the following methods:
1. Simple constructor, which sets the topology,residue names, and
trajectory
2. concatenateTraj method to do the basic by lipid concatenation
3. alignTraj method to perform the alignment of the concatenated trajectory
4. The enveloping concatenate method
"""
def __init__(self, topology: Topology, traj, lipid_resname: str):
"""
Constructor for Concatenator:
topology - topology for lipid
traj - MDAnalysis trajectory
lipid_resname - lipid resname in the trajectory
"""
self.topology = topology
self.traj = traj
self.lipid_resname = lipid_resname
if self.topology.is_merge_needed():
self.headlist, self.tail1list, self.tail2list = \
self.topology.run_merger()
# TODO: raise if length of 3 lists is not equal
else:
self.headlist = None
self.tail1list = None
self.tail2list = None
[docs]
def concatenate_traj(self):
"""
concatenateTraj performs basic trajectory concatination. First, it extracts
coordinates from trajectory, next, it reshapes the coordinate array, swaps
time and resid axes to obtain continuous trajectories of individual lipids
(this is needed for autocorrelation time analysis), and finally merges
individual lipid trajectories.
"""
traj = self.traj.trajectory
n_frames = len(traj)
heavy_atoms_topology = self.traj.select_atoms(
f"resname {self.lipid_resname} and not name H*"
)
n_atoms_lipid = len(self.topology.atom_names())
n_lipid = heavy_atoms_topology.n_residues
if n_lipid * n_atoms_lipid != heavy_atoms_topology.n_atoms:
n_lipid = heavy_atoms_topology.n_atoms // n_atoms_lipid
# Get all coordinates n_frames, n_lipid * n_atoms_lipid
coords = (
AnalysisFromFunction(lambda ag: ag.positions.copy(),
heavy_atoms_topology)
.run()
.results["timeseries"]
)
# Adding axis to separate individual lipid trajectories
coords = coords.reshape((n_frames, n_lipid, n_atoms_lipid, 3))
# Swapping time frame with lipid axis
# Now we have continuous lipid trajectory
coords = np.swapaxes(coords, 0, 1)
# Reshaping to desired shape
coords = coords.reshape((n_frames * n_lipid, n_atoms_lipid, 3))
# Creating new Universe from the concatenated coordinates
atom_resindex = np.repeat(0, n_atoms_lipid)
concatenated_traj = mda.Universe.empty(
n_atoms_lipid, 1, atom_resindex=atom_resindex, trajectory=True
)
concatenated_traj.add_TopologyAttr("resname", [self.lipid_resname])
concatenated_traj.load_new(coords, in_memory=False)
return concatenated_traj, n_lipid, n_frames * n_lipid
[docs]
def concatenate_traj_with_merging(self):
"""
concatenateTrajWithMerging performs basic trajectory concatination. In
contrast to basic concatenateTraj it additionally merges splitted lipids.
First, it creates extracts coordinates from trajectory, next, it reshapes
the coordinate array, swaps time and resid axes to obtain continuous
trajectories of individual lipids (this is needed for autocorrelation
time analysis), and finally merges individual lipid trajectories.
"""
traj = self.traj.trajectory
n_frames = len(traj)
heavy_atoms_topology = \
self.headlist[0] + \
self.tail1list[0] + \
self.tail2list[0]
for head, sn1, sn2 in zip(
self.headlist[1:], self.tail1list[1:], self.tail2list[1:]
):
heavy_atoms_topology = heavy_atoms_topology.union(head + sn1 + sn2)
n_atoms_lipid = len(self.topology.atom_names())
n_lipid = heavy_atoms_topology.n_atoms // n_atoms_lipid
# TODO: add check
# n_atoms_lipid == heavy_atoms_topology.n_atoms
# Get all coordinates n_frames, n_lipid * n_atoms_lipid
coords = (
AnalysisFromFunction(lambda ag: ag.positions.copy(),
heavy_atoms_topology)
.run()
.results["timeseries"]
)
# Adding axis to separate individual lipid trajectories
coords = coords.reshape((n_frames, n_lipid, n_atoms_lipid, 3))
# Swapping time frame with lipid axis
# Now we have continuous lipid trajectory
coords = np.swapaxes(coords, 0, 1)
# Reshaping to desired shape
coords = coords.reshape((n_frames * n_lipid, n_atoms_lipid, 3))
# Creating new Universe from the concatenated coordinates
atom_resindex = np.repeat(0, n_atoms_lipid)
concatenated_traj = mda.Universe.empty(
n_atoms_lipid, 1, atom_resindex=atom_resindex, trajectory=True
)
concatenated_traj.add_TopologyAttr("resname", [self.lipid_resname])
concatenated_traj.load_new(coords, in_memory=False)
return concatenated_traj, n_lipid, n_frames * n_lipid
"""
alignTraj alignes the concatenated trajectory in two steps: (1) it computes
average structure after alignment to the first frame, and (2) it alignes
the structure to the calculated average structure in (1).
"""
[docs]
def align_traj(self, concatenated_traj):
# Compute average structure after alignment to the first frame
av = align.AverageStructure(concatenated_traj, ref_frame=0).run()
# Align to average structure
align.AlignTraj(concatenated_traj, av.results.universe).run()
# Compute average structure after second alignment
coords = (
AnalysisFromFunction(
lambda ag: ag.positions.copy(),
concatenated_traj.select_atoms("all")
)
.run()
.results["timeseries"]
)
return coords.reshape(-1, 3), coords.mean(axis=0).reshape(1, -1)
"""
Simple enveloping function to perform concatenation
"""
[docs]
def concatenate(self):
print(f"Concatenator: Concatenating lipid with resname {self.lipid_resname}")
if not self.topology.is_merge_needed():
# Merging is not needed
concatenated_traj, n_lipid, n_frames = self.concatenate_traj()
else:
concatenated_traj, n_lipid, n_frames = \
self.concatenate_traj_with_merging()
aligned_traj, av_pos = self.align_traj(concatenated_traj)
return aligned_traj, av_pos, n_lipid, n_frames
[docs]
class PCA:
"""
Class PCA is a class that actually performs PCA. It has the following methods:
1. Simple constructor, which sets the aligned trajtory, average coordinates,
number of lipids, number of frames in the concatenated trajectory and
trajectory length in ns
2. PCA prepares the trajectory coordinates for analysis and calculates
principal components
3. get_proj projects the trajectory on principal components
4. get_lipid_autocorrelation calculates the autocorrelation timeseries for
individual lipid
5. get_autocorrelations calculates the autocorrelation timeseries for
trajectory
"""
def __init__(self, aligned_traj, av_pos, n_lipid, n_frames, traj_time):
"""
Constructor for PCA:
aligned_traj - np.array with positions of concatenated and aligned
trajectory
av_pos - np.array with average positions for the lipid
n_lipid - number of lipids of particular type in the system
n_frames - number of frames in the concatenated trajectory
traj_time - trajectory length in ns
"""
self.aligned_traj = aligned_traj
self.av_pos = av_pos
self.n_lipid = n_lipid
self.n_frames = n_frames
self.traj_time = traj_time
[docs]
def PCA(self): # noqa: N802
"""
PCA calculates the PCA. First the data is centered and then covariance
matrix is calculated manually.
"""
# centering of positions relative to the origin
x = self.aligned_traj.astype(np.float64)
x = x.reshape(self.n_frames, self.av_pos.shape[1]) - self.av_pos
# the sum of all coordinates (to calculate mean)
x_1 = x.sum(axis=0)
# production of X and X^T
x_x = np.tensordot(x, x, axes=(0, 0))
# covariance matrix calculation
cov_mat = (
x_x
- np.dot(x_1.reshape(len(x_1), 1), (x_1.reshape(len(x_1), 1)).T)
/ self.n_frames
) / (self.n_frames - 1)
# eigenvalues and eigenvectors calculation
eig_vals, eig_vecs = np.linalg.eigh(cov_mat)
self.eig_vecs = np.flip(eig_vecs, axis=1).T
return x
[docs]
def get_proj(self, cdata):
"""
Projecting the trajectory on the 1st principal component
"""
# projection on PC1
proj = np.tensordot(cdata, self.eig_vecs[0:1], axes=(1, 1)).T
proj = np.concatenate(np.array(proj), axis=None)
self.proj = proj
[docs]
def get_lipid_autocorrelation(self, data, variance, mean):
"""
Autocorrelation calculation for individual lipid.
"""
# Centering the data
data -= mean
# Convolve the data
r = signal.fftconvolve(data, data[::-1], mode="full")[-len(data):]
# Weight the correlation to get the result in range -1 to 1
return r / (variance * (np.arange(len(data), 0, -1)))
[docs]
def get_autocorrelations(self):
"""
Autocorrelation calculation for the trajectory.
"""
variance = self.proj.var()
mean = self.proj.mean()
# extract the trajectories for individual lipids
separate_projs = [
self.proj[
len(self.proj) * i // self.n_lipid:len(self.proj)
* (i + 1) // self.n_lipid]
for i in range(self.n_lipid)
]
# calculate autocorrelations for individual lipids
r = np.array(
[self.get_lipid_autocorrelation(x, variance, mean)
for x in separate_projs]
)
r = r.mean(axis=0)
t = np.arange(len(r)) * self.traj_time / len(r)
self.autocorrelation = np.array([t, r]).T
[docs]
class TimeEstimator:
"""
Class TimeEstimator is a class that estimates equilbration time from
autocorrelation data. It includes the following methods:
1. Simple constructor, which sets the autocorrelation data
2. Helper method get_nearest_value that finds the interval in the data
where the autocorrelation falls below specific value
3. timerelax method calculates the logarithms of autocorrelation and
calculates the decay time
4. calculate_time method calculates the estimated equilibration time
"""
def __init__(self, autocorrelation):
"""
Constructor for PCA:
autocorrelation - autocorrelation data
"""
self.autocorrelation = autocorrelation
[docs]
def get_nearest_value(self, iterable, value):
"""
get_nearest_value method return the indices that frame the particular value
As an input it gets an array, which is expected to decay. The method tries
to find and index (index_A), for which the array gets below the cutoff value
for the first time. Then, for index_A-1 the array was larger than the cutoff
value for the last time. It means that the function, represented by the
array data is equal to cutoff somewhere between timesteps that correspond to
index_A-1 and index_A. It can happen, that this index_A is equal 0. Then,
method searches for the first occurance, where array is smaller than
array[0]. The method returns the interval inbetween the array gets below
cutoff.
"""
try:
a = np.where(iterable < value)[0][0]
except Exception:
print("TimeEstimator: Autocorrelations do not converge. "
"We shift to extrapolation regime.")
a = np.where(iterable == np.min(iterable))[0][0]
return a, a - 1
if a == 0:
b = np.where(iterable < iterable[a])[0][0]
else:
b = a - 1
return a, b
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def timerelax(self):
"""
Estimates autocorrelation decay time.
"""
time = self.autocorrelation[:, 0]
autocorrelation = self.autocorrelation[:, 1]
points = []
j = 1
while j < len(autocorrelation):
points.append(j)
j = int(1.5 * j) + 1
# Get timeseries for autocorrelation
t_pic = np.array([time[i] for i in points if autocorrelation[i] > 0.0])
r_pic = np.array(
[autocorrelation[i] for i in points if autocorrelation[i] > 0.0]
)
# Calculate logs for time and autocorrelation arrays
# We use log since in log-log scale autocorrelation is closer to linear
r_log = np.log(r_pic)
t_log = np.log(t_pic)
# data interpolation. We are searching for time interval where
# autocorrelations decay by e. This is the most stable method.
# Autocorrelations decay by e is equivalent to
# log(autocorrelation) < - 1
power = -1
ai, bi = self.get_nearest_value(r_log, power)
# perform interpolation
a = (t_log[bi] - t_log[ai]) / (r_log[bi] - r_log[ai])
b = t_log[ai] - a * r_log[ai]
t_relax1 = a * power + b
t_relax1 = np.exp(t_relax1)
return t_relax1
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def calculate_time(self):
"""
Basic enveloping method that estimates equilibration time from
autocorrelation decay time. They are linearly connected and the
coefficient is calculated experimentally.
"""
# relaxation time at e^1 decay
te1 = self.timerelax()
return te1 * 49 # 49 from sample data average of tkss2/tac1