/
ti_.py
129 lines (103 loc) · 4.74 KB
/
ti_.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
import alchemlyb.estimators
import numpy as np
import pandas as pd
import numkit
class TI(alchemlyb.estimators.TI):
"""Thermodynamic integration (TI) estimator
Parameters
----------
verbose : bool, optional
Set to True if verbose debug output is desired.
Attributes
----------
delta_f_ : DataFrame
The estimated dimensionless free energy difference between each state.
d_delta_f_ : DataFrame
The estimated statistical uncertainty (one standard deviation) in
dimensionless free energy differences.
delta_f_error_ : DataFrame
The estimated statistical uncertainty (one standard deviation) in
dimensionless free energy differences while taking correlated data
into account.
"""
def fit(self, dHdl, ncorrel=25000):
"""
Compute free energy differences between each state by integrating
dHdl across lambda values.
Parameters
----------
dHdl : DataFrame
dHdl[n,k] is the potential energy gradient with respect to lambda
for each configuration n and lambda k.
"""
# sort by state so that rows from same state are in contiguous blocks,
# and adjacent states are next to each other
dHdl = dHdl.sort_index(level=dHdl.index.names[1:])
# obtain the mean and variance of the mean for each state
# variance calculation assumes no correlation between points
# used to calculate mean
means = dHdl.mean(level=dHdl.index.names[1:])
variances = np.square(dHdl.sem(level=dHdl.index.names[1:]))
correlation = self._correlated_error(dHdl)
errors = correlation[0]
tc = correlation[1]
# obtain vector of delta lambdas between each state
dl = means.reset_index()[means.index.names[:]].diff().iloc[1:].values
# apply trapezoid rule to obtain DF between each adjacent state
deltas = (dl * (means.iloc[:-1].values + means.iloc[1:].values)/2).sum(axis=1)
d_deltas = (dl**2 * (variances.iloc[:-1].values + variances.iloc[1:].values)/4).sum(axis=1)
d_deltas_errors = (dl**2 * (errors.iloc[:-1].values + errors.iloc[1:].values)/4).sum(axis=1)
# build matrix of deltas between each state
adelta = np.zeros((len(deltas)+1, len(deltas)+1))
ad_delta = np.zeros_like(adelta)
ad_delta_errors = np.zeros_like(adelta)
for j in range(len(deltas)):
out = []
dout = []
douterror = []
for i in range(len(deltas) - j):
out.append(deltas[i] + deltas[i+1:i+j+1].sum())
dout.append(d_deltas[i] + d_deltas[i+1:i+j+1].sum())
douterror.append(d_deltas_errors[i] + d_deltas_errors[i+1:i+j+1].sum())
adelta += np.diagflat(np.array(out), k=j+1)
ad_delta += np.diagflat(np.array(dout), k=j+1)
ad_delta_errors += np.diagflat(np.array(douterror), k=j+1)
# yield standard delta_f_ free energies between each state
self.delta_f_ = pd.DataFrame(adelta - adelta.T,
columns=means.index.values,
index=means.index.values)
# yield standard deviation d_delta_f_ between each state
self.d_delta_f_ = pd.DataFrame(np.sqrt(ad_delta + ad_delta.T),
columns=variances.index.values,
index=variances.index.values)
self.d_delta_f_error_ = pd.DataFrame(np.sqrt(ad_delta_errors + ad_delta_errors.T),
columns=errors.index.values,
index=errors.index.values)
self.means_ = means.values
self.variances_ = variances.values
self.tc_ = tc
self.errors_ = errors.values
return self
def _correlated_error(self, dHdl, ncorrel=25000):
"""Compute errors considering correlated data from time series.
Parameters
----------
dHdl : DataFrame
dHdl is the time series of dHdl for a particular lambda window.
Returns
-------
errors of correlated data
"""
errors = []
lambdas = []
tcs = []
for name, group in dHdl.groupby(level='fep-lambda'):
t = group.index.get_level_values('time').values
y = group.values.flatten()
tc = numkit.timeseries.tcorrel(t, y, nstep=int(np.ceil(len(t)/float(ncorrel))))
lambdas.append(name)
errors.append(tc['sigma'])
tcs.append(tc['tc'])
return pd.DataFrame(errors,
index=pd.Float64Index(lambdas, name='fep-lambda'),
columns=['fep']), np.array(tcs)