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kgori/pairdist.py

Last active September 10, 2015 09:14
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Maximum likelihood distance between pairs of sequences
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pairdist.py
import numpy as np
def setup_logger():
import logging
logger = logging.getLogger()
for handler in logger.handlers:
logger.removeHandler(handler)
ch=logging.StreamHandler()
formatter = logging.Formatter('%(asctime)s - %(name)s - %(levelname)s - %(message)s')
ch.setFormatter(formatter)
logger.addHandler(ch)
logger.setLevel(logging.INFO)
return logger
logger = setup_logger()
dna_charmap = {'-': [1.0, 1.0, 1.0, 1.0],
'A': [0.0, 0.0, 1.0, 0.0],
'C': [0.0, 1.0, 0.0, 0.0],
'G': [0.0, 0.0, 0.0, 1.0],
'N': [1.0, 1.0, 1.0, 1.0],
'T': [1.0, 0.0, 0.0, 0.0],
'a': [0.0, 0.0, 1.0, 0.0],
'c': [0.0, 1.0, 0.0, 0.0],
'g': [0.0, 0.0, 0.0, 1.0],
'n': [1.0, 1.0, 1.0, 1.0],
't': [1.0, 0.0, 0.0, 0.0]}
# A R N D C Q E G H I L K M F P S T W Y V
protein_charmap = {'-': [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
'?': [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
'A': [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'R': [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'N': [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'D': [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'C': [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'Q': [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'E': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'G': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'H': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'I': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'L': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'K': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'M': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'F': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'P': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'S': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0],
'T': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],
'W': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
'Y': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],
'V': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
'X': [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
'a': [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'r': [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'n': [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'd': [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'c': [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'q': [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'e': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'g': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'h': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'i': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'l': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'k': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'm': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'f': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
'p': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
's': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0],
't': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],
'w': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
'y': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],
'v': [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
'x': [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]}
lg = np.array(
[[ 0. , 0.425093, 0.276818, 0.395144, 2.489084, 0.969894, 1.038545, 2.06604 , 0.358858, 0.14983 , 0.395337, 0.536518, 1.124035, 0.253701, 1.177651, 4.727182, 2.139501, 0.180717, 0.218959, 2.54787 ],
[ 0.425093, 0. , 0.751878, 0.123954, 0.534551, 2.807908, 0.36397 , 0.390192, 2.426601, 0.126991, 0.301848, 6.326067, 0.484133, 0.052722, 0.332533, 0.858151, 0.578987, 0.593607, 0.31444 , 0.170887],
[ 0.276818, 0.751878, 0. , 5.076149, 0.528768, 1.695752, 0.541712, 1.437645, 4.509238, 0.191503, 0.068427, 2.145078, 0.371004, 0.089525, 0.161787, 4.008358, 2.000679, 0.045376, 0.612025, 0.083688],
[ 0.395144, 0.123954, 5.076149, 0. , 0.062556, 0.523386, 5.24387 , 0.844926, 0.927114, 0.01069 , 0.015076, 0.282959, 0.025548, 0.017416, 0.394456, 1.240275, 0.42586 , 0.02989 , 0.135107, 0.037967],
[ 2.489084, 0.534551, 0.528768, 0.062556, 0. , 0.084808, 0.003499, 0.569265, 0.640543, 0.320627, 0.594007, 0.013266, 0.89368 , 1.105251, 0.075382, 2.784478, 1.14348 , 0.670128, 1.165532, 1.959291],
[ 0.969894, 2.807908, 1.695752, 0.523386, 0.084808, 0. , 4.128591, 0.267959, 4.813505, 0.072854, 0.582457, 3.234294, 1.672569, 0.035855, 0.624294, 1.223828, 1.080136, 0.236199, 0.257336, 0.210332],
[ 1.038545, 0.36397 , 0.541712, 5.24387 , 0.003499, 4.128591, 0. , 0.348847, 0.423881, 0.044265, 0.069673, 1.807177, 0.173735, 0.018811, 0.419409, 0.611973, 0.604545, 0.077852, 0.120037, 0.245034],
[ 2.06604 , 0.390192, 1.437645, 0.844926, 0.569265, 0.267959, 0.348847, 0. , 0.311484, 0.008705, 0.044261, 0.296636, 0.139538, 0.089586, 0.196961, 1.73999 , 0.129836, 0.268491, 0.054679, 0.076701],
[ 0.358858, 2.426601, 4.509238, 0.927114, 0.640543, 4.813505, 0.423881, 0.311484, 0. , 0.108882, 0.366317, 0.697264, 0.442472, 0.682139, 0.508851, 0.990012, 0.584262, 0.597054, 5.306834, 0.119013],
[ 0.14983 , 0.126991, 0.191503, 0.01069 , 0.320627, 0.072854, 0.044265, 0.008705, 0.108882, 0. , 4.145067, 0.159069, 4.273607, 1.112727, 0.078281, 0.064105, 1.033739, 0.11166 , 0.232523, 10.649107],
[ 0.395337, 0.301848, 0.068427, 0.015076, 0.594007, 0.582457, 0.069673, 0.044261, 0.366317, 4.145067, 0. , 0.1375 , 6.312358, 2.592692, 0.24906 , 0.182287, 0.302936, 0.619632, 0.299648, 1.702745],
[ 0.536518, 6.326067, 2.145078, 0.282959, 0.013266, 3.234294, 1.807177, 0.296636, 0.697264, 0.159069, 0.1375 , 0. , 0.656604, 0.023918, 0.390322, 0.748683, 1.136863, 0.049906, 0.131932, 0.185202],
[ 1.124035, 0.484133, 0.371004, 0.025548, 0.89368 , 1.672569, 0.173735, 0.139538, 0.442472, 4.273607, 6.312358, 0.656604, 0. , 1.798853, 0.099849, 0.34696 , 2.020366, 0.696175, 0.481306, 1.898718],
[ 0.253701, 0.052722, 0.089525, 0.017416, 1.105251, 0.035855, 0.018811, 0.089586, 0.682139, 1.112727, 2.592692, 0.023918, 1.798853, 0. , 0.094464, 0.361819, 0.165001, 2.457121, 7.803902, 0.654683],
[ 1.177651, 0.332533, 0.161787, 0.394456, 0.075382, 0.624294, 0.419409, 0.196961, 0.508851, 0.078281, 0.24906 , 0.390322, 0.099849, 0.094464, 0. , 1.338132, 0.571468, 0.095131, 0.089613, 0.296501],
[ 4.727182, 0.858151, 4.008358, 1.240275, 2.784478, 1.223828, 0.611973, 1.73999 , 0.990012, 0.064105, 0.182287, 0.748683, 0.34696 , 0.361819, 1.338132, 0. , 6.472279, 0.248862, 0.400547, 0.098369],
[ 2.139501, 0.578987, 2.000679, 0.42586 , 1.14348 , 1.080136, 0.604545, 0.129836, 0.584262, 1.033739, 0.302936, 1.136863, 2.020366, 0.165001, 0.571468, 6.472279, 0. , 0.140825, 0.245841, 2.188158],
[ 0.180717, 0.593607, 0.045376, 0.02989 , 0.670128, 0.236199, 0.077852, 0.268491, 0.597054, 0.11166 , 0.619632, 0.049906, 0.696175, 2.457121, 0.095131, 0.248862, 0.140825, 0. , 3.151815, 0.18951 ],
[ 0.218959, 0.31444 , 0.612025, 0.135107, 1.165532, 0.257336, 0.120037, 0.054679, 5.306834, 0.232523, 0.299648, 0.131932, 0.481306, 7.803902, 0.089613, 0.400547, 0.245841, 3.151815, 0. , 0.249313],
[ 2.54787 , 0.170887, 0.083688, 0.037967, 1.959291, 0.210332, 0.245034, 0.076701, 0.119013, 10.649107, 1.702745, 0.185202, 1.898718, 0.654683, 0.296501, 0.098369, 2.188158, 0.18951 , 0.249313, 0. ]])
lg_freqs = np.array([0.079066, 0.055941, 0.041977, 0.053052, 0.012937, 0.040767, 0.071586, 0.057337, 0.022355, 0.062157, 0.099081, 0.064600, 0.022951, 0.042302, 0.044040, 0.061197, 0.053287, 0.012066, 0.034155, 0.069147])
def seq_to_partials(seq, alphabet='dna'):
return np.array(
[(dna_charmap[char] if alphabet=='dna' else protein_charmap[char])
for char in seq]
)
def get_q_matrix(rates, freqs):
q = rates.dot(np.diag(freqs))
q.flat[::len(freqs)+1] -= q.sum(1)
q /= (-(np.diag(q)*freqs).sum())
return q
def get_b_matrix(q_matrix, sqrtfreqs):
sqrtfreqs
return np.diag(sqrtfreqs).dot(q_matrix).dot(np.diag(1/sqrtfreqs))
def get_eigen(q_matrix, freqs=None):
if freqs is not None:
rootf = np.sqrt(freqs)
mtx = get_b_matrix(q_matrix, rootf)
l, r = np.linalg.eigh(mtx)
u = np.diag(1/rootf).dot(r)
uinv = r.T.dot(np.diag(rootf))
else:
mtx = q_matrix
l, u = np.linalg.eig(mtx)
sort_ix = np.argsort(l)
l = l[sort_ix]
u = u[:, sort_ix]
uinv = np.linalg.inv(u)
return u, l, uinv
class EigenDecomp(object):
def __init__(self, qmatrix, freqs=None):
u, l, uinv = get_eigen(qmatrix, freqs)
self.u = u
self.l = l
self.uinv = uinv
def values(self):
return self.u, self.l, self.uinv
class TransitionMatrix(object):
def __init__(self, eigen):
self.values = eigen.values()
self.size = len(self.values[1])
def get_p_matrix(self, t):
"""
P = transition probabilities
"""
u, l, uinv = self.values
return u.dot(np.diag(np.exp(l*t))).dot(uinv)
def get_dp_matrix(self, t):
"""
First derivative of P
"""
u, l, uinv = self.values
return u.dot(np.diag(l*np.exp(l*t))).dot(uinv)
def get_d2p_matrix(self, t):
"""
Second derivative of P
"""
u, l, uinv = self.values
return u.dot(np.diag(l*l*np.exp(l*t))).dot(uinv)
class PairLikelihood(object):
"""
See Yang, (2000) "Maximum Likelihood Estimation on Large Phylogenies and Analysis of
Adaptive Evolution in Human Influenza Virus A", J. Mol. Evol.
"""
def __init__(self, transmat, edgelen):
self.transmat = transmat
self.update_transmat(edgelen)
def update_transmat(self, edgelen):
""" Update transition probabilities for new branch lengths """
self.p = self.transmat.get_p_matrix(edgelen)
self.dp = self.transmat.get_dp_matrix(edgelen)
self.d2p = self.transmat.get_d2p_matrix(edgelen)
def _f(self, partial_a, partial_b, freqs):
return (freqs*self.p*partial_a*partial_b[:,np.newaxis]).sum()
def _df(self, partial_a, partial_b, freqs):
return (freqs*self.dp*partial_a*partial_b[:,np.newaxis]).sum()
def _d2f(self, partial_a, partial_b, freqs):
return (freqs*self.d2p*partial_a*partial_b[:,np.newaxis]).sum()
def calculate(self, partials_a, partials_b, freqs):
lnl = 0
dlnl = 0
d2lnl = 0
for sa, sb in zip(sites_a, sites_b):
f = self._f(sa, sb, freqs)
df = self._df(sa, sb, freqs)
d2f = self._d2f(sa, sb, freqs)
lnl += np.log(f)
dlnl += df / f
d2lnl += (f * d2f - df * df) / (f * f)
return lnl, dlnl, d2lnl
class Likelihood(object):
"""
See Yang, (2000) "Maximum Likelihood Estimation on Large Phylogenies and Analysis of
Adaptive Evolution in Human Influenza Virus A", J. Mol. Evol.
"""
def __init__(self, transmat, edgelen_left, edgelen_right=0):
""" Initialise object with TransitionMatrix and a branch lengths.
"""
self.transmat = transmat
self.update_transmat(edgelen_left, edgelen_right)
self.size = transmat.size
def update_transmat(self, edgelen_left, edgelen_right=0):
""" Update transition probabilities for new branch lengths """
self.p_left = self.transmat.get_p_matrix(edgelen_left)
self.p_right = self.transmat.get_p_matrix(edgelen_right)
self.dp = self.transmat.get_dp_matrix(edgelen_left+edgelen_right)
self.d2p = self.transmat.get_d2p_matrix(edgelen_left+edgelen_right)
def _likvec(self, partial_a, partial_b):
""" Calculate the likelihood vector for a site """
return (self.p_left*partial_a).sum(1) * (self.p_right*partial_b).sum(1)
def _f(self, partial_a, partial_b, freqs):
""" Calculate the root likelihood for a site """
vec = self._likvec(partial_a, partial_b)
return (vec*freqs).sum()
def _df(self, partial_a, partial_b, freqs):
""" Calculate the root first derivative of the likelihood for a site """
return (freqs*self.dp*partial_a*partial_b[:,np.newaxis]).sum()
def _d2f(self, partial_a, partial_b, freqs):
""" Calculate the root second derivative of the likelihood for a site """
return (freqs*self.d2p*partial_a*partial_b[:,np.newaxis]).sum()
def calculate(self, sites_a, sites_b, pi):
""" Calculate log likelihood and first and second derivatives over all sites.
Sites need to be given as partials (i.e. conditional probability vectors) """
lnl = 0
dlnl = 0
d2lnl = 0
for sa, sb in zip(sites_a, sites_b):
f = self._f(sa, sb, pi)
df = self._df(sa, sb, pi)
d2f = self._d2f(sa, sb, pi)
lnl += np.log(f)
dlnl += df / f
d2lnl += (f * d2f - df * df) / (f * f)
return lnl, dlnl, d2lnl
class OptWrapper(object):
"""
Wrapper for use with scipy optimiser (e.g. brenth/brentq)
"""
def __init__(self, likelihood, sites_a, sites_b, freqs):
self.lik = likelihood
self.sites_a = sites_a
self.sites_b = sites_b
self.freqs = freqs
self.updated = None
def update(self, brlen):
if self.updated == brlen:
return
else:
self.updated = brlen
self.lik.update_transmat(brlen)
self.lnl, self.dlnl, self.d2lnl = self.lik.calculate(self.sites_a, self.sites_b, self.freqs)
def get_dlnl(self, brlen):
self.update(brlen)
return self.dlnl
def get_d2lnl(self, brlen):
self.update(brlen)
return self.d2lnl
def __str__(self):
return 'Branch length={}, Variance={}, Likelihood+derivatives = {} {} {}'.format(self.updated, -1/self.d2lnl, self.lnl, self.dlnl, self.d2lnl)
def optimise(likelihood, partials_a, partials_b, frequencies, min_brlen=0.00001, max_brlen=10, verbose=True):
"""
Optimise ML distance between two partials. min and max set brackets
likelihood = Likelihood or PairLikelihood object. PairLikelihood is slightly faster.
"""
from scipy.optimize import brenth
wrapper = OptWrapper(likelihood, partials_a, partials_b, frequencies)
brlen = 0.5
n=brenth(wrapper.get_dlnl, min_brlen, max_brlen)
if verbose:
print(wrapper)
return n, -1/wrapper.get_d2lnl(n)
if __name__ == '__main__':
kappa = 1
k80 = np.array([[0,kappa,1,1],[kappa,0,1,1],[1,1,0,kappa],[1,1,kappa,0]], dtype=np.float)
k80f = np.array([0.25,0.25,0.25,0.25])
# Simulated data from K80, kappa=1, distance = 0.8
sites_a = seq_to_partials('ACCCTCCGCGTTGGGTAGTCCTAGGCCCAATGGCGTTTATGCCTCGATTTTTAGTTCTACCGTCCCTACAGATGGATGCCGTCGCATAGACACTGTCAATTCCATTCGGCAGGCTTCACACTGTTGCATTTTCATTTTGTACACGGTACCAACATAGGAGTGCTGTATTGCTATATTTCCAGTACACGGCGTTGAGTCGGATGGAAACGCCGGCGGAAGACAGCTTGGCGGGTCTTCACGCATCACCGCGGGGTCTGAAAGGTATTATCGCTGCTTAAATCAGACCGGTCAAGCTTCCTGGCGGAAGGCGGCAAGGTCCAGCCACAGCATGCTTATTCCTTGTCACGCCGGGTGGAAATCTAGAGCGTCCGGTGGACACAGAGTGATTTTGTACGGGGGGTTCCATACCAGGACATTAGGGTCGGTTTACGGTCTGAGATGTATGTTGCCTTGCGGTCGACGAGCACTGATTCCCCTGAACTTCGTAAGACACATATAGTTTTAATGAAATCCCCAAAACGAGCATGGTTTCAGTATACGCGACAACTTAGGATACAACATACTGAACCAGTCCGCATTGAGGTGCCAATCAAACGGGACCGGGACTGATAAGTATAAAATAGGTTTCCCTGTCCTCTACCTACGTTATCCTCGCGTCGATTTTGATTCTTACCAAGACTGCTAATCAGGCCCTGTGGCCTGCATGTCACCATGTCAGCGTGTTTGGCTAAATTCACGGGATTGGCCTTACCGACTTACATCAGTATTTCATACATAGTTACTCGAGTTTAACGTTGACAGTTAGTCCCATGATACGGCAAAGCCTGGTTCGGCGGATTTCCGAGTACAGCATCTTCGCCCCCGAGATTGCCGCCAATGGACACCCTCCTGAGATGCAGATATGAGTGTTTTTGACACTCTGAGGCTGAGATCCTCACACTTCCGGAGCTTCCGCGATAGTCACGTGGTTATTAGACTTACGGCAGGAAAAATCATGTTA', alphabet='dna')
sites_b = seq_to_partials('AAGCTCCGCGTAAGCTAACGACCAGTCAGCTAGGTTTAGTGCCACCAGTATGGCTAGTTCCGGAGGGCAAACCGGATGCTACCGATTGGTCACCCTCAGGGTGATTTCGCAGGGCGCTCACTTATTCCTTTTAAATCCTGCCAACAGACTAAGAAAGTTGTACGGTATTCCTATATCTTCAGTACTGCTCTTGGCCGTGCATGTAGCCGAACGACGAGGACGGTACATGAGTTTCTCACCAATTACAGGCGGTTCCATTAGGCAGTAGCTGCGGTTAGTTCATACTGCTAAAGAATCTTCTTGGAACGTGCCAAGGACCAGTCACACACATGTTGTAGTCCCTCATCGTGGTAGGCGTTCCAGACCGTCCGTGGTACACATACCAAATTTCGTACCGGCTGACTCAAAGCGGGAGTTCGCATGATACCAGGGAACGAGATGTTCAAAACGATCAGGTAGTGCCGCCATCTTTCAGGTTCTTTCGTTTCGTCCTATGATACTTGAGTAGCGGTCAAACGAAGCTCGTAGGTGACAGTTACGAGACATGCTGGGATGCAACATACTTTCGCAGTTAGCTAGTAGGTACCTATCTAGCGAATCGAGCTAGGATACCCTGATTATGCTTGTCTCCGTCCTCTTACTATGATCTCCTCGCGTGGTTTTTGCTGCTTAACCGTTGTGCCGTATAAAACAAGAGGCGGGAGTTTAGCTGTGGGAACTTCGTAGACCTTGTAAGCTGGATAGGCCCGTCCGTCGTAATTAATTACCTAAAAGAGAGTCAAACAAGCTTAAGTCGCCGAGTTAGTCGGATAAGAAGCCATTCTCTGGTCCGCCAACCTTCCCATGCCAGTACGGTTGCCGAGGTCCATTCGGTGACTGTGGGATAACCGTTGCCGGAGCTATGAGATCCATTACAACTCTGCGCCTAGGATGTTAACTCTACCGAAGTTTGCGACCCCGGAACCTGTAAATTGTCCTTAGGGTCGTAACATTTTCAAGC', alphabet='dna')
ed = EigenDecomp(get_q_matrix(k80, k80f), k80f)
tm = TransitionMatrix(ed)
lk = PairLikelihood(tm, 0)
optimise(lk, sites_a, sites_b, k80f)
# Example from Section 4.2 of Ziheng's book - his value for node 6 is wrong!
np.set_printoptions(precision=6)
partials_1 = np.array([1, 0, 0, 0], dtype=np.float)
partials_2 = np.array([0, 1, 0, 0], dtype=np.float)
partials_3 = np.array([0, 0, 1, 0], dtype=np.float)
partials_4 = np.array([0, 1, 0, 0], dtype=np.float)
partials_5 = np.array([0, 1, 0, 0], dtype=np.float)
lik_inner = Likelihood(tm, 0.1, 0.1)
lik_outer = Likelihood(tm, 0.2, 0.2)
lik_inner_outer = Likelihood(tm, 0.1, 0.2)
partials_7 = lik_outer._likvec(partials_1, partials_2)
partials_8 = lik_outer._likvec(partials_4, partials_5)
partials_6 = lik_inner_outer._likvec(partials_7, partials_3)
partials_0 = lik_inner._likvec(partials_6, partials_8)
for partial in [partials_0, partials_6, partials_8, partials_7]:
print partial
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