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mda.py
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mda.py
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# -*- coding: utf-8 -*-
import numpy as np
from scipy.stats import norm, gamma
from scipy.special import gammaln
import random
import sys
from collections import defaultdict
import json
import pickle
import shutil
from argparse import ArgumentParser
from json_utils import load_json_file, load_json_stream
from rand_utils import rand_partition_log
from hmc import hmc
from autologistic import WeightedNeighborGraph
class MatrixDecompositionAutologistic(object):
S_X_CAT = 1
S_X_BIN = 2
S_X_CNT = 3
S_Z = 4
S_W_MH = 5
S_W_HMC = 6
# S_Z_V = 7
S_Z_H = 8
S_Z_A = 9
# backward compatibility
hmc_l = 10
hmc_epsilon = 0.05
def __init__(self, mat, flist,
sigma= 1.0, # 0.1, # 1.0,
# vnet=None,
hnet=None,
K=50, mvs=None,
bias=False,
only_alphas=False,
# drop_vs=False,
drop_hs=False,
norm_sigma = 5.0,
const_h = None,
gamma_shape = 1.0,
gamma_scale = 0.001,
hmc_l = 10,
hmc_epsilon = 0.05,
):
self.mat = mat # X: L x P matrix
self.flist = flist
self.hmc_l = hmc_l
self.hmc_epsilon = hmc_epsilon
# L: # of langs
# P: # of surface features
# M: # of linearlized weight elements
# K: # of latent parameters
# l: current idx of langs
# p: current idx of surface features
# T: size of the current feature
# j: linearlized idx of the current feature
self.L, self.P = self.mat.shape
self.M = sum(map(lambda x: x["size"], self.flist))
self.K = K
self.j2pt = np.empty((self.M, 2), dtype=np.int32)
self.p2jT = np.empty((self.P, 2), dtype=np.int32)
binsize = 0
for fstruct in self.flist:
self.p2jT[fstruct["fid"]] = [binsize, fstruct["size"]]
for t in range(fstruct["size"]):
self.j2pt[binsize+t] = [fstruct["fid"], t]
binsize += fstruct["size"]
# self.vnet = vnet
self.hnet = hnet
self.bias = bias
self.only_alphas = only_alphas
# self.drop_vs = drop_vs
self.drop_hs = drop_hs
assert(mvs is None or mat.shape == mvs.shape)
self.mvs = mvs # missing values; (i,p) => bool (True: missing value)
self.mv_list = []
if self.mvs is not None:
for l in range(self.L):
for p in range(self.P):
if self.mvs[l,p]:
self.mv_list.append((l,p))
self.norm_sigma = norm_sigma
self.gamma_shape = gamma_shape
self.gamma_scale = gamma_scale
self.alphas = 0.5 * np.random.normal(loc=0.0, scale=self.norm_sigma, size=self.K)
if not (self.only_alphas or self.drop_hs):
if const_h is None:
self.is_h_fixed = False
self.hks = gamma.rvs(self.gamma_shape, scale=self.gamma_scale, size=self.K).astype(np.float32)
sys.stderr.write("{}\n".format(self.hks))
else:
self.is_h_fixed = True
# self.hks = 0.0001 * np.ones(self.K, dtype=np.float32)
self.hks = const_h * np.ones(self.K, dtype=np.float32)
else:
self.is_h_fixed = True
self.hks = np.zeros(self.K, dtype=np.float32)
self.zmat = np.zeros((self.K, self.L), dtype=np.bool_)
for k, alpha in enumerate(self.alphas):
thres = 1.0 / (1.0 + np.exp(-alpha))
self.zmat[k] = (np.random.rand(self.L) < thres)
self.sigma = sigma # Normal
self.wmat = gamma.rvs(self.sigma, scale=1.0, size=(self.K, self.M))
# np.absolute(0.1 * np.random.standard_t(df=self.sigma, size=(self.K, self.M)))
self.theta_tilde = np.zeros((self.L, self.M), dtype=np.float32)
self.theta = np.ones((self.L, self.M), dtype=np.float32)
self.calc_theta()
self.init_tasks()
def init_with_clusters(self):
# # use only K-1 binary features
min_mu = 0.99
# 1st feature: fully active
self.alphas[0] = np.log(min_mu / (1.0 - min_mu))
self.zmat[0,:] = True
freqlist = []
for p in range(self.P):
freqlist.append(defaultdict(int))
for l in range(self.L):
for p in range(self.P):
if self.mvs is None or self.mvs[l,p] == False:
freqlist[p][self.mat[l,p]] += 1
for p in range(self.P):
j_start, T = self.p2jT[p]
freq = np.array([freqlist[p][t] for t in range(T)], dtype=np.float32) + 0.5
freq /= freq.sum()
# w = np.log(freq)
# w -= max(w.min(), -10.0)
# self.wmat[0,j_start:j_start+T] = w
# subsequent K-1 features
for k in range(1, self.K):
min_mu = max(min_mu * min(np.random.beta(19.0, 1.0), 0.99), 0.01)
self.alphas[k] = np.log(min_mu / (1.0 - min_mu))
# self.wmat[k] = np.random.normal(loc=0.0, scale=0.1, size=self.M)
self.zmat[k,:] = (np.random.rand(self.L) < min_mu)
# sys.stderr.write("{}\n".format(min_mu))
# sys.stderr.write("{}\n".format(self.zmat[k].sum()))
self.calc_theta()
def calc_loglikelihood(self):
# self.calc_theta()
ll = 0.0
ls = np.arange(self.L, dtype=np.int32)
for p in range(self.P):
j_start, T = self.p2jT[p]
xs = self.mat[:,p]
ll += np.log(self.theta[ls,j_start+xs] + 1E-20).sum()
return ll
def calc_theta(self):
self.theta_tilde[...] = np.matmul(self.zmat.T, self.wmat) # (K x L)^T x (K x M) -> (L x M)
for p in range(self.P):
j_start, T = self.p2jT[p]
e_theta_tilde = np.exp(self.theta_tilde[:,j_start:j_start+T] - self.theta_tilde[:,j_start:j_start+T].max(axis=1).reshape(self.L, 1))
self.theta[:,j_start:j_start+T] = e_theta_tilde / e_theta_tilde.sum(axis=1).reshape(self.L, 1)
def init_tasks(self, a_repeat=1, sample_w=True):
self.tasks = []
for l, p in self.mv_list:
self.tasks.append((self.S_X_CAT, (l, p)))
for k in range(self.K):
if self.bias and k == 0:
continue
for a in range(a_repeat):
if not self.only_alphas:
if not(self.drop_hs) and not(self.is_h_fixed):
self.tasks.append((self.S_Z_H, k))
self.tasks.append((self.S_Z_A, k))
for l in range(self.L):
if self.bias:
self.tasks += map(lambda k: (self.S_Z, (l, k)), range(1, self.K))
else:
self.tasks += map(lambda k: (self.S_Z, (l, k)), range(self.K))
if sample_w:
# self.tasks += map(lambda p: (self.S_W_HMC, p), range(self.P))
self.tasks += map(lambda k: (self.S_W_HMC, k), range(self.K))
def sample(self, _iter=0, maxanneal=0, itemp=-1):
# inverse of temperature
if itemp > 0:
sys.stderr.write("\t\titemp\t{}\n".format(itemp))
elif _iter >= maxanneal:
itemp = 1.0
else:
itemp = 0.1 + 0.9 * _iter / maxanneal
sys.stderr.write("\t\titemp\t{}\n".format(itemp))
c_x_cat = [0, 0]
c_z = [0, 0]
c_zx = [0, 0] # changed, total
c_z_h = [0, 0]
c_z_a = [0, 0]
c_w_hmc = [0, 0]
random.shuffle(self.tasks)
for t_type, t_val in self.tasks:
if t_type == self.S_X_CAT:
l, p = t_val
changed = self.sample_x_cat(l, p)
c_x_cat[changed] += 1
elif t_type == self.S_Z:
l, k = t_val
# changed = self.sample_z(l, k, itemp=itemp)
changed, c, t = self.sample_zx(l, k, itemp=itemp)
c_z[changed] += 1
c_zx[0] += c
c_zx[1] += t
elif t_type == self.S_W_HMC:
changed = self.sample_w_hmc(t_val)
c_w_hmc[changed] += 1
elif t_type == self.S_Z_H:
assert(not self.is_h_fixed)
changed = self.sample_autologistic(t_type, t_val)
c_z_h[changed] += 1
elif t_type == self.S_Z_A:
changed = self.sample_autologistic(t_type, t_val)
c_z_a[changed] += 1
else:
raise NotImplementedError
self.calc_theta() # fix numerical errors
if sum(c_x_cat) > 0:
sys.stderr.write("\tx_cat\t{}\n".format(float(c_x_cat[1]) / sum(c_x_cat)))
sys.stderr.write("\tz\t{}\n".format(float(c_z[1]) / sum(c_z)))
if c_zx[1] > 0:
sys.stderr.write("\tzx\t{}\n".format(float(c_zx[0]) / c_zx[1]))
if sum(c_w_hmc) > 0:
sys.stderr.write("\tw_hmc\t{}\n".format(float(c_w_hmc[1]) / sum(c_w_hmc)))
if not self.only_alphas:
if sum(c_z_h) > 0:
sys.stderr.write("\tz_h\t{}\n".format(float(c_z_h[1]) / sum(c_z_h)))
if sum(c_z_a) > 0:
sys.stderr.write("\tz_a\t{}\n".format(float(c_z_a[1]) / sum(c_z_a)))
if not self.only_alphas:
sys.stderr.write("\th\tavg\t{}\tmax\t{}\n".format(self.hks.mean(), self.hks.max()))
sys.stderr.write("\ta\tavg\t{}\tvar\t{}\n".format(self.alphas.mean(), self.alphas.var()))
sys.stderr.write("\tw\tavg\t{}\tmin\t{}\tmax\t{}\tvar\t{}\n".format(self.wmat.mean(), self.wmat.min(), self.wmat.max(), self.wmat.var()))
def sample_x_cat(self, l, p):
assert(self.mvs is not None and self.mvs[l,p])
j_start, T = self.p2jT[p]
x_old = self.mat[l,p]
self.mat[l,p] = np.random.choice(T, p=self.theta[l,j_start:j_start+T])
return False if x_old == self.mat[l,p] else True
def sample_z(self, l, k, itemp=1.0):
assert(not self.bias or not k == 0)
z_old = self.zmat[k,l]
logprob0, logprob1 = 0.0, 0.0
if not self.only_alphas:
idxs, weights = self.hnet.js[l]
vals = self.zmat[k,idxs]
logprob0 += self.hks[k] * ((vals == 0) * weights).sum()
logprob1 += self.hks[k] * ((vals == 1) * weights).sum()
logprob1 += self.alphas[k]
theta_new = np.empty_like(self.theta[l,:])
theta_tilde_new = np.copy(self.theta_tilde[l,:])
if z_old == False:
# proposal: 1
theta_tilde_new += self.wmat[k,:]
logprob_old, logprob_new = logprob0, logprob1
else:
# proposal: 0
theta_tilde_new -= self.wmat[k,:]
logprob_old, logprob_new = logprob1, logprob0
for p in range(self.P):
j_start, T = self.p2jT[p]
x = self.mat[l,p]
logprob_old += np.log(self.theta[l,j_start+x] + 1E-20)
e_theta_tilde = np.exp(theta_tilde_new[j_start:j_start+T] - theta_tilde_new[j_start:j_start+T].max())
theta_new[j_start:j_start+T] = e_theta_tilde / e_theta_tilde.sum()
logprob_new += np.log(theta_new[j_start+x] + 1E-20)
if itemp != 1.0:
logprob_old *= itemp
logprob_new *= itemp
accepted = np.bool_(rand_partition_log((logprob_old, logprob_new)))
if accepted:
if z_old == False:
# 0 -> 1
self.zmat[k,l] = True
else:
# 1 -> 0
self.zmat[k,l] = False
self.theta_tilde[l,:] = theta_tilde_new
self.theta[l,:] = theta_new
return True
else:
return False
def sample_zx(self, l, k, itemp=1.0):
assert(not self.bias or not k == 0)
z_old = self.zmat[k,l]
logprob0, logprob1 = 0.0, 0.0
if not self.only_alphas:
idxs, weights = self.hnet.js[l]
vals = self.zmat[k,idxs]
logprob0 += self.hks[k] * ((vals == 0) * weights).sum()
logprob1 += self.hks[k] * ((vals == 1) * weights).sum()
logprob1 += self.alphas[k]
theta_new = np.empty_like(self.theta[l,:])
theta_tilde_new = np.copy(self.theta_tilde[l,:])
if z_old == False:
# proposal: 1
theta_tilde_new += self.wmat[k,:]
logprob_old, logprob_new = logprob0, logprob1
else:
# proposal: 0
theta_tilde_new -= self.wmat[k,:]
logprob_old, logprob_new = logprob1, logprob0
xs_new = self.mat[l,:].copy()
for p, (x, is_missing) in enumerate(zip(self.mat[l,:], self.mvs[l,:])):
j_start, T = self.p2jT[p]
e_theta_tilde = np.exp(theta_tilde_new[j_start:j_start+T] - theta_tilde_new[j_start:j_start+T].max())
theta_new[j_start:j_start+T] = e_theta_tilde / e_theta_tilde.sum()
if is_missing:
xs_new[p] = np.random.choice(T, p=theta_new[j_start:j_start+T])
else:
logprob_old += np.log(self.theta[l,j_start+x] + 1E-20)
logprob_new += np.log(theta_new[j_start+xs_new[p]] + 1E-20)
if itemp != 1.0:
logprob_old *= itemp
logprob_new *= itemp
accepted = np.bool_(rand_partition_log((logprob_old, logprob_new)))
if accepted:
if z_old == False:
# 0 -> 1
self.zmat[k,l] = True
else:
# 1 -> 0
self.zmat[k,l] = False
self.theta_tilde[l,:] = theta_tilde_new
self.theta[l,:] = theta_new
changed = (self.mat[l,:] != xs_new).sum()
self.mat[l,:] = xs_new
return True, changed, self.mvs[l,:].sum()
else:
return False, 0, self.mvs[l,:].sum()
def sample_autologistic(self, t_type, k):
logr = 0.0
if t_type == self.S_Z_A:
oldval = self.alphas[k]
pivot = min((self.zmat[k].sum() + 0.01) / self.L, 0.99)
pivot = np.log(pivot / (1.0 - pivot))
oldmean = (oldval + pivot) / 2.0
oldscale = max(abs(oldval - pivot), 0.001)
newval = np.random.normal(loc=oldmean, scale=oldscale)
newmean = (newval + pivot) / 2.0
newscale = max(abs(newval - pivot), 0.001)
# q(theta|theta', x) / q(theta'|theta, x)
logr += -((oldval - newmean) ** 2) / (2.0 * newscale * newscale) - np.log(newscale) \
+ ((newval - oldmean) ** 2) / (2.0 * oldscale * oldscale) + np.log(oldscale)
# P(theta') / P(theta)
logr += (oldval * oldval - newval * newval) / (2.0 * self.norm_sigma * self.norm_sigma)
# skip: q(theta|theta', x) / q(theta'|theta, x) for symmetric proposal
h, a = self.hks[k], newval
else:
assert(not self.only_alphas)
assert(not (t_type == self.S_Z_H and self.drop_hs))
oldval = self.hks[k]
P_SIGMA = 0.5
rate = np.random.lognormal(mean=0.0, sigma=P_SIGMA)
irate = 1.0 / rate
newval = rate * oldval
lograte = np.log(rate)
logirate = np.log(irate)
# P(theta') / P(theta)
logr += (self.gamma_shape - 1.0) * (np.log(newval) - np.log(oldval)) \
- (newval - oldval) / self.gamma_scale
# q(theta|theta', x) / q(theta'|theta, x)
logr += (lograte * lograte - logirate * logirate) / (2.0 * P_SIGMA * P_SIGMA) + lograte - logirate
h, a = newval, self.alphas[k]
net = self.hnet
zvect = self.zmat[k].copy()
llist = np.arange(self.L)
np.random.shuffle(llist)
for l in llist:
logprob0, logprob1 = (0.0, 0.0)
if not self.only_alphas:
idxs, weights = self.hnet.js[l]
vals = zvect[idxs]
logprob0 += h * ((vals == 0) * weights).sum()
logprob1 += h * ((vals == 1) * weights).sum()
logprob1 += a
zvect[l] = rand_partition_log([logprob0, logprob1])
if t_type == self.S_Z_A:
logr += (oldval - newval) * (zvect.sum() - self.zmat[k].sum())
if logr >= 0 or np.log(np.random.rand()) < logr:
# accept
self.alphas[k] = newval
return True
else:
return False
else:
oldsum = self._neighbor_sum(self.zmat[k])
newsum = self._neighbor_sum(zvect)
logr += (oldval - newval) * (newsum - oldsum)
if logr >= 0 or np.log(np.random.rand()) < logr:
# accept
self.hks[k] = newval
return True
else:
return False
def _neighbor_sum(self, vec):
s = 0.0
for l in range(self.L):
idxs, weights = self.hnet.js[l]
s += ((vec[idxs] == vec[l]) * weights).sum()
return s / 2
def sample_w_hmc(self, k):
def U(logMvect):
logMvect = np.minimum(logMvect, 10.0) # avoid overflow
Mvect = np.exp(logMvect)
ll = -((self.sigma - 1.0) * logMvect - Mvect).sum()
for l in range(self.L):
if self.zmat[k,l] == False:
continue
theta_tilde = self.theta_tilde[l] - self.wmat[k] + Mvect
for p in range(self.P):
j_start, T = self.p2jT[p]
x = self.mat[l,p]
theta_tilde2 = theta_tilde[j_start:j_start+T] - theta_tilde[j_start:j_start+T].max()
ll -= theta_tilde2[x] - np.log(np.exp(theta_tilde2).sum())
return ll
def gradU(logMvect):
if (logMvect > 300.0).sum() > 0:
sys.stderr.write("{}: overflow\n".format(k))
logMvect = np.minimum(logMvect, 10.0) # avoid overflow
Mvect = np.exp(logMvect)
grad = -((self.sigma - 1.0) / Mvect - 1.0)
for l in range(self.L):
if self.zmat[k,l] == False:
continue
theta_tilde = self.theta_tilde[l] - self.wmat[k] + Mvect
for p in range(self.P):
j_start, T = self.p2jT[p]
x = self.mat[l,p]
e_theta_tilde = np.exp(theta_tilde[j_start:j_start+T] - theta_tilde[j_start:j_start+T].max())
theta = e_theta_tilde / e_theta_tilde.sum()
grad[j_start:j_start+T] += theta
grad[j_start + x] -= 1
grad *= Mvect
return grad
accepted, logMvect = hmc(U, gradU, self.hmc_epsilon, self.hmc_l, np.log(self.wmat[k]))
if accepted:
# update theta_tilde
logMvect = np.minimum(logMvect, 10.0) # avoid overflow
Mvect = np.exp(logMvect)
for l in range(self.L):
if self.zmat[k,l] == False:
continue
self.theta_tilde[l] += Mvect - self.wmat[k]
for p in range(self.P):
j_start, T = self.p2jT[p]
e_theta_tilde = np.exp(self.theta_tilde[l,j_start:j_start+T] - self.theta_tilde[l,j_start:j_start+T].max())
self.theta[l,j_start:j_start+T] = e_theta_tilde / e_theta_tilde.sum()
# assert(all(self.theta_tilde[i] > 0))
self.wmat[k] = np.minimum(Mvect, 100.0)
# self.hmc_epsilon = min(self.hmc_epsilon * 1.1, 1.0)
return True
else:
self.wmat[k] = np.minimum(self.wmat[k], 100.0)
# self.hmc_epsilon = max(self.hmc_epsilon * 0.5, 0.001)
return False
def create_mat(langs, flist):
P = len(flist)
mat = np.zeros((len(langs), P), dtype=np.int32)
mvs = np.zeros((len(langs), P), dtype=np.bool_)
for l, lang in enumerate(langs):
for p, v in enumerate(lang["catvect"]):
if v < 0:
mvs[l,p] = True
v = np.random.randint(0, flist[p]["size"])
mat[l,p] = v
return mat, mvs
def main():
parser = ArgumentParser()
parser.add_argument("-s", "--seed", metavar="INT", type=int, default=None,
help="random seed")
parser.add_argument("--bias", action="store_true", default=False,
help="bias term in Z")
parser.add_argument("--only_alphas", action="store_true", default=False,
help="autologistic: ignore v and h")
parser.add_argument("--drop_hs", action="store_true", default=False,
help="autologistic: ignore h")
parser.add_argument("-i", "--iter", dest="_iter", metavar="INT", type=int, default=1000,
help="# of iterations")
parser.add_argument("--save_interval", metavar="INT", type=int, default=-1,
help="save interval")
parser.add_argument("--K", metavar="INT", type=int, default=100,
help="K")
parser.add_argument('--norm_sigma', type=float, default=5.0,
help='standard deviation of Gaussian prior for u')
parser.add_argument('--gamma_shape', type=float, default=1.0,
help='shape of Gamma prior for v and h')
parser.add_argument('--gamma_scale', type=float, default=0.001,
help='scale of Gamma prior for v and h')
parser.add_argument("--hmc_l", metavar="INT", type=int, default=10)
parser.add_argument('--hmc_epsilon', type=float, default=0.05,
help='HMC epsilon')
parser.add_argument("--maxanneal", metavar="INT", type=int, default=0)
parser.add_argument("--output", dest="output", metavar="FILE", default=None,
help="save the model to the specified path")
parser.add_argument("--resume", metavar="FILE", default=None,
help="resume training from model dump")
parser.add_argument("--resume_if", action="store_true", default=False,
help="resume training if the output exists")
parser.add_argument('--bins', type=str, default=None)
parser.add_argument('--bins_iter', type=int, default=100)
parser.add_argument("langs", metavar="LANG", default=None)
parser.add_argument("flist", metavar="FLIST", default=None)
args = parser.parse_args()
sys.stderr.write("args\t{}\n".format(args))
if args.seed is not None:
np.random.seed(args.seed)
random.seed(args.seed)
flist = load_json_file(args.flist)
offset = 0
if args.resume_if:
if os.path.isfile(args.output + ".current"):
args.resume = args.output + ".current"
elif os.path.isfile(args.output + ".best"):
args.resume = args.output + ".best"
if args.resume:
sys.stderr.write("loading model from {}\n".format(args.resume))
spec = pickle.load(open(args.resume, "rb"))
mda = spec["model"]
sys.stderr.write("iter {}: {}\n".format(spec["iter"] + 1, spec["ll"]))
offset = spec["iter"] + 1
else:
langs = list(load_json_stream(open(args.langs)))
mat, mvs = create_mat(langs, flist)
sys.stderr.write("building hnet\n")
hnet = WeightedNeighborGraph(langs)
mda = MatrixDecompositionAutologistic(mat, flist,
hnet=hnet,
K=args.K, mvs=mvs,
bias=args.bias,
only_alphas=args.only_alphas,
drop_hs=args.drop_hs,
norm_sigma=args.norm_sigma,
# const_h = 0.03253780242472478,
gamma_shape=args.gamma_shape,
gamma_scale=args.gamma_scale,
hmc_l=args.hmc_l,
hmc_epsilon=args.hmc_epsilon)
mda.init_with_clusters()
sys.stderr.write("iter 0: {}\n".format(mda.calc_loglikelihood()))
ll_max = -np.inf
for _iter in range(offset, args._iter):
mda.sample(_iter=_iter, maxanneal=args.maxanneal)
ll = mda.calc_loglikelihood()
sys.stderr.write("iter {}: {}\n".format(_iter + 1, ll))
sys.stderr.flush()
if args.save_interval >= 0 and (_iter + 1) % args.save_interval == 0:
with open(args.output + ".{}".format(_iter), "wb") as f:
obj = { "model": mda, "iter": _iter, "ll": ll }
if args.output is not None:
with open(args.output + ".current", "wb") as f:
obj = { "model": mda, "iter": _iter, "ll": ll }
pickle.dump(obj, f)
if ll > ll_max:
ll_max = ll
shutil.copyfile(args.output + ".current", args.output + ".best")
if args.output is not None:
with open(args.output + ".final", "wb") as f:
obj = { "model": mda, "iter": _iter, "ll": ll }
pickle.dump(obj, f)
if args.bins is not None:
zmats = [np.copy(mda.zmat)]
wmats = [np.copy(mda.wmat)]
hkss = [np.copy(mda.hks)]
for i in range(args.bins_iter):
mda.sample()
zmats.append(np.copy(mda.zmat))
wmats.append(np.copy(mda.wmat))
hkss.append(np.copy(mda.hks))
avg_zmat = np.sum(zmats, axis=0) / float(len(zmats))
avg_wmat = np.sum(wmats, axis=0) / float(len(wmats))
avg_hks = np.sum(hkss, axis=0) / float(len(hkss))
with open(args.bins, 'w') as f:
f.write("{}\n".format(json.dumps({
"avg_zmat": avg_zmat.tolist(),
"avg_wmat": avg_wmat.tolist(),
"avg_hks": avg_hks.tolist(),
})))
if __name__ == "__main__":
main()