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utils.py
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utils.py
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import numpy as np
import theano as th
from theano import tensor as T
from theano.tensor import nlinalg, slinalg
from fastlin.myCholesky import myCholesky
def t_repeat(x, num_repeats, axis):
'''Repeats x along an axis num_repeats times. Axis has to be 0 or 1, x has to be a matrix.'''
if num_repeats == 1:
return x
else:
if axis == 0:
return T.alloc(x.dimshuffle(1, 0, 'x'), x.shape[1], x.shape[0], num_repeats)\
.reshape((x.shape[1], num_repeats*x.shape[0]))\
.dimshuffle(1, 0)
elif axis == 1:
return T.alloc(x.dimshuffle(0, 'x', 1), x.shape[0], num_repeats, x.shape[1]).reshape((x.shape[0], num_repeats*x.shape[1]))
def srng(seed=123):
return MRG_RandomStreams(seed=seed)
def invLogDet( C ):
# Return inv(A) and log det A where A = C . C^T
iC = nlinalg.matrix_inverse(C)
iC.name = 'i' + C.name
iA = T.dot(iC.T, iC)
iA.name = 'i' + C.name[1:]
logDetA = 2.0*T.sum(T.log(T.abs_(T.diag(C))))
logDetA.name = 'logDet' + C.name[1:]
return(iA, logDetA)
def jitterChol(A, dim, jitter):
A_jitter = A + jitter * T.eye(dim)
cA = myCholesky()(A_jitter)
cA.name = 'c' + A.name
return cA
def cholInvLogDet(A, dim, jitter, fast=False):
A_jitter = A + jitter * T.eye(dim)
cA = myCholesky()(A_jitter)
cA.name = 'c' + A.name
if fast:
(iA,logDetA) = invLogDet(cA)
else:
iA = nlinalg.matrix_inverse(A_jitter)
#logDetA = T.log( nlinalg.Det()(A_jitter) )
logDetA = 2.0*T.sum(T.log(T.abs_(T.diag(cA))))
iA.name = 'i' + A.name
logDetA.name = 'logDet' + A.name
return(cA, iA, logDetA)
def diagCholInvLogDet_fromLogDiag(logdiag, name):
diag = T.diag(T.exp(logdiag.flatten()))
inv = T.diag(T.exp(-logdiag.flatten()))
chol = T.diag(T.exp(0.5 * logdiag.flatten()))
logDet = T.sum(logdiag) # scalar
diag.name = name
chol.name = 'c' + name
inv.name = 'i' + name
logDet.name = 'logDet' + name
return(diag,chol,inv,logDet)
def diagCholInvLogDet_fromDiag(diag_vec, name):
diag_mat = T.diag(diag_vec.flatten())
inv = T.diag(1.0/diag_vec.flatten())
chol = T.diag(T.sqrt(diag_vec.flatten()))
logDet = T.sum(T.log(diag_vec.flatten())) # scalar
diag_mat.name = name
chol.name = 'c' + name
inv.name = 'i' + name
logDet.name = 'logDet' + name
return(diag_mat,chol,inv,logDet)
def log_mean_exp_stable(x, axis):
m = T.max(x, axis=axis, keepdims=True)
return m + T.log(T.mean(T.exp(x - m), axis=axis, keepdims=True))
def np_log_mean_exp_stable(x, axis=0):
m = np.max(x, axis=axis, keepdims=True)
return m + np.log(np.mean(np.exp(x - m), axis=axis, keepdims=True))
def sharedZeroMatrix(M, N, name, dtype=th.config.floatX, broadcastable=[]):
if len(broadcastable) == 0:
return th.shared(np.asarray(np.zeros((M, N)), dtype), name=name)
else:
return th.shared(np.asarray(np.zeros((M, N)), dtype), name=name, broadcastable=broadcastable)
def sharedZeroVector(M, name, dtype=th.config.floatX, broadcastable=[]):
return sharedZeroMatrix(M, 1, name, dtype, broadcastable)
def sharedZeroArray(M, name, dtype=th.config.floatX):
return th.shared(np.zeros((M,)).astype(dtype), name=name)
def shared_zeros_like(shared_var):
return th.shared(np.zeros(shared_var.get_value(borrow=True).shape).astype(shared_var.dtype),
broadcastable=shared_var.broadcastable)
def shared_ones_like(shared_var):
return th.shared(np.ones(shared_var.get_value(borrow=True).shape).astype(shared_var.dtype),
broadcastable=shared_var.broadcastable)
def getname(T):
if type(T) == int or type(T) == float:
name = str(T)
elif hasattr(T, 'name') and not T.name == None:
name = T.name
else:
name = '?'
return name
def inName(A, B, op, name=None):
if name == None:
Aname = getname(A)
Bname = getname(B)
Cname = '(' + Aname + op + Bname + ')'
else:
Cname = name
return Cname
def dot(A, B, name=None):
C = T.dot(A,B)
C.name = inName(A, B, ' . ', name)
return C
def minus(A, B, name=None):
C = A - B
C.name = inName(A, B, ' - ', name)
return C
def plus(A, B, name=None):
C = A + B
C.name = inName(A, B, ' + ', name)
return C
def mul(A, B, name=None):
C = A * B
C.name = inName(A, B, ' * ', name)
return C
def div(A, B, name=None):
C = A / B
C.name = inName(A, B, ' / ', name)
return C
def softplus(A, name=None):
return namedFunction(A, T.nnet.softplus, 'softplus', name)
def sigmoid(A, name=None):
return namedFunction(A, T.nnet.sigmoid, 'sigmoid', name)
def trace(A, name=None):
return namedFunction(A, nlinalg.trace, 'trace', name)
def tanh(A, name=None):
return namedFunction(A, T.tanh, 'tanh', name)
def namedFunction(A, func, funcname, name):
B = func(A)
if name == None:
Aname = getname(A)
B.name = funcname + '(' + Aname + ')'
else:
B.name = name
return B