def _update_indicator(self,K,L):
""" update the indicator """
_update = {'term': self.n_terms*SP.ones((K,L)).T.ravel(),
'row': SP.kron(SP.arange(K)[:,SP.newaxis],SP.ones((1,L))).T.ravel(),
'col': SP.kron(SP.ones((K,1)),SP.arange(L)[SP.newaxis,:]).T.ravel()}
for key in _update.keys():
self.indicator[key] = SP.concatenate([self.indicator[key],_update[key]])
def _LMLgrad_s(self,hyperparams,debugging=False):
"""
evaluate gradients with respect to covariance matrix Sigma
"""
try:
KV = self.get_covariances(hyperparams, debugging=debugging)
except LA.LinAlgError:
LG.error('linalg exception in _LMLgrad_x_sigma')
return {'X_s':SP.zeros(hyperparams['X_s'].shape)}
Si = 1./KV['Stilde_os']
SS = SP.dot(unravel(Si,self.n,self.t).T,KV['Stilde_o'])
USU = SP.dot(KV['USi_c'],KV['Utilde_s'])
Yhat = unravel(Si * ravel(KV['UYtildeU_os']),self.n,self.t)
RV = {}
if 'X_s' in hyperparams:
USUY = SP.dot(USU,Yhat.T)
USUYSYUSU = SP.dot(USUY,(KV['Stilde_o']*USUY).T)
LMLgrad = SP.zeros((self.t,self.covar_s.n_dimensions))
LMLgrad_det = SP.zeros((self.t,self.covar_s.n_dimensions))
LMLgrad_quad = SP.zeros((self.t,self.covar_s.n_dimensions))
for d in xrange(self.covar_s.n_dimensions):
Kd_grad = self.covar_s.Kgrad_x(hyperparams['covar_s'],d)
UsU = SP.dot(Kd_grad.T,USU)*USU
LMLgrad_det[:,d] = SP.dot(UsU,SS.T)
# calculate gradient of squared form
LMLgrad_quad[:,d] = -(USUYSYUSU*Kd_grad).sum(0)
LMLgrad = LMLgrad_det + LMLgrad_quad
RV['X_s'] = LMLgrad
if debugging:
_LMLgrad = SP.zeros((self.t,self.covar_s.n_dimensions))
for t in xrange(self.t):
for d in xrange(self.covar_s.n_dimensions):
Kgrad_x = self.covar_s.Kgrad_x(hyperparams['covar_s'],d,t)
Kgrad_x = SP.kron(Kgrad_x,KV['K_o'])
_LMLgrad[t,d] = 0.5*(KV['W']*Kgrad_x).sum()
assert SP.allclose(LMLgrad,_LMLgrad,rtol=1E-3,atol=1E-2), 'ouch, something is wrong: %.2f'%LA.norm(LMLgrad-_LMLgrad)
if 'covar_s' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_s']))
for i in range(len(theta)):
Kgrad_s = self.covar_s.Kgrad_theta(hyperparams['covar_s'],i)
UdKU = SP.dot(USU.T, SP.dot(Kgrad_s, USU))
SYUdKU = SP.dot(UdKU,KV['Stilde_o'] * Yhat.T)
LMLgrad_det = SP.sum(Si*SP.kron(SP.diag(UdKU),KV['Stilde_o']))
LMLgrad_quad = -(Yhat.T*SYUdKU).sum()
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
if debugging:
Kd = SP.kron(Kgrad_s, KV['K_o'])
_LMLgrad = 0.5 * (KV['W']*Kd).sum()
assert SP.allclose(LMLgrad,_LMLgrad,rtol=1E-3,atol=1E-2), 'ouch, something is wrong: %.2f'%LA.norm(LMLgrad-_LMLgrad)
RV['covar_s'] = theta
return RV
def LMLdebug(self):
"""
LML function for debug
"""
assert self.N*self.P<5000, 'gp2kronSum:: N*P>=5000'
y = SP.reshape(self.Y,(self.N*self.P), order='F')
V = SP.kron(SP.eye(self.P),self.F)
XX = SP.dot(self.Xr,self.Xr.T)
K = SP.kron(self.Cr.K(),XX)
K += SP.kron(self.Cn.K()+self.offset*SP.eye(self.P),SP.eye(self.N))
# inverse of K
cholK = LA.cholesky(K)
Ki = LA.cho_solve((cholK,False),SP.eye(self.N*self.P))
# Areml and inverse
Areml = SP.dot(V.T,SP.dot(Ki,V))
cholAreml = LA.cholesky(Areml)
Areml_i = LA.cho_solve((cholAreml,False),SP.eye(self.K*self.P))
# effect sizes and z
b = SP.dot(Areml_i,SP.dot(V.T,SP.dot(Ki,y)))
z = y-SP.dot(V,b)
Kiz = SP.dot(Ki,z)
# lml
lml = y.shape[0]*SP.log(2*SP.pi)
lml += 2*SP.log(SP.diag(cholK)).sum()
lml += 2*SP.log(SP.diag(cholAreml)).sum()
lml += SP.dot(z,Kiz)
lml *= 0.5
return lml
def _LMLgrad_covar_debug(self,covar):
assert self.N*self.P<2000, 'gp2kronSum:: N*P>=2000'
y = SP.reshape(self.Y,(self.N*self.P), order='F')
K = SP.kron(self.Cg.K(),self.XX)
K += SP.kron(self.Cn.K()+self.offset*SP.eye(self.P),SP.eye(self.N))
cholK = LA.cholesky(K).T
Ki = LA.cho_solve((cholK,True),SP.eye(y.shape[0]))
Kiy = LA.cho_solve((cholK,True),y)
if covar=='Cr': n_params = self.Cr.getNumberParams()
elif covar=='Cg': n_params = self.Cg.getNumberParams()
elif covar=='Cn': n_params = self.Cn.getNumberParams()
RV = SP.zeros(n_params)
for i in range(n_params):
#0. calc grad_i
if covar=='Cg':
C = self.Cg.Kgrad_param(i)
Kgrad = SP.kron(C,self.XX)
elif covar=='Cn':
C = self.Cn.Kgrad_param(i)
Kgrad = SP.kron(C,SP.eye(self.N))
#1. der of log det
RV[i] = 0.5*(Ki*Kgrad).sum()
#2. der of quad form
RV[i] -= 0.5*(Kiy*SP.dot(Kgrad,Kiy)).sum()
return RV
def AlphaBetaCoeffs_old(n, a, b):
" Construct the alpha and beta coefficient matrices. "
Z = sp.matrix([[1,0],[0,-1]])
I = sp.identity(2)
alpha = sp.zeros((2**n,2**n))
beta = sp.zeros((2**n,2**n))
m1 = []
m2 = []
for i in range(0,n):
for m in range(0,n-1): m1.append(I)
m1.insert(i, Z)
temp1 = m1[0]
m1.pop(0)
while (len(m1) != 0):
temp1 = sp.kron(temp1, m1[0])
m1.pop(0)
alpha += temp1*a[i]
for j in range(i+1, n):
for m in range(0, n-2): m2.append(I)
m2.insert(i, Z)
m2.insert(j, Z)
temp2 = m2[0]
m2.pop(0)
while (len(m2) != 0):
temp2 = sp.kron(temp2, m2[0])
m2.pop(0)
beta += (temp2)*b[i,j]
return [alpha, beta]
def sqrtm3(X):
M = sp.copy(X)
m, fb, fe = block_structure(M)
n = M.shape[0]
for i in range(0,m):
M[fb[i]:fe[i],fb[i]:fe[i]] = twobytworoot(M[fb[i]:fe[i],fb[i]:fe[i]])
#print M
for j in range(1,m):
for i in range(0,m-j):
#print M[fb[i]:fe[i],fb[JJ]:fe[JJ]]
JJ = i+j
Tnoto = M[fb[i]:fe[i],fb[JJ]:fe[JJ]] #dopo togliere il copy
#print "Tnot: "
#print Tnoto
for k in range(i+1,JJ):
Tnoto -= (M[fb[i]:fe[i],fb[k]:fe[k]]).dot(M[fb[k]:fe[k],fb[JJ]:fe[JJ]])
#print M[fb[i]:fe[i],fb[k]:fe[k]]
#print M[fb[k]:fe[k],fb[JJ]:fe[JJ]]
if((M[fb[i]:fe[i],fb[JJ]:fe[JJ]]).shape==(1,1)):
#print "forma 1"
#print M[fb[i]:fe[i],fb[JJ]:fe[JJ]] # Uij
#print M[fb[i]:fe[i],fb[i]:fe[i]] # Uii
#print M[fb[JJ]:fe[JJ],fb[JJ]:fe[JJ]] # Ujj
M[fb[i]:fe[i],fb[JJ]:fe[JJ]] = Tnoto/(M[fb[i]:fe[i],fb[i]:fe[i]] + M[fb[JJ]:fe[JJ],fb[JJ]:fe[JJ]])
else:
Uii = M[fb[i]:fe[i],fb[i]:fe[i]]
Ujj = M[fb[JJ]:fe[JJ],fb[JJ]:fe[JJ]]
shapeUii = Uii.shape[0]
shapeUjj = Ujj.shape[0]
"""
print "------------"
print Tnoto
print Tnoto.shape
print sp.kron(sp.eye(shapeUjj),Uii)
print sp.kron(Ujj.T,sp.eye(shapeUii))
print Tnoto
"""
#M[fb[i]:fe[i],fb[JJ]:fe[JJ]] = sp.linalg.solve_sylvester(Uii, Ujj, Tnoto)
"""
x, scale, info = dtrsyl(Uii, Ujj, Tnoto
if (scale==1.0):
= x
else:
M[fb[i]:fe[i],fb[JJ]:fe[JJ]] = x*scale
print "scale!=0"
"""
Tnoto = Tnoto.reshape((shapeUii*shapeUjj),1,order="F")
M[fb[i]:fe[i],fb[JJ]:fe[JJ]] = \
linalg.solve(sp.kron(sp.eye(shapeUjj),Uii) +
sp.kron(Ujj.T,sp.eye(shapeUii)),
Tnoto).reshape(shapeUii,shapeUjj,order="F")
return M
def diag_Ctilde_o_Sr(self, i):
if i < self.Cg.getNumberParams():
r = sp.kron(sp.diag(self.LcGradCgLc(i)), self.Sr())
else:
_i = i - self.Cg.getNumberParams()
r = sp.kron(sp.diag(self.LcGradCnLc(_i)), sp.ones(self.dim_r))
return r
def varMLE(self):
""" calculate inverse of fisher information """
self._update_cache()
Sr = {}
Sr['Cg'] = self.cache['Srstar']
Sr['Cn'] = SP.ones(self.N)
n_params = self.Cg.getNumberParams()+self.Cn.getNumberParams()
fisher = SP.zeros((n_params,n_params))
header = SP.zeros((n_params,n_params),dtype='|S10')
C1 = SP.zeros((self.P,self.P))
C2 = SP.zeros((self.P,self.P))
idx1 = 0
for key1 in ['Cg','Cn']:
for key1_p1 in range(self.P):
for key1_p2 in range(key1_p1,self.P):
C1[key1_p1,key1_p2] = C1[key1_p2,key1_p1] = 1
LCL1 = SP.dot(self.cache['Lc'],SP.dot(C1,self.cache['Lc'].T))
CSr1 = SP.kron(Sr[key1][:,SP.newaxis,SP.newaxis],LCL1[SP.newaxis,:])
DCSr1 = self.cache['D'][:,:,SP.newaxis]*CSr1
idx2 = 0
for key2 in ['Cg','Cn']:
for key2_p1 in range(self.P):
for key2_p2 in range(key2_p1,self.P):
C2[key2_p1,key2_p2] = C2[key2_p2,key2_p1] = 1
LCL2 = SP.dot(self.cache['Lc'],SP.dot(C2,self.cache['Lc'].T))
CSr2 = SP.kron(Sr[key2][:,SP.newaxis,SP.newaxis],LCL2[SP.newaxis,:])
DCSr2 = self.cache['D'][:,:,SP.newaxis]*CSr2
fisher[idx1,idx2] = 0.5*(DCSr1*DCSr2).sum()
header[idx1,idx2] = '%s%d%d_%s%d%d'%(key1,key1_p1,key1_p1,key2,key2_p1,key2_p2)
C2[key2_p1,key2_p2] = C2[key2_p2,key2_p1] = 0
idx2+=1
C1[key1_p1,key1_p2] = C1[key1_p2,key1_p1] = 0
idx1+=1
RV = LA.inv(fisher)
return RV,header
def K(self):
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
rv = sp.kron(self.Cg.K(), self.R) + sp.kron(self.Cn.K(), sp.eye(self.dim_r))
return rv
def _LMLgrad_covar(self,hyperparams,debugging=False):
"""
evaluates the gradient of the log marginal likelihood with respect to the
hyperparameters of the covariance function
"""
try:
KV = self.get_covariances(hyperparams,debugging=debugging)
except LA.LinAlgError:
LG.error('linalg exception in _LMLgrad_covar')
return {'covar_r':SP.zeros(len(hyperparams['covar_r'])),'covar_c':SP.zeros(len(hyperparams['covar_c'])),'covar_r':SP.zeros(len(hyperparams['covar_r']))}
except ValueError:
LG.error('value error in _LMLgrad_covar')
return {'covar_r':SP.zeros(len(hyperparams['covar_r'])),'covar_c':SP.zeros(len(hyperparams['covar_c'])),'covar_r':SP.zeros(len(hyperparams['covar_r']))}
RV = {}
Si = unravel(1./KV['S'],self.n,self.t)
if 'covar_r' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_r']))
for i in range(len(theta)):
Kgrad_r = self.covar_r.Kgrad_theta(hyperparams['covar_r'],i)
d=(KV['U_r']*SP.dot(Kgrad_r,KV['U_r'])).sum(0)
LMLgrad_det = SP.dot(d,SP.dot(Si,KV['S_c']))
UdKU = SP.dot(KV['U_r'].T,SP.dot(Kgrad_r,KV['U_r']))
SYUdKU = SP.dot(UdKU,(KV['Ytilde']*SP.tile(KV['S_c'][SP.newaxis,:],(self.n,1))))
LMLgrad_quad = - (KV['Ytilde']*SYUdKU).sum()
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
if debugging:
Kd = SP.kron(KV['K_c'], Kgrad_r)
_LMLgrad = 0.5 * (KV['W']*Kd).sum()
assert SP.allclose(LMLgrad,_LMLgrad), 'ouch, gradient is wrong for covar_r'
RV['covar_r'] = theta
if 'covar_c' in hyperparams:
theta = SP.zeros(len(hyperparams['covar_c']))
for i in range(len(theta)):
Kgrad_c = self.covar_c.Kgrad_theta(hyperparams['covar_c'],i)
d=(KV['U_c']*SP.dot(Kgrad_c,KV['U_c'])).sum(0)
LMLgrad_det = SP.dot(KV['S_r'],SP.dot(Si,d))
UdKU = SP.dot(KV['U_c'].T,SP.dot(Kgrad_c,KV['U_c']))
SYUdKU = SP.dot((KV['Ytilde']*SP.tile(KV['S_r'][:,SP.newaxis],(1,self.t))),UdKU.T)
LMLgrad_quad = -SP.sum(KV['Ytilde']*SYUdKU)
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
theta[i] = LMLgrad
if debugging:
Kd = SP.kron(Kgrad_c, KV['K_r'])
_LMLgrad = 0.5 * (KV['W']*Kd).sum()
assert SP.allclose(LMLgrad,_LMLgrad), 'ouch, gradient is wrong for covar_c'
RV['covar_c'] = theta
return RV
def get_linds(N, eps):
#Lindblad operators must have same range as Hamiltonian terms. In this case they are nearest-neighbour.
Sp1 = (sp.kron(Sp, sp.eye(2))).reshape(2, 2, 2, 2)
Sm2 = (sp.kron(sp.eye(2), Sm)).reshape(2, 2, 2, 2)
L1 = (1, sp.sqrt(eps) * Sp1)
L2 = (N-1, sp.sqrt(eps) * Sm2)
return [L1, L2]
def _fit(self, type, vc=False):
#2. init
if type=='null':
self.gp[type].covar.Cg.setCovariance(0.5*self.covY)
self.gp[type].covar.Cn.setCovariance(0.5*self.covY)
elif type=='full':
Cg0_K = self.gp['null'].covar.Cg.K()
Cn0_K = self.gp['null'].covar.Cn.K()
self.gp[type].covar.Cr.setCovariance((Cn0_K+Cg0_K)/3.)
self.gp[type].covar.Cg.setCovariance(2.*Cg0_K/3.)
self.gp[type].covar.Cn.setCovariance(2.*Cn0_K/3.)
elif type=='block':
Crf_K = self.gp['full'].covar.Cr.K()
Cnf_K = self.gp['full'].covar.Cn.K()
self.gp[type].covar.Cr.scale = sp.mean(Crf_K)
self.gp[type].covar.Cn.setCovariance(Cnf_K)
elif type=='rank1':
Crf_K = self.gp['full'].covar.Cr.K()
Cnf_K = self.gp['full'].covar.Cn.K()
self.gp[type].covar.Cr.setCovariance(Crf_K)
self.gp[type].covar.Cn.setCovariance(Cnf_K)
else:
print('poppo')
self.gp[type].optimize(factr=self.factr, verbose=False)
RV = {'Cg': self.gp[type].covar.Cg.K(),
'Cn': self.gp[type].covar.Cn.K(),
'LML': sp.array([self.gp[type].LML()]),
'LMLgrad': sp.array([sp.mean((self.gp[type].LML_grad()['covar'])**2)])}
if type=='null': RV['Cr'] = sp.zeros(RV['Cg'].shape)
else: RV['Cr'] = self.gp[type].covar.Cr.K()
if vc:
# tr(P CoR) = tr(C)tr(R) - tr(Ones C) tr(Ones R) / float(NP)
# = tr(C)tr(R) - C.sum() * R.sum() / float(NP)
trRr = (self.Xr**2).sum()
var_r = sp.trace(RV['Cr'])*trRr / float(self.Y.size-1)
var_g = sp.trace(RV['Cg'])*self.trRg / float(self.Y.size-1)
var_n = sp.trace(RV['Cn'])*self.Y.shape[0]
var_n-= RV['Cn'].sum() / float(RV['Cn'].shape[0])
var_n/= float(self.Y.size-1)
RV['var'] = sp.array([var_r, var_g, var_n])
if 0 and self.Y.size<5000:
pdb.set_trace()
Kr = sp.kron(RV['Cr'], sp.dot(self.Xr, self.Xr.T))
Kn = sp.kron(RV['Cn'], sp.eye(self.Y.shape[0]))
_var_r = sp.trace(Kr-Kr.mean(0)) / float(self.Y.size-1)
_var_n = sp.trace(Kn-Kn.mean(0)) / float(self.Y.size-1)
_var = sp.array([_var_r, var_g, _var_n])
print(((_var-RV['var'])**2).mean())
if type=='full':
# calculate within region vcs
Cr_block = sp.mean(RV['Cr']) * sp.ones(RV['Cr'].shape)
Cr_rank1 = lowrank_approx(RV['Cr'], rank=1)
var_block = sp.trace(Cr_block)*trRr / float(self.Y.size-1)
var_rank1 = sp.trace(Cr_rank1)*trRr / float(self.Y.size-1)
RV['var_r'] = sp.array([var_block, var_rank1-var_block, var_r-var_rank1])
return RV
def test_inv(self):
C = self.C
L = sp.kron(C.Lc(), sp.eye(C.dim_r))
W = sp.kron(C.Wc(), C.Wr())
WdW = sp.dot(W.T, C.d()[:, sp.newaxis] * W)
I_WdW = sp.eye(C.dim_c * C.dim_r) - WdW
inv1 = sp.dot(L.T, sp.dot(I_WdW, L))
inv2 = C.inv()
np.testing.assert_array_almost_equal(inv1, inv2)
def distanz(x, y=None):
r"""
Calculate the distanz between two colon vectors
Parameters
----------
x : ndarray
First colon vector
y : ndarray
Second colon vector
Returns
-------
d : ndarray
Distance between x and y
Examples
--------
>>> import numpy as np
>>> from pygsp import utils
>>> x = np.random.rand(16)
>>> y = np.random.rand(16)
>>> distanz = utils.distanz(x, y)
"""
try:
x.shape[1]
except IndexError:
x = x.reshape(1, x.shape[0])
if y is None:
y = x
else:
try:
y.shape[1]
except IndexError:
y = y.reshape(1, y.shape[0])
rx, cx = x.shape
ry, cy = y.shape
# Size verification
if rx != ry:
raise("The sizes of x and y do not fit")
xx = (x*x).sum(axis=0)
yy = (y*y).sum(axis=0)
xy = np.dot(x.T, y)
d = abs(sp.kron(sp.ones((cy, 1)), xx).T +
sp.kron(sp.ones((cx, 1)), yy) - 2*xy)
return np.sqrt(d)
def diag_Ctilde_o_Sr(self, i):
np_r = self.Cr.getNumberParams()
np_g = self.Cg.getNumberParams()
if i < np_r:
r = sp.kron(sp.diag(self.LcGradCrLc(i)), self.diagWrWr())
elif i < (np_r + np_g):
_i = i - np_r
r = sp.kron(sp.diag(self.LcGradCgLc(_i)), self.Sr())
else:
_i = i - np_r - np_g
r = sp.kron(sp.diag(self.LcGradCnLc(_i)), sp.ones(self.dim_r))
return r
def get_full_op(op):
fop = sp.zeros((2**N, 2**N), dtype=sp.complex128)
for n in range(1, min(len(op), N + 1)):
if op[n] is None:
continue
n_sites = len(op[n].shape) / 2
opn = op[n].reshape(2**n_sites, 2**n_sites)
fop_n = sp.kron(sp.eye(2**(n - 1)), sp.kron(opn, sp.eye(2**(N - n - n_sites + 1))))
assert fop.shape == fop_n.shape
fop += fop_n
return fop
def IsingHamiltonian_old(n, h, J, g):
### Construct Hamiltonian ###
Z = sp.matrix([[1,0],[0,-1]])
X = sp.matrix([[0,1],[1,0]])
I = sp.identity(2)
alpha = sp.zeros((2**n,2**n))
beta = sp.zeros((2**n,2**n))
delta = sp.zeros((2**n,2**n))
matrices = []
# Calculate alpha
for i in range(0,n):
for m in range(0,n-1):
matrices.append(I)
matrices.insert(i, Z)
temp = matrices[0]
matrices.pop(0)
while (len(matrices) != 0):
temp = sp.kron(temp, matrices[0])
matrices.pop(0)
alpha = alpha + temp*h[i]
temp = 0
# Calculate beta
for i in range(0,n):
for j in range(0,n):
if (i != j):
for m in range(0,n-2):
matrices.append(I)
matrices.insert(i, Z)
matrices.insert(j, Z)
temp = matrices[0]
matrices.pop(0)
while (len(matrices) != 0):
temp = sp.kron(temp, matrices[0])
matrices.pop(0)
beta = beta + temp*J[i,j]
beta = beta + g*sp.identity(2**n)
temp = 0
# Calculate delta
for i in range(0,n) :
for m in range(0,n-1):
matrices.append(I)
matrices.insert(i, X)
temp = matrices[0]
matrices.pop(0)
while (len(matrices) != 0):
temp = sp.kron(temp, matrices[0])
matrices.pop(0)
delta += temp
return [alpha, beta, delta]
def GenerateLabels(n):
" Get proper labeling for output states. "
# Generate bitstrings
bitstring = []
for i in range(0, n + 1):
bitstring.append(kbits(n, i))
# Flatten
bitstring = list(itertools.chain.from_iterable(bitstring))
# Generate unit vectors
statelist = []
poslist = []
pos = 0
unit0 = sp.array([1, 0])
unit1 = sp.array([0, 1])
for i in range(len(bitstring)):
# Construct unit vector corresponding to bitstring
state = unit1 if (bitstring[i][0] == '1') else unit0
for j in range(n - 1):
state = sp.kron(state, unit1 if
(bitstring[i][j + 1] == '1') else unit0)
statelist.append(state)
# Record orientation of unit vector (using position of 1 value)
for j in range(2**n):
if (statelist[-1][j]):
pos = j
break
poslist.append(pos)
# Sort the states
sortperm = sp.array(poslist).argsort()
bitstring = [bitstring[i] for i in sortperm]
return bitstring
def LW(self):
R = sp.zeros((self.mean.Y.size, self.mean.n_covs))
istart = 0
for ti in range(self.mean.n_terms):
iend = istart + self.mean.F[ti].shape[1] * self.mean.A[ti].shape[0]
R[:, istart:iend] = sp.kron(self.ALc()[ti].T, self.LrF()[ti])
return R
def _LML_covar(self, hyperparams):
#calculate marginal likelihood of kronecker GP
#1. get covariance structures needed:
try:
KV = self.get_covariances(hyperparams)
except linalg.LinAlgError:
LG.error("exception caught (%s)" % (str(hyperparams)))
return 1E6
#2. build lml
LML = 0
LMLc = 0.5 * self.nd * SP.log(2.0 * SP.pi)
#constant part of negative lml
#quadratic form
Si = KV['Si']
LMLq = 0.5 * SP.dot(KV['y_rot'].ravel(), KV['YSi'].ravel())
#determinant stuff
LMLd = -0.5 * SP.log(Si).sum()
if VERBOSE:
print "costly verbose debugging on"
K = SP.kron(KV['Kr'], KV['Kc']) + SP.diag(KV['Knoise'])
Ki = SP.linalg.inv(K)
LMLq_ = 0.5 * SP.dot(SP.dot(self.y.ravel(), Ki), self.y.ravel())
LMLd_ = 0.5 * 2 * SP.log(SP.linalg.cholesky(K).diagonal()).sum()
check_dist(LMLq, LMLq_)
check_dist(LMLd, LMLd_)
return LMLc + LMLq + LMLd
def W(self):
R = sp.zeros((self.Y.size, self.n_covs))
istart = 0
for ti in range(self.n_terms):
iend = istart + self.F[ti].shape[1] * self.A[ti].shape[0]
R[:, istart:iend] = sp.kron(self.A[ti].T, self.F[ti])
return R
def L_basic_red(rate_mat, rate_dic, rowList, rowLen, pb=0.5, kex=300.0):
# populate the Liouvillian with relaxation and chemical exchange terms
a = np.zeros((1 + 2 * rowLen, 1 + 2 * rowLen), dtype=complex)
# relaxation bits
pa = 1.0 - pb
a += rate_mat
cnt = 0
for i, prod in enumerate(prodList):
if i in rowList:
if prod == 'Iz': # these are for the return of magnetisation to equilibrium
a[cnt, 0] -= rate_dic['Iz'] * pa
a[cnt + rowLen, 0] -= rate_dic['Iz'] * pb
elif prod == 'Rz':
a[cnt, 0] -= rate_dic['Rz'] * pa
a[cnt + rowLen, 0] -= rate_dic['Rz'] * pb
elif prod == 'Sz':
a[cnt, 0] -= rate_dic['Sz'] * pa
a[cnt + rowLen, 0] -= rate_dic['Sz'] * pb
cnt += 1
# add exchange
k_ge = kex * pb
k_eg = kex * pa
k_mat = np.array([[-k_ge, k_eg], [k_ge, -k_eg]])
k_mat = kron(k_mat, np.eye(rowLen))
a[1:2 * rowLen + 1, 1:2 * rowLen + 1] -= k_mat # signs are important!
return a
def gaussian_checkerboard_kernel(L, sigma=10):
'''
Computes a gaussian checkerboard kernel of shape (2L+1, 2L+1)
The result is the Hadamar (element-wise) product of a centered 2D gaussian
pdf of std `sigma` evaluated on (-L:L)x(-L:L) with a checkerboard kernel.
Thus the resulting matrix is split into 4 quarts : 2 negatives quarts and
2 positive parts.
INPUTS:
- L : half length of the kernel
- sigma : optional parameter : the std of the gaussian part of the kernel
OUTPUS:
- np.ndarray representing a gaussian checkerboard kernel of shape (2L+1)
'''
# get gaussian part
x, y = np.mgrid[-L:L, -L:L]
pos = np.empty(x.shape + (2, ))
pos[:, :, 0] = x
pos[:, :, 1] = y
rv = st.multivariate_normal([0, 0], sigma * np.eye(2))
pdf = rv.pdf(pos)
# get checkerboard part
checkerboard = kron(np.array([[1, -1], [-1, 1]]), np.ones(shape=(L, L)))
# return
return checkerboard * pdf
def GenerateLabels(n):
" Get proper labeling for output states. "
# Generate bitstrings
bitstring = []
for i in range(0,n+1):
bitstring.append(kbits(n, i))
# Flatten
bitstring = list(itertools.chain.from_iterable(bitstring))
# Generate unit vectors
statelist = []
poslist = []
pos = 0
unit0 = sp.array([1,0])
unit1 = sp.array([0,1])
for i in range(len(bitstring)):
# Construct unit vector corresponding to bitstring
state = unit1 if (bitstring[i][0] == '1') else unit0
for j in range(n-1):
state = sp.kron(state,
unit1 if (bitstring[i][j+1] == '1') else unit0)
statelist.append(state)
# Record orientation of unit vector (using position of 1 value)
for j in range(2**n):
if (statelist[-1][j]):
pos = j
break
poslist.append(pos)
# Sort the states
sortperm = sp.array(poslist).argsort()
bitstring = [ bitstring[i] for i in sortperm ]
return bitstring
def ALcCtildeLcA_o_FRF(self, i):
if i < self.covar.Cr.getNumberParams():
FRF = self.FGGF()
else:
FRF = self.FF()
ALcCtildeALc = sp.dot(self.ALc(), self.CtildeLcA(i))
return sp.kron(ALcCtildeALc, FRF)
def WcCtildeLcA_o_WrRF(self, i):
if i < self.covar.Cr.getNumberParams():
self.WrRF = self.WrGGF()
else:
self.WrRF = self.WrF()
WcCtildeLcA = sp.dot(self.covar.Wc(), self.CtildeLcA(i))
return sp.kron(WcCtildeLcA, self.WrRF)
def _LMLgrad_lik(self,hyperparams):
"""
evaluates the gradient of the log marginal likelihood with respect to
the hyperparameters of the likelihood function
"""
try:
KV = self.get_covariances(hyperparams)
except LA.LinAlgError:
LG.error('linalg exception in _LML_covar')
return {'lik':SP.zeros(len(hyperparams['lik']))}
except ValueError:
LG.error('value error in _LML_covar')
return {'lik':SP.zeros(len(hyperparams['lik']))}
YtildeVec = ravel(KV['Ytilde'])
Kd_diag = self.likelihood.Kdiag_grad_theta(hyperparams['lik'],self.n,0)
temp = SP.kron(SP.dot(KV['U_c'].T, SP.dot(KV['Binv'], SP.dot(KV['Binv'].T, KV['U_c']))),SP.diag(Kd_diag))
LMLgrad_det = SP.diag(SP.dot(SP.diag(1./KV['S']),temp)).sum() # Needs more optimization
sigma_grad = 2 * SP.exp(2 * hyperparams['lik'])
LMLgrad_quad = - (sigma_grad * YtildeVec *
ravel(SP.dot(SP.eye(self.n), SP.dot(KV['Ytilde'],KV['UBinvBinvU'].T)))).sum()
LMLgrad = 0.5*(LMLgrad_det + LMLgrad_quad)
return {'lik':SP.array([LMLgrad])}
def ALcCtildeLcA_o_FRF(self, i):
if i < self.covar.Cr.getNumberParams():
FRF = self.FGGF()
else:
FRF = self.FF()
ALcCtildeALc = sp.dot(self.ALc(), self.CtildeLcA(i))
return sp.kron(ALcCtildeALc, FRF)
def WcCtildeLcA_o_WrRF(self, i):
if i < self.covar.Cr.getNumberParams():
self.WrRF = self.WrGGF()
else:
self.WrRF = self.WrF()
WcCtildeLcA = sp.dot(self.covar.Wc(), self.CtildeLcA(i))
return sp.kron(WcCtildeLcA, self.WrRF)
def _LML_covar(self, hyperparams):
#calculate marginal likelihood of kronecker GP
#1. get covariance structures needed:
try:
KV = self.get_covariances(hyperparams)
except linalg.LinAlgError:
LG.error("exception caught (%s)" % (str(hyperparams)))
return 1E6
#2. build lml
LML = 0
LMLc = 0.5* self.nd * SP.log(2.0 * SP.pi)
#constant part of negative lml
#quadratic form
Si = KV['Si']
LMLq = 0.5 * SP.dot(KV['y_rot'].ravel(),KV['YSi'].ravel() )
#determinant stuff
LMLd = -0.5 * SP.log(Si).sum()
if VERBOSE:
print "costly verbose debugging on"
K = SP.kron(KV['Kr'],KV['Kc']) + SP.diag(KV['Knoise'])
Ki = SP.linalg.inv(K)
LMLq_ = 0.5* SP.dot(SP.dot(self.y.ravel(),Ki),self.y.ravel())
LMLd_ = 0.5* 2 * SP.log(SP.linalg.cholesky(K).diagonal()).sum()
check_dist(LMLq,LMLq_)
check_dist(LMLd,LMLd_)
return LMLc+LMLq+LMLd
def fitKronApprox(a):
Sbg = SP.zeros_like(S[0])
Kbg = SP.zeros_like(K[0])
for i in range(len(S)): Sbg+= a[i]*S[i]
for i in range(len(K)): Kbg+= a[i+len(S)]*K[i]
Gamma1 = SP.kron(Sbg,Kbg)
return ((Gamma-Gamma1)**2).sum()
def L_basic(rate_mat, rate_dic, pb=0.5, kex=300.0):
# populate the Liouvillian with relaxation and chemical exchange terms
a = np.zeros((127, 127), dtype=complex)
# relaxation bits
pa = 1.0 - pb
a += rate_mat
for i, prod in enumerate(prodList):
if prod == 'Iz': # these are for the return of magnetisation to equilibrium
a[i, 0] -= rate_dic['Iz'] * pa
a[i + 63, 0] -= rate_dic['Iz'] * pb
elif prod == 'Rz':
a[i, 0] -= rate_dic['Rz'] * pa
a[i + 63, 0] -= rate_dic['Rz'] * pb
elif prod == 'Sz':
a[i, 0] -= rate_dic['Sz'] * pa
a[i + 63, 0] -= rate_dic['Sz'] * pb
# add exchange
k_ge = kex * pb
k_eg = kex * pa
k_mat = np.array([[-k_ge, k_eg], [k_ge, -k_eg]])
k_mat = kron(k_mat, np.eye(63))
a[1:127, 1:127] -= k_mat # signs are important!
return a
def getVarianceKron(C, R, verbose=False):
""" get variance scaling of kron(C,R)"""
n_K = len(C) * len(R)
c = SP.kron(SP.diag(C), SP.diag(R)).sum() - 1. / n_K * SP.dot(
R.T, SP.dot(SP.ones((R.shape[0], C.shape[0])), C)).sum()
scalar = (n_K - 1) / c
return 1.0 / scalar
def HamiltonianGen_old(n, a, b, d):
""" Generate default Hamiltonian coefficients. """
### Construct Hamiltonian ###
Z = sp.matrix([[1,0],[0,-1]])
X = sp.matrix([[0,1],[1,0]])
I = sp.identity(2)
alpha = sp.zeros((2**n,2**n))
beta = sp.zeros((2**n,2**n))
delta = sp.zeros((2**n,2**n))
matrices = []
# Calculate alpha
for i in range(0,n):
for m in range(0,n-1): matrices.append(I)
matrices.insert(i, Z)
temp = matrices[0]
matrices.pop(0)
while (len(matrices) != 0):
temp = sp.kron(temp, matrices[0])
matrices.pop(0)
alpha = alpha + temp*a[i]
temp = 0
# Calculate beta
for i in range(0,n):
for j in range(i+1,n):
if (i != j):
for m in range(0,n-2): matrices.append(I)
matrices.insert(i, Z)
matrices.insert(j, Z)
temp = matrices[0]
matrices.pop(0)
while (len(matrices) != 0):
temp = sp.kron(temp, matrices[0])
matrices.pop(0)
beta = beta + temp*b[i,j]
temp = 0
# Calculate delta
for i in range(0,n):
for m in range(0,n-1):
matrices.append(I)
matrices.insert(i, X)
temp = matrices[0]
matrices.pop(0)
while (len(matrices) != 0):
temp = sp.kron(temp, matrices[0])
matrices.pop(0)
delta += temp*d[i]
return [alpha, beta, delta]
def _multiplex(self, bottom_gate, bottom_qubit_index, list_of_angles):
"""
Internal recursive method to create gates to perform rotations on the
imaginary qubits: works by rotating LSB (and hence ALL imaginary
qubits) by combo angle and then flipping sign (by flipping the bit,
hence moving the complex amplitudes) of half the imaginary qubits
(CNOT) followed by another combo angle on LSB, therefore executing
conditional (on MSB) rotations, thereby disentangling LSB.
"""
list_len = len(list_of_angles)
target_qubit = self.nth_qubit_from_least_sig_qubit(bottom_qubit_index)
# Case of no multiplexing = base case for recursion
if list_len == 1:
return bottom_gate(list_of_angles[0], target_qubit)
local_num_qubits = int(math.log2(list_len)) + 1
control_qubit = self.nth_qubit_from_least_sig_qubit(
local_num_qubits - 1 + bottom_qubit_index)
# calc angle weights, assuming recursion (that is the lower-level
# requested angles have been correctly implemented by recursion
angle_weight = scipy.kron([[0.5, 0.5], [0.5, -0.5]],
numpy.identity(2 ** (local_num_qubits - 2)))
# calc the combo angles
list_of_angles = (angle_weight * numpy.matrix(
list_of_angles).transpose()).reshape(-1).tolist()[0]
combine_composite_gates = CompositeGate(
"multiplex" + local_num_qubits.__str__(), [], self.arg)
# recursive step on half the angles fulfilling the above assumption
combine_composite_gates._attach(
self._multiplex(bottom_gate, bottom_qubit_index,
list_of_angles[0:(list_len // 2)]))
# combine_composite_gates.cx(control_qubit,target_qubit) -> does not
# work as expected because checks circuit
# so attach CNOT as follows, thereby flipping the LSB qubit
combine_composite_gates._attach(CnotGate(control_qubit, target_qubit))
# implement extra efficiency from the paper of cancelling adjacent
# CNOTs (by leaving out last CNOT and reversing (NOT inverting) the
# second lower-level multiplex)
sub_gate = self._multiplex(
bottom_gate, bottom_qubit_index, list_of_angles[(list_len // 2):])
if isinstance(sub_gate, CompositeGate):
combine_composite_gates._attach(sub_gate.reverse())
else:
combine_composite_gates._attach(sub_gate)
# outer multiplex keeps final CNOT, because no adjacent CNOT to cancel
# with
if self.num_qubits == local_num_qubits + bottom_qubit_index:
combine_composite_gates._attach(CnotGate(control_qubit,
target_qubit))
return combine_composite_gates
def _multiplex(self, bottom_gate, bottom_qubit_index, list_of_angles):
"""
Internal recursive method to create gates to perform rotations on the
imaginary qubits: works by rotating LSB (and hence ALL imaginary
qubits) by combo angle and then flipping sign (by flipping the bit,
hence moving the complex amplitudes) of half the imaginary qubits
(CNOT) followed by another combo angle on LSB, therefore executing
conditional (on MSB) rotations, thereby disentangling LSB.
"""
list_len = len(list_of_angles)
target_qubit = self.nth_qubit_from_least_sig_qubit(bottom_qubit_index)
# Case of no multiplexing = base case for recursion
if list_len == 1:
return bottom_gate(list_of_angles[0], target_qubit)
local_num_qubits = int(math.log2(list_len)) + 1
control_qubit = self.nth_qubit_from_least_sig_qubit(
local_num_qubits - 1 + bottom_qubit_index)
# calc angle weights, assuming recursion (that is the lower-level
# requested angles have been correctly implemented by recursion
angle_weight = scipy.kron([[0.5, 0.5], [0.5, -0.5]],
numpy.identity(2 ** (local_num_qubits - 2)))
# calc the combo angles
list_of_angles = (angle_weight * numpy.matrix(
list_of_angles).transpose()).reshape(-1).tolist()[0]
combine_composite_gates = CompositeGate(
"multiplex" + local_num_qubits.__str__(), [], self.arg)
# recursive step on half the angles fulfilling the above assumption
combine_composite_gates._attach(
self._multiplex(bottom_gate, bottom_qubit_index,
list_of_angles[0:(list_len // 2)]))
# combine_composite_gates.cx(control_qubit,target_qubit) -> does not
# work as expected because checks circuit
# so attach CNOT as follows, thereby flipping the LSB qubit
combine_composite_gates._attach(CnotGate(control_qubit, target_qubit))
# implement extra efficiency from the paper of cancelling adjacent
# CNOTs (by leaving out last CNOT and reversing (NOT inverting) the
# second lower-level multiplex)
sub_gate = self._multiplex(
bottom_gate, bottom_qubit_index, list_of_angles[(list_len // 2):])
if isinstance(sub_gate, CompositeGate):
combine_composite_gates._attach(sub_gate.reverse())
else:
combine_composite_gates._attach(sub_gate)
# outer multiplex keeps final CNOT, because no adjacent CNOT to cancel
# with
if self.num_qubits == local_num_qubits + bottom_qubit_index:
combine_composite_gates._attach(CnotGate(control_qubit,
target_qubit))
return combine_composite_gates
def _multiplex(self, target_gate, list_of_angles):
"""
Return a recursive implementation of a multiplexor circuit,
where each instruction itself has a decomposition based on
smaller multiplexors.
The LSB is the multiplexor "data" and the other bits are multiplexor "select".
Args:
target_gate (Gate): Ry or Rz gate to apply to target qubit, multiplexed
over all other "select" qubits
list_of_angles (list[float]): list of rotation angles to apply Ry and Rz
Returns:
DAGCircuit: the circuit implementing the multiplexor's action
"""
list_len = len(list_of_angles)
local_num_qubits = int(math.log2(list_len)) + 1
q = QuantumRegister(local_num_qubits)
circuit = QuantumCircuit(q)
circuit.name = "multiplex" + local_num_qubits.__str__()
lsb = q[0]
msb = q[local_num_qubits - 1]
# case of no multiplexing: base case for recursion
if local_num_qubits == 1:
circuit.append(target_gate(list_of_angles[0]), [q[0]])
return circuit
# calc angle weights, assuming recursion (that is the lower-level
# requested angles have been correctly implemented by recursion
angle_weight = scipy.kron([[0.5, 0.5], [0.5, -0.5]],
np.identity(2 ** (local_num_qubits - 2)))
# calc the combo angles
list_of_angles = angle_weight.dot(np.array(list_of_angles)).tolist()
# recursive step on half the angles fulfilling the above assumption
multiplex_1 = self._multiplex(target_gate, list_of_angles[0:(list_len // 2)])
circuit.append(multiplex_1.to_instruction(), q[0:-1])
# attach CNOT as follows, thereby flipping the LSB qubit
circuit.append(CnotGate(), [msb, lsb])
# implement extra efficiency from the paper of cancelling adjacent
# CNOTs (by leaving out last CNOT and reversing (NOT inverting) the
# second lower-level multiplex)
multiplex_2 = self._multiplex(target_gate, list_of_angles[(list_len // 2):])
if list_len > 1:
circuit.append(multiplex_2.to_instruction().mirror(), q[0:-1])
else:
circuit.append(multiplex_2.to_instruction(), q[0:-1])
# attach a final CNOT
circuit.append(CnotGate(), [msb, lsb])
return circuit
def make_E_2s(A1, A2, B1, B2, op):
res = sp.zeros((A1.shape[1]**2, A2.shape[2]**2), dtype=A1.dtype)
for s in range(A1.shape[0]):
for t in range(A2.shape[0]):
for u in range(A1.shape[0]):
for v in range(A2.shape[0]):
res += sp.kron(A1[s].dot(A2[t]), B1[u].dot(B2[v]).conj()) * op[u, v, s, t]
return res
def make_E_2s(A1, A2, B1, B2, op):
res = sp.zeros((A1.shape[1]**2, A2.shape[2]**2), dtype=A1.dtype)
for s in xrange(A1.shape[0]):
for t in xrange(A2.shape[0]):
for u in xrange(A1.shape[0]):
for v in xrange(A2.shape[0]):
res += sp.kron(A1[s].dot(A2[t]), B1[u].dot(B2[v]).conj()) * op[u, v, s, t]
return res
def LW(self):
R = sp.zeros((self.mean.Y.size, self.mean.n_covs))
istart = 0
for ti in range(self.mean.n_terms):
iend = istart + self.mean.F[ti].shape[1] * self.mean.A[ti].shape[0]
R[:, istart:iend] = sp.kron(self.ALc()[ti].T, self.LrF()[ti])
istart += iend
return R
def getGradient(self,j): """ get rotated gradient for fixed effect i """ self._rotate() i = int(self.indicator['term'][j]) r = int(self.indicator['row'][j]) c = int(self.indicator['col'][j]) rv = -SP.kron(self.Fr[i][:,[r]],self.Ar[i][[c],:]) return rv
def getGradient(self, j):
""" get rotated gradient for fixed effect i """
self._rotate()
i = int(self.indicator['term'][j])
r = int(self.indicator['row'][j])
c = int(self.indicator['col'][j])
rv = -SP.kron(self.Fr[i][:, [r]], self.Ar[i][[c], :])
return rv
def predict(self, hyperparams, Xstar_r, compute_cov = False, debugging = False):
"""
predict on Xstar
"""
self._update_inputs(hyperparams)
KV = self.get_covariances(hyperparams,debugging=debugging)
self.covar_r.Xcross = Xstar_r
Kstar_r = self.covar_r.Kcross(hyperparams['covar_r'])
Kstar_c = self.covar_c.K(hyperparams['covar_c'])
KinvY = SP.dot(KV['U_r'],SP.dot(KV['Ytilde'],KV['U_c'].T))
Ystar = SP.dot(Kstar_r.T,SP.dot(KinvY,Kstar_c))
Ystar = unravel(Ystar,self.covar_r.n_cross,self.t)
if debugging:
Kstar = SP.kron(Kstar_c,Kstar_r)
Ynaive = SP.dot(Kstar.T,KV['alpha'])
Ynaive = unravel(Ynaive,self.covar_r.n_cross,self.t)
assert SP.allclose(Ystar,Ynaive), 'ouch, prediction does not work out'
Ystar_covar = []
if compute_cov:
CU = fast_dot(Kstar_c, KV['U_c'])
s_rev = 1./KV['S']
Ystar_covar = SP.zeros([Xstar_r.shape[0], self.Y.shape[1]])
printProgressBar(0, Xstar_r.shape[0], prefix = 'Computing perdiction varaince:', suffix = 'Complete', length = 20)
for i in range(Xstar_r.shape[0]):
R_star_star = self.covar_r.K(hyperparams['covar_r'], SP.expand_dims(Xstar_r[i,:],axis=0))
self.covar_r.Xcross = SP.expand_dims(Xstar_r[i,:],axis=0)
R_tr_star = self.covar_r.Kcross(hyperparams['covar_r'])
RU = SP.dot(R_tr_star.T, KV['U_r'])
q = SP.kron(SP.diag(Kstar_c), R_star_star)
t = SP.zeros([self.t])
for j in range(self.t):
temp = SP.kron(CU[j,:], RU)
t[j,] = SP.sum((s_rev * temp).T * temp.T, axis = 0)
Ystar_covar[i,:] = q - t
if (i + 1) % (Xstar_r.shape[0]/10) == 0:
printProgressBar(i+1, Xstar_r.shape[0], prefix = 'Computing perdiction varaince:', suffix = 'Complete', length = 20)
self.covar_r.Xcross = Xstar_r
return Ystar, Ystar_covar
def fitKronApprox(a):
Sbg = SP.zeros_like(S[0])
Kbg = SP.zeros_like(K[0])
for i in range(len(S)):
Sbg += a[i] * S[i]
for i in range(len(K)):
Kbg += a[i + len(S)] * K[i]
Gamma1 = SP.kron(Sbg, Kbg)
return ((Gamma - Gamma1)**2).sum()
def getK_verbose(KV,noise=True):
if 'K' not in KV.keys():
K = SP.kron(KV['Kr'],KV['Kc'])
if noise:
K += SP.diag(KV['Knoise'])
Ki = SP.linalg.inv(K)
KV['K'] = K
KV['Ki'] =Ki
return [KV['K'],KV['Ki']]
def W(self):
R = sp.zeros((self.Y.size, self.n_covs))
istart = 0
for ti in range(self.n_terms):
iend = istart + self.F[ti].shape[1] * self.A[ti].shape[0]
R[:, istart:iend] = sp.kron(self.A[ti].T, self.F[ti])
if self._miss:
R = R[self._veIok, :]
return R
def getK_verbose(KV, noise=True):
if 'K' not in KV.keys():
K = SP.kron(KV['Kr'], KV['Kc'])
if noise:
K += SP.diag(KV['Knoise'])
Ki = SP.linalg.inv(K)
KV['K'] = K
KV['Ki'] = Ki
return [KV['K'], KV['Ki']]
def varMLE(self):
""" calculate inverse of fisher information """
self._update_cache()
Sr = {}
Sr['Cg'] = self.cache['Srstar']
Sr['Cn'] = SP.ones(self.N)
n_params = self.Cg.getNumberParams() + self.Cn.getNumberParams()
fisher = SP.zeros((n_params, n_params))
header = SP.zeros((n_params, n_params), dtype='|S10')
C1 = SP.zeros((self.P, self.P))
C2 = SP.zeros((self.P, self.P))
idx1 = 0
for key1 in ['Cg', 'Cn']:
for key1_p1 in range(self.P):
for key1_p2 in range(key1_p1, self.P):
C1[key1_p1, key1_p2] = C1[key1_p2, key1_p1] = 1
LCL1 = SP.dot(self.cache['Lc'],
SP.dot(C1, self.cache['Lc'].T))
CSr1 = SP.kron(Sr[key1][:, SP.newaxis, SP.newaxis],
LCL1[SP.newaxis, :])
DCSr1 = self.cache['D'][:, :, SP.newaxis] * CSr1
idx2 = 0
for key2 in ['Cg', 'Cn']:
for key2_p1 in range(self.P):
for key2_p2 in range(key2_p1, self.P):
C2[key2_p1, key2_p2] = C2[key2_p2, key2_p1] = 1
LCL2 = SP.dot(self.cache['Lc'],
SP.dot(C2, self.cache['Lc'].T))
CSr2 = SP.kron(
Sr[key2][:, SP.newaxis, SP.newaxis],
LCL2[SP.newaxis, :])
DCSr2 = self.cache['D'][:, :,
SP.newaxis] * CSr2
fisher[idx1,
idx2] = 0.5 * (DCSr1 * DCSr2).sum()
header[idx1, idx2] = '%s%d%d_%s%d%d' % (
key1, key1_p1, key1_p1, key2, key2_p1,
key2_p2)
C2[key2_p1, key2_p2] = C2[key2_p2, key2_p1] = 0
idx2 += 1
C1[key1_p1, key1_p2] = C1[key1_p2, key1_p1] = 0
idx1 += 1
RV = LA.inv(fisher)
return RV, header
def K_grad_i(self,i):
nCg = self.Cg.getNumberParams()
if i >= self.getNumberParams():
raise ValueError("Trying to retrieve the gradient over a "
"parameter that is inactive.")
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(msg_too_expensive_dim(my_name(),
_MAX_DIM))
i = self._actindex2index(i)
if i < nCg:
rv= sp.kron(self.Cg.K_grad_i(i), self.R)
else:
_i = i - nCg
rv = sp.kron(self.Cn.K_grad_i(_i), sp.eye(self.dim_r))
return rv
def K_grad_i(self, i):
nCg = self.Cg.getNumberParams()
if i >= self.getNumberParams():
raise ValueError("Trying to retrieve the gradient over a "
"parameter that is inactive.")
if self.dim > _MAX_DIM:
raise TooExpensiveOperationError(
msg_too_expensive_dim(my_name(), _MAX_DIM))
i = self._actindex2index(i)
if i < nCg:
rv = sp.kron(self.Cg.K_grad_i(i), self.R)
else:
_i = i - nCg
rv = sp.kron(self.Cn.K_grad_i(_i), sp.eye(self.dim_r))
return rv
def aveCC2F(grid):
"Construct the averaging operator on cell cell centers to faces."
if grid.ndim == 1:
aveCC2F = av_extrap(grid.shape[0])
elif grid.ndim == 2:
aveCC2F = sp.vstack(
(sp.kron(speye(grid.shape[1]), av_extrap(grid.shape[0])),
sp.kron(av_extrap(grid.shape[1]), speye(grid.shape[0]))),
format="csr")
elif grid.ndim == 3:
aveCC2F = sp.vstack(
(kron3(speye(grid.shape[2]), speye(grid.shape[1]),
av_extrap(grid.shape[0])),
kron3(speye(grid.shape[2]), av_extrap(grid.shape[1]),
speye(grid.shape[0])),
kron3(av_extrap(grid.shape[2]), speye(grid.shape[1]),
speye(grid.shape[0]))),
format="csr")
return aveCC2F
def predict(self,
hyperparams,
xstar_r=None,
xstar_c=None,
var=False,
hyperparams_star=None):
"""
Predict mean and variance for given **Parameters:**
hyperparams : {}
hyperparameters in logSpace
xstar : [double]
prediction inputs
var : boolean
return predicted variance
interval_indices : [ int || bool ]
Either scipy array-like of boolean indicators,
or scipy array-like of integer indices, denoting
which x indices to predict from data.
hyperparams_star: optional alternative hyperparameters for cross covariance
output : output dimension for prediction (0)
"""
if var:
print "predictive varinace not supported yet"
if hyperparams_star is None:
hyperparams_star = hyperparams
#1. get covariance sturcture
KV = self.get_covariances(hyperparams)
#cross covariance:
Kr_star = self.covar_r.K(hyperparams_star['covar_r'], self.x_r,
xstar_r)
Kc_star = self.covar_c.K(hyperparams_star['covar_c'], self.x_c,
xstar_c)
Kr_starU = SP.dot(Kr_star, KV['Ur'])
Kc_starU = SP.dot(Kc_star, KV['Uc'])
mu = kronravel(Kr_starU, Kc_starU, KV['YSi'])
if VERBOSE:
#trivial computations
[K, Ki] = getK_verbose(KV)
Kstar = SP.kron(Kr_star, Kc_star)
yt = SP.dot(Ki, self.y.ravel())
mu_slow = SP.dot(Kstar, yt)
check_dist(mu.ravel(), mu_slow)
return mu
def fullrho(qu, squ):
print("#Starting full density matrix simulation!")
#Build state from pure states received from the MPS processes
rho = sp.zeros((2**N, 2**N), dtype=sp.complex128)
psis = [None] * N_samp
for n in range(N_samp):
pnum, psi = squ.get()
psis[pnum] = psi
rho += sp.outer(psi, psi.conj())
squ.task_done()
rho /= sp.trace(rho)
Hfull = get_full_op(get_ham(N, lam))
linds = get_linds(N, eps)
linds = [(n, L.reshape(tuple([sp.prod(L.shape[:sp.ndim(L)/2])]*2))) for (n, L) in linds]
linds_full = [sp.kron(sp.eye(2**(n-1)), sp.kron(L, sp.eye(2**(N - n + 1) / L.shape[0]))) for (n, L) in linds]
for L in linds_full:
assert L.shape == Hfull.shape
Qfull = -1.j * Hfull - 0.5 * sp.sum([L.conj().T.dot(L) for L in linds_full], axis=0)
szs = [None] + [sp.kron(sp.kron(sp.eye(2**(n - 1)), Sz), sp.eye(2**(N - n))) for n in range(1, N + 1)]
for i in range(N_steps + 1):
rho /= sp.trace(rho)
esz = []
for n in range(1, N + 1):
esz.append(sp.trace(szs[n].dot(rho)).real)
if i % res_every == 0:
if qu is None:
print(esz)
else:
qu.put([-1, i, esz])
qu.put([-2, i, [sp.NaN] * N]) #this slot is reserved for a second "exact" result
#Do Euler steps, approximately integrating the Lindblad master equation
rho += dt * (Qfull.dot(rho) + rho.dot(Qfull.conj().T) +
sum([L.dot(rho).dot(L.conj().T) for L in linds_full]))
def christof_trick(A1, F1, D, A2=None, F2=None):
if A2 is None:
A2 = A1
if F2 is None:
F2 = F1
out = sp.zeros([A1.shape[1] * F1.shape[1], A2.shape[1] * F2.shape[1]])
for c in range(A1.shape[0]):
Oc = sp.dot(A1[[c], :].T, A2[[c], :])
Or = sp.dot(F1.T, D[:, [c]] * F2)
out += sp.kron(Oc, Or)
return out
def Trans_prof(self, rho, phi, z):
coef = sp.sqrt(2 * math.factorial(self._p) /
((1 + sp.kron(0, self._m)) * sp.pi *
math.factorial(self._m + self._p)))
gouy = sp.exp(1j * (2 * self._p + self._m + 1) *
self.Gouy(z)) / self.Spot_size(z)
expon = sp.exp(-1j * self.k * rho**2 / (2 * self.R_curve(z)) -
rho**2 / self.Spot_size(z)**2 + 1j * self._m * phi)
return coef * gouy * (sp.sqrt(2) * rho /
self.Spot_size(z))**self._m * genlaguerre(
self._p, self._m)(rho) * expon
def LMLdebug(self):
"""
LML function for debug
"""
assert self.N*self.P<2000, 'gp2kronSum:: N*P>=2000'
y = SP.reshape(self.Y,(self.N*self.P), order='F')
K = SP.kron(self.Cg.K(),self.XX)
K += SP.kron(self.Cn.K()+self.offset*SP.eye(self.P),SP.eye(self.N))
cholK = LA.cholesky(K)
Kiy = LA.cho_solve((cholK,False),y)
lml = y.shape[0]*SP.log(2*SP.pi)
lml += 2*SP.log(SP.diag(cholK)).sum()
lml += SP.dot(y,Kiy)
lml *= 0.5
return lml
def _update_cache(self):
"""
Update cache
"""
cov_params_have_changed = self.Cr.params_have_changed or self.Cn.params_have_changed
if self.Xr_has_changed:
start = TIME.time()
""" Row SVD Bg + Noise """
Urstar, S, V = NLA.svd(self.Xr)
self.cache['Srstar'] = SP.concatenate(
[S**2, SP.zeros(self.N - S.shape[0])])
self.cache['Lr'] = Urstar.T
self.mean.setRowRotation(Lr=self.cache['Lr'])
smartSum(self.time, 'cache_XXchanged', TIME.time() - start)
smartSum(self.count, 'cache_XXchanged', 1)
if cov_params_have_changed:
start = TIME.time()
""" Col SVD Noise """
S2, U2 = LA.eigh(self.Cn.K() + self.offset * SP.eye(self.P))
self.cache['Sc2'] = S2
US2 = SP.dot(U2, SP.diag(SP.sqrt(S2)))
USi2 = SP.dot(U2, SP.diag(SP.sqrt(1. / S2)))
""" Col SVD region """
A = SP.reshape(self.Cr.getParams(), (self.P, self.rank), order='F')
Astar = SP.dot(USi2.T, A)
Ucstar, S, V = NLA.svd(Astar)
self.cache['Scstar'] = SP.concatenate(
[S**2, SP.zeros(self.P - S.shape[0])])
self.cache['Lc'] = SP.dot(Ucstar.T, USi2.T)
""" pheno """
self.mean.setColRotation(self.cache['Lc'])
if cov_params_have_changed or self.Xr_has_changed:
""" S """
self.cache['s'] = SP.kron(self.cache['Scstar'],
self.cache['Srstar']) + 1
self.cache['d'] = 1. / self.cache['s']
self.cache['D'] = SP.reshape(self.cache['d'], (self.N, self.P),
order='F')
""" pheno """
self.cache['LY'] = self.mean.evaluate()
self.cache['DLY'] = self.cache['D'] * self.cache['LY']
smartSum(self.time, 'cache_colSVDpRot', TIME.time() - start)
smartSum(self.count, 'cache_colSVDpRot', 1)
self.Y_has_changed = False
self.Xr_has_changed = False
self.Cr.params_have_changed = False
self.Cn.params_have_changed = False
def data_simulation(n_samples, n_dimensions, n_tasks, n_latent, train_portion):
# true parameters
true_param = dict()
true_param['X_c'] = SP.random.randn(n_tasks, n_latent)
true_param['X_s'] = SP.random.randn(n_tasks, n_latent)
X = SP.random.randn(n_samples, n_dimensions) #/ SP.sqrt(n_dimensions)
R = SP.dot(X, X.T)
true_param['C'] = SP.dot(true_param['X_c'], true_param['X_c'].T)
true_param['Sigma'] = SP.dot(true_param['X_s'], true_param['X_s'].T)
K = SP.kron(true_param['C'], R) + SP.kron(true_param['Sigma'],
SP.eye(n_samples))
y = SP.random.multivariate_normal(SP.zeros(n_tasks * n_samples), K)
Y = SP.reshape(y, (n_samples, n_tasks), order='F')
temp = SP.random.permutation(n_samples)
idx_train = temp[0:np.int(train_portion * n_samples), ]
idx_test = temp[np.int(train_portion * n_samples):, ]
X_train = X[idx_train, :]
X_test = X[idx_test, :]
Y_train = Y[idx_train, :]
Y_test = Y[idx_test, :]
return X_train, X_test, Y_train, Y_test, true_param
def genNoise(self, vTot=0.4, vCommon=0.2):
vSpecifc = vTot - vCommon
# common
Yc = SP.kron(SP.randn(self.N, 1), SP.randn(1, self.P))
Yc *= SP.sqrt(vCommon / Yc.var(0).mean())
# independent
Yi = SP.randn(self.N, self.P)
Yi *= SP.sqrt(vSpecifc / Yi.var(0).mean())
return Yc, Yi