def g_PY_Beta(Nu, Beta, Omega, Y, SigmaY, B0, Ngene, Ncell, Nsample):
# Ngene by Nsample
Exp = ExpQ(Nu, Beta, Omega, Ngene, Ncell, Nsample)
Var = VarQ(Nu, Beta, Omega, Ngene, Ncell, Nsample)
# Nsample by Ncell be Ngene
g_Exp = g_Exp_Beta(Nu, Omega, Beta, B0, Ngene, Ncell, Nsample)
g_Var = g_Var_Beta(Nu, Omega, Beta, B0, Ngene, Ncell, Nsample)
# Nsample by Ncell by Ngene
a = np.empty((Nsample, Ncell, Ngene))
for c in range(Ncell):
a[:,c,:] = np.divide((g_Var[:,c,:] * t(Exp) - 2 * g_Exp[:,c,:]*t(Var)),np.power(t(Exp),3))
b = np.empty((Nsample, Ncell, Ngene))
Var_Exp2 = np.divide(Var, 2*np.square(Exp))
for s in range(Nsample):
for c in range(Ncell):
for g in range(Ngene):
b[s,c,g] = - (Y[g,s] - np.log(Exp[g,s]) - Var_Exp2[g,s]) *(2*np.divide(g_Exp[s,c,g],Exp[g,s]) + a[s,c,g])
grad_PY = np.zeros((Nsample, Ncell))
for s in range(Nsample):
for c in range(Ncell):
grad_PY[s,c] = grad_PY[s,c] - np.sum(0.5 / np.square(SigmaY[:,s]) * (a[s,c,:] + b[s,c,:]))
return grad_PY
def conjugate_gradient(A, b, x0):
"""
Applies conjugate gradient algorithm to find the minimum of function
Algorithm from laboratory nr 8
:param A: matrix 2x2
:param b: matrix 1x2
:param x0: starting point (eg [0,0])
:return: all the solutions, the last one being the most accurate
"""
eps = 1e-10
x = x0
dk = rk = b - dot(A, x)
solutions = []
while norm(rk) > eps:
rate = dot(t(rk), rk) / dot(dot(t(dk), A), dk)
x = x + rate * dk
rk_n = rk - rate * dot(A, dk)
bk = dot(t(rk_n), rk_n) / dot(t(rk), rk)
rk = rk_n
dk = rk + bk * dk
solutions.append(x)
return solutions
def LR_smooth(Y, X_):
X = add_intercept(X_)
yhat = np.zeros(Y.shape)
theta = np.zeros(2)
theta = dot(np.linalg.inv(dot(t(X), X)), dot(t(X), Y))
yhat = dot(X, theta)[:, np.newaxis]
return yhat, theta
def CreateLmComp(self):
'''
This function generates components for the linear model: hrf, whitening matrix, autocorrelation matrix and CX
'''
# hrf
self.canonical()
# contrasts
# expand contrasts to resolution
self.CX = np.array(np.kron(self.C, np.eye(self.laghrf)))
assert(self.CX.shape[0]==self.C.shape[0]*self.laghrf)
assert(self.CX.shape[1]==self.n_stimuli*self.laghrf)
# drift
self.S = self.drift(np.arange(0, self.n_scans)) # [tp x 1]
assert(self.S.shape == (3,self.n_scans))
self.S = np.matrix(self.S)
# square of the whitening matrix
base = [1 + self.rho**2, -1 * self.rho] + [0] * (self.n_scans - 2)
self.V2 = scipy.linalg.toeplitz(base)
# set first and last to 1
self.V2[0, 0] = 1
self.V2[self.n_scans - 1, self.n_scans - 1] = 1
self.V2 = np.matrix(self.V2)
self.white = self.V2 - self.V2 * \
t(self.S) * np.linalg.pinv(self.S *
self.V2 * t(self.S)) * self.S * self.V2
return self
def LM(Y, Z, X, beta_0):
Z_PI = Z @ PI_tilde(Y, Z, X, beta_0)
P_zpi = np.outer(Z_PI, t(Z_PI)) * \
((t(Z_PI) @ Z_PI) ** (-1))
LM = ((1 / sigma_eps_eps(Y, Z, X, beta_0)) *
((t(Y - X * beta_0)) @ P_zpi @ (Y - X * beta_0)))
return LM
def B_init(dim_hid,dim_vis): B = rd.uniform(size = (dim_hid+1,dim_vis+1)) B[:,0] = 0 B[0,:] = 0 B[0,0] = 1 B = t(t(B) / np.sum(B, axis = 1)) return B
def hessian(x, y, theta): #constructing hessian matrix
H = 0
for i in range(len(y)):
H+=np.exp(-y[i]*np.dot(t(theta),x[i,]))*y[i]**2\
*np.outer(x[i],t(x[i]))*sigmoid(y[i],x[i,],theta)**2
H /= len(y)
return H
def g_Exp_Beta_python(Nu, Omega, Beta, B0, Ngene, Ncell, Nsample):
g_Exp = t(np.tile(np.exp(Nu + 0.5*np.square(Omega))[:,:,np.newaxis], [1,1,Nsample]), (2,1,0))\
/np.tile(B0[:,np.newaxis, np.newaxis], [1,Ncell, Ngene])\
- t(np.tile(np.sum( # Nsample Ncell Ngenes
t(np.tile(np.exp(Nu + 0.5*np.square(Omega))[:,:,np.newaxis], [1,1,Nsample]), (2,1,0))\
*np.tile((Beta/np.tile(np.square(B0)[:,np.newaxis], [1,Ncell]))[:,:, np.newaxis], [1,1, Ngene]), axis=1
)[:,:,np.newaxis], [1,1,Ncell]), (0,2,1))
return g_Exp
def PI_tilde(Y, Z, X, beta_0):
M_z = np.identity(n=N) - Z @ inv(t(Z) @ Z) @ t(Z)
sigma_e_e = sigma_eps_eps(Y, Z, X, beta_0)
sigma_e_V = sigma_eps_V(Y, Z, X, beta_0)
eps = Y - X * beta_0
ro_hat = sigma_e_V / sigma_e_e
PI_tilde = inv(t(Z) @ Z) @ t(Z) @ (X - eps * ro_hat)
return (PI_tilde)
def eval_f(A, b, x):
"""
:param A: function component
:param b: function component
:param x: value to evaluate
:return: f(x) where f is the function represented by A & b
"""
return 0.5 * dot(dot(x, A), t(x)) - dot(x, t(b))
def pearsonr(signals, nstim):
cor = []
varcov = np.zeros([len(signals), len(signals)])
for sig1 in range(len(signals)):
for sig2 in range(sig1, len(signals)):
cors = np.diag(np.corrcoef(
t(signals[sig1]), t(signals[sig2]))[nstim:, :nstim])
varcov[sig1, sig2] = np.mean(cors)
varcov[sig2, sig1] = np.mean(cors)
return varcov
def LWR_smooth(Y, X, tau): #locally weighted regression
Y_hat = np.zeros(Y.shape) #initialize
for i in range(len(Y)):
W = np.diag(np.exp(-(X[i] - X)**2 / 2 /
tau**2)) ## construct weight matrix
Y_hat[i] = X[i] * reduce(dot, [t(X), W, X])**(-1) * reduce(
dot, [t(X), W, Y])
##reduce is for triple dot product
##return prediction
return Y_hat
def FdCalc(self, Design):
W = np.matrix(Design['Z'])
X = t(W) * self.white * W
invM = scipy.linalg.pinv(X)
CMC = np.matrix(self.C) * invM * np.matrix(t(self.C))
if self.Aoptimality == True:
Design["Fd"] = float(self.rc / np.matrix.trace(CMC))
else:
Design["Fd"] = float(np.linalg.det(CMC)**(-1 / self.rc))
return Design
def FdCalc(self,Design):
W = np.matrix(Design['Z'])
X = t(W)*self.white*W
invM = scipy.linalg.pinv(X)
CMC = np.matrix(self.C)*invM*np.matrix(t(self.C))
if self.Aoptimality == True:
Design["Fd"] = float(self.rc/np.matrix.trace(CMC))
else:
Design["Fd"] = float(np.linalg.det(CMC)**(-1/self.rc))
return Design
def r_beta_0(Y, Z, X, beta_0):
M_z = np.identity(n=N) - Z @ inv(t(Z) @ Z) @ t(Z)
SIGMA_VV = 1 / (N - k) * t(X) @ M_z @ X
SIGMA_VV_eps = SIGMA_VV - \
((sigma_eps_V(Y, Z, X, beta_0) ** 2) / sigma_eps_eps(Y, Z, X, beta_0))
PI_tld = PI_tilde(Y, Z, X, beta_0)
Z_PI = Z @ PI_tld
r_beta = (1 / SIGMA_VV_eps) * \
t(Y - X * beta_0) * (t(Z_PI) @ Z_PI) @ (Y - X * beta_0)
return r_beta
def RsT(R, n, s):
"""
:param R: 3 dimensional matrix
:param n: integer
:param s: integer
:return: integer
"""
B = []
for k in range(0, (n - 2)):
B.append(Beta(k + 1))
# print(t(R[0][s,0:(n - 2 - s)]))
rst = sum(t(t(R[0][s, 0:(n - 2 - s)]) * B[0:(n - 2 - s)]))
return rst
def compute_hydraulic_p(qc):
# Débits des arcs
q = q0 + dot(B, qc)
# Pertes de charge des arcs
z = r * abs(q) * q
# Flux des noeuds
f = np.zeros(m)
f[:mr] = dot(Ar, q)
f[mr:] = fd
# Pression aux noeuds
p = np.zeros(m)
p[:mr] = pr
p[mr:] = -dot(t(AdI), (dot(t(Ar), pr) + z)[:md])
return q, z, f, p
def FdCalc(self, Aoptimality=True):
'''
Compute detection power.
:param Aoptimality: Kind of optimality to optimize: A- or D-optimality
:type Aoptimality: boolean
'''
DES = {"order": self.order, "ITI": self.ITI}
pickle.dump(DES, open("/home/jdurnez/SVDerrorCheck/design.p", "wb"))
try:
invM = scipy.linalg.inv(self.Z)
except scipy.linalg.LinAlgError:
try:
invM = scipy.linalg.pinv(self.Z)
except numpy.linalg.linalg.LinAlgError:
invM = np.nan
sys.exc_clear()
invM = np.array(invM)
CMC = np.matrix(self.C) * invM * np.matrix(t(self.C))
if Aoptimality == True:
self.Fd = float(len(self.C) / np.matrix.trace(CMC))
else:
self.Fd = float(np.linalg.det(CMC)**(-1 / len(self.C)))
self.Fd = self.Fd / self.experiment.FdMax
return self
def norm_rnd(sigma):
h = chol(sigma)
size = shape(sigma)
rv = randn(size = (size[0],1))
y = t(h) @ rv
return y
def FeCalc(self, Aoptimality=True):
'''
Compute estimation efficiency.
:param Aoptimality: Kind of optimality to optimize, A- or D-optimality
:type Aoptimality: boolean
'''
try:
invM = scipy.linalg.inv(self.X)
except scipy.linalg.LinAlgError:
try:
invM = scipy.linalg.pinv(self.X)
except numpy.linalg.linalg.LinAlgError:
invM = np.nan
sys.exc_clear()
print("step1")
invM = np.array(invM)
print("step2")
st1 = np.dot(self.CX, invM)
print("step3")
CMC = np.dot(st1, t(self.CX))
if Aoptimality == True:
self.Fe = float(self.CX.shape[0] / np.matrix.trace(CMC))
else:
self.Fe = float(np.linalg.det(CMC)**(-1 / len(self.C)))
self.Fe = self.Fe / self.experiment.FeMax
return self
def fit_sgd(X, Y, epoch=1000, lr=0.0001):
w = np.zeros(X.shape[1])
b = 0
lr = lr
for epoch in range(epoch):
for x, y in zip(X, Y): # mini batches of size 1
pred = squeeze(t(w).dot(t(x)) + b)
err = (y - pred)
grad_w = (-2 * x) * err
grad_b = (-2) * err
w = w - lr * grad_w
b = b - lr * grad_b
def f(x):
return squeeze(t(w).dot(t(x)) + b)
return f
def verify_equilibrum(q, z, f, p):
# Ecarts maximaux sur les lois de Kirschoff
tol_debits = max(abs(dot(A, q) - f))
tol_pression = max(abs(dot(t(A), p) + z))
# Affichage
print("Vérification des équations d'équilibre du réseau")
print("Sur les débits : {}".format(tol_debits))
print("Sur les pressions : {}".format(tol_pression))
def my_nlrm(y, x, beta_0, v_0, h_0, nu_0):
b0_cov = nu_0 * h_0**(-1) / (nu_0 -
2) * v_0 # analogie (3.16) z Koop (2003)
b0_std = np.array([[sqrt(var)] for var in diag(b0_cov)])
h0_std = sqrt(2 * h_0 / nu_0) # analogie odmocniny z (3.19) z Koop (2003)
n = len(y) # pocet pozorovani
b_ols = inv(t(x) @ x) @ t(x) @ y # (3.5) z Koop (2003)
nu_ols = n - x.shape[1] # (3.4) z Koop (2003)
s2_ols = 1 / nu_ols * t(y - x @ b_ols) @ (y - x @ b_ols
) # (3.6) z Koop (2003)
v_1 = inv(inv(v_0) + t(x) @ x) # (3.9) z Koop (2003)
beta_1 = v_1 @ (inv(v_0) @ beta_0 + t(x) @ x @ b_ols
) # (3.11) z Koop (2003)
nu_1 = nu_0 + n # (3.12) z Koop (2003)
h_1 = nu_1 / (
nu_0 / h_0 + nu_ols * s2_ols +
t(b_ols - beta_0) @ inv(v_0 + inv(t(x) @ x)) @ (b_ols - beta_0))
# (3.13) z Koop (2003), kdy h_1 = s2_1^-1
b1_cov = nu_1 / h_1 / (nu_1 - 2) * v_1 # (3.16) z Koop (2003)
b1_std = np.array([[sqrt(var)] for var in diag(b1_cov)])
h1_std = sqrt(2 * h_1 / nu_1) # odmocnina z (3.19) z Koop (2003)
log_c = gammaln(nu_1 / 2) + nu_0 / 2 * log(nu_0 / h_0) - gammaln(
nu_0 / 2) - n / 2 * log(pi)
# logaritmus (3.35) z Koop (2003)
log_ml = log_c + 1 / 2 * (log(det(v_1)) - log(det(v_0))) - nu_1 / 2 * log(
nu_1 / h_1)
# logaritmus (3.34) z Koop (2003)
results = {
'x': x,
'y': y,
'beta_0': beta_0,
'v_0': v_0,
'h_0': h_0,
'nu_0': nu_0,
'b0_cov': b0_cov,
'b0_std': b0_std,
'h0_std': h0_std,
'n': n,
'b_ols': b_ols,
'nu_ols': nu_ols,
's2_ols': s2_ols,
'beta_1': beta_1,
'h_1': h_1,
'v_1': v_1,
'nu_1': nu_1,
'b1_cov': b1_cov,
'b1_std': b1_std,
'h1_std': h1_std,
'log_c': log_c,
'log_ml': log_ml
}
return results
def my_nlrm(y, X, beta_0, V_0, h_0, nu_0):
# Vypocet charakteristik apriornich hustot
# Vypocet kovariancni matice pro beta
b0_cov = nu_0 * (1 / h_0) / (nu_0 -
2) * V_0 # analogie (3.16) z Koop (2003)
b0_std = [sqrt(cov) for cov in diag(b0_cov)]
# Apriorni sm. odchylka pro h
h0_std = sqrt(2 * h_0 / nu_0) # analogie (3.19) z Koop (2003)
# Vypocet aposteriornich hyperparametru
N = len(y)
# Odhady OLS
b_OLS = inv(t(X) @ X) @ t(X) @ y # (3.5) z Koop (2003)
nu_OLS = N - shape(X)[1] # (3.4) z Koop (2003)
s2_OLS = t(y - dot(X, b_OLS)) @ (
y - dot(X, b_OLS)) / nu_OLS # (3.6) z Koop (2003)
# Aposteriorni hyperparametry
V_1 = inv(inv(V_0) + (t(X) @ X)) # (3.10) z Koop (2003)
beta_1 = V_1 @ inv(V_0) @ beta_0 + t(X) @ dot(
X, b_OLS) # (3.11) z Koop (2003)
beta_1 = asmatrix(beta_1)
nu_1 = nu_0 + N # (3.12) z Koop (2003)
h_1 = nu_1 * 1/(nu_0 * 1/h_0 + nu_OLS * s2_OLS + \
t(b_OLS - beta_0) @ inv(V_0 + \
inv(t(X) @ X)) @ (b_OLS - beta_0)) # (3.13) z Koop (2003)
# Aposteriorni kovariancni matice a smerodatne odchylky
b1_cov = (nu_1 * 1 / h_1) / (nu_1 - 2) * V_1 # (3.16) z Koop (2003)
b1_std = [sqrt(cov) for cov in diag(b1_cov)]
# Aposteriorni smerodatna odchylka pro presnost chyby h
h1_std = sqrt(2 * h_1 / nu_1) # (3.19) z Koop (2003), odmocneno
# Logaritmus marginalni verohodnosti
log_c = lgamma(nu_1/2) + nu_0/2 * log(nu_0/h_0) - \
lgamma(nu_0/2) - N/2 * log(pi) # (3.35) z Koop (2003), logaritmovano
log_ML = log_c + 1/2 * (log(det(V_1)) - log(det(V_0))) - \
nu_1/2 * log(nu_1/h_1) # (3.34) z Koop (2003), logaritmovano
# Ulozeni vysledku
results = {
'b0_cov': b0_cov,
'b0_std': b0_std,
'h0_std': h0_std,
'beta_1': beta_1,
'h_1': h_1,
'V_1': V_1,
'nu_1': nu_1,
'b1_cov': b1_cov,
'b1_std': b1_std,
'h1_std': h1_std,
'log_ML': log_ML
}
return results
def oracle(u, compute_gradient=True, compute_hessian=False):
q, delta = q_hat(u)
# Critère
# on prend l'opposée du critère réel pour passer à un problème de minimisation
loss = -(1./3*dot(q, r*q*np.abs(q)) + dot(pr, dot(Ar, q)) + dot(u, dot(Ad, q) - fd))
# Dérivée du critère par rapport à u
# On prend l'opposée du critère réel pour passer à un problème de minimisation
gradient = -( dot(Ad, q) - fd) if compute_gradient else None
hessian = -dot(dot(Ad, delta), t(Ad)) if compute_hessian else None
return loss, gradient, hessian
def g_PY_Beta_python(Nu, Beta, Omega, Y, SigmaY, B0, Ngene, Ncell, Nsample):
# Ngene by Ncell by Nsample
Exp = t(np.tile(ExpQ(Nu, Beta, Omega, Ngene, Ncell, Nsample)[:,:,np.newaxis], [1,1,Ncell]), (0,2,1))
Var = t(np.tile(VarQ(Nu, Beta, Omega, Ngene, Ncell, Nsample)[:,:,np.newaxis], [1,1,Ncell]), (0,2,1))
# Nsample by Ncell be Ngene
g_Exp = g_Exp_Beta(Nu, Omega, Beta, B0, Ngene, Ncell, Nsample)
g_Var = g_Var_Beta(Nu, Omega, Beta, B0, Ngene, Ncell, Nsample)
# Nsample by Ncell by Ngene
a = (g_Var * t(Exp, (2,1,0)) - 2*g_Exp*t(Var, (2,1,0)))/t(np.power(Exp,3), (2,1,0))
b = - (\
t(np.tile(Y[:,:,np.newaxis], [1,1,Ncell]), (1,2,0))\
- t(np.log(Exp+0.000001), (2,1,0))- t(Var/(2*np.square(Exp)), (2,1,0))\
)*(2*g_Exp/t(Exp, (2,1,0)) + a)
grad_PY = -np.sum( 0.5 / t(np.tile(np.square(SigmaY)[:,:,np.newaxis], [1,1,Ncell]), (1,2,0)) \
* ( a + b ), axis=2)
return grad_PY
def fit_normal_equation(X, Y):
X = np.c_[np.ones((len(X), 1)),
X] # adding ones for bias in affine functions
tX = t(X)
w = inv(tX.dot(X)).dot(tX).dot(Y)
def f(x):
x = np.c_[np.ones((len(x), 1)),
x] # adding ones for bias in affine functions
return squeeze(t(w).dot(t(x)))
return f
def g_Exp_Beta(Nu, Omega, Beta, B0, Ngene, Ncell, Nsample):
ExpX = np.exp(Nu)
for i in range(Nsample):
ExpX[i,:,:] = ExpX[i,:,:]*np.exp(0.5*np.square(Omega)) #Nsample by Ngene by Ncell
B0mat = np.empty(Beta.shape)
for c in range(Ncell):
B0mat[:,c] =Beta[:,c]/np.square(B0)
#B0mat = np.dot(B0mat, t(ExpX)) # Nsample by Ngene
tmp = np.empty((Nsample, Ngene))
for i in range(Nsample):
tmp[i,:] = np.dot(B0mat[i,:], t(ExpX[i,:,:]))
B0mat = tmp
g_Exp = np.empty((Nsample, Ncell, Ngene))
for s in range(Nsample):
for c in range(Ncell):
g_Exp[s,c,:] = t(ExpX[s,:,c] / B0[s]) - B0mat[s,:]
return g_Exp
def Optimize(logY, SigmaY, Mu0, Alpha, Alpha0, Beta0, Kappa0, Nu_Init, Omega_Init, Nsample, Ncell, Init_Fraction):
Beta_Init = np.random.gamma(shape=1, size=(Nsample, Ncell)) * 0.1 + t(Init_Fraction) * 10
obs = BLADE(logY, SigmaY, Mu0, Alpha, Alpha0, Beta0, Kappa0,
Nu_Init, Omega_Init, Beta_Init, fix_Nu=True, fix_Omega=True)
obs.Optimize()
#obs.Fix_par['Beta'] = True
obs.Fix_par['Nu'] = False
obs.Fix_par['Omega'] = False
obs.Optimize()
#obs.Fix_par['Beta'] = False
#obs.Optimize()
return obs
def CreateLmComp(self):
# compute components for linear model (drift, autocorrelation, projection of drift)
# drift
self.S = self.drift(np.arange(0, self.duration, self.TR)) #[tp x 1]
self.S = np.matrix(self.S)
# square of the whitening matrix
base = [1 + self.rho**2, -1 * self.rho] + [0] * (self.tp - 2)
self.V2 = scipy.linalg.toeplitz(base)
self.V2[0, 0] = 1
self.V2[self.tp - 1, self.tp - 1] = 1
self.V2 = np.matrix(self.V2)
self.V = scipy.linalg.sqrtm(self.V2)
P = t(self.S) * np.linalg.pinv(self.S * t(self.S)) * self.S
self.white = t(self.V) * (np.eye(self.tp) - P) * self.V
# orthogonal projection of whitened drift
#VS = self.V*self.S
#self.Pvs = reduce(np.dot,[VS,np.linalg.pinv(np.dot(t(VS),VS)),t(VS)])
return self
def __init__(self, dfy, dfX, numeigen = 0, minproportion = 0, vce = None, cluster = None):
print("PCA Regression:")
self.vce = vce
self.cluster = cluster
self.varlist = dfX.columns
self.X = dfX.values
self.Xt = self.X.transpose()
self.XtX = self.Xt @ self.X
self.lam, self.v = np.linalg.eigh(self.XtX)
idx = self.lam.argsort()[::-1]
self.v = self.v[:,idx]
self.lam = self.lam[idx]
self.lp = self.lam/sum(self.lam)
self.dfA = pd.DataFrame(self.X @ self.v, columns = np.arange(len(self.lam))+1)
self.l = len(self.lam)
if numeigen > 0 and minproportion > 0:
print("Error, only one is required")
pass
elif minproportion > 0:
proportion = 0
self.num = 0
for i in range(len(self.lp)):
self.num = self.num + 1
proportion = proportion + self.lp[i]
if proportion >= minproportion:
break
elif numeigen > 0:
self.num = numeigen
else:
print("Selecting all components")
self.num = len(self.lam)
print("Number of components selected: {}".format(self.num))
self.est = OLS(dfy, self.dfA.iloc[:,0:self.num], nocons = True, vce = self.vce, cluster = self.cluster)
self.g = self.est.b
self.SEg = self.est.SEb
self.b = self.v[:,0:self.num] @ self.g
self.Varb = self.v[:,0:self.num] @ self.est.Varb1 @ self.v[:,0:self.num].transpose()
if np.any(np.diag(self.Varb) < 0):
print("Non Positive Semi-Definite VCE Matrix! Cameron, Gelbach & Miller (2011) Transformation Used")
lb, vb = eigh(self.Varb)
idx = lb.argsort()[::-1]
vb = vb[:,idx]
lb = lb[idx]
for i in range(len(lb)):
lb[i] = max(0, lb[i])
diag = lb * np.identity(len(lb))
self.Varb = vb @ diag @ t(vb)
self.SEb = np.sqrt(np.diag(self.Varb))
self.t = self.b/self.SEb
self.pval = 2*ss.t.cdf(-abs(self.t), self.est.df)
def CreateLmComp(self):
# compute components for linear model (drift, autocorrelation, projection of drift)
# drift
self.S = self.drift(np.arange(0,self.duration,self.TR)) #[tp x 1]
self.S = np.matrix(self.S)
# square of the whitening matrix
base = [1+self.rho**2,-1*self.rho]+[0]*(self.tp-2)
self.V2 = scipy.linalg.toeplitz(base)
self.V2[0,0] = 1
self.V2[self.tp-1,self.tp-1] = 1
self.V2 = np.matrix(self.V2)
self.V = scipy.linalg.sqrtm(self.V2)
P = t(self.S)*np.linalg.pinv(self.S*t(self.S))*self.S
self.white = t(self.V)*(np.eye(self.tp)-P)*self.V
# orthogonal projection of whitened drift
#VS = self.V*self.S
#self.Pvs = reduce(np.dot,[VS,np.linalg.pinv(np.dot(t(VS),VS)),t(VS)])
return self
def compute_hydraulic_d(pd):
# Pressions aux noeuds
p = np.zeros(m)
p[:mr] = pr
p[mr:m] = pd
# Pertes de charge des arcs
z = dot(-t(A), p)
# Debits des arcs
q = z / np.sqrt(r * abs(z))
# Flux aux noeuds
f = np.zeros(m)
f[:mr] = dot(Ar, q)
f[mr:m] = fd
return q, z, f, p
def diag(mat):
return t(matrix(diagonal(matrix(mat))))
def downWin(self):
x = t(self.board).tolist()
return self.straightWin(x)
def A_init(dim_hid): A = rd.uniform(size = (dim_hid+1,dim_hid+1)) A[:,0] = 0 A[0,1:(dim_hid+1)] = 1./dim_hid A = t(t(A) / np.sum(A, axis = 1)) return A