def _sample_effects_block_garcia(self):
self._update_mm_equations()
C = self.mmeq_C
# sample loc_star
# -- fixed locations are left as 0 since they don't affect result (GC&S claim)
sigma2b = self.theta[self.sigma2_b_idx]
self.loc_star[self.num_fixed:,0] = gt.rmvn(0,cholL=self.cholG,sigma=sigma2b)
# Sample y*
sigma2e = self.theta[self.sigma2_e_idx]
Ie = np.matrix(np.identity(self.num_y), copy=False)
e_star = gt.rmvn(0,cholLU=Ie,lower=True,sigma=sigma2e)
self.y_star = self.W*self.loc_star + e_star
cholC = np.asmatrix(scipy.linalg.cholesky(C,lower=True))
rhs = self.W.T * (self.y - self.y_star)
self.loc_tilde = np.asmatrix(scipy.linalg.cho_solve((cholC,True),rhs))
# Sampling result
self.theta[0:self.num_locations,0] = self.loc_star - self.loc_tilde
def lmm_sample(beta,Gs,sigma2=[],X=[5,30]):
p = len(beta)
beta = np.matrix(beta).reshape(p,1)
c = len(Gs)
qs = [np.shape(g)[0] for g in Gs]
q = sum(qs)
n = qs[0]
if (isinstance(X,list)):
# X contains list of ranges
rangex0 = X[0]
rangex1 = X[1]
X = np.matrix(np.zeros((n,p)))
X[:,0] = 1
X[:,1] = rangex0 + (rangex1-rangex0)*np.random.rand(n).reshape(n,1)
else:
assert(isinstance(X,np.matrix))
(n1,p1) = np.shape(X)
assert((n1==n)and(p1==n))
# Create Z: n x q --- Sparse
# sparse(y)
zs = [sparse.eye(n)]
data = [1 for u in range(0,n)]
for qi in qs[1:]:
# col = [random.randint(0,qi-1) for i in range(0,n)]
col = [i%qi for i in range(0,n)]
zi = sparse.csc_matrix((data,(range(0,n),col)),shape=(n,qi))
zs.append(zi)
Z = sparse.hstack(zs)
assert(len(sigma2)==(c+1))
# Sample random effects
us = []
cholLs=[]
for g,s2 in zip(Gs,sigma2[:-1]):
cholL = np.linalg.cholesky(g)
cholLs.append(cholL)
ui = gt.rmvn(0,cholL=cholL,sigma=s2)
us.append(ui)
u = np.vstack(us)
# Sample residual
sigma2_e = sigma2[-1]
R = np.asmatrix(np.eye(n))
cholL = np.linalg.cholesky(R)
e = gt.rmvn(0,cholL=cholL,sigma=sigma2_e)
# Calculate y
y = X*beta + Z*u + e
return (y,X,Z,cholLs,u,e)
def _sample_effects_block(self):
self._update_mm_equations()
C = self.mmeq_C
invC = np.linalg.inv(C)
# Compute location estimators - expected values
# Equation C * loc = rhs -> loc = C^{-1}*rhs
self.loc_hat = invC * self.mmeq_rhs
# Sample from multivariate normal
self.theta[0:self.num_locations,0] = gt.rmvn(self.loc_hat,V=invC,sigma=self.theta[self.sigma2_e_idx])
def lmmsample(tree):
# The script
#tree = PhyloTree(treeFile, schema='newick')
#tree.normalize()
G = tree.getV()
(n,n) = np.shape(G)
num_fixed = 2
# Create Beta
beta = np.matrix([15,2.5]).reshape(num_fixed,1)
# Create X
rangex0 = 5
rangex1 = 30
X = np.matrix(np.zeros((n,num_fixed)))
X[:,0] = 1
X[:,1] = rangex0 + (rangex1-rangex0)*np.random.rand(n).reshape(n,1)
# Create Z
Z = np.asmatrix(np.eye(n))
# Sample b ~ N(0,sigma2_b * V)
sigma2_b = 5
cholL = np.linalg.cholesky(G)
b = gt.rmvn(0,cholL=cholL,sigma=sigma2_b)
# Sample residual e ~ N(0, sigma2_e * R)
sigma2_e = 1.0
R = np.asmatrix(np.eye(n))
cholL = np.linalg.cholesky(R)
e = gt.rmvn(0,cholL=cholL,sigma=sigma2_e)
# Calculate y
y = X*beta + Z*b + e
#yl = y.ravel().tolist()[0]
#xl = X[:,1].ravel().tolist()[0]
#plt.plot(xl,yl,'ro')
#ymax = max(yl)
#plt.axis([0,rangex1,0, 10*(int(ymax/10)+1)])
#plt.show()
return (y,X,beta,Z,b,G,cholL,sigma2_b,R,sigma2_e)
def _sample_effects_block_chol(self):
# self._update_mm_equations()
C = self.mmeq_C
L = np.linalg.cholesky(C)
# L = np.asmatrix(scipy.linalg.cholesky(C,lower=True))
# print 'before solve'
self.theta_hat = np.asmatrix(scipy.linalg.cho_solve((L, True), self.mmeq_rhs))
# print 'after solve'
# invChol = np.linalg.inv(cholC)
sigma2_e0 = self.sigma2_e[0, 0]
self.theta[:, 0] = gt.rmvn(self.theta_hat, cholL=L, inverse=True, sigma=sigma2_e0)
def _sample_effects_block_chol(self):
self._update_mm_equations()
C = self.mmeq_C
L = np.linalg.cholesky(C)
#L = np.asmatrix(scipy.linalg.cholesky(C,lower=True))
print 'before solve'
print L
print self.mmeq_rhs
self.loc_hat = np.asmatrix(scipy.linalg.cho_solve((L,True),self.mmeq_rhs))
print "first loc hat"
print self.loc_hat
#print 'after solve'
# invChol = np.linalg.inv(cholC)
sigma2e = self.theta[self.sigma2_e_idx]
self.theta[0:self.num_locations,0] = gt.rmvn(self.loc_hat,cholL=L,inverse=True,sigma=sigma2e)
print 'sample'
print self.theta[0:self.num_locations,0]
exit(0)
