def def_pos(self,distance,k): major_axis = True # Project along major or minor axes? # Load Ellipticity Data for 100 Halos pkl_file = open(self.root+'/nkern/Stacking/Halo_Shape/100_halo_ellipticities.pkl','rb') input = pkl.Unpickler(pkl_file) d = input.load() eig_vec = d['eig_vec'] eig_val = d['eig_val'] # Define theta and phi for unit vector and construt unit vector in cartesian coordinates if major_axis == True: eig_vec = eig_vec[k][0] r = norm(eig_vec) theta = np.arccos(eig_vec[2]/r) phi = np.arctan(eig_vec[1]/eig_vec[0]) if major_axis == False: eig_vec = eig_vec[k][1] r = norm(eig_vec) theta = np.arccos(eig_vec[2]/r) phi = np.arctan(eig_vec[1]/eig_vec[0]) # if random.random()<.5: # eig_vec *= -1. theta = random.normal(theta,.075) phi = random.normal(phi,.075) x = np.sin(theta)*np.cos(phi) y = np.sin(theta)*np.sin(phi) z = np.cos(theta) unit = np.array([x,y,z])/norm(np.array([x,y,z])) return unit*distance
def func(self, X, V):
k = self.C.TFdata.k
v1 = self.C.TFdata.v1
w1 = self.C.TFdata.w1
if k >=0:
J_coords = self.F.sysfunc.J_coords
w = sqrt(k)
q = v1 - (1j/w)*matrixmultiply(self.F.sysfunc.J_coords,v1)
p = w1 + (1j/w)*matrixmultiply(transpose(self.F.sysfunc.J_coords),w1)
p /= linalg.norm(p)
q /= linalg.norm(q)
p = reshape(p,(p.shape[0],))
q = reshape(q,(q.shape[0],))
direc = conjugate(1/matrixmultiply(transpose(conjugate(p)),q))
p = direc*p
l1 = firstlyapunov(X, self.F.sysfunc, w, J_coords=J_coords, p=p, q=q)
return array([l1])
else:
return array([1])
def test_c_samples_scaling():
"""Test C scaling by n_samples
"""
X = iris.data[iris.target != 2]
y = iris.target[iris.target != 2]
X2 = np.r_[X, X]
y2 = np.r_[y, y]
clfs = [svm.SVC(tol=1e-6, kernel='linear', C=0.1),
svm.SVR(tol=1e-6, kernel='linear', C=100),
svm.LinearSVC(tol=1e-6, C=0.1),
linear_model.LogisticRegression(penalty='l1', tol=1e-6, C=100),
linear_model.LogisticRegression(penalty='l2', tol=1e-6),
svm.NuSVR(tol=1e-6, kernel='linear')]
for clf in clfs:
clf.set_params(scale_C=False)
coef_ = clf.fit(X, y).coef_
coef2_ = clf.fit(X2, y2).coef_
error_no_scale = linalg.norm(coef2_ - coef_) / linalg.norm(coef_)
assert_true(error_no_scale > 1e-3)
clf.set_params(scale_C=True)
coef_ = clf.fit(X, y).coef_
coef2_ = clf.fit(X2, y2).coef_
error_with_scale = linalg.norm(coef2_ - coef_) / linalg.norm(coef_)
assert_true(error_with_scale < 1e-5)
def poseLinearCalibration(objectPoints, imagePoints, cameraMatrix, distCoeffs, model, retMatrix=False):
'''
takes calibration points and estimate linearly camera pose. re
'''
# map coordinates with z=0
xm, ym = objectPoints.T[:2]
# undistort ccd points, x,y homogenous undistorted
xp, yp = cl.ccd2homUndistorted(imagePoints, cameraMatrix, distCoeffs, model)
A = dataMatrixPoseCalib(xm, ym, xp, yp)
_, s, v = ln.svd(A)
m = v[-1] # select right singular vector of smaller singular value
# normalize and ensure that points are in front of the camera
m /= np.sqrt(ln.norm(m[:3])*ln.norm(m[3:6])) * np.sign(m[-1])
# rearrange as rVec, tVec
R = np.array([m[:3], m[3:6], np.cross(m[:3], m[3:6])]).T
rVec = cv2.Rodrigues(R)[0]
tVec = m[6:]
if retMatrix:
return rVec, tVec, A
return rVec, tVec
def fgmres(self,rhs,tol=1e-6,restrt=None,maxiter=None,callback=None):
if maxiter == None:
maxiter = len(rhs)
if restrt == None:
restrt = 2*maxiter
# implemented as in [Saad, 1993]
# start
x = zeros(len(rhs))
H = zeros((restrt+1, restrt))
V = zeros((len(rhs),restrt))
Z = zeros((len(rhs),restrt))
# Arnoldi process (with modified Gramm-Schmidt)
res = 1.
j = 0
r = rhs - self.point.matvec(x)
beta = norm(r)
V[:,0]=r/beta
while j < maxiter and res > tol:
Z[:,j] = self.point.psolve(V[:,j])
w = self.point.matvec(Z[:,j])
for i in range(j+1):
H[i,j]=dot(w,V[:,i])
w = w - H[i,j]*V[:,i]
H[j+1,j] = norm(w)
V[:,j+1]=w/H[j+1,j]
e = zeros(j+2)
e[0]=1.
y, res, rank, sing_val = lstsq(H[:j+2,:j+1],beta*e)
j += 1
print "# GMRES| iteration :", j, "res: ", res/beta
self.resid = r_[self.resid,res/beta]
Zy = dot(Z[:,:j],y)
x = x + Zy
info = 1
return (x,info)
def _help_expm_cond_search(A, A_norm, X, X_norm, eps, p):
p = np.reshape(p, A.shape)
p_norm = norm(p)
perturbation = eps * p * (A_norm / p_norm)
X_prime = expm(A + perturbation)
scaled_relative_error = norm(X_prime - X) / (X_norm * eps)
return -scaled_relative_error
def pcosine(u, v):
"""Computes the Cosine distance (positive space) between 1-D arrays.
The Cosine distance (positive space) between `u` and `v` is defined as
.. math::
d(u, v) = 1 - abs \\left( \\frac{u \\cdot v}{||u||_2 ||v||_2} \\right)
where :math:`u \\cdot v` is the dot product of :math:`u` and :math:`v`.
Parameters
----------
u : array
Input array.
v : array
Input array.
Returns
-------
cosine : float
Cosine distance between `u` and `v`.
"""
# validate vectors like scipy does
u = ssd._validate_vector(u)
v = ssd._validate_vector(v)
dist = 1. - np.abs(np.dot(u, v) / (linalg.norm(u) * linalg.norm(v)))
return dist
def power_iteration_oPCA(data, num_pcs, tolerance=0.01, max_iter=1000):
"""Compute OPCs recursively with the power iteration method.
Parameters
----------
data : array
see offsetPCA
num_pcs : int
Then number of oPCs to be computed.
tolerance : float, optional
The criterion for fractional difference between subsequent estimates
used to determine when to terminate the algorithm. Default: 0.01.
max_iter : int, optional
The maximum number of iterations. Default: 1000.
Returns
-------
see offsetPCA
WARNING: INCOMPLETE!!!!!!!!!!!
"""
for X in (data):
U0 = X.reshape(1, -1)
p = X.shape
break
eivects, eivals = [], []
Z = np.zeros((1, p))
for pc_idx in range(num_pcs):
U = U0 / norm(U0) # np.random.randn(num_pcs, p)
iter_count = 0
while True:
print iter_count
iter_count += 1
if iter_count > max_iter:
warnings.warn("max_iter reached by power_iteration_oPCA")
break
_opca._Z_update(Z, U, data)
U_new = np.dot(np.dot(np.dot(U, U.T), inv(np.dot(Z, U.T))), Z)
error = norm(U_new - U) / norm(U)
U = U_new / norm(U_new)
if error < tolerance:
break
eivects.append(U.T)
eivals.append(float(np.dot(Z, U.T) /
np.dot(U, U.T)) / (2. * (X.shape[0] - 1.)))
"""
XUtU = np.dot(np.dot(X, U.T), U)
X -= XUtU
OX[1:] -= XUtU[:-1]
OX[:-1] -= XUtU[1:] # TODO: isn't this wrong???
"""
print 'Eigenvalue', pc_idx + 1, 'found'
eivects = np.concatenate(eivects, axis=1)
for i in range(eivects.shape[1]):
eivects[:, i] /= norm(eivects[:, i])
eivals = np.array(eivals)
idx = np.argsort(-eivals)
return eivals[idx], eivects[:, idx], np.dot(X, eivects[:, idx])
def getVelocity(self,p, V, E, last=False):
"""
This function calculates the velocity for the robot with RRT.
The inputs are (given in order):
p = the current x-y position of the robot
E = edges of the tree (2 x No. of nodes on the tree)
V = points of the tree (2 x No. of vertices)
last = True, if the current region is the last region
= False, if the current region is NOT the last region
"""
pose = mat(p).T
#dis_cur = distance between current position and the next point
dis_cur = vstack((V[1,E[1,self.E_current_column]],V[2,E[1,self.E_current_column]]))- pose
heading = E[1,self.E_current_column] # index of the current heading point on the tree
if norm(dis_cur) < 1.5*self.radius: # go to next point
if not heading == shape(V)[1]-1:
self.E_current_column = self.E_current_column + 1
dis_cur = vstack((V[1,E[1,self.E_current_column]],V[2,E[1,self.E_current_column]]))- pose
#else:
# dis_cur = vstack((V[1,E[1,self.E_current_column]],V[2,E[1,self.E_current_column]]))- vstack((V[1,E[0,self.E_current_column]],V[2,E[0,self.E_current_column]]))
Vel = zeros([2,1])
Vel[0:2,0] = dis_cur/norm(dis_cur)*0.5 #TUNE THE SPEED LATER
return Vel
def test_lasso_lars_vs_lasso_cd(verbose=False):
# Test that LassoLars and Lasso using coordinate descent give the
# same results.
X = 3 * diabetes.data
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
for c, a in zip(lasso_path.T, alphas):
if a == 0:
continue
lasso_cd.alpha = a
lasso_cd.fit(X, y)
error = linalg.norm(c - lasso_cd.coef_)
assert_less(error, 0.01)
# similar test, with the classifiers
for alpha in np.linspace(1e-2, 1 - 1e-2, 20):
clf1 = linear_model.LassoLars(alpha=alpha, normalize=False).fit(X, y)
clf2 = linear_model.Lasso(alpha=alpha, tol=1e-8,
normalize=False).fit(X, y)
err = linalg.norm(clf1.coef_ - clf2.coef_)
assert_less(err, 1e-3)
# same test, with normalized data
X = diabetes.data
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
tol=1e-8)
for c, a in zip(lasso_path.T, alphas):
if a == 0:
continue
lasso_cd.alpha = a
lasso_cd.fit(X, y)
error = linalg.norm(c - lasso_cd.coef_)
assert_less(error, 0.01)
def test_lasso_lars_vs_lasso_cd_early_stopping(verbose=False):
# Test that LassoLars and Lasso using coordinate descent give the
# same results when early stopping is used.
# (test : before, in the middle, and in the last part of the path)
alphas_min = [10, 0.9, 1e-4]
for alpha_min in alphas_min:
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
alpha_min=alpha_min)
lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
lasso_cd.alpha = alphas[-1]
lasso_cd.fit(X, y)
error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
assert_less(error, 0.01)
# same test, with normalization
for alpha_min in alphas_min:
alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
alpha_min=alpha_min)
lasso_cd = linear_model.Lasso(fit_intercept=True, normalize=True,
tol=1e-8)
lasso_cd.alpha = alphas[-1]
lasso_cd.fit(X, y)
error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
assert_less(error, 0.01)
def _assert_cov(cov, cov_desired, tol=0.005, nfree=True):
assert_equal(cov.ch_names, cov_desired.ch_names)
err = (linalg.norm(cov.data - cov_desired.data, ord='fro') /
linalg.norm(cov.data, ord='fro'))
assert_true(err < tol, msg='%s >= %s' % (err, tol))
if nfree:
assert_equal(cov.nfree, cov_desired.nfree)
def test_rank_deficient_design():
# consistency test that checks that LARS Lasso is handling rank
# deficient input data (with n_features < rank) in the same way
# as coordinate descent Lasso
y = [5, 0, 5]
for X in ([[5, 0],
[0, 5],
[10, 10]],
[[10, 10, 0],
[1e-32, 0, 0],
[0, 0, 1]],
):
# To be able to use the coefs to compute the objective function,
# we need to turn off normalization
lars = linear_model.LassoLars(.1, normalize=False)
coef_lars_ = lars.fit(X, y).coef_
obj_lars = (1. / (2. * 3.)
* linalg.norm(y - np.dot(X, coef_lars_)) ** 2
+ .1 * linalg.norm(coef_lars_, 1))
coord_descent = linear_model.Lasso(.1, tol=1e-6, normalize=False)
coef_cd_ = coord_descent.fit(X, y).coef_
obj_cd = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, coef_cd_)) ** 2
+ .1 * linalg.norm(coef_cd_, 1))
assert_less(obj_lars, obj_cd * (1. + 1e-8))
def calculate_examples(mean, sigma, weights, c = 2):
from scipy.linalg import norm
mean_p = mean + c * (weights/norm(weights)) * norm(sigma)
mean_m = mean - c * (weights/norm(weights)) * norm(sigma)
return np.array([mean_p, mean_m])
def get_neuromag_transform(lpa, rpa, nasion):
"""Creates a transformation matrix from RAS to Neuromag-like space
Resets the origin to mid-distance of peri-auricular points with nasion
passing through y-axis.
(mne manual, pg. 97)
Parameters
----------
lpa : numpy.array, shape = (1, 3)
Left peri-auricular point coordinate.
rpa : numpy.array, shape = (1, 3)
Right peri-auricular point coordinate.
nasion : numpy.array, shape = (1, 3)
Nasion point coordinate.
Returns
-------
trans : numpy.array, shape = (3, 3)
Transformation matrix to Neuromag-like space.
"""
origin = (lpa + rpa) / 2
nasion = nasion - origin
lpa = lpa - origin
rpa = rpa - origin
axes = np.empty((3, 3))
axes[1] = nasion / linalg.norm(nasion)
axes[2] = np.cross(axes[1], lpa - rpa)
axes[2] /= linalg.norm(axes[2])
axes[0] = np.cross(axes[1], axes[2])
trans = linalg.inv(axes)
return trans
def test_orthogonal_procrustes():
np.random.seed(1234)
for m, n in ((6, 4), (4, 4), (4, 6)):
# Sample a random target matrix.
B = np.random.randn(m, n)
# Sample a random orthogonal matrix
# by computing eigh of a sampled symmetric matrix.
X = np.random.randn(n, n)
w, V = eigh(X.T + X)
assert_allclose(inv(V), V.T)
# Compute a matrix with a known orthogonal transformation that gives B.
A = np.dot(B, V.T)
# Check that an orthogonal transformation from A to B can be recovered.
R, s = orthogonal_procrustes(A, B)
assert_allclose(inv(R), R.T)
assert_allclose(A.dot(R), B)
# Create a perturbed input matrix.
A_perturbed = A + 1e-2 * np.random.randn(m, n)
# Check that the orthogonal procrustes function can find an orthogonal
# transformation that is better than the orthogonal transformation
# computed from the original input matrix.
R_prime, s = orthogonal_procrustes(A_perturbed, B)
assert_allclose(inv(R_prime), R_prime.T)
# Compute the naive and optimal transformations of the perturbed input.
naive_approx = A_perturbed.dot(R)
optim_approx = A_perturbed.dot(R_prime)
# Compute the Frobenius norm errors of the matrix approximations.
naive_approx_error = norm(naive_approx - B, ord='fro')
optim_approx_error = norm(optim_approx - B, ord='fro')
# Check that the orthogonal Procrustes approximation is better.
assert_array_less(optim_approx_error, naive_approx_error)
def hess(A):
"""Computes the upper Hessenberg form of A using Householder reflectors.
input: A, mxn array
output: Q, orthogonal mxm array
H, upper Hessenberg
s.t. Q.dot(H).dot(Q.T) = A
"""
# similar approach as the householder function.
# again, not perfectly optimized, but good enough.
Q = np.eye(A.shape[0]).T
H = np.array(A, order="C")
# initialize m and n for convenience
m, n = H.shape
# avoid reallocating v in the for loop
v = np.empty(A.shape[1]-1)
for k in xrange(n-2):
# get a slice of the temporary array
vk = v[k:]
# fill it with corresponding values from R
vk[:] = H[k+1:,k]
# add in the term that makes the reflection work
vk[0] += copysign(la.norm(vk), vk[0])
# normalize it so it's an orthogonal transform
vk /= la.norm(vk)
# apply projection to H on the left
H[k+1:,k:] -= 2 * np.outer(vk, vk.dot(H[k+1:,k:]))
# apply projection to H on the right
H[:,k+1:] -= 2 * np.outer(H[:,k+1:].dot(vk), vk)
# Apply it to Q
Q[k+1:] -= 2 * np.outer(vk, vk.dot(Q[k+1:]))
return Q, H
def test_bar3( self ):
'''Clamped bar with recursive constraints (load at right end)
[0]-[1]-[2]-[3]
u[1] = 0.2 * u[2], u[2] = 0.2 * u[3], R[3] = 10
'''
self.domain.coord_max = (3,0,0)
self.domain.shape = (3,)
self.ts.bcond_list = [BCDof(var='u', dof = 0, value = 0.),
BCDof(var='u', dof = 1, link_dofs = [2], link_coeffs = [0.5] ),
BCDof(var='u', dof = 2, link_dofs = [3], link_coeffs = [1.] ),
BCDof(var='f', dof = 3, value = 1 ) ]
# system solver
u = self.tloop.eval()
# expected solution
u_ex = array([-0. , 0.1 , 0.2 , 0.2],
dtype = float )
difference = sqrt( norm( u-u_ex ) )
self.assertAlmostEqual( difference, 0 )
return
#
# '---------------------------------------------------------------'
# 'Clamped bar with recursive constraints (displ at right end)'
# 'u[1] = 0.5 * u[2], u[2] = 1.0 * u[3], u[3] = 1'
self.ts.bcond_list = [BCDof(var='u', dof = 0, value = 0.),
BCDof(var='u', dof = 1, link_dofs = [2], link_coeffs = [0.5] ),
BCDof(var='u', dof = 2, link_dofs = [3], link_coeffs = [1.] ),
BCDof(var='u', dof = 3, value = 1 ) ]
u = self.tloop.eval()
# expected solution
u_ex = array([0. , 0.5 , 1 , 1], dtype = float )
difference = sqrt( norm( u-u_ex ) )
self.assertAlmostEqual( difference, 0 )
def test_orthogonal_procrustes_skbio_example():
# This transformation is also exact.
# It uses translation, scaling, and reflection.
#
# |
# | a
# | b
# | c d
# --+---------
# |
# | w
# |
# | x
# |
# | z y
# |
#
A_orig = np.array([[4, -2], [4, -4], [4, -6], [2, -6]], dtype=float)
B_orig = np.array([[1, 3], [1, 2], [1, 1], [2, 1]], dtype=float)
B_standardized = np.array([
[-0.13363062, 0.6681531],
[-0.13363062, 0.13363062],
[-0.13363062, -0.40089186],
[0.40089186, -0.40089186]])
A, A_mu = _centered(A_orig)
B, B_mu = _centered(B_orig)
R, s = orthogonal_procrustes(A, B)
scale = s / np.square(norm(A))
B_approx = scale * np.dot(A, R) + B_mu
assert_allclose(B_approx, B_orig)
assert_allclose(B / norm(B), B_standardized)
def getRank(M, beta = 0.8, eps = 1e-6):
''' Loop until get right rank
Args: M: rank matrix; beta: non-teleport weight; eps: epsilon
Returns: Each node's Rank
'''
# Preparation
n1, n2 = M.shape
r1 = 1.0 / n2 * np.ones((n2, 1))
r0 = np.ones((n2, 1))
n = 0
print '|Loop| epsilon|time(s)|'
print '|----|---------|-------|'
# Loop
while norm(r1 - r0, 1) > eps:
t0 = time.clock()
n += 1
r0 = r1
r1 = beta * M.dot(r0)
r1 = r1 + (1 - beta) / n2
sum_r1 = r1.sum()
r1 = r1 + (1 - sum_r1) / n2
t1 = time.clock() - t0
print '|%4d|%6.3e|%7.3f|' % (n, norm(r1 - r0, 1), t1)
return r1
def initial_cond(coords, mass, dipole, temp, F):
cm_coords = coords - tile(center_of_mass(coords, mass), (coords.shape[0], 1))
print "computing inertia tensor and principal axes of inertia"
mol_I, mol_Ix = eig(inertia_tensor(cm_coords, mass))
mol_I.sort()
print "principal moments of inertia are: ", mol_I
# compute the ratio of the dipole energy to the
# rotational energy
print "x = (mu*F / kB*T_R) = ", norm(dipole) * F / kB_au / temp
# random initial angular velocity vector
# magnitude set so that 0.5 * I * w**2.0 = kT
w_mag = sqrt(2.0 * kB_au * temp / mol_I.mean())
w0 = 2.0 * rand(3) - 1.0
w0 = w0 / norm(w0) * w_mag
# random initial orientation / random unit quaternion
q0 = 2.0 * rand(4) - 1.0
q0 = q0 / norm(q0)
return q0, w0
def test_randomized_svd_power_iteration_normalizer():
# randomized_svd with power_iteration_normalized='none' diverges for
# large number of power iterations on this dataset
rng = np.random.RandomState(42)
X = make_low_rank_matrix(100, 500, effective_rank=50, random_state=rng)
X += 3 * rng.randint(0, 2, size=X.shape)
n_components = 50
# Check that it diverges with many (non-normalized) power iterations
U, s, V = randomized_svd(X, n_components, n_iter=2,
power_iteration_normalizer='none')
A = X - U.dot(np.diag(s).dot(V))
error_2 = linalg.norm(A, ord='fro')
U, s, V = randomized_svd(X, n_components, n_iter=20,
power_iteration_normalizer='none')
A = X - U.dot(np.diag(s).dot(V))
error_20 = linalg.norm(A, ord='fro')
assert_greater(np.abs(error_2 - error_20), 100)
for normalizer in ['LU', 'QR', 'auto']:
U, s, V = randomized_svd(X, n_components, n_iter=2,
power_iteration_normalizer=normalizer,
random_state=0)
A = X - U.dot(np.diag(s).dot(V))
error_2 = linalg.norm(A, ord='fro')
for i in [5, 10, 50]:
U, s, V = randomized_svd(X, n_components, n_iter=i,
power_iteration_normalizer=normalizer,
random_state=0)
A = X - U.dot(np.diag(s).dot(V))
error = linalg.norm(A, ord='fro')
assert_greater(15, np.abs(error_2 - error))
def compute_innovationFactor(y, H, m_minus):
innov = y - np.dot(H, m_minus)
if la.norm(innov) > (1.0/3.0):
innov_s = sigmaUnitSwitch(y) - np.dot(H, m_minus)
if la.norm(innov_s) < la.norm(innov):
innov = innov_s
return innov
def batched_decode(df):
s = time.time()
data = []
r_data = []
df = df.reindex(numpy.random.permutation(df.index))
for start_i in range(0, len(df), batch_size):
if verbose:
print(start_i)
batched_df = df[start_i:start_i+batch_size]
text_embeddings, text_masks, hypothesis_embeddings, hypothesis_masks, labels = \
prepare(batched_df, model['utable'], worddict, model['uoptions'], use_eos)
uff = model['f_w2v'](text_embeddings, text_masks, hypothesis_embeddings, hypothesis_masks)
r_uff = model['f_w2v'](hypothesis_embeddings, hypothesis_masks, text_embeddings, text_masks)
text_embeddings, text_masks, hypothesis_embeddings, hypothesis_masks, labels = \
prepare(batched_df, model['btable'], worddict, model['boptions'], use_eos)
bff = model['f_w2v2'](text_embeddings, text_masks, hypothesis_embeddings, hypothesis_masks)
r_bff = model['f_w2v2'](hypothesis_embeddings, hypothesis_masks, text_embeddings, text_masks)
if use_norm:
for j in range(len(uff)):
uff[j] /= norm(uff[j])
bff[j] /= norm(bff[j])
r_uff[j] /= norm(r_uff[j])
r_bff[j] /= norm(r_bff[j])
ff = numpy.concatenate([uff, bff], axis=1)
r_ff = numpy.concatenate([r_uff, r_bff], axis=1)
data.append(ff)
r_data.append(r_ff)
data = numpy.concatenate(data)
r_data = numpy.concatenate(r_data)
print('used {0} seconds'.format(time.time() - s))
return data, r_data, df.label.values
def _admm_ips(S, support, rho=1., tau_inc=2., tau_decr=2., mu=None, tol=1e-6,
max_iter=100, Xinit=None):
"""
returns:
-------
Z : numpy.ndarray
the split variable with correct support
r_ : list of floats
normalised norm of difference between split variables
s_ : list of floats
convergence of the variable Z in normalised norm
r_.append(linalg.norm(X - Z))
s_.append(np.inf)
normalisation is based on division by the number of elements
"""
p = S.shape[0]
dof = np.count_nonzero(support)
Z = (1 + rho) * np.identity(p)
U = np.zeros((p, p))
if Xinit is None:
X = np.identity(p)
else:
X = Xinit
r_ = list()
s_ = list()
f_vals_ = list()
rho_ = [rho]
r_.append(linalg.norm(X - Z) / dof)
s_.append(np.inf)
f_vals_.append(_pen_neg_log_likelihood(X, S))
iter_count = 0
while True:
try:
Z_old = Z.copy()
# closed form optimization for X
eigvals, eigvecs = linalg.eigh(rho * (Z - U) - S)
eigvals = (eigvals + (eigvals ** 2 + rho) ** (1. / 2)) / rho
X = eigvecs.dot(np.diag(eigvals).dot(eigvecs.T))
# proximal operator for Z: projection on support
Z = support * (X + U)
# update scaled dual variable
U = U + X - Z
r_.append(linalg.norm(X - Z) / (p ** 2))
s_.append(linalg.norm(Z - Z_old) / dof)
func_val = -np.linalg.slogdet(support * X)[1] + \
np.sum(S * X * support)
f_vals_.append(func_val)
if mu is not None:
rho = _update_rho(U, rho, r_[-1], s_[-1],
mu, tau_inc, tau_decr)
rho_.append(rho)
iter_count += 1
if (_check_convergence(X, Z, Z_old, U, rho, tol_abs=tol) or
iter_count > max_iter):
raise StopIteration
except StopIteration:
return X, Z, r_, s_, f_vals_, rho_
def PicardTolerance(x,u_k,b_k,FSpaces,dim,NormType,iter):
X = IO.vecToArray(x)
uu = X[0:dim[0]]
bb = X[dim[0]+dim[1]:dim[0]+dim[1]+dim[2]]
u = Function(FSpaces[0])
u.vector()[:] = u.vector()[:] + uu
diffu = u.vector().array() - u_k.vector().array()
b = Function(FSpaces[2])
b.vector()[:] = b.vector()[:] + bb
diffb = b.vector().array() - b_k.vector().array()
if (NormType == '2'):
epsu = splin.norm(diffu)/sqrt(dim[0])
epsb = splin.norm(diffb)/sqrt(dim[0])
elif (NormType == 'inf'):
epsu = splin.norm(diffu, ord=np.Inf)
epsb = splin.norm(diffb, ord=np.Inf)
else:
print "NormType must be 2 or inf"
quit()
print 'iter=%d: u-norm=%g b-norm=%g ' % (iter, epsu,epsb)
u_k.assign(u)
b_k.assign(b)
return u_k,b_k,epsu,epsb
def _check_dipoles(dipoles, fwd, stc, evoked, residual=None):
src = fwd['src']
pos1 = fwd['source_rr'][np.where(src[0]['vertno'] ==
stc.vertices[0])]
pos2 = fwd['source_rr'][np.where(src[1]['vertno'] ==
stc.vertices[1])[0] +
len(src[0]['vertno'])]
# Check the position of the two dipoles
assert_true(dipoles[0].pos[0] in np.array([pos1, pos2]))
assert_true(dipoles[1].pos[0] in np.array([pos1, pos2]))
ori1 = fwd['source_nn'][np.where(src[0]['vertno'] ==
stc.vertices[0])[0]][0]
ori2 = fwd['source_nn'][np.where(src[1]['vertno'] ==
stc.vertices[1])[0] +
len(src[0]['vertno'])][0]
# Check the orientation of the dipoles
assert_true(np.max(np.abs(np.dot(dipoles[0].ori[0],
np.array([ori1, ori2]).T))) > 0.99)
assert_true(np.max(np.abs(np.dot(dipoles[1].ori[0],
np.array([ori1, ori2]).T))) > 0.99)
if residual is not None:
picks_grad = mne.pick_types(residual.info, meg='grad')
picks_mag = mne.pick_types(residual.info, meg='mag')
rel_tol = 0.02
for picks in [picks_grad, picks_mag]:
assert_true(linalg.norm(residual.data[picks], ord='fro') <
rel_tol *
linalg.norm(evoked.data[picks], ord='fro'))
def power_method(A, N=20, tol=1e-12):
"""Compute the dominant eigenvalue of A and a corresponding eigenvector
via the power method.
Inputs:
A ((n,n) ndarray): A square matrix.
N (int): The maximum number of iterations.
tol (float): The stopping tolerance.
Returns:
(foat): The dominant eigenvalue of A.
((n, ) ndarray): An eigenvector corresponding to the dominant
eigenvalue of A.
"""
# Choose a random x_0 with norm 1.
x = np.random.random(A.shape[0])
x /= la.norm(x)
for _ in xrange(N):
# x_{k+1} = Ax_k / ||Ax_k||
y = np.dot(A, x)
x_new = y / la.norm(y)
# Check for convergence.
if la.norm(x_new - x) < tol:
x = x_new
break
# Move to the next iteration.
x = x_new
return np.dot(x, np.dot(A, x)), x
def dogleg(gk,Hk,rk):
"""Calculate the dogleg minimizer of the quadratic model function.
Parameters:
gk : ndarray of shape (n,)
The current gradient of the objective function
Hk : ndarray of shape (n,n)
The current (or approximate) hessian
rk : float
The current trust region radius
Returns:
pk : ndarray of shape (n,)
The dogleg minimizer of the model function.
"""
pB = la.solve(-Hk,gk)
pU = -(gk.T.dot(gk))/(gk.T.dot(Hk.dot(gk)))*gk
if la.norm(pB) <= rk:
return pB
if la.norm(pU) >= rk:
return rk*pU/la.norm(pU)
a = pB.T.dot(pB) - 2.*pB.T.dot(pU) + pU.T.dot(pU)
b = 2*pB.T.dot(pU) -2.*pU.T.dot(pU)
c = pU.T.dot(pU) - rk**2
t = 1. + (-b + np.sqrt(b**2-4.*a*c))/(2.*a)
return pU + (t-1.)*(pB-pU)
def test_cov_estimation_on_raw_segment():
"""Test estimation from raw on continuous recordings (typically empty room)
"""
tempdir = _TempDir()
raw = Raw(raw_fname, preload=False)
cov = compute_raw_data_covariance(raw)
cov_mne = read_cov(erm_cov_fname)
assert_true(cov_mne.ch_names == cov.ch_names)
assert_true(linalg.norm(cov.data - cov_mne.data, ord='fro')
/ linalg.norm(cov.data, ord='fro') < 1e-4)
# test IO when computation done in Python
cov.save(op.join(tempdir, 'test-cov.fif')) # test saving
cov_read = read_cov(op.join(tempdir, 'test-cov.fif'))
assert_true(cov_read.ch_names == cov.ch_names)
assert_true(cov_read.nfree == cov.nfree)
assert_array_almost_equal(cov.data, cov_read.data)
# test with a subset of channels
picks = pick_channels(raw.ch_names, include=raw.ch_names[:5])
cov = compute_raw_data_covariance(raw, picks=picks)
assert_true(cov_mne.ch_names[:5] == cov.ch_names)
assert_true(linalg.norm(cov.data - cov_mne.data[picks][:, picks],
ord='fro') / linalg.norm(cov.data, ord='fro') < 1e-4)
# make sure we get a warning with too short a segment
raw_2 = raw.crop(0, 1)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
cov = compute_raw_data_covariance(raw_2)
assert_true(len(w) == 1)
def _gradient_descent(objective,
p0,
it,
n_iter,
objective_error=None,
n_iter_check=1,
n_iter_without_progress=50,
momentum=0.5,
learning_rate=1000.0,
min_gain=0.01,
min_grad_norm=1e-7,
min_error_diff=1e-7,
verbose=0,
args=None,
kwargs=None):
"""Batch gradient descent with momentum and individual gains.
Parameters
----------
objective : function or callable
Should return a tuple of cost and gradient for a given parameter
vector. When expensive to compute, the cost can optionally
be None and can be computed every n_iter_check steps using
the objective_error function.
p0 : array-like, shape (n_params,)
Initial parameter vector.
it : int
Current number of iterations (this function will be called more than
once during the optimization).
n_iter : int
Maximum number of gradient descent iterations.
n_iter_check : int
Number of iterations before evaluating the global error. If the error
is sufficiently low, we abort the optimization.
objective_error : function or callable
Should return a tuple of cost and gradient for a given parameter
vector.
n_iter_without_progress : int, optional (default: 30)
Maximum number of iterations without progress before we abort the
optimization.
momentum : float, within (0.0, 1.0), optional (default: 0.5)
The momentum generates a weight for previous gradients that decays
exponentially.
learning_rate : float, optional (default: 1000.0)
The learning rate should be extremely high for t-SNE! Values in the
range [100.0, 1000.0] are common.
min_gain : float, optional (default: 0.01)
Minimum individual gain for each parameter.
min_grad_norm : float, optional (default: 1e-7)
If the gradient norm is below this threshold, the optimization will
be aborted.
min_error_diff : float, optional (default: 1e-7)
If the absolute difference of two successive cost function values
is below this threshold, the optimization will be aborted.
verbose : int, optional (default: 0)
Verbosity level.
args : sequence
Arguments to pass to objective function.
kwargs : dict
Keyword arguments to pass to objective function.
Returns
-------
p : array, shape (n_params,)
Optimum parameters.
error : float
Optimum.
i : int
Last iteration.
"""
if args is None:
args = []
if kwargs is None:
kwargs = {}
p = p0.copy().ravel()
update = np.zeros_like(p)
gains = np.ones_like(p)
error = np.finfo(np.float).max
best_error = np.finfo(np.float).max
best_iter = 0
for i in range(it, n_iter):
new_error, grad = objective(p, *args, **kwargs)
grad_norm = linalg.norm(grad)
inc = update * grad >= 0.0
dec = np.invert(inc)
gains[inc] += 0.05
gains[dec] *= 0.95
np.clip(gains, min_gain, np.inf)
grad *= gains
update = momentum * update - learning_rate * grad
p += update
if (i + 1) % n_iter_check == 0:
if new_error is None:
new_error = objective_error(p, *args)
error_diff = np.abs(new_error - error)
error = new_error
if verbose >= 2:
m = "[t-SNE] Iteration %d: error = %.7f, gradient norm = %.7f"
print(m % (i + 1, error, grad_norm))
if error < best_error:
best_error = error
best_iter = i
elif i - best_iter > n_iter_without_progress:
if verbose >= 2:
print("[t-SNE] Iteration %d: did not make any progress "
"during the last %d episodes. Finished." %
(i + 1, n_iter_without_progress))
break
if grad_norm <= min_grad_norm:
if verbose >= 2:
print("[t-SNE] Iteration %d: gradient norm %f. Finished." %
(i + 1, grad_norm))
break
if error_diff <= min_error_diff:
if verbose >= 2:
m = "[t-SNE] Iteration %d: error difference %f. Finished."
print(m % (i + 1, error_diff))
break
if new_error is not None:
error = new_error
return p, error, i
for j1 in range(6):
mu=muinit*(ps_step**j1)
opterr1=n_s*100
end1=2
optmu21=mu2init
for j2 in range(6):
mu2=mu2init*(ps_step**j2)
err=0
for k in range(1): #5 for full 5 fold CV
train1_idx=SP.concatenate((train_idx[:int(n_train*k*0.2)],train_idx[int(n_train*(k+1)*0.2):n_train]))
valid_idx=train_idx[int(n_train*k*0.2):int(n_train*(k+1)*0.2)]
res1=lmm_lasso.train(X[train1_idx],K[train1_idx][:,train1_idx],y[train1_idx],mu,mu2,group,w0=w0)
w1=res1['weights']
w0=w1
yhat = lmm_lasso.predict(y[train1_idx],X[train1_idx,:],X[valid_idx,:],K[train1_idx][:,train1_idx],K[valid_idx][:,train1_idx],res1['ldelta0'],w1)
err += LA.norm(yhat-y[valid_idx])
print mu, mu2, err
if err<=opterr1:
opterr1=err
optmu21=mu2
end1=2
else:
end1-=1
if end1==0:
break
if opterr1<=opterr:
opterr=opterr1
optmu=mu
optmu2=optmu21
end=2
def encode(model,
X,
use_norm=True,
verbose=True,
batch_size=128,
use_eos=False):
"""
Encode sentences in the list X. Each entry will return a vector
"""
# first, do preprocessing
X = preprocess(X)
# word dictionary and init
d = defaultdict(lambda: 0)
for w in model['utable'].keys():
d[w] = 1
ufeatures = numpy.zeros((len(X), model['uoptions']['dim']),
dtype='float32')
bfeatures = numpy.zeros((len(X), 2 * model['boptions']['dim']),
dtype='float32')
# length dictionary
ds = defaultdict(list)
captions = [s.split() for s in X]
for i, s in enumerate(captions):
ds[len(s)].append(i)
# Get features. This encodes by length, in order to avoid wasting computation
for k in ds.keys():
if verbose:
print(k)
numbatches = int(len(ds[k]) / batch_size + 1) #changed by Debanjan
for minibatch in range(int(numbatches)):
caps = ds[k][minibatch::numbatches]
if use_eos:
uembedding = numpy.zeros(
(k + 1, len(caps), model['uoptions']['dim_word']),
dtype='float32')
bembedding = numpy.zeros(
(k + 1, len(caps), model['boptions']['dim_word']),
dtype='float32')
else:
uembedding = numpy.zeros(
(k, len(caps), model['uoptions']['dim_word']),
dtype='float32')
bembedding = numpy.zeros(
(k, len(caps), model['boptions']['dim_word']),
dtype='float32')
for ind, c in enumerate(caps):
caption = captions[c]
for j in range(len(caption)):
if d[caption[j]] > 0:
uembedding[j, ind] = model['utable'][caption[j]]
bembedding[j, ind] = model['btable'][caption[j]]
else:
uembedding[j, ind] = model['utable']['UNK']
bembedding[j, ind] = model['btable']['UNK']
if use_eos:
uembedding[-1, ind] = model['utable']['<eos>']
bembedding[-1, ind] = model['btable']['<eos>']
if use_eos:
uff = model['f_w2v'](uembedding,
numpy.ones((len(caption) + 1, len(caps)),
dtype='float32'))
bff = model['f_w2v2'](bembedding,
numpy.ones((len(caption) + 1, len(caps)),
dtype='float32'))
else:
uff = model['f_w2v'](uembedding,
numpy.ones((len(caption), len(caps)),
dtype='float32'))
bff = model['f_w2v2'](bembedding,
numpy.ones((len(caption), len(caps)),
dtype='float32'))
if use_norm:
for j in range(len(uff)):
uff[j] /= norm(uff[j])
bff[j] /= norm(bff[j])
for ind, c in enumerate(caps):
ufeatures[c] = uff[ind]
bfeatures[c] = bff[ind]
features = numpy.c_[ufeatures, bfeatures]
return features
Ny = utils.optimize_fftsize(Ny, fft_max_prime) dx = Lx/np.float(Nx) dy = Ly/np.float(Ny) # X-Y vector - linespace can be problematic, refinement with arange x = np.linspace(-Lx/2., Lx/2., Nx) x = (np.arange(x.size) - x.size/2) * (x[1]-x[0]) y = np.linspace(-Ly/2., Ly/2., Ny) y = (np.arange(y.size) - y.size/2) * (y[1]-y[0]) x, y = np.meshgrid(x, y) # Currents current = current_mag * np.array([np.cos(current_dir), np.sin(current_dir)]) U_eff_vec = (wind_U * np.array([np.cos(wind_dir), np.sin(wind_dir)]) - current) wind_U_eff = linalg.norm(U_eff_vec) wind_dir_eff = np.arctan2(U_eff_vec[1], U_eff_vec[0]) # Kx-Ky meshgrid kx = 2.*np.pi*np.fft.fftfreq(Nx, dx) ky = 2.*np.pi*np.fft.fftfreq(Ny, dy) kx, ky = np.meshgrid(kx, ky) # Kx-Ky resolution kx_res = kx[0, 1] - kx[0, 0] ky_res = ky[1, 0] - ky[0, 0] # K-theta meshgrid (Polar, wind direction shifted) k = np.sqrt(kx**2 + ky**2) good_k = np.where(k > np.min(np.array([kx_res, ky_res]))/2.0) kinv = np.zeros(k.shape)
def _gradient_descent(objective,
p0,
it,
n_iter,
objective_error=None,
n_iter_check=1,
n_iter_without_progress=50,
momentum=0.5,
learning_rate=1000.0,
min_gain=0.01,
min_grad_norm=1e-7,
min_error_diff=1e-7,
verbose=0,
args=None,
kwargs=None,
urls=[],
text=[],
colors=[],
n_samples=0,
n_components=0):
"""Batch gradient descent with momentum and individual gains.
Parameters
----------
objective : function or callable
Should return a tuple of cost and gradient for a given parameter
vector. When expensive to compute, the cost can optionally
be None and can be computed every n_iter_check steps using
the objective_error function.
p0 : array-like, shape (n_params,)
Initial parameter vector.
it : int
Current number of iterations (this function will be called more than
once during the optimization).
n_iter : int
Maximum number of gradient descent iterations.
n_iter_check : int
Number of iterations before evaluating the global error. If the error
is sufficiently low, we abort the optimization.
objective_error : function or callable
Should return a tuple of cost and gradient for a given parameter
vector.
n_iter_without_progress : int, optional (default: 30)
Maximum number of iterations without progress before we abort the
optimization.
momentum : float, within (0.0, 1.0), optional (default: 0.5)
The momentum generates a weight for previous gradients that decays
exponentially.
learning_rate : float, optional (default: 1000.0)
The learning rate should be extremely high for t-SNE! Values in the
range [100.0, 1000.0] are common.
min_gain : float, optional (default: 0.01)
Minimum individual gain for each parameter.
min_grad_norm : float, optional (default: 1e-7)
If the gradient norm is below this threshold, the optimization will
be aborted.
min_error_diff : float, optional (default: 1e-7)
If the absolute difference of two successive cost function values
is below this threshold, the optimization will be aborted.
verbose : int, optional (default: 0)
Verbosity level.
args : sequence
Arguments to pass to objective function.
kwargs : dict
Keyword arguments to pass to objective function.
Returns
-------
p : array, shape (n_params,)
Optimum parameters.
error : float
Optimum.
i : int
Last iteration.
"""
#connect to database
conn = r.connect(host="localhost", port=28015, db="messagedb")
#keep track of total distance each point has moved
global point_distances
if args is None:
args = []
if kwargs is None:
kwargs = {}
p = p0.copy().ravel()
update = np.zeros_like(p)
gains = np.ones_like(p)
error = np.finfo(np.float).max
best_error = np.finfo(np.float).max
best_iter = 0
for i in range(it, n_iter):
new_error, grad = objective(p, *args, **kwargs)
grad_norm = linalg.norm(grad)
# track which keys to remove from dictionary
to_remove = []
# check client changes
if (len(changes) > 0):
for change in changes:
index = urls.index(str(change["new_val"]["id"]))
print(index)
print(changes)
print(p[index * 2])
print(p[index * 2 + 1])
print(change["old_val"]["x"])
print(change["old_val"]["y"])
print(change["new_val"]["x"])
print(change["new_val"]["y"])
p[index * 2] = change["new_val"]["x"]
p[index * 2 + 1] = change["new_val"]["y"]
to_remove.append(change)
for item in to_remove:
print(len(changes))
changes.remove(item)
print(len(changes))
inc = update * grad >= 0.0
dec = np.invert(inc)
gains[inc] += 0.05
gains[dec] *= 0.95
np.clip(gains, min_gain, np.inf)
grad *= gains
update = momentum * update - learning_rate * grad
p += update
if (i + 1) % n_iter_check == 0:
if new_error is None:
new_error = objective_error(p, *args)
error_diff = np.abs(new_error - error)
error = new_error
if verbose >= 2:
m = "[t-SNE] Iteration %d: error = %.7f, gradient norm = %.7f"
print((m % (i + 1, error, grad_norm)))
if error < best_error:
best_error = error
best_iter = i
elif i - best_iter > n_iter_without_progress:
if verbose >= 2:
print(("[t-SNE] Iteration %d: did not make any progress "
"during the last %d episodes. Finished." %
(i + 1, n_iter_without_progress)))
break
if grad_norm <= min_grad_norm:
if verbose >= 2:
print(
("[t-SNE] Iteration %d: gradient norm %f. Finished." %
(i + 1, grad_norm)))
break
if error_diff <= min_error_diff:
if verbose >= 2:
m = "[t-SNE] Iteration %d: error difference %f. Finished."
print((m % (i + 1, error_diff)))
break
if (i + 1) % 5 == 0:
#save to database every so often
embedded_array = p.reshape(n_samples, n_components)
#array of packaged message objects
data = []
#combine url, xy coords, and text into one object and add to data array
for idx in range(len(urls)):
urls[idx] = urls[idx].replace('\ufeff', '')
tempUrl = int(urls[idx])
if (len(colors) > 0):
data.append({
"id": tempUrl,
"x": embedded_array[idx][0],
"y": embedded_array[idx][1],
"distance": point_distances[idx],
"text": text[idx],
"color": colors[idx],
"modified_by": "server"
})
else:
data.append({
"id": tempUrl,
"x": embedded_array[idx][0],
"y": embedded_array[idx][1],
"distance": point_distances[idx],
"text": text[idx],
"modified_by": "server"
})
#insert data into the database, updating if it already exists
results = r.table("messages").insert(
data, conflict="update", return_changes="always").run(conn)
for k in range(len(results["changes"])):
if results["changes"][k]["old_val"] == None:
break
delta = math.sqrt(
math.pow(
results["changes"][k]["new_val"]["x"] -
results["changes"][k]["old_val"]["x"], 2) + math.pow(
results["changes"][k]["new_val"]["y"] -
results["changes"][k]["old_val"]["y"], 2))
point_distances[k] += delta
if new_error is not None:
error = new_error
#close database connection
conn.close()
return p, error, i
def _test_lstsq_reg_single(k, d, r):
"""Do one test of utils._solver.lstsq_reg()."""
A = np.random.random((k, d))
b = np.random.random(k)
B = np.random.random((k, r))
I = np.eye(d)
# VECTOR TEST
x = la.lstsq(A, b)[0]
# Ensure that the least squares solution is the usual one when P=0.
x_ = roi.utils.lstsq_reg(A, b, P=0)[0]
assert np.allclose(x, x_)
# Ensure that the least squares solution is the usual one when P=0 (matrix)
x_ = roi.utils.lstsq_reg(A, b, np.zeros((d, d)))[0]
assert np.allclose(x, x_)
# Check that the regularized least squares solution has decreased norm.
x_ = roi.utils.lstsq_reg(A, b, P=2)[0]
assert la.norm(x_) <= la.norm(x)
x_ = roi.utils.lstsq_reg(A, b, P=2 * I)[0]
assert la.norm(x_) <= la.norm(x)
# MATRIX TEST
X = la.lstsq(A, B)[0]
# Ensure that the least squares solution is the usual one when P=0.
X_ = roi.utils.lstsq_reg(A, B, P=0)[0]
assert np.allclose(X, X_)
# Ensure that the least squares solution is the usual one when P=0 (matrix)
X_ = roi.utils.lstsq_reg(A, B, P=0)[0]
assert np.allclose(X, X_)
# Ensure that the least squares solution is the usual one when P=0 (list)
X_ = roi.utils.lstsq_reg(A, B, P=[np.zeros((d, d))] * r)[0]
assert np.allclose(X, X_)
# Ensure that the least squares problem decouples correctly.
Ps = [l * I for l in range(r)]
X_ = roi.utils.lstsq_reg(A, B, P=Ps)[0]
for j in range(r):
xj_ = roi.utils.lstsq_reg(A, B[:, j], P=Ps[j])[0]
assert np.allclose(xj_, X_[:, j])
# Check that the regularized least squares solution has decreased norm.
X_ = roi.utils.lstsq_reg(A, B, P=2)[0]
assert la.norm(X_) <= la.norm(X)
X_ = roi.utils.lstsq_reg(A, B, P=2)[0]
assert la.norm(X_) <= la.norm(X)
X_ = roi.utils.lstsq_reg(A, B, P=[2] * r)[0]
assert la.norm(X_) <= la.norm(X)
X_ = roi.utils.lstsq_reg(A, B, P=[2 * I] * r)[0]
assert la.norm(X_) <= la.norm(X)
# Test residuals actually give the Frobenius norm squared of the misfit.
Acond = np.linalg.cond(A)
X_, res, rnk, svdvals = roi.utils.lstsq_reg(A, B, P=0)
assert np.isclose(np.sum(res), np.sum((A @ X_ - B)**2))
assert np.isclose(abs(svdvals[0] / svdvals[-1]), Acond)
# Ensure residuals larger, condition numbers smaller with regularization.
X_, res, rnk, svdvals = roi.utils.lstsq_reg(A, B, P=2)
assert np.sum(res) > np.sum((A @ X_ - B)**2)
assert abs(svdvals[0] / svdvals[-1]) < Acond
X_, res, rnk, svdvals = roi.utils.lstsq_reg(A, B, P=[2 * I] * r)
assert np.sum(res) > np.sum((A @ X_ - B)**2)
assert abs(svdvals[0] / svdvals[-1]) < Acond
def check_solver(self, solver, fit_intercept=True, model='logreg',
decimal=1):
"""Check solver instance finds same parameters as scipy BFGS
Parameters
----------
solver : `Solver`
Instance of a solver to be tested
fit_intercept : `bool`, default=True
Model uses intercept is `True`
model : 'linreg' | 'logreg' | 'poisreg', default='logreg'
Name of the model used to test the solver
decimal : `int`, default=1
Number of decimals required for the test
"""
# Set seed for data simulation
np.random.seed(12)
n_samples = TestSolver.n_samples
n_features = TestSolver.n_features
coeffs0 = weights_sparse_gauss(n_features, nnz=5)
if fit_intercept:
interc0 = 2.
else:
interc0 = None
if model == 'linreg':
X, y = SimuLinReg(coeffs0, interc0, n_samples=n_samples,
verbose=False, seed=123).simulate()
model = ModelLinReg(fit_intercept=fit_intercept).fit(X, y)
elif model == 'logreg':
X, y = SimuLogReg(coeffs0, interc0, n_samples=n_samples,
verbose=False, seed=123).simulate()
model = ModelLogReg(fit_intercept=fit_intercept).fit(X, y)
elif model == 'poisreg':
X, y = SimuPoisReg(coeffs0, interc0, n_samples=n_samples,
verbose=False, seed=123).simulate()
# Rescale features to avoid overflows in Poisson simulations
X /= np.linalg.norm(X, axis=1).reshape(n_samples, 1)
model = ModelPoisReg(fit_intercept=fit_intercept).fit(X, y)
else:
raise ValueError("``model`` must be either 'linreg', 'logreg' or"
" 'poisreg'")
solver.set_model(model)
strength = 1e-2
prox = ProxL2Sq(strength, (0, model.n_features))
if type(solver) is not SDCA:
solver.set_prox(prox)
else:
solver.set_prox(ProxZero())
solver.l_l2sq = strength
coeffs_solver = solver.solve()
# Compare with BFGS
bfgs = BFGS(max_iter=100,
verbose=False).set_model(model).set_prox(prox)
coeffs_bfgs = bfgs.solve()
np.testing.assert_almost_equal(coeffs_solver, coeffs_bfgs,
decimal=decimal)
# We ensure that reached coeffs are not equal to zero
self.assertGreater(norm(coeffs_solver), 0)
self.assertAlmostEqual(
solver.objective(coeffs_bfgs), solver.objective(coeffs_solver),
delta=1e-2)
def adaptive_graal_terminate(J,
F,
prox_g,
x1,
numb_iter=100,
phi=1.5,
tol=1e-6,
output=False):
""" Adaptive Golden Ratio algorithm with termination criteria.
Input
-----
J : function that computes residual in every iteration.
Takes x as input.
F : main operator.
Takes x as input.
prox_g: proximal operator.
Takes two parameters x and a scalar as input.
x1: Strating point.
np.array, be consistent with J, F and prox_g.
numb_iter: number of iteration to run rhe algorithm.
phi: a key parameter for the algorithm.
Must be between 1 and the golden ratio, 1.618... Choice
phi=1.5 seems to be one of the best.
tol: a positive number.
Required accuracy for termination of the algorithm.
output: boolean.
If true, prints the length of a stepsize in every iteration. Useful
for monitoring.
Return
------
values: 1d array
Collects all values that were computed in every iteration with J(x).
x : last iterate.
i: positive integer, number of iteration to reach desired accuracy.
time_list: list of time stamps in every iteration.
Useful for monitoring.
"""
begin = perf_counter()
x, x_ = x1.copy(), x1.copy()
x0 = x + np.random.randn(x.shape[0])
Fx = F(x)
la = phi / 2 * LA.norm(x - x0) / LA.norm(Fx - F(x0))
rho = 1. / phi + 1. / phi**2
values = [J(x)]
time_list = [perf_counter() - begin]
th = 1
i = 1
while i <= numb_iter and values[-1] > tol:
i += 1
x1 = prox_g(x_ - la * Fx, la)
Fx1 = F(x1)
n1 = LA.norm(x1 - x)
n2 = LA.norm(Fx1 - Fx)
n1_div_n2 = np.exp(2 * (np.log(n1) - np.log(n2)))
la1 = min(rho * la, 0.25 * phi * th / la * n1_div_n2, 1e6)
x_ = ((phi - 1) * x1 + x_) / phi
if output:
print(i, la, LA.norm(x1), LA.norm(Fx), LA.norm(x_))
th = phi * la1 / la
x, la, Fx = x1, la1, Fx1
values.append(J(x))
time_list.append(perf_counter() - begin)
end = perf_counter()
print("Time execution of aGRAAL:", end - begin)
return np.array(values), x, i, time_list
def M(axis, theta):
return expm(np.cross(np.eye(3), axis / norm(axis) * theta))
def adaptive_graal(J, F, prox_g, x0, numb_iter=100, phi=1.5, output=False):
""" Adaptive Golden Ratio algorithm.
Input
-----
J : function that computes residual in every iteration.
Takes x as input.
F : main operator.
Takes x as input.
prox_g: proximal operator.
Takes two parameters x and a scalar as input.
x0: Starting point.
np.array, be consistent with J, F and prox_g.
numb_iter: number of iteration to run rhe algorithm.
phi: a key parameter for the algorithm.
Must be between 1 and the golden ratio, 1.618... Choice
phi=1.5 seems to be one of the best.
output: boolean.
If true, prints the length of a stepsize in every iteration.
Useful for monitoring.
Return
------
values: 1d array
Collects all values that were computed in every iteration with J(x)
x, x_ : last iterates
time_list: list of time stamps in every iteration.
Useful for monitoring.
"""
begin = perf_counter()
x, x_ = x0.copy(), x0.copy()
x0 = x + np.random.randn(x.shape[0]) * 1e-9
Fx = F(x)
la = phi / 2 * LA.norm(x - x0) / LA.norm(Fx - F(x0))
rho = 1. / phi + 1. / phi**2
values = [J(x)]
time_list = [perf_counter() - begin]
th = 1
for i in range(numb_iter):
x1 = prox_g(x_ - la * Fx, la)
Fx1 = F(x1)
n1 = LA.norm(x1 - x)**2
n2 = LA.norm(Fx1 - Fx)**2
n1_div_n2 = np.exp(np.log(n1) - np.log(n2))
la1 = min(rho * la, 0.25 * phi * th / la * n1_div_n2, 1e6)
x_ = ((phi - 1) * x1 + x_) / phi
if output:
print(i, la)
th = phi * la1 / la
x, la, Fx = x1, la1, Fx1
values.append(J(x))
time_list.append(perf_counter() - begin)
end = perf_counter()
print("Time execution of adaptive GRAAL:", end - begin)
return np.array(values), x, x_, time_list
def iqml_recon_ri(G, a, K, noise_level, max_ini=100, stop_cri='mse'):
"""
Here we assume both the measurements a and the linear transformation G are real-valued
"""
# make sure the assumption (real-valued) is true
assert not np.iscomplexobj(a) and not np.iscomplexobj(G)
compute_mse = (stop_cri == 'mse')
GtG = np.dot(G.T, G)
Gt_a = np.dot(G.T, a)
two_Lp1 = G.shape[1]
assert two_Lp1 % 2 == 1
L = np.int((two_Lp1 - 1) / 2.)
sz_T0 = 2 * (L - K + 1)
sz_T1 = 2 * (K + 1)
sz_G1 = 2 * L + 1
sz_R0 = sz_T0
sz_R1 = 2 * L + 1
sz_coef = 2 * (K + 1)
D = expansion_mtx_pos(L + 1)
max_iter = 50
min_error = float('inf')
beta = linalg.lstsq(G, a)[0]
Tbeta = Tmtx_ri_half(beta, K, D) # has 2(K+1) columns
rhs = np.concatenate((np.zeros(sz_T1 + sz_T0 + sz_G1), [1.]))
rhs_bl = np.concatenate((Gt_a, np.zeros(sz_R0)))
for ini in xrange(max_ini):
c_ri = np.random.randn(2 * (K + 1)) # first half of c_ri: c_real, second half: c_imag
c0 = c_ri.copy()
error_seq = np.zeros(max_iter)
# R has (2L + 1) columns
R_loop = Rmtx_ri_half(c_ri, K, L + 1, D)
for loop in xrange(max_iter):
Mtx_loop = np.vstack((np.hstack((np.zeros((sz_T1, sz_T1)), Tbeta.T, np.zeros((sz_T1, sz_R1)),
c0[:, np.newaxis])),
np.hstack((Tbeta, np.zeros((sz_T0, sz_T0)), -R_loop, np.zeros((sz_T0, 1)))),
np.hstack((np.zeros((sz_R1, sz_T1)), -R_loop.T, GtG, np.zeros((sz_G1, 1)))),
np.hstack((c0[np.newaxis, :], np.zeros((1, sz_T0 + sz_R1 + 1))))
))
# matrix should be Hermitian symmetric
Mtx_loop = (Mtx_loop + Mtx_loop.T) / 2.
c_ri = linalg.solve(Mtx_loop, rhs)[:sz_coef]
R_loop = Rmtx_ri_half(c_ri, K, L + 1, D)
Mtx_brecon = np.vstack((np.hstack((GtG, R_loop.T)),
np.hstack((R_loop, np.zeros((sz_R0, sz_R0))))
))
# matrix should be Hermitian symmetric
Mtx_brecon = (Mtx_brecon + Mtx_brecon.T) / 2.
b_recon_ri = linalg.solve(Mtx_brecon, rhs_bl)[:sz_G1]
error_seq[loop] = linalg.norm(a - np.dot(G, b_recon_ri))
if error_seq[loop] < min_error:
min_error = error_seq[loop]
b_opt = b_recon_ri[:L+1] + 1j * np.concatenate((np.array([0]),
b_recon_ri[L+1:]))
c_opt = c_ri[:K+1] + 1j * c_ri[K+1:]
if min_error < noise_level and compute_mse:
break
if min_error < noise_level and compute_mse:
break
return b_opt, min_error, c_opt, ini
def _cholesky_omp(X,
y,
n_nonzero_coefs,
tol=None,
copy_X=True,
return_path=False):
"""Orthogonal Matching Pursuit step using the Cholesky decomposition.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Input dictionary. Columns are assumed to have unit norm.
y : ndarray of shape (n_samples,)
Input targets.
n_nonzero_coefs : int
Targeted number of non-zero elements.
tol : float, default=None
Targeted squared error, if not None overrides n_nonzero_coefs.
copy_X : bool, default=True
Whether the design matrix X must be copied by the algorithm. A false
value is only helpful if X is already Fortran-ordered, otherwise a
copy is made anyway.
return_path : bool, default=False
Whether to return every value of the nonzero coefficients along the
forward path. Useful for cross-validation.
Returns
-------
gamma : ndarray of shape (n_nonzero_coefs,)
Non-zero elements of the solution.
idx : ndarray of shape (n_nonzero_coefs,)
Indices of the positions of the elements in gamma within the solution
vector.
coef : ndarray of shape (n_features, n_nonzero_coefs)
The first k values of column k correspond to the coefficient value
for the active features at that step. The lower left triangle contains
garbage. Only returned if ``return_path=True``.
n_active : int
Number of active features at convergence.
"""
if copy_X:
X = X.copy("F")
else: # even if we are allowed to overwrite, still copy it if bad order
X = np.asfortranarray(X)
min_float = np.finfo(X.dtype).eps
nrm2, swap = linalg.get_blas_funcs(("nrm2", "swap"), (X, ))
(potrs, ) = get_lapack_funcs(("potrs", ), (X, ))
alpha = np.dot(X.T, y)
residual = y
gamma = np.empty(0)
n_active = 0
indices = np.arange(X.shape[1]) # keeping track of swapping
max_features = X.shape[1] if tol is not None else n_nonzero_coefs
L = np.empty((max_features, max_features), dtype=X.dtype)
if return_path:
coefs = np.empty_like(L)
while True:
lam = np.argmax(np.abs(np.dot(X.T, residual)))
if lam < n_active or alpha[lam]**2 < min_float:
# atom already selected or inner product too small
warnings.warn(premature, RuntimeWarning, stacklevel=2)
break
if n_active > 0:
# Updates the Cholesky decomposition of X' X
L[n_active, :n_active] = np.dot(X[:, :n_active].T, X[:, lam])
linalg.solve_triangular(
L[:n_active, :n_active],
L[n_active, :n_active],
trans=0,
lower=1,
overwrite_b=True,
check_finite=False,
)
v = nrm2(L[n_active, :n_active])**2
Lkk = linalg.norm(X[:, lam])**2 - v
if Lkk <= min_float: # selected atoms are dependent
warnings.warn(premature, RuntimeWarning, stacklevel=2)
break
L[n_active, n_active] = sqrt(Lkk)
else:
L[0, 0] = linalg.norm(X[:, lam])
X.T[n_active], X.T[lam] = swap(X.T[n_active], X.T[lam])
alpha[n_active], alpha[lam] = alpha[lam], alpha[n_active]
indices[n_active], indices[lam] = indices[lam], indices[n_active]
n_active += 1
# solves LL'x = X'y as a composition of two triangular systems
gamma, _ = potrs(L[:n_active, :n_active],
alpha[:n_active],
lower=True,
overwrite_b=False)
if return_path:
coefs[:n_active, n_active - 1] = gamma
residual = y - np.dot(X[:, :n_active], gamma)
if tol is not None and nrm2(residual)**2 <= tol:
break
elif n_active == max_features:
break
if return_path:
return gamma, indices[:n_active], coefs[:, :n_active], n_active
else:
return gamma, indices[:n_active], n_active
def do_solve(**kw):
count[0] = 0
x0, flag = lgmres(A, b, x0=zeros(A.shape[0]), inner_m=6, tol=1e-14, **kw)
count_0 = count[0]
assert_(allclose(A*x0, b, rtol=1e-12, atol=1e-12), norm(A*x0-b))
return x0, count_0
# ## Linear Algebra Methods in SciPy # In[98]: import scipy.linalg as sl A = array([[1,2], [-6,4]]) [LU,piv] = sl.lu_factor(A) # In[99]: bi = array([1,1]) xi=sl.lu_solve((LU,piv),bi) xi # ### Solving a least squares problem with SVD # In[100]: import scipy.linalg as sl A = array([[1, 2], [-6, 4], [0, 8]]) b = array([1,1,1]) [U1, Sigma_1, VT] = sl.svd(A, full_matrices = False, compute_uv = True) xast = dot(VT.T, dot(U1.T, b)/ Sigma_1) r = dot(A, xast) - b # computes the residual nr = sl.norm(r, 2) # computes the Euclidean norm of the residual nr
def grasp_callback(my_grasp):
my_pose = geometry_msgs.msg.PoseStamped()
my_pose.header.stamp = my_grasp.markers[0].header.stamp
my_pose.header.frame_id = "/xtion_rgb_optical_frame"
pose_target = geometry_msgs.msg.Pose()
pose_target.position.x = my_grasp.markers[0].points[0].x
pose_target.position.y = my_grasp.markers[0].points[0].y
pose_target.position.z = my_grasp.markers[0].points[0].z
## Convert to quaternion
u = [1, 0, 0]
norm = linalg.norm([
my_grasp.markers[i].points[0].x - my_grasp.markers[0].points[1].x,
my_grasp.markers[0].points[0].y - my_grasp.markers[0].points[1].y,
my_grasp.markers[0].points[0].z - my_grasp.markers[0].points[1].z
])
v = asarray([
my_grasp.markers[0].points[0].x - my_grasp.markers[0].points[1].x,
my_grasp.markers[0].points[0].y - my_grasp.markers[0].points[1].y,
my_grasp.markers[0].points[0].z - my_grasp.markers[0].points[1].z
]) / norm
if (array_equal(u, v)):
pose_target.orientation.w = 1
pose_target.orientation.x = 0
pose_target.orientation.y = 0
pose_target.orientation.z = 0
elif (array_equal(u, negative(v))):
pose_target.orientation.w = 0
pose_target.orientation.x = 0
pose_target.orientation.y = 0
pose_target.orientation.z = 1
else:
half = [u[0] + v[0], u[1] + v[1], u[2] + v[2]]
pose_target.orientation.w = dot(u, half)
temp = cross(u, half)
pose_target.orientation.x = temp[0]
pose_target.orientation.y = temp[1]
pose_target.orientation.z = temp[2]
norm = math.sqrt(pose_target.orientation.x * pose_target.orientation.x +
pose_target.orientation.y * pose_target.orientation.y +
pose_target.orientation.z * pose_target.orientation.z +
pose_target.orientation.w * pose_target.orientation.w)
if norm == 0:
norm = 1
my_pose.pose.orientation.x = pose_target.orientation.x / norm
my_pose.pose.orientation.y = pose_target.orientation.y / norm
my_pose_.pose.orientation.z = pose_target.orientation.z / norm
my_pose.pose.orientation.w = pose_target.orientation.w / norm
pose_target_trans = geometry_msgs.msg.PoseStamped()
pose_target_trans.header.stamp = pose_target.header.stamp
pose_target_trans.header.frame_id = "/map"
now = rospy.Time.now()
listener.waitForTransform("/map", "/xtion_rgb_optical_frame", now,
rospy.Duration(1.0))
pose_target_trans = listener.transformPose("/map", pose_target)
my_grasp_pub.publish(pose_target_trans)
qbhistvec = qbhistvec.astype(np.complex)
# %%
sqr2D = sqr2D.astype(np.complex)
# %%
#prob_detect_v = np.kron(np.eye(32), sqr2D) @ qbhistvec
#
# More direct route, without going through histories
i, j = find_best()
prob_detect_v = \
(np.kron(EnergyCorrectionMatricesT[i], sqr2D) @ eigenvectors.T[i]) + \
(np.kron(EnergyCorrectionMatricesT[j], sqr2D) @ eigenvectors.T[j])
# normalize
prob_detect_v = prob_detect_v / norm(prob_detect_v)
# %%
prob_detect = np.zeros(32)
for t_idx in range(32):
prob_detect[t_idx] = \
np.abs(prob_detect_v[2*t_idx])**2 + np.abs(prob_detect_v[2*t_idx+1])**2
# %%
plt.plot(times, prob_detect, 'bs')
# %%
detect_fft = \
np.kron(F, np.eye(2)) @ prob_detect_v
detect_fft = detect_fft / norm(detect_fft)
def _run_modeling(cls, dataset_reader, **kwargs):
def one_or_nan(x):
y = np.ones(x.shape)
y[np.isnan(x)] = float('nan')
return y
if 'subject_rejection' in kwargs and kwargs[
'subject_rejection'] is True:
assert False, 'SubjectAwareGenerativeModel must not and need not ' \
'apply subject rejection.'
x_es = cls._get_opinion_score_2darray_with_preprocessing(
dataset_reader, **kwargs)
E, S = x_es.shape
use_log = kwargs['use_log'] if 'use_log' in kwargs else False
# === initialization ===
mos = pd.DataFrame(x_es).mean(axis=1)
x_e = mos # use MOS as initial value for x_e
b_s = np.zeros(S)
r_es = x_es - np.tile(x_e, (S, 1)).T # r_es: residual at e, s
v_s = np.array(pd.DataFrame(r_es).std(axis=0, ddof=0))
log_v_s = np.log(v_s)
# === iteration ===
MAX_ITR = 5000
REFRESH_RATE = 0.1
DELTA_THR = 1e-8
print '=== Belief Propagation ==='
itr = 0
while True:
x_e_prev = x_e
# (8) b_s
num = pd.DataFrame(x_es - np.tile(x_e, (S, 1)).T).sum(
axis=0) # sum over e
den = pd.DataFrame(one_or_nan(x_es)).sum(axis=0) # sum over e
b_s_new = num / den
b_s = b_s * (1.0 - REFRESH_RATE) + b_s_new * REFRESH_RATE
a_es = x_es - np.tile(x_e, (S, 1)).T - np.tile(b_s, (E, 1))
if use_log:
# (9') log_v_s
num = pd.DataFrame(-np.ones([E, S]) +
a_es**2 / np.tile(v_s**2, (E, 1))).sum(
axis=0) # sum over e
den = pd.DataFrame(-2 * a_es**2 / np.tile(v_s**2, (E, 1))).sum(
axis=0) # sum over e
log_v_s_new = log_v_s - num / den
log_v_s = log_v_s * (1.0 -
REFRESH_RATE) + log_v_s_new * REFRESH_RATE
v_s = np.exp(log_v_s)
else:
# (9) v_s
num = pd.DataFrame(2 * np.ones([E, S]) *
np.tile(v_s**3, (E, 1)) -
4 * np.tile(v_s, (E, 1)) * a_es**2).sum(
axis=0) # sum over e
den = pd.DataFrame(
np.ones([E, S]) * np.tile(v_s**2, (E, 1)) -
3 * a_es**2).sum(axis=0) # sum over e
v_s_new = num / den
v_s = v_s * (1.0 - REFRESH_RATE) + v_s_new * REFRESH_RATE
# v_s = np.maximum(v_s, np.zeros(v_s.shape))
# (7) x_e
num = pd.DataFrame(
(x_es - np.tile(b_s, (E, 1))) / np.tile(v_s**2, (E, 1))).sum(
axis=1) # sum along s
den = pd.DataFrame(one_or_nan(x_es) / np.tile(v_s**2, (E, 1))).sum(
axis=1) # sum along s
x_e_new = num / den
x_e = x_e * (1.0 - REFRESH_RATE) + x_e_new * REFRESH_RATE
itr += 1
delta_x_e = linalg.norm(x_e_prev - x_e)
msg = 'Iteration {itr:4d}: change {delta_x_e}, mean x_e {x_e}, mean b_s {b_s}, mean v_s {v_s}'.\
format(itr=itr, delta_x_e=delta_x_e, x_e=np.mean(x_e), b_s=np.mean(b_s), v_s=np.mean(v_s))
sys.stdout.write(msg + '\r')
sys.stdout.flush()
# time.sleep(0.001)
if delta_x_e < DELTA_THR:
break
if itr >= MAX_ITR:
break
sys.stdout.write("\n")
result = {
'quality_scores': list(x_e),
'observer_bias': list(b_s),
'observer_inconsistency': list(v_s),
}
try:
observers = dataset_reader._get_list_observers() # may not exist
result['observers'] = observers
except AssertionError:
pass
return result
def get_medoids(df):
"""
Parameters
----------
df : pandas.DataFrame
Dataframe returned by `cluster` function
Returns
--------
Nested dictionary, first key is cluster id. Nested keys are:
'data': with the representative data for each cluster (medoid)
'size' : size of the cluster in days/weeks (weight)
'dates': pandas.datetimeindex with dates of original data of clusters.
"""
# calculate hours of the group (e.g. 24 for day, 168 for week etc)
hours = int(len(df) / len(set(df.index.get_level_values('group'))))
# Finding medoids, clustersizes, etc.
cluster_group = {}
cluster_size = {}
medoids = {}
# this is necessary fors weeks, because there might be no cluster for
# elements inside the dataframe, i.e. no complete weeks
cluster_ids = [
i for i in df.index.get_level_values('cluster_id').unique()
if not np.isnan(i)
]
for c in cluster_ids:
print('Computing medoid for cluster: ', c, '...')
# days in the cluster is the df subset indexed by the cluster id 'c'
cluster_group[c] = df.loc[c]
# the size for daily clusters is the length of all hourly vals / 24
cluster_size[c] = len(df.loc[c]) / hours
# store the cluster 'days' i.e. all observations of cluster in 'cluster'
# TODO: Maybe rather use copy() to keep cluster_days untouched (reference problem)
cluster = cluster_group[c]
#pdb.set_trace()
# Finding medoids (this is a little hackisch but should work correctly):
# 1) create emtpy distance matrix with size of cluster
# 2) loop through matrix and add the distance between two 'days'
# 3) As we want days, we have to slice 24*i...
Yc = np.empty((
int(cluster_size[c]),
int(cluster_size[c]),
))
Yc[:] = np.NAN
for i in range(len(Yc)):
for j in range(len(Yc[i, :])):
A = cluster.iloc[hours * i:hours * i + hours].values
B = cluster.iloc[hours * j:hours * j + hours].values
Yc[i, j] = norm(A - B, ord='fro')
# taking the index with the minimum summed distance as medoid
mid = np.argmin(Yc.sum(axis=0))
# store data about medoids
medoids[c] = {}
# find medoid
medoids[c]['data'] = cluster.iloc[hours * mid:hours * mid + hours]
# size ( weight)
medoids[c]['size'] = cluster_size[c]
# dates from original data
medoids[c]['dates'] = medoids[c]['data'].index.get_level_values(
'datetime')
return medoids
def cost_func(y):
dists = np.array([norm(x - y) for x in X])
return np.sum(dists)
def _run_modeling(cls, dataset_reader, **kwargs):
# mode: DEFAULT - subject and content-aware
# NO_SUBJECT - subject-unaware
# NO_CONTENT - content-unaware
if 'subject_rejection' in kwargs and kwargs[
'subject_rejection'] is True:
assert False, '{} must not and need not apply subject rejection.'.format(
cls.__name__)
gradient_method = kwargs[
'gradient_method'] if 'gradient_method' in kwargs else cls.DEFAULT_GRADIENT_METHOD
assert gradient_method == 'simplified' or gradient_method == 'original' or gradient_method == 'numerical'
def sum_over_content_id(xs, cids):
assert len(xs) == len(cids)
num_c = np.max(cids) + 1
for cid in set(cids):
assert cid in range(num_c), \
'content id must be in [0, {num_c}), but is {cid}'.format(num_c=num_c, cid=cid)
sums = np.zeros(num_c)
for x, cid in zip(xs, cids):
sums[cid] += x
return sums
def std_over_subject_and_content_id(x_es, cids):
assert x_es.shape[0] == len(cids)
num_c = np.max(cids) + 1
for cid in set(cids):
assert cid in range(num_c), \
'content id must be in [0, {num_c}), but is {cid}'.format(num_c=num_c, cid=cid)
ls = [[] for _ in range(num_c)]
for idx_cid, cid in enumerate(cids):
ls[cid] = ls[cid] + list(x_es[idx_cid, :])
stds = []
for l in ls:
stds.append(pd.Series(l).std(ddof=0))
return np.array(stds)
def one_or_nan(x):
y = np.ones(x.shape)
y[np.isnan(x)] = float('nan')
return y
x_es = cls._get_opinion_score_2darray_with_preprocessing(
dataset_reader, **kwargs)
E, S = x_es.shape
C = dataset_reader.max_content_id_of_ref_videos + 1
# === initialization ===
mos = np.array(
MosModel(dataset_reader).run_modeling()['quality_scores'])
r_es = x_es - np.tile(mos, (S, 1)).T # r_es: residual at e, s
sigma_r_s = pd.DataFrame(r_es).std(axis=0, ddof=0) # along e
sigma_r_c = std_over_subject_and_content_id(
r_es, dataset_reader.content_id_of_dis_videos)
x_e = mos # use MOS as initial value for x_e
b_s = np.zeros(S)
v_s = np.zeros(S) if cls.mode == 'NO_SUBJECT' else sigma_r_s
a_c = np.zeros(C) if cls.mode == 'NO_CONTENT' else sigma_r_c
x_e_std = None
b_s_std = None
v_s_std = None
a_c_std = None
# === iterations ===
MAX_ITR = 10000
REFRESH_RATE = 0.1
DELTA_THR = 1e-8
EPSILON = 1e-3
print '=== Belief Propagation ==='
itr = 0
while True:
x_e_prev = x_e
# ==== (12) b_s ====
if gradient_method == 'simplified':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
num_num = x_es - np.tile(x_e, (S, 1)).T
num_den = np.tile(v_s**2, (E, 1)) + np.tile(a_c_e**2, (S, 1)).T
num = pd.DataFrame(num_num / num_den).sum(axis=0) # sum over e
den_num = one_or_nan(x_es) # 1 and nan
den_den = num_den
den = pd.DataFrame(den_num / den_den).sum(axis=0) # sum over e
b_s_new = num / den
b_s = b_s * (1.0 - REFRESH_RATE) + b_s_new * REFRESH_RATE
b_s_std = 1.0 / np.sqrt(den) # calculate std of x_e
elif gradient_method == 'original':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
vs2_add_ace2 = np.tile(v_s**2,
(E, 1)) + np.tile(a_c_e**2, (S, 1)).T
order1 = (x_es - np.tile(x_e, (S, 1)).T -
np.tile(b_s, (E, 1))) / vs2_add_ace2
order1 = pd.DataFrame(order1).sum(axis=0) # sum over e
order2 = -one_or_nan(x_es) / vs2_add_ace2
order2 = pd.DataFrame(order2).sum(axis=0) # sum over e
b_s_new = b_s - order1 / order2
b_s = b_s * (1.0 - REFRESH_RATE) + b_s_new * REFRESH_RATE
b_s_std = 1.0 / np.sqrt(-order2) # calculate std of x_e
elif gradient_method == 'numerical':
axis = 0 # sum over e
order1 = (cls.loglikelihood_fcn(
x_es,
x_e,
b_s + EPSILON / 2.0,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) - cls.loglikelihood_fcn(
x_es,
x_e,
b_s - EPSILON / 2.0,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON
order2 = (cls.loglikelihood_fcn(
x_es,
x_e,
b_s + EPSILON,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) - 2 * cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) + cls.loglikelihood_fcn(
x_es,
x_e,
b_s - EPSILON,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON**2
b_s_new = b_s - order1 / order2
b_s = b_s * (1.0 - REFRESH_RATE) + b_s_new * REFRESH_RATE
b_s_std = 1.0 / np.sqrt(-order2) # calculate std of x_e
else:
assert False
if cls.mode == 'NO_SUBJECT':
b_s = np.zeros(S) # forcing zero, hence disabling
b_s_std = np.zeros(S)
# ==== (14) v_s ====
if gradient_method == 'simplified':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
a_es = x_es - np.tile(x_e, (S, 1)).T - np.tile(b_s, (E, 1))
vs2_add_ace2 = np.tile(v_s**2,
(E, 1)) + np.tile(a_c_e**2, (S, 1)).T
vs2_minus_ace2 = np.tile(v_s**2,
(E, 1)) - np.tile(a_c_e**2, (S, 1)).T
num = -np.tile(v_s, (E, 1)) / vs2_add_ace2 + np.tile(
v_s, (E, 1)) * a_es**2 / vs2_add_ace2**2
num = pd.DataFrame(num).sum(axis=0) # sum over e
poly_term = np.tile(a_c_e**4, (S, 1)).T \
- 3 * np.tile(v_s**4, (E, 1)) \
- 2 * np.tile(v_s**2, (E, 1)) * np.tile(a_c_e**2, (S, 1)).T
den = vs2_minus_ace2 / vs2_add_ace2**2 + a_es**2 * poly_term / vs2_add_ace2**4
den = pd.DataFrame(den).sum(axis=0) # sum over e
v_s_new = v_s - num / den
v_s = v_s * (1.0 - REFRESH_RATE) + v_s_new * REFRESH_RATE
# calculate std of v_s
lpp = pd.DataFrame(vs2_minus_ace2 / vs2_add_ace2**2 +
a_es**2 * poly_term / vs2_add_ace2**4).sum(
axis=0) # sum over e
v_s_std = 1.0 / np.sqrt(-lpp)
elif gradient_method == 'original':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
a_es = x_es - np.tile(x_e, (S, 1)).T - np.tile(b_s, (E, 1))
vs2_add_ace2 = np.tile(v_s**2,
(E, 1)) + np.tile(a_c_e**2, (S, 1)).T
vs2_minus_ace2 = np.tile(v_s**2,
(E, 1)) - np.tile(a_c_e**2, (S, 1)).T
poly_term = np.tile(a_c_e**4, (S, 1)).T \
- 3 * np.tile(v_s**4, (E, 1)) \
- 2 * np.tile(v_s**2, (E, 1)) * np.tile(a_c_e**2, (S, 1)).T
order1 = -np.tile(v_s, (E, 1)) / vs2_add_ace2 + np.tile(
v_s, (E, 1)) * a_es**2 / vs2_add_ace2**2
order1 = pd.DataFrame(order1).sum(axis=0) # sum over e
order2 = vs2_minus_ace2 / vs2_add_ace2**2 + a_es**2 * poly_term / vs2_add_ace2**4
order2 = pd.DataFrame(order2).sum(axis=0) # sum over e
v_s_new = v_s - order1 / order2
v_s = v_s * (1.0 - REFRESH_RATE) + v_s_new * REFRESH_RATE
v_s_std = 1.0 / np.sqrt(-order2) # calculate std of v_s
elif gradient_method == 'numerical':
axis = 0 # sum over e
order1 = (cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s + EPSILON / 2.0,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) - cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s - EPSILON / 2.0,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON
order2 = (cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s + EPSILON,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) - 2 * cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) + cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s - EPSILON,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON**2
v_s_new = v_s - order1 / order2
v_s = v_s * (1.0 - REFRESH_RATE) + v_s_new * REFRESH_RATE
v_s_std = 1.0 / np.sqrt(-order2) # calculate std of v_s
else:
assert False
# force non-negative
v_s = np.maximum(v_s, 0.0 * np.ones(v_s.shape))
if cls.mode == 'NO_SUBJECT':
v_s = np.zeros(S) # forcing zero, hence disabling
v_s_std = np.zeros(S)
# ==== (15) a_c ====
if gradient_method == 'simplified':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
a_es = x_es - np.tile(x_e, (S, 1)).T - np.tile(b_s, (E, 1))
vs2_add_ace2 = np.tile(v_s**2,
(E, 1)) + np.tile(a_c_e**2, (S, 1)).T
vs2_minus_ace2 = np.tile(v_s**2,
(E, 1)) - np.tile(a_c_e**2, (S, 1)).T
num = -np.tile(a_c_e, (S, 1)).T / vs2_add_ace2 + np.tile(
a_c_e, (S, 1)).T * a_es**2 / vs2_add_ace2**2
num = pd.DataFrame(num).sum(axis=1) # sum over s
num = sum_over_content_id(
num, dataset_reader.content_id_of_dis_videos
) # sum over e:c(e)=c
poly_term = np.tile(v_s**4, (E, 1)) \
- 3 * np.tile(a_c_e**4, (S, 1)).T \
- 2 * np.tile(v_s**2, (E, 1)) * np.tile(a_c_e**2, (S, 1)).T
den = -vs2_minus_ace2 / vs2_add_ace2**2 + a_es**2 * poly_term / vs2_add_ace2**4
den = pd.DataFrame(den).sum(axis=1) # sum over s
den = sum_over_content_id(
den, dataset_reader.content_id_of_dis_videos
) # sum over e:c(e)=c
a_c_new = a_c - num / den
a_c = a_c * (1.0 - REFRESH_RATE) + a_c_new * REFRESH_RATE
# calculate std of a_c
lpp = sum_over_content_id(
pd.DataFrame(-vs2_minus_ace2 / vs2_add_ace2**2 +
a_es**2 * poly_term / vs2_add_ace2**4).sum(
axis=1), dataset_reader.
content_id_of_dis_videos) # sum over e:c(e)=c
a_c_std = 1.0 / np.sqrt(-lpp)
elif gradient_method == 'original':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
a_es = x_es - np.tile(x_e, (S, 1)).T - np.tile(b_s, (E, 1))
vs2_add_ace2 = np.tile(v_s**2,
(E, 1)) + np.tile(a_c_e**2, (S, 1)).T
vs2_minus_ace2 = np.tile(v_s**2,
(E, 1)) - np.tile(a_c_e**2, (S, 1)).T
poly_term = np.tile(v_s**4, (E, 1)) \
- 3 * np.tile(a_c_e**4, (S, 1)).T \
- 2 * np.tile(v_s**2, (E, 1)) * np.tile(a_c_e**2, (S, 1)).T
order1 = -np.tile(a_c_e, (S, 1)).T / vs2_add_ace2 + np.tile(
a_c_e, (S, 1)).T * a_es**2 / vs2_add_ace2**2
order1 = pd.DataFrame(order1).sum(axis=1) # sum over s
order1 = sum_over_content_id(
order1, dataset_reader.content_id_of_dis_videos
) # sum over e:c(e)=c
order2 = -vs2_minus_ace2 / vs2_add_ace2**2 + a_es**2 * poly_term / vs2_add_ace2**4
order2 = pd.DataFrame(order2).sum(axis=1) # sum over s
order2 = sum_over_content_id(
order2, dataset_reader.content_id_of_dis_videos
) # sum over e:c(e)=c
a_c_new = a_c - order1 / order2
a_c = a_c * (1.0 - REFRESH_RATE) + a_c_new * REFRESH_RATE
a_c_std = 1.0 / np.sqrt(-order2) # calculate std of a_c
elif gradient_method == 'numerical':
axis = 1 # sum over s
order1 = (cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c + EPSILON / 2.0,
dataset_reader.content_id_of_dis_videos,
axis=axis) - cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c - EPSILON / 2.0,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON
order2 = (cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c + EPSILON,
dataset_reader.content_id_of_dis_videos,
axis=axis) - 2 * cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) + cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c - EPSILON,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON**2
order1 = sum_over_content_id(
order1, dataset_reader.content_id_of_dis_videos
) # sum over e:c(e)=c
order2 = sum_over_content_id(
order2, dataset_reader.content_id_of_dis_videos
) # sum over e:c(e)=c
a_c_new = a_c - order1 / order2
a_c = a_c * (1.0 - REFRESH_RATE) + a_c_new * REFRESH_RATE
a_c_std = 1.0 / np.sqrt(-order2) # calculate std of a_c
else:
assert False
# force non-negative
a_c = np.maximum(a_c, 0.0 * np.ones(a_c.shape))
if cls.mode == 'NO_CONTENT':
a_c = np.zeros(C) # forcing zero, hence disabling
a_c_std = np.zeros(C)
# (11) ==== x_e ====
if gradient_method == 'simplified':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
num_num = x_es - np.tile(b_s, (E, 1))
num_den = np.tile(v_s**2, (E, 1)) + np.tile(a_c_e**2, (S, 1)).T
num = pd.DataFrame(num_num / num_den).sum(axis=1) # sum over s
den_num = one_or_nan(x_es) # 1 and nan
den_den = num_den
den = pd.DataFrame(den_num / den_den).sum(axis=1) # sum over s
x_e_new = num / den
x_e = x_e * (1.0 - REFRESH_RATE) + x_e_new * REFRESH_RATE
x_e_std = 1.0 / np.sqrt(den) # calculate std of x_e
elif gradient_method == 'original':
a_c_e = np.array(
map(lambda i: a_c[i],
dataset_reader.content_id_of_dis_videos))
a_es = x_es - np.tile(x_e, (S, 1)).T - np.tile(b_s, (E, 1))
vs2_add_ace2 = np.tile(v_s**2,
(E, 1)) + np.tile(a_c_e**2, (S, 1)).T
order1 = a_es / vs2_add_ace2
order1 = pd.DataFrame(order1).sum(axis=1) # sum over s
order2 = -one_or_nan(x_es) / vs2_add_ace2
order2 = pd.DataFrame(order2).sum(axis=1) # sum over s
x_e_new = x_e - order1 / order2
x_e = x_e * (1.0 - REFRESH_RATE) + x_e_new * REFRESH_RATE
x_e_std = 1.0 / np.sqrt(-order2) # calculate std of x_e
elif gradient_method == 'numerical':
axis = 1 # sum over s
order1 = (cls.loglikelihood_fcn(
x_es,
x_e + EPSILON / 2.0,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) - cls.loglikelihood_fcn(
x_es,
x_e - EPSILON / 2.0,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON
order2 = (cls.loglikelihood_fcn(
x_es,
x_e + EPSILON,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) - 2 * cls.loglikelihood_fcn(
x_es,
x_e,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis) + cls.loglikelihood_fcn(
x_es,
x_e - EPSILON,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=axis)) / EPSILON**2
x_e_new = x_e - order1 / order2
x_e = x_e * (1.0 - REFRESH_RATE) + x_e_new * REFRESH_RATE
x_e_std = 1.0 / np.sqrt(-order2) # calculate std of x_e
else:
assert False
itr += 1
delta_x_e = linalg.norm(x_e_prev - x_e)
likelihood = np.sum(
cls.loglikelihood_fcn(x_es,
x_e,
b_s,
v_s,
a_c,
dataset_reader.content_id_of_dis_videos,
axis=1))
msg = 'Iteration {itr:4d}: change {delta_x_e}, likelihood {likelihood}, x_e {x_e}, b_s {b_s}, v_s {v_s}, a_c {a_c}'.\
format(itr=itr, delta_x_e=delta_x_e, likelihood=likelihood, x_e=np.nanmean(x_e), b_s=np.nanmean(b_s), v_s=np.nanmean(v_s), a_c=np.nanmean(a_c))
sys.stdout.write(msg + '\r')
sys.stdout.flush()
# time.sleep(0.001)
if delta_x_e < DELTA_THR:
break
if itr >= MAX_ITR:
break
sys.stdout.write("\n")
assert x_e_std is not None
assert b_s_std is not None
result = {
'quality_scores': list(x_e),
'quality_scores_std': list(x_e_std),
}
if cls.mode != 'NO_SUBJECT':
result['observer_bias'] = list(b_s)
result['observer_bias_std'] = list(b_s_std)
result['observer_inconsistency'] = list(v_s)
result['observer_inconsistency_std'] = list(v_s_std)
if cls.mode != 'NO_CONTENT':
result['content_ambiguity'] = list(a_c)
result['content_ambiguity_std'] = list(a_c_std)
try:
observers = dataset_reader._get_list_observers() # may not exist
result['observers'] = observers
except AssertionError:
pass
return result
def basicFunc(self, c, d, beta):
return np.exp(beta * norm(c - d)**2)
def BinarySolver(func, h0, x0, rho, maxIter, sigma=100):
"""
Use exact penalty method to solve optimization problem with binary constraints
min_x func(x)
s.t. x \in {-1,1}
Inputs:
- func: Function that needs to be minimized
- x0: Initialization
This implementation uses a novel method invented by HKT Team
Copyright 2018 HKT
Refereces: https://www.facebook.com/dangkhoasdc
"""
n = len(x0)
#xt, vt: Values of x and v at the previous iteration, which are used to update x and v at the current iteration, respectively
#h0 = x0.copy()
xt = x0 #np.zeros(x0.shape) #np.sign(x0)
vt = np.ones(xt.shape) - xt #np.zeros(xt.shape) # Initialize v to zeros!!!!!!! Note on this
# Lagrangian duals
y1 = np.zeros(x0.shape)
y2 = np.zeros(x0.shape)
def fcost(x):
return func(x) + sigma*np.sum((x-h0)**2)
print("Initial cost with sign: %f without sign = %f" %(fcost(xt), fcost(h0)))
print("reconstruction: %f" %(func(x0)))
print("Encoder error: %f" %(sigma*np.sum((x0-h0)**2)))
# pdb.set_trace()
def fx(x): # Fix v, solve for x
return func(x) + sigma*np.sum(np.power(x-h0,2))
+ np.dot(y1, vt - np.ones(xt.shape) + x) + 0.5*rho*(np.sum(np.power(vt + x - np.ones(xt.shape), 2)))
+ np.dot (y2, np.multiply(vt, x+np.ones(x0.shape))) + 0.5*rho*np.sum(np.power(np.multiply(vt, x+np.ones(x0.shape)),2))
def fv(x): # Fix x, solve for v
return np.dot(y1, x - np.ones(x0.shape) + xt) + 0.5*rho*np.sum(np.power(x - np.ones(x0.shape), 2))
+ np.dot(y2, np.multiply(x, np.ones(x0.shape)+xt)) + 0.5*rho*np.sum(np.power(np.multiply(x, np.ones(x0.shape)+xt),2))
# Define the lower and upper bounds for fx, i.e., -1 <= x <= 1
xbounds= [(-1,1) for i in range(n)]
vbounds = [(0, 2) for i in range(n)]
# Now, let the iterations begin
converged = False
iter = 0
while iter < maxIter and not converged:
# Fix v, minimize x
print('----Updating x ')
x_res = minimize(fx, xt, bounds = xbounds)
x = x_res.x
# print min(x), max(x)
# Fix x, update v
print('----Updating v')
v_res = minimize(fv, vt, bounds = vbounds)
v = v_res.x
# print min(v), max(v)
y1 = y1 + rho*(v + x - np.ones(x0.shape))
y2 = y2 + rho*(np.multiply(v, np.ones(x0.shape) + x))
print("Iter: %d , fx = %.3f, prev_fx = %.3f, x diff: %.3f, rho = %.3f reconstruction: %f"
%(iter, fcost(x), fcost(xt), norm(x - xt), rho, func(x)))
print("reconstruction: %f" %(func(x)))
print("Encoder error: %f" %(sigma*np.sum((x-h0)**2)))
# Check for convergence
# if iter > 4 and ((norm(v - vt) < 1e-6 and abs(func(x) - func(xt) < 1e-6)) or (n-np.dot(xt, vt))**2<1.5):
if iter > 1 and ( (norm(x - xt) < 1e-6 or
abs(fcost(x)-fcost(xt))<1e-6 ) ):
converged = True
print('--------Using LINF - Converged---------')
return xt #np.ones(x0.shape) - vt
#print (xt)
rho = rho*1.05
xt = x
vt = v
iter = iter + 1
return xt #np.ones(x0.shape) - vt
uop_sd.set_uniq_amps_(x_rand)
upsi = uop_sd (psi)
upsi_h = fockspace.fock2hilbert (upsi, norb, nelec)
uTupsi = uop_sd (upsi, transpose=True)
for ix in range (2**(2*norb)):
if np.any (np.abs ([psi[ix], upsi[ix], uTupsi[ix]]) > 1e-8):
print (pbin (ix), psi[ix], upsi[ix], uTupsi[ix])
print ("<psi|psi> =",psi.dot (psi), "<psi|U|psi> =",psi.dot (upsi),"<psi|U'U|psi> =",upsi.dot (upsi))
print ("<psi|S**2|psi> =",spin_square (psi, norb)[0],
"<psi|U'S**2U|psi> =",spin_square (upsi, norb)[0], spin_op.spin_square (upsi_h, norb, nelec)[0])
ndet = cistring.num_strings (norb, nelec//2)
np.random.seed (0)
tpsi = 1-(2*np.random.rand (ndet))
tpsi = np.multiply.outer (tpsi, tpsi).ravel ()
tpsi /= linalg.norm (tpsi)
tpsi = fockspace.hilbert2fock (tpsi, norb, (nelec//2, nelec//2)).ravel ()
from scipy import optimize
def obj_test (uop_test):
def obj_fun (x):
uop_test.set_uniq_amps_(x)
upsi = uop_test (psi)
ut = upsi.dot (tpsi)
err = upsi.dot (upsi) - (ut**2)
jac = np.zeros (uop_test.ngen)
for ix, dupsi in enumerate (uop_test.gen_deriv1 (psi)):
jac[ix] += 2*dupsi.dot (upsi - ut*tpsi)
jac = uop_test.product_rule_pack (jac)
print (err, linalg.norm (jac))
return err, jac
a = inner(q(u_k)*nabla_grad(u), nabla_grad(v))*dx
f = Constant(0.0)
L = f*v*dx
# Picard iterations
u = Function(V) # new unknown function
eps = 1.0 # error measure ||u-u_k||
rho = 0 # convergence rate
tol = 1.0E-6 # tolerance
iter = 0 # iteration counter
maxiter = 25 # max no of iterations allowed
for iter in range(maxiter):
solve(a == L, u, bcs)
diff = u.vector().array() - u_k.vector().array()
oldeps = eps
eps = la.norm(diff, ord=np.Inf) / la.norm(u.vector().array(), ord=np.Inf)
rho = eps/oldeps
print 'iter=%d: norm=%g, rho=%g' % (iter, eps, rho)
if eps < tol * (1.0-rho)
break
u_k.assign(u) # update for next iteration
convergence = 'convergence after %d Picard iterations' % iter
if iter >= maxiter:
convergence = 'no ' + convergence
print convergence
# Find max error
u_exact = Expression('pow((pow(2, m+1)-1)*x[0] + 1, 1.0/(m+1)) - 1', m=m)
u_e = interpolate(u_exact, V)
diff = la.norm((u_e.vector().array() - u.vector().array()), ord=np.Inf)
def compute_coordinate():
'''
Compute the magnet's position in cartesian space.
INPUTS:
- No inputs.
OUTPUT:
- position: The most current and updated position
of the magnet in cartesian space.
'''
global initialGuess # Modify from within function
start = time() # Call clock() for accurate time readings
# Data acquisition
(H1, H2, H3, H4, H5, H6) = getData(IMU) # Get data from MCU
# Compute norms
HNorm = [
float(norm(H1)),
float(norm(H2)), #
float(norm(H3)),
float(norm(H4)), # Compute L2 vector norms
float(norm(H5)),
float(norm(H6))
] #
# Solve system of equations
sol = root(
LHS,
initialGuess,
args=(K, HNorm),
method='lm', # Invoke solver using the
options={
'ftol': 1e-10,
'xtol': 1e-10,
'maxiter': 1000, # Levenberg-Marquardt
'eps': 1e-8,
'factor': 0.001
}) # Algorithm (aka LMA)
# Store solution in array
position = np.array(
(
sol.x[0] * 1000, # x-axis
sol.x[1] * 1000, # y-axis
sol.x[2] * 1000, # z-axis
time() - start),
dtype='float64') # time
# Check value
if (position[2] < 0): position[2] = -1 * position[2] # Make sure z-value
else: pass # ... is ALWAYS +ve
# Print solution (coordinates) to screen
print("(x, y, z, t): (%.3f, %.3f, %.3f, %.3f)" %
(position[0], position[1], position[2], position[3]))
# Check if solution makes sense
if (abs(sol.x[0] * 1000) > 500) or (abs(sol.x[1] * 1000) > 500) or (abs(
sol.x[2] * 1000) > 500):
initialGuess = findIG(
getData(IMU)) # Determine initial guess based on magnet's location
return (compute_coordinate()) # Recursive call of function()
# Update initial guess with current position and feed back to solver
else:
initialGuess = np.array(
(
sol.x[0] + dx,
sol.x[1] + dx, # Update the initial guess as the
sol.x[2] + dx),
dtype='float64') # current position and feed back to LMA
return (position) # Return position
def sensitivity_map(fwd,
projs=None,
ch_type='grad',
mode='fixed',
exclude=[],
verbose=None):
"""Compute sensitivity map
Such maps are used to know how much sources are visible by a type
of sensor, and how much projections shadow some sources.
Parameters
----------
fwd : dict
The forward operator.
projs : list
List of projection vectors.
ch_type : 'grad' | 'mag' | 'eeg'
The type of sensors to use.
mode : str
The type of sensitivity map computed. See manual. Should be 'free',
'fixed', 'ratio', 'radiality', 'angle', 'remaining', or 'dampening'
corresponding to the argument --map 1, 2, 3, 4, 5, 6 and 7 of the
command mne_sensitivity_map.
exclude : list of string | str
List of channels to exclude. If empty do not exclude any (default).
If 'bads', exclude channels in fwd['info']['bads'].
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Return
------
stc : SourceEstimate
The sensitivity map as a SourceEstimate instance for
visualization.
"""
# check strings
if not ch_type in ['eeg', 'grad', 'mag']:
raise ValueError("ch_type should be 'eeg', 'mag' or 'grad (got %s)" %
ch_type)
if not mode in [
'free', 'fixed', 'ratio', 'radiality', 'angle', 'remaining',
'dampening'
]:
raise ValueError('Unknown mode type (got %s)' % mode)
# check forward
if is_fixed_orient(fwd, orig=True):
raise ValueError('fwd should must be computed with free orientation')
fwd = convert_forward_solution(fwd,
surf_ori=True,
force_fixed=False,
verbose=False)
if not fwd['surf_ori'] or is_fixed_orient(fwd):
raise RuntimeError('Error converting solution, please notify '
'mne-python developers')
# limit forward
if ch_type == 'eeg':
fwd = pick_types_forward(fwd, meg=False, eeg=True, exclude=exclude)
else:
fwd = pick_types_forward(fwd, meg=ch_type, eeg=False, exclude=exclude)
gain = fwd['sol']['data']
# Make sure EEG has average
if ch_type == 'eeg':
if projs is None or not _has_eeg_average_ref_proj(projs):
eeg_ave = [make_eeg_average_ref_proj(fwd['info'])]
else:
eeg_ave = []
projs = eeg_ave if projs is None else projs + eeg_ave
# Construct the projector
if projs is not None:
proj, ncomp, U = make_projector(projs,
fwd['sol']['row_names'],
include_active=True)
# do projection for most types
if mode not in ['angle', 'remaining', 'dampening']:
gain = np.dot(proj, gain)
# can only eggie the last couple methods if there are projectors
elif mode in ['angle', 'remaining', 'dampening']:
raise ValueError('No projectors used, cannot compute %s' % mode)
n_sensors, n_dipoles = gain.shape
n_locations = n_dipoles // 3
sensitivity_map = np.empty(n_locations)
for k in range(n_locations):
gg = gain[:, 3 * k:3 * (k + 1)]
if mode != 'fixed':
s = linalg.svd(gg, full_matrices=False, compute_uv=False)
if mode == 'free':
sensitivity_map[k] = s[0]
else:
gz = linalg.norm(gg[:, 2]) # the normal component
if mode == 'fixed':
sensitivity_map[k] = gz
elif mode == 'ratio':
sensitivity_map[k] = gz / s[0]
elif mode == 'radiality':
sensitivity_map[k] = 1. - (gz / s[0])
else:
if mode == 'angle':
co = linalg.norm(np.dot(gg[:, 2], U))
sensitivity_map[k] = co / gz
else:
p = linalg.norm(np.dot(proj, gg[:, 2]))
if mode == 'remaining':
sensitivity_map[k] = p / gz
elif mode == 'dampening':
sensitivity_map[k] = 1. - p / gz
else:
raise ValueError('Unknown mode type (got %s)' % mode)
# only normalize fixed and free methods
if mode in ['fixed', 'free']:
sensitivity_map /= np.max(sensitivity_map)
vertices = [fwd['src'][0]['vertno'], fwd['src'][1]['vertno']]
subject = _subject_from_forward(fwd)
stc = SourceEstimate(sensitivity_map[:, np.newaxis],
vertices=vertices,
tmin=0,
tstep=1,
subject=subject)
return stc
def power_diagram(face, uv, h=None, dh=None):
if h is None:
h = np.zeros((uv.shape[0], 1))
if dh is None:
dh = h * 0
nf = face.shape[0]
c = 1
while True:
h = h - c * dh
pl = np.concatenate((uv, np.reshape(np.square(norm(uv, axis=1)), (-1, 1)) - h), axis=1)
hull = ConvexHull(pl, qhull_options='Qt')
face = hull.simplices
# fix ups for the convex hull, as the orientation may inverse
fn_from_hull = hull.equations[:,2]
fn = calculate_face_normal(face, pl)
for i in range(face.shape[0]):
if fn[i,2] * fn_from_hull[i] < 0 : # orientation difff
face[i,:] = face[i,[0, 2, 1]]
for i in range(face.shape[0]):
mif = np.argmin(face[i,:])
face[i, :] = face[i, np.mod(np.arange(mif,mif+3),3)]
face = face[np.argsort(face[:, 0] * np.max(face) + face[:, 1]), :]
fn = calculate_face_normal(face, pl)
ind = fn[:, 2] < 0
if np.sum(ind) < nf:
h = h + c * dh
c = c / 2
else:
break
if np.max(abs(dh)) == 0:
break
fn = calculate_face_normal(face, pl)
ind = fn[:, 2] < 0
face = face[ind, :]
pd = dict()
pd['face'] = face
vr = compute_vertex_ring(face, uv, ordered=True)
pd['uv'] = uv
pd['dp'] = np.zeros((face.shape[0], 2))
pd['cell'] = [[] for i in range(pl.shape[0])]
for i in range(face.shape[0]):
dp = face_dual_uv(pl[face[i,:],:])
pd['dp'][i,:] = dp
K = ConvexHull(uv, qhull_options='Qt').vertices
ks = np.argmin(K)
K = np.concatenate((K[ks::], K[0:ks]), axis=0)
K = np.append(K,K[0])
vb = np.zeros((K.shape[0] - 1, 2))
mindp = np.min(pd["dp"], axis=0) - 1
maxdp = np.max(pd["dp"], axis=0) + 1
minx = mindp[0]
miny = mindp[1]
maxx = maxdp[0]
maxy = maxdp[1]
box = np.array([minx, miny, maxx, miny, maxx, maxy, minx, maxy, minx, miny]).reshape((-1,2))
for i in range(K.shape[0]- 1):
i1 = K[i]
i2 = K[i + 1]
vec = uv[i2,:] - uv[i1,:]
vec = np.array([vec[1], -vec[0]])
mid = (uv[i2,:] + uv[i1,:]) / 2.0
intersect = intersectRayPolygon(mid, vec, box)
vb[i,:] = intersect
pd["dpe"] = np.concatenate((pd["dp"], vb), axis=0)
vvif, _, _= compute_connectivity(face)
for i in range(uv.shape[0]):
vri = vr[i]
pb = np.argwhere(K==i)
if pb.size > 0 :
pb = pb[0][0]
fr = np.zeros((len(vri) + 1,)).astype(int)
fr[-1] = face.shape[0] + pb
if pb == 0:
fr[0] = face.shape[0] + K.shape[0]-2
else:
fr[0] = face.shape[0] + pb - 1
for j in range(len(vri) - 1):
fr[j+1] = vvif[i, vri[j]]
else:
fr = np.zeros((len(vri),)).astype(int)
for j in range(len(vri)):
fr[j] = vvif[i, vri[j]]
pd["cell"][i] = np.flip(fr)
return pd, h
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import scipy as sc
from scipy import linalg
from numpy import linalg as linalg2
H5 = linalg.hilbert(5)
H10 = linalg.hilbert(10)
H20 = linalg.hilbert(20)
print('\nnorma(H5)=', linalg.norm(H5, np.inf))
print('k(H5)=', linalg2.cond(H5, np.inf))
print('\nnorma(H10)=', linalg.norm(H10, np.inf))
print('k(H10)=', linalg2.cond(H10, np.inf))
print('\nnorma(H220)=', linalg.norm(H20, np.inf))
print('k(H20)=', linalg2.cond(H20, np.inf))
np.random.seed(0)
mask = np.ones([size, size], dtype=bool)
coef = np.zeros((size, size))
coef[0:roi_size, 0:roi_size] = -1.0
coef[-roi_size:, -roi_size:] = 1.0
X = np.random.randn(n_samples, size ** 2)
for x in X: # smooth data
x[:] = ndimage.gaussian_filter(x.reshape(size, size), sigma=1.0).ravel()
X -= X.mean(axis=0)
X /= X.std(axis=0)
y = np.dot(X, coef.ravel())
noise = np.random.randn(y.shape[0])
noise_coef = (linalg.norm(y, 2) / np.exp(snr / 20.0)) / linalg.norm(noise, 2)
y += noise_coef * noise # add noise
# #############################################################################
# Compute the coefs of a Bayesian Ridge with GridSearch
cv = KFold(2) # cross-validation generator for model selection
ridge = BayesianRidge()
cachedir = tempfile.mkdtemp()
mem = Memory(location=cachedir, verbose=1)
# Ward agglomeration followed by BayesianRidge
connectivity = grid_to_graph(n_x=size, n_y=size)
ward = FeatureAgglomeration(n_clusters=10, connectivity=connectivity, memory=mem)
clf = Pipeline([("ward", ward), ("ridge", ridge)])
# Select the optimal number of parcels with grid search
clf = GridSearchCV(clf, {"ward__n_clusters": [10, 20, 30]}, n_jobs=1, cv=cv)
def dmg_seed_50_1D(colnum):
#INITIALIZING STUFF
Nmitral = 50
Ngranule = np.copy(Nmitral) #number of granule cells pg. 383 of Li/Hop
Ndim = Nmitral + Ngranule #total number of cells
# t_inh = 25 ; # time when inhalation starts
# t_exh = 205; #time when exhalation starts
# Ndamagetotal = Nmitral*2 + 1 #number of damage steps
Ndamage = 3 #steps to reduce entire matrix to zero
Ncols = int(Nmitral / 2) #define number of columns to damage
finalt = 395
# end time of the cycle
#y = zeros(ndim,1);
P_odor0 = np.zeros((Nmitral, 1)) #odor pattern, no odor
P_odor1 = P_odor0 + .00429 #Odor pattern 1
# P_odor2 = 1/70*np.array([.6,.5,.5,.5,.3,.6,.4,.5,.5,.5])
# P_odor3 = 4/700*np.array([.7,.8,.5,1.2,.7,1.2,.8,.7,.8,.8])
#control_odor = control_order + .00429
#control_odor = np.zeros((Nmitral,1)) #odor input for adaptation
#controllevel = 1 #1 is full adaptation
H0 = np.zeros((Nmitral, Ngranule)) #weight matrix: to mitral from granule
W0 = np.zeros((Ngranule, Nmitral)) #weights: to granule from mitral
H0 = np.load('H0_50_53Hz.npy') #load weight matrix
W0 = np.load('W0_50_53Hz.npy') #load weight matrix
#H0 = H0 + H0*np.random.rand(np.shape(H0))
#W0 = W0+W0*np.random.rand(np.shape(W0))
M = 5 #average over 5 trials for each level of damage
#initialize iterative variables
d1it, d2it, d3it, d4it = np.zeros(M), np.zeros(M), np.zeros(M), np.zeros(M)
IPRit, IPR2it, pnit = np.zeros(M), np.zeros(M), np.zeros(M)
frequencyit = np.zeros(M)
pwrit = np.zeros(M)
yout2, Sh2 = np.zeros((finalt, Ndim)), np.zeros((finalt, Ndim))
psi = np.copy(Sh2[:, :Nmitral])
#initialize quantities to be returned at end of the process
dmgpct1 = np.zeros(Ncols * (Ndamage - 1) + 1)
eigfreq1 = np.zeros(Ncols * (Ndamage - 1) + 1)
d11 = np.zeros(Ncols * (Ndamage - 1) + 1)
d21 = np.zeros(Ncols * (Ndamage - 1) + 1)
d31 = np.zeros(Ncols * (Ndamage - 1) + 1)
d41 = np.zeros(Ncols * (Ndamage - 1) + 1)
pwr1 = np.zeros(Ncols * (Ndamage - 1) + 1)
IPR1 = np.zeros(Ncols * (Ndamage - 1) + 1)
IPR2 = np.zeros(Ncols * (Ndamage - 1) + 1)
pn1 = np.zeros(Ncols * (Ndamage - 1) + 1)
freq1 = np.zeros(Ncols * (Ndamage - 1) + 1)
cell_act = np.zeros((finalt, Ndim, Ncols * (Ndamage - 1) + 1))
damage = 0
dam = np.ones(Nmitral)
#Get the base response first
Omean1,Oosci1,Omeanbar1,Ooscibar1 = np.zeros((Nmitral,M))+0j,\
np.zeros((Nmitral,M))+0j,np.zeros(M)+0j,np.zeros(M)+0j
for m in np.arange(M):
yout,y0out,Sh,t,OsciAmp1,Omean1[:,m],Oosci1[:,m],Omeanbar1[m],\
Ooscibar1[m],freq0,maxlam = olf_bulb_10(Nmitral,H0,W0,P_odor1,dam)
counter = 0 #to get the right index for each of the measures
damage = 0
dam[colnum] += .5 #so it starts on zero damage
for col in range(Ncols):
cols = int(np.mod(colnum + col, Nmitral))
for lv in np.arange(Ndamage):
#reinitialize all iterative variables to zero (really only need to do for distance measures, but good habit)
d1it, d2it, d3it, d4it = np.zeros(M), np.zeros(M), np.zeros(
M), np.zeros(M)
IPRit, IPR2it, pnit = np.zeros(M), np.zeros(M), np.zeros(M)
frequencyit = np.zeros(M)
pwrit = np.zeros(M)
if not (
lv == 0 and cols != colnum
): #if it's the 0th level for any but the original col, skip
dam[cols] = dam[cols] - .5
dam[dam < 1e-10] = 0
damage = np.sum(1 - dam)
for m in np.arange(M):
#Then get respons of damaged network
yout2[:,:],y0out2,Sh2[:,:],t2,OsciAmp2,Omean2,Oosci2,Omeanbar2,\
Ooscibar2,freq2,grow_eigs2 = olf_bulb_10(Nmitral,H0,W0,P_odor1,dam)
#calculate distance measures
print(time.time() - tm1)
for i in np.arange(M):
d1it[m] += 1 - Omean1[:, m].dot(Omean2) / (
lin.norm(Omean1[:, m]) * lin.norm(Omean2))
d2it[m] += 1 - lin.norm(Oosci1[:, m].dot(
np.conjugate(Oosci2))) / (lin.norm(Oosci1[:, m]) *
lin.norm(Oosci2))
d3it[m] += (Omeanbar1[m] - Omeanbar2) / (Omeanbar1[m] +
Omeanbar2)
d4it[m] += np.real((Ooscibar1[m] - Ooscibar2) /
(Ooscibar1[m] + Ooscibar2))
d1it[m] = d1it[
m] / M #average over comparison with all control trials
d2it[m] = d2it[m] / M
d3it[m] = d3it[m] / M
d4it[m] = d4it[m] / M
#calculate spectral density and "wave function" to get average power and IPR
P_den = np.zeros(
(501,
Nmitral)) #only calculate the spectral density from
for i in np.arange(
Nmitral
): #t=125 to t=250, during the main oscillations
f, P_den[:, i] = signal.periodogram(Sh2[125:250, i],
nfft=1000,
fs=1000)
psi = np.zeros(Nmitral)
for p in np.arange(Nmitral):
psi[p] = np.sum(P_den[:, p])
psi = psi / np.sqrt(np.sum(psi**2))
psi2 = np.copy(OsciAmp2)
psi2 = psi2 / np.sqrt(np.sum(psi2**2))
maxAmp = np.max(OsciAmp2)
pnit[m] = len(OsciAmp2[OsciAmp2 > maxAmp / 2])
IPRit[m] = 1 / np.sum(psi**4)
IPR2it[m] = 1 / np.sum(psi2**4)
pwrit[m] = np.sum(P_den) / Nmitral
#get the frequency according to the adiabatic analysis
maxargs = np.argmax(P_den, axis=0)
argf = stats.mode(maxargs[maxargs != 0])
frequencyit[m] = f[argf[0][0]]
# print(cols)
# print(time.time()-tm1)
#
# print('level',lv)
#Get the returned variables for each level of damage
dmgpct1[counter] = damage / Nmitral
IPR1[counter] = np.average(IPRit) #Had to do 1D list, so
pwr1[counter] = np.average(
pwrit) #it goes column 0 damage counterl
freq1[counter] = np.average(
frequencyit) #0,1,2,3,4...Ndamage-1, then
#col 1 damage level 0,1,2...
# IPRsd[counter]=np.std(IPRit)
# pwrsd[counter]=np.std(pwrit)
# freqsd[counter]=np.std(frequencyit)
IPR2[counter] = np.average(IPR2it)
pn1[counter] = np.average(pnit)
d11[counter] = np.average(d1it)
d21[counter] = np.average(d2it)
d31[counter] = np.average(d3it)
d41[counter] = np.average(d4it)
# d1sd[counter] = np.std(d1it)
# d2sd[counter] = np.std(d2it)
# d3sd[counter]=np.std(d3it)
# d4sd[counter]=np.std(d4it)
eigfreq1[counter] = np.copy(freq2)
if (colnum == 0 or colnum == int(Nmitral / 2)):
cell_act[:, :, counter] = np.copy(yout2)
counter += 1
return dmgpct1, eigfreq1, d11, d21, d31, d41, pwr1, IPR1, IPR2, pn1, freq1, cell_act