def synth_meas_watson_SH_cyl_neuman_PGSE( self, x, grad_dirs, G, delta, smalldel, fibredir, roots ):
d=x[0]
R=x[1]
kappa=x[2]
l_q = grad_dirs.shape[0]
# Parallel component
LePar = self.cyl_neuman_le_par_PGSE(d, G, delta, smalldel)
# Perpendicular component
LePerp = self.cyl_neuman_le_perp_PGSE(d, R, G, delta, smalldel, roots)
ePerp = np.exp(LePerp)
# Compute the Legendre weighted signal
Lpmp = LePerp - LePar
lgi = self.legendre_gaussian_integral(Lpmp, 6)
# Compute the spherical harmonic coefficients of the Watson's distribution
coeff = self.watson_SH_coeff(kappa)
coeffMatrix = matlib.repmat(coeff, l_q, 1)
# Compute the dot product between the symmetry axis of the Watson's distribution
# and the gradient direction
#
# For numerical reasons, cosTheta might not always be between -1 and 1
# Due to round off errors, individual gradient vectors in grad_dirs and the
# fibredir are never exactly normal. When a gradient vector and fibredir are
# essentially parallel, their dot product can fall outside of -1 and 1.
#
# BUT we need make sure it does, otherwise the legendre function call below
# will FAIL and abort the calculation!!!
#
cosTheta = np.dot(grad_dirs,fibredir)
badCosTheta = abs(cosTheta)>1
cosTheta[badCosTheta] = cosTheta[badCosTheta]/abs(cosTheta[badCosTheta])
# Compute the SH values at cosTheta
sh = np.zeros(coeff.shape)
shMatrix = matlib.repmat(sh, l_q, 1)
for i in range(7):
shMatrix[:,i] = np.sqrt((i+1 - .75)/np.pi)
# legendre function returns coefficients of all m from 0 to l
# we only need the coefficient corresponding to m = 0
# WARNING: make sure to input ROW vector as variables!!!
# cosTheta is expected to be a COLUMN vector.
tmp = np.zeros((l_q))
for pol_i in range(l_q):
tmp[pol_i] = scipy.special.lpmv(0, 2*i, cosTheta[pol_i])
shMatrix[:,i] = shMatrix[:,i]*tmp
E = np.sum(lgi*coeffMatrix*shMatrix, 1)
# with the SH approximation, there will be no guarantee that E will be positive
# but we need to make sure it does!!! replace the negative values with 10% of
# the smallest positive values
E[E<=0] = np.min(E[E>0])*0.1
E = 0.5*E*ePerp
return E
def con2vert(A, b):
"""
Convert sets of constraints to a list of vertices (of the feasible region).
If the shape is open, con2vert returns False for the closed property.
"""
# Python implementation of con2vert.m by Michael Kleder (July 2005),
# available: http://www.mathworks.com/matlabcentral/fileexchange/7894
# -con2vert-constraints-to-vertices
# Author: Michael Kelder (Original)
# Andre Campher (Python implementation)
c = linalg.lstsq(mat(A), mat(b))[0]
btmp = mat(b)-mat(A)*c
D = mat(A)/matlib.repmat(btmp, 1, A.shape[1])
fmatv = qhull(D, "Ft") #vertices on facets
G = zeros((fmatv.shape[0], D.shape[1]))
for ix in range(0, fmatv.shape[0]):
F = D[fmatv[ix, :], :].squeeze()
G[ix, :] = linalg.lstsq(F, ones((F.shape[0], 1)))[0].transpose()
V = G + matlib.repmat(c.transpose(), G.shape[0], 1)
ux = uniqm(V)
eps = 1e-13
Av = dot(A, ux.T)
bv = tile(b, (1, ux.shape[0]))
closed = sciall(Av - bv <= eps)
return ux, closed
def get_lap_matrix_self_tuning(data):
start_time = time.clock()
sls2 = -2 * np.mat(data) * np.mat(data.T)
sls1 = np.mat(np.sum(data ** 2, 1))
w_matrix = sls2 + repmat(sls1, len(sls1), 1) + repmat(sls1.T, 1, len(sls1))
w_matrix = np.array(w_matrix)
sigma = list()
m = len(w_matrix)
sort_w_matrix = np.sort(w_matrix)
for i in range(m):
sigma.append(np.sqrt(sort_w_matrix[i, 7]))
"""for i in range(m):
print(i)
idx = np.argsort(w_matrix[i, :])
idx = get_k_min_index(w_matrix[i, :].tolist(), 7)
sigma.append(np.sqrt(w_matrix[i, idx]))
"""
for row in range(m):
for col in range(m):
w_matrix[row][col] /= float(sigma[row] * sigma[col])
w_matrix = np.exp(-np.mat(w_matrix))
w_matrix = np.array(w_matrix)
d_matrix = np.diag(np.sum(w_matrix, 1))
d_matrix_square_inv = np.linalg.inv(d_matrix ** 0.5)
dot_matrix = np.dot(d_matrix_square_inv, w_matrix)
lap_matrix = np.dot(dot_matrix, d_matrix_square_inv)
end_time = time.clock()
print("calc self_tuning laplace matrix spends %f seconds" % (end_time - start_time))
return lap_matrix
def deltas(x, w=9):
"""
Calculate the deltas (derivatives) of a sequence
Use a W-point window (W odd, default 9) to calculate deltas using a
simple linear slope. This mirrors the delta calculation performed
in feacalc etc. Each row of X is filtered separately.
Notes:
x is your data matrix where each feature corresponds to a row (so you may have to transpose the data you
pass as an argument) and then transpose the output of the function).
:param x: x is your data matrix where each feature corresponds to a row.
(so you may have to transpose the data you pass as an argument)
and then transpose the output of the function)
:param w: window size, defaults to 9
:return: derivatives of a sequence
"""
# compute the shape of the input
num_row, num_cols = x.shape
# define window shape
hlen = w // 2 # floor integer divide
w = 2 * hlen + 1 # odd number
win = np.arange(hlen, -hlen - 1, -1, dtype=np.float32)
# pad the data by repeating the first and last columns
a = matlab.repmat(x[:, 1], 1, hlen).reshape((num_row, hlen), order='F')
b = matlab.repmat(x[:, -1], 1, hlen).reshape((num_row, hlen), order='F')
xx = np.concatenate((a, x, b), axis=1)
# apply the delta filter, see matlab 1D filter
d = signal.lfilter(win, 1, xx, 1)
# trim the edges
return d[:, hlen*2: hlen*2 + num_cols]
def dlnprob(self, theta):
if self.batchsize > 0:
batch = [ i % self.N for i in range(self.iter * self.batchsize, (self.iter + 1) * self.batchsize) ]
ridx = self.permutation[batch]
self.iter += 1
else:
ridx = np.random.permutation(self.X.shape[0])
Xs = self.X[ridx, :]
Ys = self.Y[ridx]
w = theta[:, :-1] # logistic weights
alpha = np.exp(theta[:, -1]) # the last column is logalpha
d = w.shape[1]
wt = np.multiply((alpha / 2), np.sum(w ** 2, axis=1))
coff = np.matmul(Xs, w.T)
y_hat = 1.0 / (1.0 + np.exp(-1 * coff))
dw_data = np.matmul(((nm.repmat(np.vstack(Ys), 1, theta.shape[0]) + 1) / 2.0 - y_hat).T, Xs) # Y \in {-1,1}
dw_prior = -np.multiply(nm.repmat(np.vstack(alpha), 1, d) , w)
dw = dw_data * 1.0 * self.X.shape[0] / Xs.shape[0] + dw_prior # re-scale
dalpha = d / 2.0 - wt + (self.a0 - 1) - self.b0 * alpha + 1 # the last term is the jacobian term
return np.hstack([dw, np.vstack(dalpha)]) # % first order derivative
def fastsvds(M,r):
"""
"Fast" but less accurate SVD by computing the SVD of MM^T or M^TM
***IF*** one of the dimensions of M is much smaller than the other.
Note. This is numerically less stable, but useful for large hyperspectral
images.
"""
m,n = M.shape
rationmn = 10 # Parameter, should be >= 1
if m < rationmn*n:
MMt = np.dot(M,M.T)
u,s,v = svds(MMt,r)
s = np.diag(s)
v = np.dot(M.T, u)
v = np.multiply(v,repmat( (sum(v**2)+1e-16)**(-0.5),n,1))
s = np.sqrt(s)
elif n < rationmn*m:
MtM = np.dot(M.T,M)
u,s,v = svds(MtM,r)
s = np.diag(s)
u = np.dot(M,v)
u = np.multiply(u,repmat( (sum(u**2)+1e-16)**(-0.5),m,1))
s = np.sqrt(s)
else:
u,s,v = svds(M,r)
s = np.diag(s)
return (u,s,v)
def computeGradient( nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lamda ): Theta1, Theta2 = paramRollback( nn_params, input_layer_size, hidden_layer_size, num_labels ) # print shape(Theta1), shape(Theta2) m, n = shape(X) a1, z2, a2, z3, h = feedForward( Theta1, Theta2, X, m ) yVec = ( (matlib.repmat(arange(1, num_labels+1), m, 1) == matlib.repmat(y, 1, num_labels)) + 0) D1 = zeros(shape(Theta1)) D2 = zeros(shape(Theta2)) sigma3 = h - yVec.T sigma2 = Theta2.T.dot(sigma3) * sigmoidGradient( r_[ ones((1,m)), z2 ] ) sigma2 = sigma2[1:,:] # print shape(sigma2) delta1 = sigma2.dot( a1.T ) delta2 = sigma3.dot( a2.T ) D1[:,1:] = delta1[:,1:]/m + (Theta1[:,1:] * lamda / m) D2[:,1:] = delta2[:,1:]/m + (Theta2[:,1:] * lamda / m) D1[:,0] = delta1[:,0]/m D2[:,0] = delta2[:,0]/m grad = array([D1.T.reshape(-1).tolist() + D2.T.reshape(-1).tolist()]).T # print D1, shape(D1) # print D2, shape(D2) return ndarray.flatten(grad)
def trueFeatureStats(T, R, fMap, discountFactor, stateProp=1, MAT_LIMIT=1e8):
""" Gather the statistics needed for LSTD,
assuming infinite data (true probabilities).
Option: if stateProp is < 1, then only a proportion of all
states will be seen as starting state for transitions """
dim = len(fMap)
numStates = len(T)
statMatrix = zeros((dim, dim))
statResidual = zeros(dim)
ss = range(numStates)
repVersion = False
if stateProp < 1:
ss = random.sample(ss, int(numStates * stateProp))
elif dim * numStates**2 < MAT_LIMIT:
repVersion = True
# two variants, depending on how large we can afford our matrices to become.
if repVersion:
tmp1 = tile(fMap, (numStates,1,1))
tmp2 = transpose(tmp1, (2,1,0))
tmp3 = tmp2 - discountFactor * tmp1
tmp4 = tile(T, (dim,1,1))
tmp4 *= transpose(tmp1, (1,2,0))
statMatrix = tensordot(tmp3, tmp4, axes=[[0,2], [1,2]]).T
statResidual = dot(R, dot(fMap, T).T)
else:
for sto in ss:
tmp = fMap - discountFactor * repmat(fMap[:, sto], numStates, 1).T
tmp2 = fMap * repmat(T[:, sto], dim, 1)
statMatrix += dot(tmp2, tmp.T)
statResidual += R[sto] * dot(fMap, T[:, sto])
return statMatrix, statResidual
def env_init(self):
"""
Based on the levin model, the dispersion probability is initialized.
"""
self.dispersionModel = InvasiveUtility.Levin
notDirectedG = networkx.Graph(self.simulationParameterObj.graph)
adjMatrix = adjacency_matrix(notDirectedG)
edges = self.simulationParameterObj.graph.edges()
simulationParameterObj = self.simulationParameterObj
if self.dispersionModel == InvasiveUtility.Levin:
parameters = InvasiveUtility.calculatePath(notDirectedG,adjMatrix, edges, simulationParameterObj.downStreamRate,
simulationParameterObj.upStreamRate)
C = (1 - simulationParameterObj.upStreamRate * simulationParameterObj.downStreamRate) / (
(1 - 2 * simulationParameterObj.upStreamRate) * (1 - simulationParameterObj.downStreamRate))
self.dispertionTable = np.dot(1 / C, parameters)
self.germinationObj = GerminationDispersionParameterClass(1, 1)
#calculating the worst case fully invaded rivers cost
worst_case = repmat(1, 1, self.simulationParameterObj.nbrReaches * self.simulationParameterObj.habitatSize)[0]
cost_state_unit = InvasiveUtility.get_unit_invaded_reaches(worst_case,
self.simulationParameterObj.habitatSize) * self.actionParameterObj.costPerReach
stateCost = cost_state_unit + InvasiveUtility.get_invaded_reaches(
worst_case) * self.actionParameterObj.costPerTree
stateCost = stateCost + InvasiveUtility.get_empty_slots(worst_case) * self.actionParameterObj.emptyCost
costAction = InvasiveUtility.get_budget_cost_actions(repmat(3, 1, self.simulationParameterObj.nbrReaches)[0],
worst_case, self.actionParameterObj)
networkx.adjacency_matrix(self.simulationParameterObj.graph)
return "VERSION RL-Glue-3.0 PROBLEMTYPE non-episodic DISCOUNTFACTOR " + str(
self.discountFactor) + " OBSERVATIONS INTS (" + str(
self.simulationParameterObj.nbrReaches * self.simulationParameterObj.habitatSize) + " 1 3) ACTIONS INTS (" + str(
self.simulationParameterObj.nbrReaches) + " 1 4) REWARDS (" + str(self.Bad_Action_Penalty)+" "+str(
-1 * (costAction + stateCost)) + ") EXTRA "+str(self.simulationParameterObj.graph.edges()) + " BUDGET "+str(self.actionParameterObj.budget) +" by Majid Taleghan."
def samples_to_cluster_object(data, label):
m = len(label)
assert len(data) == len(label)
Cluster.n_samples = m
for i in range(m):
cluster_object = Cluster()
cluster_object.data = data[i, :]
cluster_object.cluster = label[i]
Cluster.samples_list.append(cluster_object)
start_time = time.clock()
sls2 = -2 * np.mat(data) * np.mat(data.T)
sls1 = np.mat(np.sum(data ** 2, 1))
Cluster.w_matrix = sls2 + repmat(sls1, len(sls1), 1) + repmat(sls1.T, 1, len(sls1))
Cluster.w_matrix = np.array(Cluster.w_matrix) ** 0.5
end_time = time.clock()
print("calc distance matrix' time is %f seconds" % (end_time - start_time))
outfile = open("distance.txt", "w+")
print("writing distance to file ...")
for i in range(m - 1):
for j in range(i + 1, m):
Cluster.distances.append(Cluster.w_matrix[i, j])
str_d = str(i + 1) + "\t" + str(j + 1) + "\t" + str(Cluster.w_matrix[i, j]) + "\n"
outfile.write(str_d)
print("write done")
del cluster_object
def fit(self, X): if self.components==0: self.components=X.shape[0] self.X = X N = X.shape[0] K = np.zeros((N,N)) for row in range(N): for col in range(N): K[row,col] = self._kernel_func(X[row,:], X[col,:]) self._K_sum = np.sum(K) self._K_cached_sumcols = np.sum(K, axis=0) K_c = K - repmat(np.reshape(np.sum(K, axis=1), (N,1)), 1, N)/N - repmat(self._K_cached_sumcols, N, 1)/N + self._K_sum/N**2 # kernel matrix must be symmetric, so using symmetric matrix eigenvalue solver self._eigenvalues, self._eigenvectors = eigh(K_c) self._eigenvalues = np.real(self._eigenvalues) self._eigenvectors = np.real(self._eigenvectors) key = np.argsort(self._eigenvalues) key = key[::-1] self._eigenvalues = self._eigenvalues[key] self._eigenvectors = self._eigenvectors[:,key] self.X = self.X[key,:] self._K_cached_sumcols = self._K_cached_sumcols[key]
def __check_and_repmat__(self, attrib, angles):
"""
Checks whether the attribute is a single value and repeats it into an array if it is
:rtype: None
:param attrib: string
:param angles: np.ndarray
"""
old_attrib = getattr(self, attrib)
if type(old_attrib) in [float, int, np.float32, np.float64]:
new_attrib = matlib.repmat(old_attrib, 1, angles.shape[0])[0]
setattr(self, attrib, new_attrib)
elif type(old_attrib) == np.ndarray:
if old_attrib.ndim == 1:
if old_attrib.shape in [(3,), (2,), (1,)]:
new_attrib = matlib.repmat(old_attrib, angles.shape[0], 1)
setattr(self, attrib, new_attrib)
elif old_attrib.shape == (angles.shape[0],):
pass
else:
if old_attrib.shape == (angles.shape[0], old_attrib.shape[1]):
pass
else:
raise AttributeError(attrib + " with shape: " + str(old_attrib.shape) +
" not compatible with shapes: " + str([(angles.shape[0],),
(angles.shape[0], old_attrib.shape[1]),
(3,), (2,), (1,)]))
else:
raise TypeError(
"Data type not understood for: geo." + attrib + " with type = " + str(type(getattr(self, attrib))))
def julia_sets(complex_number, n, maxIter=30, a=-1, b=1):
"""
This function computes the Julia set of the comlex number passed in
according to the function f(x) = x**2 + c.
Inputs:
complex_number: The comlpex number for which you would like to find
the Julia set.
n: The size of the square (n x n) matrix that will contain plot
information.
maxIter: The maximum number of iterations to pass x though f(x).
a: The lower bound for both the real and complex axes.
b: The upper bound for both the real and complex axes.
Outputs:
plot: There is no output that can be stored to a variable. When this
function is called a plot is automatically generated.
"""
if n % 2 != 0:
print 'Value Error: We need n to be an even number'
return
X = sp.zeros((n,n), dtype = 'complex64')
Xj = sp.zeros((n,n), dtype = 'complex64')
x = sp.linspace(a,b,n)
xj = x * 1j
X = repmat(x, n, 1)
Xj = repmat(xj, n, 1)
start_grid = X + Xj.T
answer_grid = sp.zeros((n,n), dtype = 'complex64')
func = lambda x: x**2 + complex_number
for i in range(n):
for j in range(n):
x = start_grid[i,j]
for m in range(maxIter):
x = func(x)
m += 1
answer_grid[i,j] = x
for i in range(n):
for j in range(n):
if math.isnan(answer_grid[i,j]):
answer_grid[i,j] = 0
E = sp.zeros((n,n), dtype = 'complex64')
for i in range(n):
for j in range(n):
E[i,j] = sp.exp(-abs(answer_grid[i,j]))
E = -1* sp.array(E, dtype = float)
plt.imshow(E)
def compute_distance_matrix(self):
X = self.X
y = self.y
self.EDM = distance_utils.calcDistanceMatrixFastEuclidean(X)
N,d = X.shape
ind = repmat(array(range(N)),N,1)
self.EDM.setfield(ind, dtype=int16)
Y = repmat(y, N, 1)
flag = (Y==Y.T)
self.EDM.setfield(flag, dtype=bool, offset=2)
def MutInf(x1, x2, Nbins=(20, 20, 20), s=1):
import numpy as np # histogramdd, array, transpose
# define data vectors/arrays
x = x1[s:] # time series data from osc_1
y = x1[:-s] # time series data from osc_1 delayed by s
z = x2[:-s] # time series data from osc_2 delayed by s
# calculate 3D histogram of size (nx,ny,nz) where nx is the number
# of bins for x, ny for y, nz for z. This is the tricky part since
# the size of bins is quite critical. However you could start with
# say nx=20, i.e. 20 bins evenly spaced between the min and max values
# of x
nx, ny, nz = Nbins
H, edges = np.histogramdd([x, y, z], bins=(nx, ny, nz))
# add small probability mass everywhere to avoid divide by zeros,
# e.g. 1e-9 (you can experiment with different values). This part
# was a bit of a fudge and should be replaced with something more
# sensible - but I never got round to it
# H = H + 1e-12
# renormalise so sums to unity
P = H / np.sum(H)
# now sum along the first dimension to create a 2D array of p(y,z)
P_yz = np.sum(P, axis=0)
# replicate the 2D array at each element in the first dimension
# so as to regain a (nx,ny,nz) array (this is purely for computational
# ease)
from numpy.matlib import repmat
P_yz = repmat(P_yz, nx, 1).reshape(nx, ny, nz)
# now sum along the first and third dimension to give 1D array of p(y)
P_y = np.sum(P, axis=(0, 2))
# replicate in both the x and z directions
P_y = repmat(P_y, nx, nz).reshape(nx, ny, nz)
P_xy = np.sum(P, axis=2)
P_xy = repmat(P_xy, nz, 1).reshape(nx, ny, nz)
# create conditional probability mass functions
P_x_given_yz = P / P_yz
P_x_given_y = P_xy / P_y
# calculate transfer entropy
logP = np.log(P_x_given_yz / P_x_given_y)
logP = np.nan_to_num(logP)
T = np.sum(P * logP)
return T
def mkfdstencil(x,xbar,k): #this funtion is sue to create finite diference method matrix maxorder = len(x) h_matrix = repmat(np.transpose(x)-xbar,maxorder,1) powerfactor_matrix = np.transpose(repmat(np.arange(0,maxorder),maxorder,1)) factorialindex = np.transpose(repmat(factorial(np.arange(0,maxorder)),maxorder,1)) taylormatrix = h_matrix ** powerfactor_matrix /factorialindex derivativeindex = np.zeros(maxorder) derivativeindex[k] = 1 u = np.linalg.solve(taylormatrix,derivativeindex) return u
def polyFeatures(X, p): m, n = shape(X) powers = matlib.repmat(range(1, p+1), m, 1) Xrep = matlib.repmat(X, 1, p) # print shape(powers), shape(Xrep) X_poly = Xrep ** powers # print shape(X_poly) # print X_poly # test = (ones((12,8))*2) ** powers # print test return X_poly
def depth_to_local_point_cloud(image, color=None, max_depth=0.9):
"""
Convert an image containing CARLA encoded depth-map to a 2D array containing
the 3D position (relative to the camera) of each pixel and its corresponding
RGB color of an array.
"max_depth" is used to omit the points that are far enough.
"""
far = 1000.0 # max depth in meters.
normalized_depth = depth_to_array(image)
# (Intrinsic) K Matrix
k = numpy.identity(3)
k[0, 2] = image.width / 2.0
k[1, 2] = image.height / 2.0
k[0, 0] = k[1, 1] = image.width / \
(2.0 * math.tan(image.fov * math.pi / 360.0))
# 2d pixel coordinates
pixel_length = image.width * image.height
u_coord = repmat(numpy.r_[image.width-1:-1:-1],
image.height, 1).reshape(pixel_length)
v_coord = repmat(numpy.c_[image.height-1:-1:-1],
1, image.width).reshape(pixel_length)
if color is not None:
color = color.reshape(pixel_length, 3)
normalized_depth = numpy.reshape(normalized_depth, pixel_length)
# Search for pixels where the depth is greater than max_depth to
# delete them
max_depth_indexes = numpy.where(normalized_depth > max_depth)
normalized_depth = numpy.delete(normalized_depth, max_depth_indexes)
u_coord = numpy.delete(u_coord, max_depth_indexes)
v_coord = numpy.delete(v_coord, max_depth_indexes)
if color is not None:
color = numpy.delete(color, max_depth_indexes, axis=0)
# pd2 = [u,v,1]
p2d = numpy.array([u_coord, v_coord, numpy.ones_like(u_coord)])
# P = [X,Y,Z]
p3d = numpy.dot(numpy.linalg.inv(k), p2d)
p3d *= normalized_depth * far
# Formating the output to:
# [[X1,Y1,Z1,R1,G1,B1],[X2,Y2,Z2,R2,G2,B2], ... [Xn,Yn,Zn,Rn,Gn,Bn]]
if color is not None:
# numpy.concatenate((numpy.transpose(p3d), color), axis=1)
return sensor.PointCloud(
image.frame_number,
numpy.transpose(p3d),
color_array=color)
# [[X1,Y1,Z1],[X2,Y2,Z2], ... [Xn,Yn,Zn]]
return sensor.PointCloud(image.frame_number, numpy.transpose(p3d))
def backcor(self,n,y,ord_cus,s,fct):
# Rescaling
N = len(n)
index = np.argsort(n)
n=np.array([n[i] for i in index])
y=np.array([y[i] for i in index])
maxy = max(y)
dely = (maxy-min(y))/2.
n = 2. * (n-n[N-1]) / float(n[N-1]-n[0]) + 1.
n=n[:,np.newaxis]
y = (y-maxy)/dely + 1
# Vandermonde matrix
p = np.array(range(ord_cus+1))[np.newaxis,:]
T = repmat(n,1,ord_cus+1) ** repmat(p,N,1)
Tinv = pinv(np.transpose(T).dot(T)).dot(np.transpose(T))
# Initialisation (least-squares estimation)
a = Tinv.dot(y)
z = T.dot(a)
# Other variables
alpha = 0.99 * 1/2 # Scale parameter alpha
it = 0 # Iteration number
zp = np.ones((N,1)) # Previous estimation
# LEGEND
while np.sum((z-zp)**2)/np.sum(zp**2) > 1e-10:
it = it + 1 # Iteration number
zp = z # Previous estimation
res = y - z # Residual
# Estimate d
if fct=='sh':
d = (res*(2*alpha-1)) * (abs(res)<s) + (-alpha*2*s-res) * (res<=-s) + (alpha*2*s-res) * (res>=s)
elif fct=='ah':
d = (res*(2*alpha-1)) * (res<s) + (alpha*2*s-res) * (res>=s)
elif fct=='stq':
d = (res*(2*alpha-1)) * (abs(res)<s) - res * (abs(res)>=s)
elif fct=='atq':
d = (res*(2*alpha-1)) * (res<s) - res * (res>=s)
else:
pass
# Estimate z
a = Tinv.dot(y+d) # Polynomial coefficients a
z = T.dot(a) # Polynomial
z=np.array([(z[list(index).index(i)]-1)*dely+maxy for i in range(len(index))])
return z,a,it,ord_cus,s,fct
def cocktail(data1, data2): global BITWIDTH dt1 = data1 / float(1<<(BITWIDTH-1)) dt2 = data2 / float(1<<(BITWIDTH-1)) xx = [dt1, dt2] p = xx - np.transpose(matlib.repmat(np.mean(xx, 1), np.shape(xx)[1], 1)) yy = np.dot(linalg.sqrtm(np.linalg.inv(np.cov(xx))), p) rr = matlib.repmat(np.sum(yy*yy, 0), np.shape(yy)[0], 1) w, s, v = np.linalg.svd(np.dot(rr*yy, np.transpose(yy))) f = np.transpose(np.dot(np.transpose(xx), w)) #w is the unmixing matrix f[0] *= float(1<<(BITWIDTH-1)) f[1] *= float(1<<(BITWIDTH-1)) return f
def spkmeans(X, init):
"""
Perform spherical k-means clustering.
X: d x n data matrix
init: k (1 x 1) or label (1 x n, 1<=label(i)<=k) or center (d x k)
Reference: Clustering on the Unit Hypersphere using Von Mises-Fisher Distributions.
by A. Banerjee, I. Dhillon, J. Ghosh and S. Sra.
Written by Michael Chen ([email protected]).
Based on matlab version @
http://www.mathworks.com/matlabcentral/fileexchange/28902-spherical-k-means/content/spkmeans.m
(and slightly modifed to run on previous verions of Matlab)
initialization
"""
d,n = X.shape
if n <= init:
label = range(1,init)
m = X
energy = 0
else:
# Normalize the columns of X
X = np.dot(X, repmat( (sum(X**2)+1e-16)**(-0.5),d,1))
if len(init) == 1:
idx = randsample(n,init)
m = X[:,idx]
[ul,label] = np.maximum(np.dot(m.T,X),[],1)
elif init.shape[0] == 1 and init.shape[1] == n:
label = init
elif init.shape[0] == d:
m = np.multiply(init, repmat( (sum(init**2)+1e-16)**(-0.5),d,1))
ul,label = np.maximum(np.dot(m.T,X),[],1)
else:
error('ERROR: init is not valid.')
## main algorithm: final version
last = 0
while (label != last).any():
u,pipi,label = np.unique(label) # remove empty clusters
k = len(u)
E = sparse.coo_matrix(range(n),label,1,n,k,n)
m = np.dot(X,E)
m = np.dot(m, repmat( (sum(m**2)+1e-16)**(-0.5),d,1))
last = label
val = np.maximum(np.dot(m.T*X),[],1)
label = np.argmax(np.dot(m.T*X),[],1)
ul,ul,label = np.unique(label) # remove empty clusters
energy = np.sum(val)
return (label, m, energy)
def get_lap_matrix_sl(data, sigma):
#高斯核函数
# s(x_i, x_j) = exp(-|x_i - x_j|^2 /(2 * sigma^2))
start_time = time.clock()
sls2 = -2 * np.mat(data) * np.mat(data.T)
sls1 = np.mat(np.sum(data ** 2, 1))
w_matrix = np.exp(-(sls2 + repmat(sls1, len(sls1), 1) + repmat(sls1.T, 1, len(sls1))) / float((2 * sigma ** 2)))
w_matrix = np.array(w_matrix)
d_matrix = np.diag(np.sum(w_matrix, 1))
lap_matrix = d_matrix - w_matrix
end_time = time.clock()
print("calc sl laplace matrix spends %f seconds" % (end_time - start_time))
return lap_matrix
def get_lap_matrix_njw(data, sigma):
#高斯核函数
# s(x_i, x_j) = exp(-|x_i - x_j|^2 /(2 * sigma^2))
start_time = time.clock()
sls2 = -2 * np.mat(data) * np.mat(data.T)
sls1 = np.mat(np.sum(data ** 2, 1))
w_matrix = np.exp(-(sls2 + repmat(sls1, len(sls1), 1) + repmat(sls1.T, 1, len(sls1))) / float((2 * sigma ** 2)))
w_matrix = np.array(w_matrix)
d_matrix = np.diag(np.sum(w_matrix, 1))
d_matrix_square_inv = np.linalg.inv(d_matrix ** 0.5)
dot_matrix = np.dot(d_matrix_square_inv, w_matrix)
lap_matrix = np.dot(dot_matrix, d_matrix_square_inv)
end_time = time.clock()
print("calc njw laplace matrix spends %f seconds" % (end_time - start_time))
return lap_matrix
def _mask(self, shape):
if len(shape) > 1:
nsynch, nsamples = shape
else:
nsamples = shape[0]
nsynch = 1
return repmat(rand(1, nsamples) < self.sparsity, nsynch, 1)
def currentLosses(self, params):
if self.batch_size > 1:
params = repmat(params, 1, self.batch_size)
res = self.loss_fun(params)
return reshape(res, (self.batch_size, self.paramdim))
else:
return self.loss_fun(params)
def currentGradients(self, params):
if self.batch_size > 1:
params = repmat(params, 1, self.batch_size)
res = self.gradient_fun(params)
return reshape(res, (self.batch_size, self.paramdim))
else:
return self.gradient_fun(params)
def testcluster(lamBda=0.00001, ncluster=2, kx=50, rate=0.001, func=sign):
S = zeros([n_total, n_total])
r_index, l_index = randindex(n_total, rate, -1)
S[r_index, l_index] = groundTruth[r_index, l_index]
# function varctorization
sign = func
sign = np.vectorize(sign)
S = sign(S + S.T)
S = sparse.csr_matrix(S)
#
U, D = idc.inductive(X, S, kx, ncluster, lamBda, 50)
#
Xresult = matrix(U[:, 0:ncluster])
Xresult = Xresult / (matlib.repmat(np.sqrt(np.square(Xresult).sum(axis=1)),
1,
ncluster) * 1.0)
label = KMeans(n_clusters=ncluster).fit_predict(Xresult)
label = array(label)
predictA = - ones([n_total, n_total])
#
for i in range(ncluster):
pos = np.where(label == i)[0]
for j in pos:
for k in pos:
predictA[j, k] = 1
#
accbias = sum(predictA != groundTruth).sum() / float(np.product(groundTruth.shape))
print 'sample rate: ', rate, " ", "err: ", accbias
def signalToNoiseRatio(self, xs):
""" What is the one-sample signal-to-noise ratio. """
rxs = repmat(xs, self.ESamples, 1).T
gs = self._df(rxs)
g2s = mean(gs **2, axis=1)
gs = mean(gs, axis=1)
return gs**2/g2s
def hw1_find_eigendigits(A):
# get mean vector by averaging the rows
A = A.astype(float)
m = mean(A, axis=1)
# replace X with X - E(X)
B = repmat(m, A.shape[1], 1)
A = A - transpose(B)
# get vec and val
print "Before Eig"
val, vec = eig(dot(transpose(A), A))
print "After Eig"
vec = dot(A, vec)
# sort e-vec and e-val
idx = val.argsort()[::-1]
val = val[idx]
vec = vec[:,idx]
# normalize columns
V = vec / norm(vec, axis=0)
V = nan_to_num(V)
V = around(V, decimals=8).real
return (m, V)
def testHand(cards,model):
if type(cards[0]) is str:
cards = [CARDS[i] for i in cards]
handCode = encodeCards(cards).reshape((1,85))
netInput = np.hstack((matlib.repmat(handCode,32,1),np_utils.to_categorical(range(32),32)))
predictions = model.predict(netInput,verbose=0)
return [np.argmax(predictions),predictions]
def phaserandomized(X):
"""Calculates phase randomized data based on real data. The full algorithm is described here Pritchard 1991.
Parameters:
-------
X : ndarray
3-D numpy array structured like (subject, channel, sample)
Returns:
-------
Xr : ndarray
3-D numpy array structured like (subject, channel, sample) with random phase added
"""
start = default_timer()
N, D, T = X.shape
print(f'\n{N} subjects, {D} sensors and {T} samples')
Xr = np.empty((N, D, T))
for subject in range(0, N):
Xfft = np.fft.rfft(X[subject, :, :], T)
ampl = np.abs(Xfft)
phi = np.angle(Xfft)
# np.random.seed(42)
phi_r = 4 * np.arccos(0) * np.random.rand(
1, int(T / 2 - 1)) - 2 * np.arccos(0)
Xfft[:, 1:int(T / 2)] = ampl[:, 1:int(T / 2)] * np.exp(
np.sqrt(-1 + 0j) *
(phi[:, 1:int(T / 2)] + npm.repmat(phi_r, D, 1)))
Xr[subject, :, :] = np.fft.irfft(Xfft, T)
stop = default_timer()
print(f'Elapsed time: {round(stop - start)} seconds.')
return Xr
def geometric_brownian_motion(allow_negative=False, **kwargs):
"""
Geometric Brownian Motion
Step 1 - Calculate the Deterministic component - drift
Alternative drift 1 - supporting random walk theory
drift = 0
Alternative drift 2 -
drift = risk_free_rate - (0.5 * sigma**2)
:return: asset path
"""
starting_value = kwargs.get("starting_value")
mu = kwargs.get("mu")
sigma = kwargs.get("sigma")
num_trading_days = kwargs.get("num_trading_days")
num_per = kwargs.get("forecast_period")
# Calculate Drift
mu = mu / num_trading_days
sigma = sigma / math.sqrt(num_trading_days) # Daily volatility
drift = mu - (0.5 * sigma**2)
# Calculate Random Shock Component
random_shock = np.random.normal(0, 1, (1, num_per))
log_ret = drift + (sigma * random_shock)
compounded_ret = np.cumsum(log_ret, axis=1)
asset_path = starting_value + (starting_value * compounded_ret)
# Include starting value
starting_value = ml.repmat(starting_value, 1, 1)
asset_path = np.concatenate((starting_value, asset_path), axis=1)
if allow_negative:
asset_path *= asset_path > 0
return asset_path.mean(axis=0)
def scattering_factor(elements, HKL, sf):
"""
Input:
elements: all the elements in a molecule -> mol.element (1*n) list
HKL: (3*N) array contains all points that we are calculating in 3D Fourier space
sf: object of class ScatterFactor, which contains information of sf for each atom
Output:
(n*N) array
"""
atomTypes = np.unique(elements)
f = np.zeros((len(elements), HKL.shape[1]))
stols = np.array([0.25 * np.sum(np.square(HKL), axis=0)])
for iType in range(atomTypes.shape[0]):
try:
sfnr = sf.label.index(atomTypes[iType])
except ValueError:
print "Cannot find " + atomTypes[iType] + " in atomsf.lib"
idx = [i for i, x in enumerate(elements) if x == atomTypes[iType]]
a = np.array(sf.a[sfnr]) # 1*4, based on the structure of the atomsf.lib file
b = np.array(sf.b[sfnr])
b.shape = len(b), 1 # 4*1
c = sf.c[sfnr]
fType = c + np.dot(a, np.exp(-b * stols)) # b * stols -> 4*N, fType-> 1*N
f[idx, :] = repmat(fType, len(idx), 1)
smallerthanzero = np.where(f < 0)
f[smallerthanzero] = np.finfo(float).eps
return f
def plot_vehicle(self,
pos: np.ndarray,
heading: float,
width: float,
length: float,
zorder: int = 10,
color_str: str = 'blue',
id_in: str = 'default') -> None:
"""
Highlight a vehicle pose with a scaled bounding box.
:param pos: position of the vehicle's center of gravity
:param heading: heading of the vehicle (0.0 beeing north) [in rad]
:param width: width of the vehicle [in m]
:param length: length of the vehicle [in m]
:param zorder: z-order of the plotted object (layer in the plot)
:param color_str: string specifying color (use default color strings)
:param id_in: sting with an unique object ID (previously plotted objects with same ID will be removed)
"""
# delete highlighted positions with handle
if id_in in self.__veh_patch.keys():
self.__veh_patch[id_in].remove()
del self.__veh_patch[id_in]
theta = heading - np.pi / 2
bbox = (npm.repmat([[pos[0]], [pos[1]]], 1, 4)
+ np.matmul([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]],
[[-length / 2, length / 2, length / 2, -length / 2],
[-width / 2, -width / 2, width / 2, width / 2]]))
patch = np.array(bbox).transpose()
patch = np.vstack((patch, patch[0, :]))
plt_patch = ptch.Polygon(patch, facecolor=color_str, zorder=zorder)
self.__veh_patch[id_in] = self.__main_ax.add_artist(plt_patch)
def get_3dim_spectrum_from_data(wav_data, frame, shift, fftl):
"""
dump_wav : channel_size * speech_size (2dim)
"""
len_sample, len_channel_vec = len(wav_data[:, 0]), 4
dump_wav = wav_data.T
dump_wav = dump_wav / np.max(np.abs(dump_wav)) * 0.7
window = sg.hanning(fftl + 1, 'periodic')[:-1]
multi_window = npm.repmat(window, len_channel_vec, 1)
st = 0
ed = frame
number_of_frame = np.int((len_sample - frame) / shift)
spectrums = np.zeros(
(len_channel_vec, number_of_frame, np.int(fftl / 2) + 1),
dtype=np.complex64)
for ii in range(0, number_of_frame):
multi_signal_spectrum = fft(dump_wav[:, st:ed], n=fftl,
axis=1)[:, 0:np.int(fftl / 2) +
1] # channel * number_of_bin
spectrums[:, ii, :] = multi_signal_spectrum
st = st + shift
ed = ed + shift
return spectrums, len_sample
def sortXYZ(xyz):
#SORTXYZ Sort 3D point in clockwise order
# The definition of clockwise order for 3D points is ill-posed. To make it well defined,
# we must first define a viewing direction. This code treats the center
# of the set of points as the viewing direction (from original point).
ori_xyz = xyz
xyz = xyz / repmat(np.sum(xyz**2, 1), 3, 1).T
center = np.mean(xyz, 0)
center = center / np.linalg.norm(center, 2)
# set up z axis at center
z = center
x = [-center[1], center[0], 0]
x = x / np.linalg.norm(x, 2)
y = np.cross(z, x)
R = np.dot(np.diag([1, 1, 1]), np.linalg.pinv(np.array([x, y, z]).T))
newXYZ = np.dot(R, (xyz.T))
A = np.arctan2(newXYZ[1, :], newXYZ[0, :])
I = np.argsort(A)
s_xyz = ori_xyz[I, :]
return [s_xyz, I]
def getLocalChart(self, point, U0=None):
"""Find the local coordinate chart to perform approximations"""
if self.sigma == None:
print("Warning: sigma not initialized - initializing with calculateSigma()")
self.calculateSigmaFromPoint(point)
if self.kd_tree == None:
print("Warning: No KD tree. Looking for neighbors one by one.")
print("currently not implemented")
raise Exception("no KD tree")
init_q = self.genInitQ(point)
if self.recompute_sigma == True:
self.calculateSigmaFromPoint(init_q)
U, q, PX0, X0, W, _ = self.findLocalCoordinatesThresh( point, init_q, self.compactWeightFunc, U0, initSVD = self.initSVD)
D, I = self.kd_tree.query(q, self.sigma) # work with neighbors according to the SIGMA_Q neighborhood (so we'll have enough)
D = D[0]
I = I[0][D<np.inf]
X0 = self.data[:,I] - nlib.repmat(q, 1, len(I))
PX0 = np.dot(U.T, X0)
F0 = self.f_data[I]
W = self.compactWeightFunc(np.linalg.norm(PX0, axis=0))
return q, X0, PX0, F0, W, U
def zscore_matrix(data, group, controlCode):
"""
Z-score data relative to a given group (author: @saratheriver)
Parameters
----------
data : pandas.DataFrame
Data matrix (e.g. thickness data), shape = (n_subject, n_region)
group : list
Group assignment (e.g, [0, 0, 0, 1, 1, 1], same length as n_subject.
controlCode : int
Value that corresponds to "baseline" group
Returns
-------
Z : pandas.DataFrame
Z-scored data relative to control code
"""
C = [i for i, x in enumerate(group) if x == controlCode]
n = len(group)
z1 = data - npm.repmat(np.mean(data.iloc[C, ]), n, 1)
z2 = np.std(data.iloc[C, ], ddof=1)
return z1 / z2
def compute_svm_cost(self, X, Y, W=None, b=None):
"""
Calculates the cost of the loss function in the SVM multi-class sense
for the given data, weights and bias.
"""
if W is None:
W = self.W
if b is None:
b = self.b
N = X.shape[1]
s = W.dot(X) + b
sy = repmat(s.T[Y.T == 1], Y.shape[0], 1)
margins = np.maximum(0, s - sy + 1)
margins[Y == 1] = 0
loss = margins.sum() / N
regularization = 0.5 * self.l * np.sum(W**2)
return loss + regularization
def diffusionMap(sigmaK, alpha=1, numEigs=6):
myHdf5 = h5py.File(fname, 'r+')
D_data = myHdf5[grpNameDM+dset_data][()]
dim = myHdf5[grpNameDM+dset_data].attrs['numHits']
D_indices = myHdf5[grpNameDM+dset_indices]
D_indptr = myHdf5[grpNameDM+dset_indptr]
P = normalizedGraphLaplacian(D_data,D_indices,D_indptr,dim,sigmaK)
tic = time.time()
s, u = eigsh(P,k=numEigs+1,which='LM')
u = np.real(u)
u = np.fliplr(u)
toc = time.time()
print "%%%%: ",toc-tic, u, u.shape, s, s.shape
U = u/repmat(np.matrix(u[:,0]).transpose(),1,numEigs+1)
Y = U[:,1:numEigs+1]
myHdf5.close()
return Y,s
def vdpmm_maximizeCNN(data, params, gammas, stddev):
D = data.shape[1]
N = data.shape[0]
K = (params['a']).shape[0]
a0 = D
beta0 = 1
mean0 = np.mean(data, axis=0)
B0 = .1 * D * np.cov(data.T)
#convenience variables first
Ns = np.sum(gammas, axis=0) + 1e-10
mus = np.zeros((K, D))
sigs = np.zeros((D, D, K))
mus = np.dot(gammas.T, data) / (repmat(Ns, D, 1).T)
for i in range(K):
diff0 = data - repmat(mus[i, :], N, 1)
diff1 = repmat(np.sqrt(gammas[:, i]), D, 1).T * diff0
sigs[:, :, i] = np.dot(diff1.T, diff1)
#now the estimates for the variational parameters
params['g'][:, 0] = 1 + np.sum(gammas, axis=0)
#g_{s,2} = Eq[alpha] + sum_n sum_{j=s+1} gamma_j^n
temp1 = (params['eq_alpha'] +
np.flipud(np.cumsum(np.flipud(np.sum(gammas, 0)))) -
np.sum(gammas, 0))
params['g'][:, 1] = temp1
params['beta'] = Ns + beta0
params['a'] = Ns + a0
tempNs = repmat(Ns, D, 1).T * mus
for k in range(K):
if k > 1:
params['mean'][k, :] = (tempNs[k] + beta0 * mean0) / (repmat(
Ns[k] + beta0, D, 1).T) + 0.1 * params['mean'][k - 1, :]
else:
params['mean'][k, :] = (tempNs[k] + beta0 * mean0) / (repmat(
Ns[k] + beta0, D, 1).T)
#for one dimension
tempStddev = np.sum(gammas * stddev, axis=0)
tempStddev.shape = (K, 1)
for i in range(K):
diff = mus[i, :] - mean0
params['B'][:, :, i] = sigs[:, :, i] + Ns[i] * beta0 * np.dot(
diff, diff.T) / (Ns[i] + beta0) + B0 + tempStddev[i]
return params
def compute_statistics_random_h_star(
h_sim: np.ndarray,
max_cell_radius=None,
simulation_number=None) -> (List[int], List[int], List[int]):
"""
Build related statistics derived from Ripley's K function, normalize K
"""
simulation_number = simulation_number or constants.analysis_config[
"RIPLEY_K_SIMULATION_NUMBER"]
max_cell_radius = max_cell_radius or constants.analysis_config[
"MAX_CELL_RADIUS"]
h_sim = np.power((h_sim * 3) / (4 * math.pi), 1. / 3) - matlib.repmat(
np.arange(1, max_cell_radius + 1), simulation_number, 1)
h_sim_sorted = np.sort(h_sim)
h_sim_sorted = np.sort(h_sim_sorted[:, ::-1], axis=0)
synth95 = h_sim_sorted[int(
np.floor(0.95 * simulation_number)
)] # TODO : difference with V0 : floor since if the numbers are high we get simulation_sumber here
synth50 = h_sim_sorted[int(np.floor(0.5 * simulation_number))]
synth5 = h_sim_sorted[int(np.floor(0.05 * simulation_number))]
return synth5, synth50, synth95
def costFunction(initial_theta, X, Y):
m = len(Y)
J = 0
for a, b in zip(Y, np.dot(X, initial_theta)):
J += -a * np.log(sigmoid(b)) - (1 - a) * np.log(1 - sigmoid(b))
J /= m
in_mat = []
for a, b in zip(np.dot(X, initial_theta), Y):
in_mat.append(sigmoid(a) - b)
in_mat = np.array(in_mat)
size_X = X.shape
in_mat = npm.repmat(in_mat, 1, size_X[1])
matsum = []
for x, y in zip(X, in_mat):
matsum.append(x * y)
return J, sum(matsum) / m
def jensen_shannon_div(query_arr, train_mat):
# normalize arrays so that they become probability distributions
query_arr = query_arr / float(np.sum(query_arr))
train_mat = np.divide(train_mat.T, np.sum(train_mat, 1)).T
query_mat = repmat(query_arr, len(train_mat), 1)
mat_sum = 0.5 * (query_mat + train_mat)
D1 = query_mat * np.log2(np.divide(query_mat, mat_sum))
D2 = train_mat * np.log2(np.divide(train_mat, mat_sum))
# convert all nans to 0
D1[np.isnan(D1)] = 0
D2[np.isnan(D2)] = 0
JS_mat = 0.5 * (np.sum(D1, 1) + np.sum(D2, 1))
return JS_mat
def h2e(v):
"""
Convert from homogeneous to Euclidean form
:param v: homogeneous vector or matrix
:type v: array_like
:return: Euclidean vector
:rtype: numpy.ndarray
- If ``v`` is an array, shape=(N,), return an array shape=(N-1,) where the elements have
all been scaled by the last element of ``v``.
- If ``v`` is a matrix, shape=(N,M), return a matrix shape=(N-1,N), where each column has
been scaled by its last element.
:seealso: e2h
"""
if argcheck.isvector(v):
# dealing with shape (N,) array
v = argcheck.getvector(v)
return v[0:-1] / v[-1]
elif isinstance(v, np.ndarray) and len(v.shape) == 2:
# dealing with matrix
return v[:-1, :] / matlib.repmat(v[-1, :], v.shape[0] - 1, 1)
def los_channel(rx_ant_coordinates, tx_ant_coordinates, wavelength):
shape = rx_ant_coordinates.shape
if (len(shape) == 1):
nr = 1
else:
nr = len(rx_ant_coordinates)
shape = tx_ant_coordinates.shape
if (len(shape) == 1):
nt = 1
else:
nt = len(tx_ant_coordinates)
rr = mat.repmat(rx_ant_coordinates, nt, 1)
tt = np.kron(tx_ant_coordinates, np.ones((nr, 1)))
diff = np.power((rr - tt), 2)
diff = np.sum(diff, axis=1)
dist = np.power(diff, 0.5)
dist = dist.reshape(nr, nt)
dist = np.array(dist)
los = np.zeros((nr, nt), dtype=complex)
for ii in range(nr):
for jj in range(nt):
los[ii][jj] = np.exp(1j * 2 * np.pi * dist[ii][jj] / wavelength)
return los
def extend_time(feats, upsampling_factor):
"""FUNCTION TO EXTEND TIME RESOLUTION
Args:
feats (ndarray): feature vector with the shape (T x D)
upsampling_factor (int): upsampling_factor
Return:
(ndarray): extend feats with the shape (upsampling_factor*T x D)
"""
# get number
n_frames = feats.shape[0]
n_dims = feats.shape[1]
# extend time
feats_extended = np.zeros((n_frames * upsampling_factor, n_dims))
for j in range(n_frames):
start_idx = j * upsampling_factor
end_idx = (j + 1) * upsampling_factor
feats_extended[start_idx:end_idx] = repmat(feats[j, :],
upsampling_factor, 1)
return feats_extended
def initialize_all(numParticles, numTimeSteps, cluster, boxLength, hDiameter, aligned, field, \
fieldAmp, angFreq, timeSteps, shape, rAvg):
"""Initializes all particles and fields."""
#create empty matrices
particleMoments, particleAxes = initialize_empty_matrices(
numParticles, numTimeSteps, shape)
#fill matrices, initialize particles and fields
particleMoments, particleAxes, mStart, nStart, hApplied, particleCoords = initialize_particles(particleMoments, \
particleAxes, numParticles, numTimeSteps, cluster, boxLength, hDiameter, aligned, field, fieldAmp, angFreq, \
timeSteps, shape)
#initialize "ghost" coordinates for periodic boundary conditions
ghostCoords, masks = initialize_ghost_coords(particleCoords, rAvg,
boxLength)
distMatrixSq = repmat(ghostCoords, len(ghostCoords), 1) - repeat(
ghostCoords, len(ghostCoords), axis=0)
distMatrixSq = distMatrixSq.reshape(
(len(ghostCoords), len(ghostCoords), 3))
distMatrix = np.sqrt(np.sum(distMatrixSq**2, axis=2))
return particleMoments, particleAxes, mStart, nStart, hApplied, particleCoords, ghostCoords, masks, \
distMatrixSq, distMatrix
def create_plot(self):
# 数据的流动
self.t = 0
pg.setConfigOption('background', 'w')
pg.setConfigOption('foreground', 'k')
self.stream_scroll = pg.PlotWidget(title='脑电图', background='w')
self.stream_scroll.setYRange(0.5, self.channel_count, padding=0.1)
self.stream_scroll_time_axis = np.linspace(-5, 0, self.samples * 4)
self.stream_scroll.setXRange(-5, 0, padding=.005)
labelStyle = {'color': '#000', 'font-size': '14pt'}
self.stream_scroll.setLabel('bottom', 'Time', 'Seconds', **labelStyle)
self.stream_scroll.setLabel('left', 'Channel', **labelStyle)
color_list = [(255, 0, 0), (0, 255, 0), (0, 0, 255), (255, 255, 0),
(0, 255, 255), (255, 0, 255), (0, 0, 0), (255, 0, 0),
(255, 0, 0), (0, 255, 0), (0, 0, 255), (255, 255, 0),
(0, 255, 255), (255, 0, 255), (0, 0, 0), (255, 0, 0)]
for i in range(self.channel_count - 1, -1, -1):
self.filtered_data['filtered_channel{}'.format(i +
1)] = matlib.repmat(
[0],
self.samples *
4, 1).T.ravel()
self.curves['curve_channel{}'.format(i +
1)] = self.stream_scroll.plot(
pen=color_list[i])
self.curves['curve_channel{}'.format(i + 1)].setData(
x=self.stream_scroll_time_axis,
y=([
point + i + 1 for point in self.filtered_data[
'filtered_channel{}'.format(i + 1)]
]))
# print(len(self.data_buffer))
self.set_layout()
def calcDistanceMatrix2(AB,
distFunc=lambda delta: sqrt(sum(delta**2, axis=1))):
assert (len(AB) in [1, 2] and type(AB) != ndarray)
if len(AB) == 2:
A, B = AB
#if (A==B).all(): return calcDistanceMatrix2([A],distFunc)
#A = array(A)
#B = array(B)
nA, dim = A.shape
assert (B.shape[1] == dim)
nB = B.shape[0]
print A.shape, nB, B.shape, nA
delta = repeat(A, nB, 0) - repmat(B, nA, 1)
dist = distFunc(delta).reshape(nA, nB) # dist[i,j] = d(A[i],B[j])
del delta
return dist
else: # elif len(AB)==1:
A = array(AB[0])
nA, dim = A.shape #max nA <= 800
rows = repeat(range(nA), nA) # 0,0,0,...,n-1,n-1
cols = array(range(nA) * nA) # 0,1,2
upper_ind = where(cols > rows)[0]
# nA == (1+sqrt(1+8*len(upper_ind))/2
##lower_ind = where(cols<rows)[0]
delta = A[rows[upper_ind], :] - A[cols[upper_ind], :]
del rows
del cols
# computes all possible combinations
#dist = zeros(nA*nA)
#partial_delta = delta[:,upper_ind]
partial_dist = distFunc(delta)
del delta
partial_dist.setfield(upper_ind, dtype=int32)
#dist[upper_ind] = partial_dist
#dist = dist.reshape(nA, nA) # dist[i,j] = d(A[i],A[j]) for i<j
#dist = dist + dist.T # make it symmetric
return partial_dist
def gbm_monte_carlo(s0, sigma, mu, nPer, nTDays, nSim):
"""
Geometric Brownian Motion Monte Carlo Simulation
#s0 - starting price
#sigma - annual volatility
#mu - annual expected return
#nPer - number of forecast period in days
#nTDays - number of trading days in one year
#nSim - number of simulations
returns simulated asset path
"""
''' Step 1 - Calculate the Deterministic component - drift
Alternative drift 1 - supporting random walk theory
drift = 0
Alternative drift 2 -
drift = risk_free_rate - (0.5 * sigma**2)
'''
#Industry standard for drift
mu = mu / nTDays #Daily return
sigma = sigma / math.sqrt(nTDays) #Daily volatility
drift = mu - (0.5 * sigma**2)
''' Step 2 - Create a matrix of stochastic component - random shock '''
z = np.random.normal(0, 1, (nSim, nPer))
log_ret = drift + (sigma * z)
''' Compound return using vectorize method
LN(Today/Yesterday) = drift + random shock * sigma
'''
compounded_ret = np.cumsum(log_ret, axis=1)
asset_path = s0 + (s0 * compounded_ret)
#Include starting value
s0 = matlib.repmat(s0, nSim, 1)
asset_path = np.concatenate((s0, asset_path), axis=1)
asset_path *= (asset_path > 0) #set negative to zero
return (asset_path)
def compute_s_prime_a(self, s_primes):
"""Given the list of next states s_prime, it returns the matrix state actions that
for each state prime the contains all the pairs s'a where a is in the action set
of s'.
"""
# Get the number of actions for each state
n_actions_per_state = list(
map(lambda x: len(x),
map(lambda s: self._actions[tuple(s)], s_primes)))
tot_n_actions = sum(n_actions_per_state)
n_states = s_primes.shape[0]
sa = np.empty((tot_n_actions, self.state_dim + self.action_dim))
end = 0
for i in range(n_states):
# set interval variables
start = end
end = end + n_actions_per_state[i]
# set state prime
i_s_prime = s_primes[i, :]
n_actions = n_actions_per_state[i]
# populate the matrix with the ith state prime
sa[start:end,
0:self.state_dim] = matlib.repmat(i_s_prime, n_actions, 1)
# populate the matrix with the actions of the action set of ith state prime
sa[start:end, self.state_dim:] =\
np.array(self._actions[tuple(i_s_prime)]).reshape((n_actions, self.action_dim))
# reset self._actions to save memory
self._actions = []
self.sprime_a = sa
self.n_actions_per_state_prime = n_actions_per_state
def find_knee(values):
# get coordinates of all the points
nPoints = len(values)
allCoord = np.vstack((range(nPoints), values)).T
# np.array([range(nPoints), values])
# get the first point
firstPoint = allCoord[0]
# get vector between first and last point - this is the line
lineVec = allCoord[-1] - allCoord[0]
lineVecNorm = lineVec / np.sqrt(np.sum(lineVec**2))
# find the distance from each point to the line:
# vector between all points and first point
vecFromFirst = allCoord - firstPoint
# To calculate the distance to the line, we split vecFromFirst into two
# components, one that is parallel to the line and one that is perpendicular
# Then, we take the norm of the part that is perpendicular to the line and
# get the distance.
# We find the vector parallel to the line by projecting vecFromFirst onto
# the line. The perpendicular vector is vecFromFirst - vecFromFirstParallel
# We project vecFromFirst by taking the scalar product of the vector with
# the unit vector that points in the direction of the line (this gives us
# the length of the projection of vecFromFirst onto the line). If we
# multiply the scalar product by the unit vector, we have vecFromFirstParallel
scalarProduct = np.sum(vecFromFirst * mb.repmat(lineVecNorm, nPoints, 1),
axis=1)
vecFromFirstParallel = np.outer(scalarProduct, lineVecNorm)
vecToLine = vecFromFirst - vecFromFirstParallel
# distance to line is the norm of vecToLine
distToLine = np.sqrt(np.sum(vecToLine**2, axis=1))
# knee/elbow is the point with max distance value
idxOfBestPoint = np.argmax(distToLine)
return idxOfBestPoint
def mf(f):
FFT = np.fft.rfft(f, axis=0) # FFT of signal
RF = np.real(FFT) # Real part of FFT
IF = np.imag(FFT) # Imaginary part of FFT
F = np.abs(FFT) # Magnitude of spectrum
# AF = np.sqrt(np.power(RF,2)+np.power(IF,2))/FFT.shape[0] # Amplitude of FFT
AF = np.abs(FFT)
PF = np.arctan(np.divide(IF, RF + np.finfo(float).eps)) # Phase of FFT
PF = np.power(F, 2) # Power of spectrum
PF[1:-1] = 2 * PF[1:-1]
sumF = 0.5 * sum(F[1:], axis=0)
sumPF = 0.5 * sum(PF[1:], axis=0)
if len(F.shape) <= 1:
F = F[:, np.newaxis]
PF = PF[:, np.newaxis]
freq = npm.repmat(
np.array(range(F.shape[0]))[:, np.newaxis], 1, F.shape[-1])
MDF = np.array([
next(i for i in range(1,
len(freq) + 1)
if sum(PF[1:i + 1, j], axis=0) >= sumPF[j])
for j in range(PF.shape[-1])
])
MMDF = np.array([
next(i for i in range(1,
len(freq) + 1)
if sum(F[1:i + 1, j], axis=0) >= sumF[j])
for j in range(F.shape[-1])
])
sumPF[sumPF == 0] = 1.
sumF[sumF == 0] = 1.
MNF = sum(np.divide(np.multiply(PF[1:], freq[1:]), sumPF), axis=0)
MMNF = sum(np.divide(np.multiply(F[1:], freq[1:]), sumF), axis=0)
out = np.concatenate((np.array([MNF, MDF, MMNF, MMDF]), RF, IF, F, AF, PF),
axis=0)
return out, np.array([MNF, MDF, MMNF,
MMDF]), RF, IF, F, AF, PF, time.time()
def _to_one_hot(self, labels, reverse=False):
""" Transform a list of labels into a 1-hot encoding.
Args:
labels: A list of class labels.
reverse: If true, then one-hot encoded samples are transformed back
to categorical labels.
Returns:
The 1-hot encoded labels.
"""
if not self.classification:
raise RuntimeError('This method can only be called for ' +
'classification datasets.')
# Initialize encoder.
if self._one_hot_encoder is None:
self._one_hot_encoder = OneHotEncoder( \
categories=[range(self.num_classes)])
num_time_steps = 1
if self.sequence:
num_time_steps = labels.shape[1] // np.prod(self.out_shape)
self._one_hot_encoder.fit(
npm.repmat(np.arange(self.num_classes), num_time_steps, 1).T)
if reverse:
# Unfortunately, there is no inverse function in the OneHotEncoder
# class. Therefore, we take the one-hot-encoded "labels" samples
# and take the indices of all 1 entries. Note, that these indices
# are returned as tuples, where the second column contains the
# original column indices. These column indices from "labels"
# mudolo the number of classes results in the original labels.
return np.reshape(
np.argwhere(labels)[:, 1] % self.num_classes,
(labels.shape[0], -1))
else:
return self._one_hot_encoder.transform(labels).toarray()
def get_3dim_spectrum(wav_name, channel_vec, start_point, stop_point, frame,
shift, fftl):
"""
dump_wav : channel_size * speech_size (2dim)
"""
samples, _ = sf.read(wav_name.replace('{}', str(channel_vec[0])),
start=start_point,
stop=stop_point,
dtype='float32')
if len(samples) == 0:
return None, None
dump_wav = np.zeros((len(channel_vec), len(samples)), dtype=np.float16)
dump_wav[0, :] = samples.T
for ii in range(0, len(channel_vec) - 1):
samples, _ = sf.read(wav_name.replace('{}', str(channel_vec[ii + 1])),
start=start_point,
stop=stop_point,
dtype='float32')
dump_wav[ii + 1, :] = samples.T
dump_wav = dump_wav / np.max(np.abs(dump_wav)) * 0.7
window = sg.hanning(fftl + 1, 'periodic')[:-1]
multi_window = npm.repmat(window, len(channel_vec), 1)
st = 0
ed = frame
number_of_frame = np.int((len(samples) - frame) / shift)
spectrums = np.zeros(
(len(channel_vec), number_of_frame, np.int(fftl / 2) + 1),
dtype=np.complex64)
for ii in range(0, number_of_frame):
multi_signal_spectrum = fft(dump_wav[:, st:ed], n=fftl,
axis=1)[:, 0:np.int(fftl / 2) +
1] # channel * number_of_bin
spectrums[:, ii, :] = multi_signal_spectrum
st = st + shift
ed = ed + shift
return spectrums, len(samples)
def sample(self, b=None, isQMDP=False):
if b is None:
b = self.current_belief
V = self.alpha_v
b = np.matrix(b)
# If Q-MDP choose action directly
if isQMDP:
Q = V * b.T
act = greedy('samp', Q)
# else: Build Q-matrix
else:
Q = np.zeros(self._nA)
for a in range(self._nA):
#b = np.matrix(b)
# Compute updated beliefs for current action and all observations
# print"b : {}".format(b)
Vaux = (b * self._P[a]).T
Vaux = np.multiply(npmat.repmat(Vaux, 1, self._nZ), self._O[a])
Vaux = V * Vaux
Vmax = np.amax(Vaux, 0)[0]
# Compute observation probabilities and multiply
Q[a] = (b * np.matrix(self._R[:, a]).T).item(
0, 0) + self._gamma * np.sum(Vmax)
# print "Q : {}".format(Q)
# raw_input()
act = greedy('prob', Q)
f_act = {self.main_act: [act]}
return f_act
def patient_staging(pi0, event_centers, likeli_post, likeli_pre, type_staging):
L_yes = np.divide(likeli_post, likeli_post + likeli_pre + 1e-100)
L_no = 1 - L_yes
event_centers_pad = np.insert(event_centers, 0, 0)
event_centers_pad = np.append(event_centers_pad, 1)
pk_s = np.diff(event_centers_pad)
# pk_s[:]=1;#?????
m = L_yes.shape
prob_stage = np.zeros((m[0], m[1] + 1))
p_no_perm = L_no[:, pi0]
p_yes_perm = L_yes[:, pi0]
for j in range(
m[1] + 1
): # np.nanprod当axis=1时横向相乘,空值设为1，p_yes_perm[:,:j]列数逐渐增多，p_no_perm[:,j:]列数逐渐减小
prob_stage[:, j] = pk_s[j] * np.multiply(
np.nanprod(p_yes_perm[:, :j], axis=1),
np.nanprod(p_no_perm[:, j:], axis=1))
all_stages_rep2 = matlib.repmat(event_centers_pad[:-1], m[0], 1)
if type_staging[0] == 'exp':
subj_stages = np.zeros(prob_stage.shape[0])
for i in range(prob_stage.shape[0]):
idx_nan = np.isnan(p_yes_perm[i, :])
pr = prob_stage[i, 1:]
ev = event_centers_pad[1:-1]
# 将每一个病人不同生物标记物的分期概率与事件中心相乘（除去空值），除以不同生物标记物的分期概率
subj_stages[i] = np.mean(
np.multiply(
np.append(prob_stage[i, 0], pr[~idx_nan]),
np.append(event_centers_pad[0], ev[~idx_nan]))) / np.mean(
np.append(prob_stage[i, 0], pr[~idx_nan]))
elif type_staging[0] == 'ml':
subj_stages = np.argmax(prob_stage, axis=1)
return subj_stages
def llc(X, D, knn=5):
# the sparse coder introduced in
# "Locality-constrained Linear Coding for Image Classification"
n_samples = X.shape[1]
n_atoms = D.shape[1]
# has the distance of
# each sample to each atom
dist = np.zeros((n_samples, n_atoms))
# calculate the distances
for i in range(n_samples):
for j in range(n_atoms):
dist[i, j] = norm(X[:, i] - D[:, j])
# has the indices of the atoms
# that are nearest neighbour to each sample
knn_idx = np.zeros((n_samples, knn)).astype(int)
for i in xrange(n_samples):
knn_idx[i, :] = np.argsort(dist[i, :])[:knn]
# the sparse coding matrix
Z = np.zeros((n_atoms, n_samples))
II = np.eye(knn)
beta = 1e-4
b = np.ones(knn)
for i in xrange(n_samples):
idx = knn_idx[i, :]
z = D.T[idx, :] - repmat(X.T[i, :], knn, 1)
C = np.dot(z, z.T)
C = C + II * beta * np.trace(C)
# solve the linear system C*c=b
c = solve(C, b)
# enforce the constraint on the sparse codes
# such that sum(c)=1
c = c / float(np.sum(c))
Z[idx, i] = c
return Z
def _create_accum_list_labeled(self, shortest_paths, maxpath, labels_t,
numlabels):
"""
Construct accumulation array matrix for one dataset
containing labaled graph data.
"""
res = lil_matrix(
np.zeros((len(shortest_paths),
(maxpath + 1) * numlabels * (numlabels + 1) / 2)))
for i, s in enumerate(shortest_paths):
labels = labels_t[i]
labels_aux = matlib.repmat(labels, 1, len(labels))
min_lab = np.minimum(labels_aux.T, labels_aux)
max_lab = np.maximum(labels_aux.T, labels_aux)
subsetter = np.triu(~(np.isinf(s)))
min_lab = min_lab[subsetter]
max_lab = max_lab[subsetter]
ind = s[subsetter] * numlabels * (numlabels + 1) / 2 + \
(min_lab - 1) * (2*numlabels + 2 - min_lab) / 2 + \
max_lab - min_lab
accum = np.zeros((maxpath + 1) * numlabels * (numlabels + 1) / 2)
accum[:ind.max() + 1] += np.bincount(ind.astype(int))
res[i] = lil_matrix(accum)
return res
