def inf(self, x, meanonly=False):
x = np.asmatrix(x)
if x.shape[1] != self.d:
if x.shape[0] == self.d:
x = x.T
else:
raise Exception('Invalid test-set dimension -- '
'expected d = ' + str(self.d) + '.')
n = x.shape[0]
# Handle empty test set
if n == 0:
return (np.zeros((0, 1)), np.zeros((0, 1)))
ms = self.kernel.mean*np.ones((n, 1))
Kbb = self.kernel(x, diag=True)
# Handle empty training set
if len(self) == 0:
return (ms, np.asmatrix(Kbb))
Kba = self.kernel(x, self.x)
m = self.kernel.mean*np.ones((len(self), 1))
fm = ms + Kba*scipy.linalg.cho_solve((self.L, True), self.y - m,
overwrite_b=True)
if meanonly:
return fm
else:
W = scipy.linalg.cho_solve((self.L, True), Kba.T)
fv = np.asmatrix(Kbb - np.sum(np.multiply(Kba.T, W), axis=0).T)
# W = np.asmatrix(scipy.linalg.solve(self.L, Kba.T, lower=True))
# fv = np.asmatrix(Kbb - np.sum(np.power(W, 2), axis=0).T)
return (fm, fv)
def add(self, x, y, update=True):
assert x.shape[0] == y.shape[0]
assert x.shape[1] == self.d
assert y.shape[1] == 1
x = np.asmatrix(x)
y = np.asmatrix(y)
if x.shape[0] > 0:
self.x = np.concatenate((self.x, x))
self.y = np.concatenate((self.y, y))
if update:
self._update()
def from_mat(cls, fname):
import scipy.io
m = scipy.io.loadmat(fname, byte_order='native')
data = {}
data['x'] = np.asmatrix(m['tc'][0][0][0][0][0][0].newbyteorder('='))
data['y'] = np.asmatrix(m['tc'][0][0][0][0][0][1].newbyteorder('='))
h = m['tc'][0][0][1][0][0].newbyteorder('=')
name = m['tc'][0][0][3][0]
hyp = {'mean': 2.4, 'cov': [5.5, 1, 0.75], 'lik': -1}
k = kernels.SE(hyp)
tc = Testcase(k, data=data, h=h, name=name)
return tc
def from_mat(cls, fname):
import scipy.io
m = scipy.io.loadmat(fname, byte_order='native')
data = {}
data['x'] = np.asmatrix(m['tc'][0][0][0][0][0][0].newbyteorder('='))
data['y'] = np.asmatrix(m['tc'][0][0][0][0][0][1].newbyteorder('='))
h = m['tc'][0][0][1][0][0].newbyteorder('=')
name = m['tc'][0][0][3][0]
hyp = {'mean': 2.4, 'cov': [5.5, 1, 0.75], 'lik': -1}
k = kernels.SE(hyp)
tc = Testcase(k, data=data, h=h, name=name)
return tc
def __call__(self, x, z=[], diag=False):
if x.shape[0] == 0:
return np.zeros((0, 0))
if diag:
return self.sf2*np.ones((x.shape[0], 1))
sx = x*self.covd
if z == []:
K = np.asmatrix(ssd.squareform(ssd.pdist(sx, 'sqeuclidean')))
else:
sz = z*self.covd
K = np.asmatrix(ssd.cdist(sx, sz, 'sqeuclidean'))
K = self.sf2*np.exp(-K/2)
return K
def computeCovariance(self):
"""
Computes the time-lagged covariance matrix :math:`C^{\\tau}` with
:math:`c_{ij}^{\\tau} = \\frac{1}{N-\\tau-1}\\sum_{t=1}^{N-\\tau}x_{ti}x_{(t+\\tau)j}`
"""
self.m_prinComp.m_dataImporter.rewind()
dataChunk = np.asarray(self.m_prinComp.m_dataImporter.get_data(self.m_prinComp.param_chunkSize), dtype=np.float32)
dimData = self.m_prinComp.m_dataImporter.get_shape_inFile()
shapeDataChunk = dataChunk.shape
m = shapeDataChunk[0]
self.m_covMatTimeLag = matlib.zeros([shapeDataChunk[1], shapeDataChunk[1]], dtype = np.float64)
normalizedPCs = matlib.zeros([shapeDataChunk[1], shapeDataChunk[1]], dtype = np.float64)
if 1 < m:
pcs = self.m_prinComp.computePCs(dataChunk, shapeDataChunk[1])
del dataChunk
normalizedPCs = self.m_prinComp.normalizePCs(pcs)
del pcs
self.m_covMatTimeLag += np.dot(normalizedPCs[0:(m - self.param_timeLag), :].T,
normalizedPCs[self.param_timeLag:m, :])
lastRowsChunkBefore = normalizedPCs[(m-self.param_timeLag):m, :]
del normalizedPCs
while self.m_prinComp.m_dataImporter.has_more_data():
dataChunk = np.asarray(self.m_prinComp.m_dataImporter.get_data(self.m_prinComp.param_chunkSize), dtype=np.float32)
shapeDataChunk = dataChunk.shape
m = shapeDataChunk[0]
pcs = self.m_prinComp.computePCs(dataChunk, shapeDataChunk[1])
del dataChunk
normalizedPCs = self.m_prinComp.normalizePCs(pcs)
del pcs
self.m_covMatTimeLag += np.dot(matlib.asmatrix(lastRowsChunkBefore).T,
matlib.asmatrix(normalizedPCs[0:self.param_timeLag, :]))
if 1 < m:
self.m_covMatTimeLag += np.dot(normalizedPCs[0:(m - self.param_timeLag), :].T,
normalizedPCs[self.param_timeLag:m, :])
lastRowsChunkBefore = normalizedPCs[(m-self.param_timeLag):m, :]
del normalizedPCs
self.m_covMatTimeLag *= 1.0 / (dimData[0] - self.param_timeLag - 1.0)
def normalizePCs(self, i_pcsChunk):
"""
This function computes the normalizes the principle components :math:`Y` of the input data :math:`X`.
Let :math:`\\Lambda` be a diagonal matrix with the ordered eigenvalues of the instantaneous
#covariance matrix :math:`C`. The normalized principle components :math:`\\tilde{Y}` are computed
by :math:`\\tilde{Y} = \\Lambda^{-\\frac{1}{2}}Y)`.
:param i_pcsChunk: A chunk of principle components.
:type i_pcsChunk: numpy.array
:return o_pcNorm: The normalized principle components :math:`\\tilde{Y}`.
:rtype: numpy.array
"""
temp = self.m_eigenDecomp.m_eigenValReal + self.param_addEpsilon
if ( any(temp < 0) or any(np.isnan(temp)) ) and self.param_useDampingAdapt:
lamb = self.naiveDampingParamAdapt()
else:
lamb = 1.0 / np.sqrt(self.m_eigenDecomp.m_eigenValReal + self.param_addEpsilon)
if not 1 < i_pcsChunk.shape[0]:
o_pcNorm = np.dot(matlib.asmatrix(i_pcsChunk), np.diag(lamb))
else:
o_pcNorm = np.dot(i_pcsChunk, np.diag(lamb))
return o_pcNorm
def get_u(self):
points = npmat.hstack([s.center_position for s in self.solids])
center = npmat.asmatrix(npmat.average(points, axis = 1)).T
centered_points = points - center
correlation_matrix = (centered_points * centered_points.T)/self.nb_solids
u = iterate(correlation_matrix, self.NB_ITERATIONS)
return u
def computePCs(self, i_dataChunk, i_domComp):
"""
This function computes the principle components of the input data :math:`X`.
Let :math:`\\Gamma` be the matrix which contains the ordered eigenvectors of the instantaneous
covariance matrix :math:`C`. The principle components :math:`Y` are computed
by :math:`Y = \\Gamma^{T}(X-mean(X))`.
:param i_dataChunk: A data chunk as a subset of hole data.
:type i_dataChunk: numpy.array
:param i_domComp: Number of dominated components which are considered.
:type i_domComp: int
:return o_pc: The principle components :math:`Y`.
:rtype: numpy.array
"""
if not 1 < i_dataChunk.shape[0]:
meanFreeChunk = i_dataChunk[:, 0:i_dataChunk.shape[1]] - self.m_colMeans
o_pc = np.dot(matlib.asmatrix(meanFreeChunk), self.m_eigenDecomp.m_eigenVecReal[:, 0:i_domComp])
del meanFreeChunk
else:
meanFreeChunk = i_dataChunk[:, 0:i_dataChunk.shape[1]] - self.m_colMeans
o_pc = np.dot( meanFreeChunk, self.m_eigenDecomp.m_eigenVecReal[:, 0:i_domComp])
del meanFreeChunk
return o_pc
def cross_product_matrix(w):
"""
Returns a matrix representing the linear function (v -> cross_product(w,v))
where w is a 3 dimensional vector
"""
x = w[0, 0]
y = w[1, 0]
z = w[2, 0]
return npmat.asmatrix([[0., -z, y], [z, 0., -x], [-y, x, 0.]])
def iterate(M, nb_iterations):
w = npmat.asmatrix(npmat.random.uniform(0., 1., size = (3, 1)))
w /= npmat.linalg.norm(w)
for i in range(nb_iterations):
w = M * w
w /= npmat.linalg.norm(w)
return w
def colliding_boxes(self):
nb_solids = self.nb_solids
points = npmat.hstack([s.center_position for s in self.solids])
center = npmat.asmatrix(npmat.average(points, axis = 1)).T
centered_points = points - center
correlation_matrix = (centered_points * centered_points.T) / nb_solids
u = iterate(correlation_matrix, self.NB_ITERATIONS)
if self.projected_bounds is None:
self.projected_bounds = []
for i in range(nb_solids):
self.projected_bounds.append((i, 0, 0.))
self.projected_bounds.append((i, 1, 0.))
min_max_projections = npmat.empty((nb_solids, 2))
for solid_id in range(nb_solids):
solid_AABB_corners = self.solids[solid_id].AABB_corners()
corners_projections = u.T * solid_AABB_corners
min_max_projections[solid_id, 0] = np.min(corners_projections)
min_max_projections[solid_id, 1] = np.max(corners_projections)
for i in range(2 * nb_solids):
solid_id, begin_or_end_id, value = self.projected_bounds[i]
new_value = min_max_projections[solid_id, begin_or_end_id]
self.projected_bounds[i] = (solid_id, begin_or_end_id, new_value)
# TODO: linear sorting
self.projected_bounds.sort(key = lambda x : x[2])
output = []
active_solids = []
for i in range(2 * nb_solids):
solid_id, begin_or_end_id, value = self.projected_bounds[i]
if begin_or_end_id == 0:
for active_solid_id in active_solids:
if self.solids[active_solid_id].AABB_intersect_with(self.solids[solid_id]):
output.append((active_solid_id, solid_id))
active_solids.append(solid_id)
else:
active_solids.remove(solid_id)
return output
def forward(self, ngrami):
aux = self.C[ngrami[0, :], :][0]
aux = aux.reshape((aux.shape[0] * aux.shape[1], 1))
x = shared(np.asmatrix(aux, 'float32'))
o = self.linear(self.H, x, self.D)
a = self.sigmoid(o)
e = self.linear(self.U, a, self.B)
z = self.dot(self.W, x)
y = np.add(e, z)
return y, a, x
def add(self, x, y, update=True):
x = np.asmatrix(x)
y = np.asmatrix(y)
if x.shape[1] != self.d:
if x.shape[0] == self.d:
x = x.T
else:
raise Exception('Invalid train-set (x) dimension -- '
'expected d = ' + str(self.d) + '.')
if y.shape[1] != 1:
if y.shape[0] == 1:
y = y.T
else:
raise Exception('Invalid train-set (y) dimension -- '
'expected d = 1.')
if y.shape[0] != x.shape[0]:
raise Exception('Incompatible train-set (x, y) lengths.')
x = np.asmatrix(x)
y = np.asmatrix(y)
if x.shape[0] > 0:
self.x = np.concatenate((self.x, x))
self.y = np.concatenate((self.y, y))
if update:
self._update()
def inf(self, x, meanonly=False):
x = np.asmatrix(x)
assert x.shape[1] == self.d
n = x.shape[0]
# Handle empty test set
if n == 0:
return (np.zeros((0, 1)), np.zeros((0, 1)))
ms = self.kernel.mean*np.ones((n, 1))
Kbb = self.kernel(x, diag=True)
# Handle empty training set
if len(self) == 0:
return (ms, np.asmatrix(np.diag(Kbb)).T)
Kba = self.kernel(x, self.x)
m = self.kernel.mean*np.ones((len(self), 1))
fm = ms + Kba*scipy.linalg.cho_solve((self.L, True), self.y - m,
overwrite_b=True)
if meanonly:
return fm
else:
W = scipy.linalg.cho_solve((self.L, True), Kba.T)
fv = np.asmatrix(Kbb - np.sum(np.multiply(Kba.T, W), axis=0).T)
# W = np.asmatrix(scipy.linalg.solve(self.L, Kba.T, lower=True))
# fv = np.asmatrix(Kbb - np.sum(np.power(W, 2), axis=0).T)
return (fm, fv)
def rotation_matrix_from_quaternion(q):
"""
Returns the rotation matrix associated to a unitary
quaternion represented by a 4 dimensional vector
"""
a, b, c, d = npmat.asarray(q).reshape(-1)
a2 = a * a
b2 = b * b
c2 = c * c
d2 = d * d
return npmat.asmatrix(
[[a2 + b2 - c2 - d2, 2. * (b * c - a * d), 2. * (a * c + b * d)],
[2. * (a * d + b * c), a2 - b2 + c2 - d2, 2. * (c * d - a * b)],
[2. * (b * d - a * c), 2. * (a * b + c * d), a2 - b2 - c2 + d2]])
def train(self, w, z, eta=0.005, epoca=1000, error=0.01):
count = 0
training_samples_pos = sample(range(w.shape[0]), min(w.shape[0], epoca))
while count < epoca:
for i in training_samples_pos:
traini = w[i, :]
y, a, x = self.forward(traini)
x = shared(np.asmatrix(y, 'float32'))
self.probs = self.softmax(y)
def haar_inverse(image, dim=2):
'''
Apply haar inverse transformation.
:param image: square matrix
:param dim: dimension
:return: None
'''
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = T.T * P.T * M.asmatrix(image[0:dim, 0:dim]) * P * T
if dim == M.shape(image)[0]:
return
haar_inverse(image, dim * 2)
def haar_inverse(image, dim=2):
'''
Apply haar inverse transformation.
:param image: square matrix
:param dim: dimension
:return: None
'''
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = T.T * P.T * M.asmatrix(image[0:dim, 0:dim]) * P * T
if dim == M.shape(image)[0]:
return
haar_inverse(image, dim * 2)
def minfo(self, x):
x = np.asmatrix(x)
assert x.shape[1] == self.d
n = x.shape[0]
# Handle empty test set
if n == 0:
return 0
Kbb = self.kernel(x)
# Handle empty training set
if len(self) == 0:
S = Kbb
else:
Kba = self.kernel(x, self.x)
S = Kbb - Kba*scipy.linalg.cho_solve((self.L, True), Kba.T)
sn2 = np.exp(2*self.kernel.lik)
(sng, mi) = numpy.linalg.slogdet(np.eye(n) + S/sn2)
return 0.5*mi
def onComputeClick():
epsilon = float(epsilonInput.get())
if matrixInput.get() == "rand":
N = int(matrixSizeInput.get())
m = generateRandMatrix(N)
elif matrixInput.get() == "conv_ex":
N = 3
m = [[6., 3., 2.], [7., 2., 3.], [5., 5., 1.]]
elif matrixInput.get() == "non_conv_ex":
N = 2
m = [[1., 1.], [0., -1.]]
maxIt =N*1000
if numPySelectionInput.get() == "no":
startComputation(m, N, epsilon, maxIt)
elif numPySelectionInput.get() == "yes":
m = matlib.asmatrix(m)
startComputation_np(m, N, epsilon, maxIt)
def haar_forward(image, dim=None, recursive=True):
'''
Apply haar transformation to image.
:param image: square matrix
:param dim: dimension
:param recursive: apply recursively
:return: None
'''
if dim is None:
dim = M.shape(image)[0]
if dim == 1: # base case
return
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = P * T * M.asmatrix(image[0:dim, 0:dim]) * T.T * P.T
if recursive:
haar_forward(image, dim / 2)
def haar_forward(image, dim=None, recursive=True):
'''
Apply haar transformation to image.
:param image: square matrix
:param dim: dimension
:param recursive: apply recursively
:return: None
'''
if dim is None:
dim = M.shape(image)[0]
if dim == 1: # base case
return
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = P * T * M.asmatrix(image[0:dim, 0:dim]) * T.T * P.T
if recursive:
haar_forward(image, dim / 2)
Simultaneous estimation of the full pose, i.e. including all six channels.
'''
import numpy as np
import numpy.matlib as mt
from kalmanfilter import Constant, exponentialSmooth, M
import kalmanfilter
from kalman_simulation2 import getTrack
def SetupKf(measurement, dt, (sigmaQ, sigmaQVPfactor, sigmaQVVfactor)):
R = mt.asmatrix([
[ 1.334363e-02 , 1.460443e-03 , 1.540213e-03 , -2.719011e-02 , -3.486926e-04 , 1.866799e-02 , ],
[ 1.460443e-03 , 5.416844e-03 , -3.137613e-03 , 1.608790e-02 , -2.012435e-03 , 8.478703e-03 , ],
[ 1.540213e-03 , -3.137613e-03 , 8.234656e-02 , 1.201560e-02 , 4.897242e-02 , -2.295807e-03 , ],
[ -2.719011e-02 , 1.608790e-02 , 1.201560e-02 , 6.615176e-01 , -2.021002e-02 , 7.779090e-03 , ],
[ -3.486926e-04 , -2.012435e-03 , 4.897242e-02 , -2.021002e-02 , 2.195976e-01 , 7.623157e-05 , ],
[ 1.866799e-02 , 8.478703e-03 , -2.295807e-03 , 7.779090e-03 , 7.623157e-05 , 5.354048e-02 , ],
])
# Stuff works better if we pretend that there are less correlations ...
R.A[...] *= (0.5 + 0.5 *np.identity(6) )
h = np.matrix([
[ 1. , 0. ],
])
H = mt.zeros((6,12))
for k in xrange(6):
H[k::6,k::6] = h
# Consider varying time delta, so system matrices change from step to step.
def computeA(k):
def __init__(self, hyp):
self.mean = hyp['mean']
self.cov = np.exp(hyp['cov'][:-1])
self.covd = np.asmatrix(np.diagflat(1/self.cov))
self.sf2 = np.exp(2*hyp['cov'][-1])
self.lik = hyp['lik']
import numpy.matlib as np
print(np.matrix('1,2;3,4'))
print(np.asmatrix('1,2;3,4'))
n = np.array(range(L)) # Дискретное нормированное время
plt.subplot(1, 1, 1)
plt.gcf().canvas.set_window_title('Discrete Triangular Impulse')
plt.title('Discrete Triangular Impulse x4(n)')
plt.stem(n, x4)
plt.xlabel('n')
plt.show()
print('\n----------------------------------------')
print('п8. Линейная комбинация дискретных гармонических сигналов')
input(
'Для вывода ГРАФИКОВ гармонических сигналов и их линейной комбинации нажмите <ENTER>'
)
n = np.array(range(5 * N - 1))
xi = np.multiply(matlib.repmat(B, len(n), 1),
np.sin(matlib.asmatrix(n).transpose() * w))
ai = matlib.repmat(A, len(n), 1)
x5 = np.sum(np.multiply(ai, xi), axis=1)
plt.subplot(4, 1, 1)
plt.gcf().canvas.set_window_title(
'Discrete Harmonic Signals and their Linear Combination')
plt.stem(n, xi[:, 0])
plt.title('First Discrete Harmonic Signal')
plt.subplot(4, 1, 2)
plt.stem(n, xi[:, 1])
plt.title('Second Discrete Harmonic Signal')
plt.subplot(4, 1, 3)
plt.stem(n, xi[:, 2])
plt.title('Third Discrete Harmonic Signal')
plt.subplot(4, 1, 4)
plt.title('Linear Combination x5(n)')
def Vect(l):
"""
Creates a vector, represented by a matrix column
"""
return npmat.asmatrix(l).reshape((-1, 1))