def sgrad(self, x, ndata=100, bound=True, average=True):
low_no = sp.random.randint(0, high=50000 - ndata)
high_no = low_no + ndata
sli = slice(low_no, high_no)
data2 = []
data2.append(self.data.train[0][sli])
data2.append(self.data.train[1][sli])
gradient = self.gradEval(x, tuple(data2))
m = int(sp.shape(gradient)[1])
'''u is the random direction matrix'''
u = sp.random.randint(0, high=m, size=sp.shape(gradient))
'''taking element wise product of u and gradient and then row wise sum to
get dot product of the matrices. dotprod is 10X1 matrix'''
dotprod = (u * gradient).sum(axis=1, keepdims=True)
stoc_grad = dotprod * u
if bound == True:
len_vec = sp.sqrt(
sp.diagonal(sp.dot(stoc_grad, sp.transpose(stoc_grad))))
#creating the list where len_vec is greater than desired value
bool_list = list(map(lambda z: z > 10, len_vec))
#converting boolean list to array of 1 0
bool_array = sp.array(bool_list, dtype=int)
#calculating factor to be divided with
norm_factor = sp.divide(bool_array, float(m) * len_vec)
norm_factor[norm_factor == 0] = 1 #replacing 0's with 1
temp_norm = sp.reshape(norm_factor,
(len(norm_factor), 1)) * sp.ones(
sp.shape(stoc_grad))
stoc_grad = sp.divide(stoc_grad, temp_norm)
'''alternatively we can use this
for i in range(len(len_vec)): #this for loop is small as len_vec len is 10
if len_vec[i] > 10:
stoc_grad[i,:] = stoc_grad[i,:]/(float(m)*float(len_vec[i]))'''
return stoc_grad
def indx_1dto3d(idx, sz):
"""
Translate 1D vector coordinates to 3D matrix coordinates for a 3D matrix of size sz.
Parameters
----------
idx : array
A 1D numpy coordinate vector.
sz : array
Shape of 3D matrix idx.
Returns
-------
x : int
x-coordinate of 3D matrix coordinates.
y : int
y-coordinate of 3D matrix coordinates.
z : int
z-coordinate of 3D matrix coordinates.
References
----------
.. Adapted from PyClusterROI
"""
from scipy import divide, prod
x = divide(idx, prod(sz[1:3]))
y = divide(idx - x * prod(sz[1:3]), sz[2])
z = idx - x * prod(sz[1:3]) - y * sz[2]
return x, y, z
def __init__(self, fc, c_vel, alp_g, mu_los, mu_nlos, a, b, noise_var, hUAV, xUAV, yUAV, xUE, yUE):
dist = sp.sqrt( sp.add(sp.square(sp.subtract(yUAV, yUE)), sp.square(sp.subtract(xUAV, xUE))) )
R_dist = sp.sqrt( sp.add(sp.square(dist), sp.square(hUAV)) )
temp1 = sp.multiply(10, sp.log10(sp.power(fc*4*sp.pi*R_dist/c_vel, alp_g)))
temp2 = sp.multiply(sp.subtract(mu_los, mu_nlos), sp.divide(1, (1+a*sp.exp(-b*sp.arctan(hUAV/dist)-a))))
temp3 = sp.add(sp.add(temp1, temp2), mu_nlos)
self.pathloss = sp.divide(sp.real(sp.power(10, -sp.divide(temp3, 10))), noise_var)
def european_option_delta(self): numerator = sp.add( sp.log( sp.divide( self.spot_price, self.strike_price ) ), sp.multiply( ( self.interest_rate - self.dividend_yield + 0.5*sp.power(self.sigma,2)), self.time_to_maturity ) ) d1 = sp.divide( numerator, sp.prod( [ self.sigma, sp.sqrt(self.time_to_maturity) ], axis=0, ) ) call_delta = self.bls_erf_value(d1) put_delta = call_delta - 1 return call_delta, put_delta
def european_option_rho(self): "Price of the call option" "the vectorized method can compute price of multiple options in array" numerator = sp.add( sp.log( sp.divide( self.spot_price, self.strike_price, ) ), sp.multiply( ( self.interest_rate - self.dividend_yield + 0.5*sp.power(self.sigma,2) ), self.time_to_maturity) ) d1 = sp.divide( numerator, sp.prod( [ self.sigma, sp.sqrt(self.time_to_maturity) ], axis=0, ) ) d2 = sp.add( d1, -sp.multiply( self.sigma, sp.sqrt(self.time_to_maturity) ) ) j = sp.product( [ self.spot_price, self.time_to_maturity, sp.exp( sp.multiply( -self.interest_rate, self.time_to_maturity ) ), ], axis=0 ) c_rho = j * self.bls_erf_value(d2) p_rho = -j * self.bls_erf_value(-d2) return c_rho, p_rho
def PointDipole(Freq,EpsB,Cell,NX,NY,NZ,Xs,Ys,Zs,XPol,YPol,ZPol):
"""Returns the incident field Ein over the computational domain,
produced by a point dipole source polarized as (XPol,YPol,ZPol)
and located at (Xs,Ys,Zs)
"""
c0=299792458.0 # speed of light in vacuum
Mu0=4.0*sci.pi*1.0e-7 # vacuum permeability
Eps0=1.0/(Mu0*c0*c0) # vacuum permittivity
Field=sci.zeros((NX,NY,NZ,3),complex)
Omega=2.0*sci.pi*Freq
EtaB=-1.0j*Omega*Eps0*EpsB
ZetaB=-1.0j*Omega*Mu0
KB=Omega*sci.sqrt(Eps0*EpsB*Mu0)
# 3D arrays of x,y,z coordinates
xx,yy,zz=sci.mgrid[0:NX*Cell:Cell,0:NY*Cell:Cell,0:NZ*Cell:Cell]
# 3D arrays of distances
dd=sci.sqrt((xx-Xs)**2+(yy-Ys)**2+(zz-Zs)**2)
dd2=dd*dd
Xd=xx-Xs
Yd=yy-Ys
Zd=zz-Zs
# 3D arrays of components of the Q-matrix
Q11=(Xd*Xd)/dd2
Q12=(Xd*Yd)/dd2
Q13=(Xd*Zd)/dd2
Q21=Q12
Q22=(Yd*Yd)/dd2
Q23=(Yd*Zd)/dd2
Q31=Q13
Q32=Q23
Q33=(Zd*Zd)/dd2
QJ1=Q11*XPol+Q12*YPol+Q13*ZPol
QJ2=Q21*XPol+Q22*YPol+Q23*ZPol
QJ3=Q31*XPol+Q32*YPol+Q33*ZPol
dd2=dd*dd
dd3=dd2*dd
Field[0:NX,0:NY,0:NZ,0]=sci.exp(1.0j*KB*dd)*\
(sci.divide((3.0*QJ1-XPol),(4.0*EtaB*sci.pi*dd3))\
+sci.divide((3.0*QJ1-XPol)*(-1.0j*KB),(4.0*EtaB*sci.pi*dd2))\
+sci.divide((QJ1-XPol),(4.0*ZetaB*sci.pi*dd)))
Field[0:NX,0:NY,0:NZ,1]=sci.exp(1.0j*KB*dd)*\
(sci.divide((3.0*QJ2-YPol),(4.0*EtaB*sci.pi*dd3))\
+sci.divide((3.0*QJ2-YPol)*(-1.0j*KB),(4.0*EtaB*sci.pi*dd2))\
+sci.divide((QJ2-YPol),(4.0*ZetaB*sci.pi*dd)))
Field[0:NX,0:NY,0:NZ,2]=sci.exp(1.0j*KB*dd)*\
(sci.divide((3.0*QJ3-ZPol),(4.0*EtaB*sci.pi*dd3))\
+sci.divide((3.0*QJ3-ZPol)*(-1.0j*KB),(4.0*EtaB*sci.pi*dd2))\
+sci.divide((QJ3-ZPol),(4.0*ZetaB*sci.pi*dd)))
return Field
def __init__(self,WeakLearner,training_data, \
bin_training_label,T,Twl):
self.T = T
self.weakLearner = WeakLearner
numOfSamples = len(training_data)
self.numOfFeatures = len(training_data[0])
self.D = [1.0/numOfSamples for _ in xrange(0,numOfSamples)]
self.w = [0.0 for _ in xrange(0,T)]
self.ht = []
for t in xrange(0,T):
if t%10==0:
print "getting weak learner number "+str(t)
wl = self.weakLearner(training_data,bin_training_label,Twl,D=self.D)
self.ht.append(wl)
epsilon=0.00001
#we want to prevent the case where epsilon=0,
#because the calculation of w relays on epsilon!=0
for i in xrange(0,numOfSamples):
h_t_xi = self.ht[t].Classify(training_data[i])
y_xi = bin_training_label[i]
if h_t_xi != y_xi :
epsilon+=self.D[i]
if epsilon>0.5:
print " warning: for the "+str(t)+" iteration got "+\
"{0:.2f}".format(epsilon)+" error the training set "
self.w[t]=0.5*math.log(1.0/epsilon-1)
for i in xrange(0,numOfSamples):
yi = labelTosign(bin_training_label[i])
hti =labelTosign(self.ht[t].Classify(training_data[i]))
self.D[i]=self.D[i]*math.exp(-1.0*self.w[t]*yi*hti)
self.D = sp.divide(self.D,sp.sum(self.D))
def density(self, x):
assert x.shape == self.dim, "Problem with the dimensionalities"
assert x.dtype == int, "x has to be an integer array"
theta = self.params['theta'].flatten()
x = x.flatten()
# return s.prod (stats.poisson.pmf(x,theta) )
return s.prod(s.divide(theta**x * s.exp(-theta), s.misc.factorial(x)))
def generate_stats(trueY, forecastY, missing=True):
""" From TRMF code """
nz_mask = trueY != 0
diff = forecastY - trueY
abs_true = sp.absolute(trueY)
abs_diff = sp.absolute(diff)
def my_mean(x):
tmp = x[sp.isfinite(x)]
assert len(tmp) != 0
return tmp.mean()
with sp.errstate(divide='ignore'):
# rmse
rmse = sp.sqrt((diff**2).mean())
# normalized root mean squared error
nrmse = sp.sqrt((diff**2).mean()) / abs_true.mean()
# baseline
abs_baseline = sp.absolute(trueY[1:, :] - trueY[:-1, :])
mase = abs_diff.mean() / abs_baseline.mean()
m_mase = my_mean(abs_diff.mean(axis=0) / abs_baseline.mean(axis=0))
mape = my_mean(sp.divide(abs_diff, abs_true, where=nz_mask))
return mape, mase, rmse
def __init__(self,WeakLearner,training_data, \
bin_training_label,T,Twl):
self.T = T
self.weakLearner = WeakLearner
numOfSamples = len(training_data)
self.numOfFeatures = len(training_data[0])
self.D = [1.0 / numOfSamples for _ in xrange(0, numOfSamples)]
self.w = [0.0 for _ in xrange(0, T)]
self.ht = []
for t in xrange(0, T):
if t % 10 == 0:
print "getting weak learner number " + str(t)
wl = self.weakLearner(training_data,
bin_training_label,
Twl,
D=self.D)
self.ht.append(wl)
epsilon = 0.00001
#we want to prevent the case where epsilon=0,
#because the calculation of w relays on epsilon!=0
for i in xrange(0, numOfSamples):
h_t_xi = self.ht[t].Classify(training_data[i])
y_xi = bin_training_label[i]
if h_t_xi != y_xi:
epsilon += self.D[i]
if epsilon > 0.5:
print " warning: for the "+str(t)+" iteration got "+\
"{0:.2f}".format(epsilon)+" error the training set "
self.w[t] = 0.5 * math.log(1.0 / epsilon - 1)
for i in xrange(0, numOfSamples):
yi = labelTosign(bin_training_label[i])
hti = labelTosign(self.ht[t].Classify(training_data[i]))
self.D[i] = self.D[i] * math.exp(-1.0 * self.w[t] * yi * hti)
self.D = sp.divide(self.D, sp.sum(self.D))
def reflect1(v, u, c):
print("Reflect by vector math variant 1:")
c = 0
center_ = eT(center(len(v)))
print("center_:", center_)
print("v:", v)
v = scipy.subtract(v, center_)
print("v:", v)
print("u:", u)
print("c:", c)
v_dot_u = scipy.dot(v, u)
print("v_dot_u:", v_dot_u)
v_dot_u_minus_c = scipy.subtract(v_dot_u, c)
print("v_dot_u_minus_c:", v_dot_u_minus_c)
u_dot_u = scipy.dot(u, u)
print("u_dot_u:", u_dot_u)
quotient = scipy.divide(v_dot_u_minus_c, u_dot_u)
print("quotient:", quotient)
subtrahend = scipy.multiply((2 * quotient), u)
print("subtrahend:", subtrahend)
reflection = scipy.subtract(v, subtrahend)
print("reflection:", reflection)
reflection = scipy.add(reflection, center_)
print("reflection:", reflection)
return reflection
def hyperplane_equation_from_dimensonality(dimensions,
transpositional_equivalence=False,
sector=1):
center_ = center(dimensions)
cyclical_region_vertices_ = cyclical_region_vertices(
dimensions, transpositional_equivalence)
for i in range(sector):
front = cyclical_region_vertices_.pop(0)
cyclical_region_vertices_.append(front)
upper_point = midpoint(cyclical_region_vertices_[1],
cyclical_region_vertices_[2])
lower_point = midpoint(cyclical_region_vertices_[0],
cyclical_region_vertices_[-1])
print("sector:", sector)
print("upper_point:", upper_point)
print("lower_point:", lower_point)
if transpositional_equivalence == True:
center_ = eT(center_)
#~ lower_point = eT(lower_point)
#~ upper_point = eT(upper_point)
normal_vector = scipy.subtract(upper_point, lower_point)
norm = scipy.linalg.norm(normal_vector)
unit_normal_vector = scipy.divide(normal_vector, norm)
constant_term = unit_normal_vector.dot(center_)
debug("hyperplane_equation_from_dimensonality for", dimensions, "voices:")
print("center:")
for e in center_:
print(e)
print("unit_normal_vector:")
for e in unit_normal_vector:
print(e)
print("constant_term:", constant_term)
print()
return unit_normal_vector, constant_term
def hyperplane_equation_by_svd_from_vectors(points, t_equivalence='True'):
t_ = []
if t_equivalence == True:
debug("original points:\n", points)
for point in points:
t_.append(eT(point))
points = t_
debug("points:\n", points)
vectors = []
subtrahend = points[-1]
debug("subtrahend:", subtrahend)
for i in range(len(points) - 1):
vector = scipy.subtract(points[i], subtrahend)
vectors.append(vector)
# debug("vectors:\n", vectors)
vectors = scipy.array(vectors)
debug("vectors:\n", vectors)
U, singular_values, V = scipy.linalg.svd(vectors)
debug("U:\n", U)
print("singular values:", singular_values)
debug("V:\n", V)
normal_vector = V[-1]
debug("normal_vector:", normal_vector)
norm = scipy.linalg.norm(normal_vector)
debug("norm:", norm)
unit_normal_vector = scipy.divide(normal_vector, norm)
print("unit_normal_vector:")
for e in unit_normal_vector:
print(e)
constant_term = scipy.dot(scipy.transpose(unit_normal_vector), subtrahend)
print("constant_term:", constant_term)
print()
return unit_normal_vector, constant_term
def hyperplane_equation_by_nullspace_from_points(points, t_equivalence='True'):
t_ = []
if t_equivalence == True:
debug("original points:\n", points)
for point in points:
t_.append(eT(point))
points = t_
debug("points:\n", points)
try:
debug("determinant of points:", scipy.linalg.det(points))
except:
pass
homogeneous_points = []
for point in points:
homogeneous_points.append(scipy.append(point, [1]))
debug("homogeneous points:", homogeneous_points)
nullspace = scipy.linalg.null_space(homogeneous_points)
nullspace = scipy.ndarray.flatten(nullspace[:-1])
debug("nullspace from homogeneous points:", nullspace)
constant_term = scipy.dot(scipy.transpose(nullspace), points[0])
debug("constant_term:", constant_term)
norm = scipy.linalg.norm(nullspace)
debug("norm:", norm)
unit_normal = scipy.divide(nullspace, norm)
print("unit normal vector:", unit_normal)
constant_term = scipy.dot(scipy.transpose(unit_normal), points[0])
print("constant_term:", constant_term)
return unit_normal, constant_term
def hyperplane_equation_by_nullspace_from_vectors(points,
t_equivalence='True'):
vectors = []
t_ = []
if t_equivalence == True:
debug("original points:", points)
for point in points:
t_.append(eT(point))
points = t_
debug("points:", points)
try:
debug("determinant of points:", scipy.linalg.det(points))
except:
pass
subtrahend = points[-1]
debug("subtrahend:", subtrahend)
for i in range(len(points) - 1):
vector = scipy.subtract(points[i], subtrahend)
debug("vector[", i, "]:", vector)
vectors.append(vector)
nullspace = scipy.linalg.null_space(vectors)
debug("nullspace from vectors:", nullspace)
norm = scipy.linalg.norm(nullspace)
debug("norm:", norm)
unit_normal_vector = scipy.divide(nullspace, norm)
print("unit_normal_vector:")
for e in unit_normal_vector:
print(e)
constant_term = scipy.dot(scipy.transpose(unit_normal_vector), subtrahend)
print("constant_term:", constant_term)
return unit_normal_vector, constant_term
def hyperplane_equation_by_cross_product(points, t_equivalence='True'):
vectors = []
t_ = []
if t_equivalence == True:
debug("original points:", points)
for point in points:
t_.append(eT(point))
points = t_
debug("points:", points)
debug("determinant of points:", scipy.linalg.det(points))
subtrahend = points[-1]
debug("subtrahend:", subtrahend)
for i in range(len(points) - 1):
vector = scipy.subtract(points[i], subtrahend)
debug("vector[", i, "]:", vector)
vectors.append(vector)
debug("vectors:", vectors)
product = generalized_cross_product(vectors)
print("generalized_cross_product:", product)
norm = scipy.linalg.norm(product)
debug("norm:", norm)
unit_normal_vector = scipy.divide(product, norm)
print("unit_normal_vector:")
for e in unit_normal_vector:
print(e)
constant_term = scipy.dot(scipy.transpose(unit_normal_vector), subtrahend)
print("constant_term:", constant_term)
return unit_normal_vector, constant_term
def BodefromTwoTimeDomainVectors(timevector,output,input,truncfreq=100):
"""This function calculates the Bode response between two time
domain signals. The timevector is used to calculate the frequency
vector, which is then used to truncate the Bode response to reduce
calculation time and return only useful information. Input and
output are time domain vectors.
The return values are
freq, magnitude ratio, phase, complex
The goal of this function is to be useful for small amounts of
data and/or as part of a routine to calculate a Bode response from
fixed sine data."""
N=len(timevector)
f=makefreqvect(timevector)
co=thresh_py(f,truncfreq)
f=f[0:co]
curin_fft=fft(input,None,0)*2/N
curout_fft=fft(output,None,0)*2/N
curin_fft=curin_fft[0:co]
curout_fft=curout_fft[0:co]
curGxx=norm2(curin_fft)
curGyy=norm2(curout_fft)
curGxy=scipy.multiply(scipy.conj(curin_fft),curout_fft)
H=scipy.divide(curGxy,curGxx)
Hmag=abs(H)
Hphase=mat_atan2(scipy.imag(H),scipy.real(H))*180.0/pi
return f,Hmag,Hphase,H
def get_F1Mean(self):
"""
Compute F1 Mean
"""
nl = sp.sum(self.confusionMatrix,axis=1,dtype=float)
nc = sp.sum(self.confusionMatrix,axis=0,dtype=float)
return 2*sp.mean( sp.divide( sp.diag(self.confusionMatrix), (nl + nc)) )
def gradEval(self, x, data1):
'''gradient form is negative for the form shown in the image'''
self.x_temp = x
self.dat_temp = data1
self.fn2 = None
map(self.secondpart, [i for i in range(10)])
gd2b = self.fn2 #DSX1
#fn_stacked creates first parts w's
self.gd_stacked = sp.ones(
784) #next two steps are req for calling stack fn
map(self.stack, data1[1], ['gd_stacked' for i in range(len(data1[1]))])
self.gd_stacked = sp.delete(
self.gd_stacked, (0),
axis=0) #deleting the first row (of ones created above)
gd2a1 = self.gd_stacked * self.dat_temp[0]
gd2a = sp.exp(gd2a1.sum(axis=1, keepdims=True)) #DSX1
temp = sp.divide(gd2a, gd2b) * self.dat_temp[0]
self.grad_vec_l = -1 * self.dat_temp[0] + temp
self.grad_vec = sp.ones((10, 1))
iter_temp = sp.array([i for i in range(784)])
map(self.grad_pooling, iter_temp)
self.grad_vec = sp.delete(self.grad_vec, (0), axis=1)
return self.grad_vec
def array_factor(number_of_elements_x, number_of_elements_y, element_spacing_x,
element_spacing_y, frequency, scan_angle_theta,
scan_angle_phi, theta, phi):
"""
Calculate the array factor for a planar uniform array.
:param number_of_elements_x: The number of elements in the x-direction.
:param number_of_elements_y: The number of elements in the y-direction.
:param element_spacing_x: The spacing of the elements in the x-direction (m).
:param element_spacing_y: The spacing of the elements in the y-direction (m).
:param frequency: The operating frequency (Hz).
:param scan_angle_theta: The scan angle in the theta-direction (rad).
:param scan_angle_phi: The scan angle in the phi-direction (rad).
:param theta: The pattern angle in theta (rad).
:param phi: The pattern angle in phi (rad).
:return: The array factor for a planar uniform array.
"""
# Calculate the wave number
k = 2.0 * pi * frequency / c
# Calculate the phase
psi_x = k * element_spacing_x * (
sin(theta) * cos(phi) - sin(scan_angle_theta) * cos(scan_angle_phi))
psi_y = k * element_spacing_y * (
sin(theta) * sin(phi) - sin(scan_angle_theta) * sin(scan_angle_phi))
# Break into numerator and denominator
numerator = sin(0.5 * number_of_elements_x * psi_x) * sin(
0.5 * number_of_elements_y * psi_y)
denominator = number_of_elements_x * number_of_elements_y * sin(
0.5 * psi_x) * sin(0.5 * psi_y)
return divide(numerator,
denominator,
ones_like(psi_x),
where=(denominator != 0.0)), psi_x, psi_y
def generate(cls, trueY, forecastY, missing=True):
nz_mask = trueY != 0
diff = forecastY - trueY
abs_true = sp.absolute(trueY)
abs_diff = sp.absolute(diff)
def my_mean(x):
tmp = x[sp.isfinite(x)]
assert len(tmp) != 0
return tmp.mean()
with sp.errstate(divide='ignore'):
nrmse = sp.sqrt((diff**2).mean()) / abs_true.mean()
m_nrmse = my_mean(
sp.sqrt((diff**2).mean(axis=0)) / abs_true.mean(axis=0))
nd = abs_diff.sum() / abs_true.sum()
m_nd = my_mean(abs_diff.sum(axis=0) / abs_true.sum(axis=0))
abs_baseline = sp.absolute(trueY[1:, :] - trueY[:-1, :])
mase = abs_diff.mean() / abs_baseline.mean()
m_mase = my_mean(abs_diff.mean(axis=0) / abs_baseline.mean(axis=0))
mape = my_mean(sp.divide(abs_diff, abs_true, where=nz_mask))
return cls(nd=nd,
mase=mase,
nrmse=nrmse,
m_nd=m_nd,
m_mase=m_mase,
m_nrmse=m_nrmse,
mape=mape)
def processing_part3(flann, gray_roi, gray_img):
orb = cv2.ORB(nfeatures=100, nlevels=4, scaleFactor=1.3)
key_points, query_descriptors = orb.detectAndCompute(gray_roi, None)
matches = flann.knnMatch(np.uint8(query_descriptors), k=6)
vote_array = np.zeros((gray_img.shape[0] / 10, gray_img.shape[1] / 10),
dtype=np.uint8)
for match in matches:
for index in match:
vectorx = (
key_points[index.queryIdx].size *
key_points_math_array[index.trainIdx].distance[0] *
scipy.cos(key_points_math_array[index.trainIdx].distance[2] +
key_points[index.queryIdx].distance[2] -
key_points_math_array[index.trainIdx].distance[2])
) / key_points_math_array[index.trainIdx].size
vectory = (
key_points[index.queryIdx].size *
key_points_math_array[index.trainIdx].distance[0] *
scipy.sin(key_points_math_array[index.trainIdx].distance[2] +
key_points[index.imgIdx].distance[2] -
key_points_math_array[index.trainIdx].distance[2])
) / key_points_math_array[index.trainIdx].size
kpx = int(
scipy.divide(key_points[index.imgIdx].pt[0] + vectorx, 10))
kpy = int(
scipy.divide(key_points[index.imgIdx].pt[1] + vectory, 10))
if (kpx > 0 and kpy > 0) and (kpx < vote_array.shape[1]
and kpy < vote_array.shape[0]):
vote_array[kpy, kpx] += 1
vote_array = cv2.resize(vote_array,
None,
fx=10,
fy=10,
interpolation=cv2.INTER_NEAREST)
max_index = np.unravel_index(vote_array.argmax(), vote_array.shape)
position = (max_index[0], max_index[1])
cv2.circle(gray_img,
position,
gray_img.shape[1] / 33, (0, 0, 255),
thickness=2)
return gray_img
def updateExpectations(self):
a, b = self.params['a'], self.params['b']
E = s.divide(a, a + b)
lnE = special.digamma(a) - special.digamma(a + b)
lnEInv = special.digamma(b) - special.digamma(
a + b) # expectation of ln(1-X)
lnEInv[s.isinf(
lnEInv)] = -s.inf # there is a numerical error in lnEInv if E=1
self.expectations = {'E': E, 'lnE': lnE, 'lnEInv': lnEInv}
def european_option_vega(self): numerator = sp.add( sp.log( sp.divide( self.spot_price, self.strike_price ) ), sp.multiply( ( self.interest_rate - self.dividend_yield + 0.5*sp.power(self.sigma,2)), self.time_to_maturity ) ) d1 = sp.divide( numerator, sp.prod( [ self.sigma, sp.sqrt(self.time_to_maturity) ], axis=0, ) ) val = sp.multiply( sp.multiply( self.spot_price, sp.exp( -sp.multiply( self.dividend_yield, self.time_to_maturity ) ) ), sp.exp(-sp.square(d1)*0.5) ) val = sp.multiply( val, sp.sqrt(self.time_to_maturity) ) vega = (1/sqrt(2*pi))*val return vega
def diffTaylor(v,i):
coeffs = polyfit(v,i,3)
vFit = linspace(min(v),max(v),100)
iFit = polyval(coeffs, vFit)
polynomial = poly1d(coeffs)
#didv = lambda ix: 6*coeffs[0]*((ix)**5) + 5*coeffs[1]*((ix)**4) + 4*coeffs[2]*((ix)**3) + 3*coeffs[3]*((ix)**2) + 2*coeffs[4]*(ix) + coeffs[5]
didv = lambda ix: 3*coeffs[0]*((ix)**2) + 2*coeffs[1]*(ix) + coeffs[2]
g = [float(didv(val)) for val in vFit]
rFit = divide(1,g)
return vFit, iFit, rFit
def loss_to_pair(self, pair, atg_a, atg_b, pl_exp=4, gamma=1e2):
dist = sp.sqrt(
sp.add(sp.square(pair.tx_x),
sp.add(sp.square(pair.tx_y), sp.square(self.h))))
phi = sp.multiply(sp.divide(180, sp.pi),
sp.arcsin(sp.divide(self.h, dist)))
pr_LOS = sp.divide(
1,
sp.add(
1,
sp.multiply(
atg_a, sp.exp(sp.multiply(-atg_b, sp.subtract(phi,
atg_a))))))
pr_NLOS = sp.subtract(1, pr_LOS)
total_loss = sp.add(
sp.multiply(pr_LOS, sp.power(dist, -pl_exp)),
sp.multiply(sp.multiply(pr_NLOS, gamma), sp.power(dist, -pl_exp)))
return total_loss
def feval(self, x, average=True):
'''I'm considering opt problem regarding parameters of each digit
independently i.e.., I have ten opt problems to solve.
loss_fn is an 10X1 matrix or vector'''
data = self.data.train
loss_fn = self.funcEval(x, data)
if average == True:
n_vals = sp.bincount(self.data.train[1]).astype(
float) #counts no of 1's 2's ..... in the dataset
loss_fn = sp.divide(loss_fn, sp.reshape(n_vals, sp.shape(loss_fn)))
return loss_fn
else:
return loss_fn
def sfeval(self, x, ndata=100, average=True):
'''slice the data, slice size is given by ndata.'''
low_no = sp.random.randint(0, high=50000 - ndata)
high_no = low_no + ndata
sli = slice(low_no, high_no)
data2 = []
data2.append(self.data.train[0][sli])
data2.append(self.data.train[1][sli])
loss_fn = self.funcEval(x, tuple(data2))
if average == True:
'''assuming that in this 100 numbers every digit happens atleast once'''
n_vals = sp.bincount(data2[1]).astype(float)
loss_fn = sp.divide(loss_fn, sp.reshape(n_vals, sp.shape(loss_fn)))
return loss_fn
else:
return loss_fn
def far_fields(radius, frequency, r, theta, phi):
"""
Calculate the electric and magnetic fields in the far field of the aperture.
:param r: The range to the field point (m).
:param theta: The theta angle to the field point (rad).
:param phi: The phi angle to the field point (rad).
:param radius: The radius of the aperture (m).
:param frequency: The operating frequency (Hz).
:return: The electric and magnetic fields radiated by the aperture (V/m), (A/m).
"""
# Calculate the wavenumber
k = 2.0 * pi * frequency / c
# Calculate the wave impedance
eta = sqrt(mu_0 / epsilon_0)
# Calculate the argument for the Bessel function
z = k * radius * sin(theta)
# Calculate the Bessel function
bessel_term = divide(jv(1, z), z, where=z != 0.0)
# Define the radial-component of the electric far field (V/m)
e_r = 0.0
# Define the theta-component of the electric far field (V/m)
e_theta = 1j * k * radius**2 * exp(
-1j * k * r) / r * sin(phi) * bessel_term
# Define the phi-component of the electric far field (V/m)
e_phi = 1j * k * radius**2 * exp(-1j * k * r) / r * cos(phi) * bessel_term
# Define the radial-component of the magnetic far field (A/m)
h_r = 0.0
# Define the theta-component of the magnetic far field (A/m)
h_theta = 1j * k * radius**2 * exp(
-1j * k * r) / r * -cos(theta) * cos(phi) / eta * bessel_term
# Define the phi-component of the magnetic far field (A/m)
h_phi = 1j * k * radius**2 * exp(
-1j * k * r) / r * sin(phi) / eta * bessel_term
# Return all six components of the far field
return e_r, e_theta, e_phi, h_r, h_theta, h_phi
def diffTaylor(v, i):
coeffs = polyfit(v, i, 3)
vFit = linspace(min(v), max(v), 100)
iFit = polyval(coeffs, vFit)
polynomial = poly1d(coeffs)
# Second order
didv = lambda ix: 3 * coeffs[0] * (
(ix)**2) + 2 * coeffs[1] * (ix) + coeffs[2]
# Fifth order
#didv = lambda ix:
# 6*coeffs[0]*((ix)**5) + 5*coeffs[1]*((ix)**4) + 4*coeffs[2]*((ix)**3) +
# 3*coeffs[3]*((ix)**2) + 2*coeffs[4]*(ix) + coeffs[5]
rFit = divide(1, [float(didv(val)) for val in vFit])
return vFit, iFit, rFit
def main():
wheel_graph = networkx.generators.classic.wheel_graph(10)
model = glove.Glove(2, learning_rate=0.01, alpha=0.2, max_count=1000)
adj_matrix = networkx.adjacency_matrix(wheel_graph)
adj_matrix = adj_matrix.toarray().astype('d')
normalized_adj_matrix = scipy.divide(adj_matrix,
adj_matrix.sum(1)[:, scipy.newaxis])
model.fit(scipy.sparse.coo_matrix(normalized_adj_matrix), epochs=1000)
vertex_positions = {
vertex_idx: tuple(model.word_vectors[vertex_idx])
for vertex_idx in range(wheel_graph.order())
}
networkx.drawing.draw(wheel_graph, pos=vertex_positions)
plt.savefig("asdf.png")
pass
def reflect(v, u, c):
print("Reflect by vector math:")
print("v:", v)
print("u:", u)
print("c:", c)
v_dot_u = scipy.dot(v, u)
print("v_dot_u:", v_dot_u)
v_dot_u_minus_c = scipy.subtract(v_dot_u, c)
print("v_dot_u_minus_c:", v_dot_u_minus_c)
u_dot_u = scipy.dot(u, u)
print("u_dot_u:", u_dot_u)
quotient = scipy.divide(v_dot_u_minus_c, u_dot_u)
print("quotient:", quotient)
subtrahend = scipy.multiply(u, (2 * quotient))
print("subtrahend:", subtrahend)
reflection = scipy.subtract(v, subtrahend)
print("reflection:", reflection)
return reflection
def build_W(self, N_x, sparsity_tuples, scaling_W):
# N_x integer
# sparsity between 0 and 1 inclusive
# scaling_W >= 1
sparsity_tuples_list = tuple([(a_row[0], a_row[1])
for a_row in sparsity_tuples])
if os.path.isfile('./W_(adjacency)/W_' + str(N_x) + '_' + str(N_x) +
'_' + str(sparsity_tuples_list) + '.txt'):
print("Loading W")
# If file already exists
W = sp.loadtxt('./W_(adjacency)/W_' + str(N_x) + '_' + str(N_x) +
'_' + str(sparsity_tuples_list) + '.txt')
else:
# If file doesn't yet exist
# No notion of locality here
# Designate connection or no connection at each element of the (N_x) by (N_x) matrix:
W_sparsity_list = []
# Rows used for each sparsity
rows_used_for_sparsity = (sp.around(
sp.multiply(sparsity_tuples[:, 1], N_x))).astype(int)
for i, sparsity_pair in enumerate(sparsity_tuples):
this_density = sparsity_pair[0]
W_sparsity_list.append(
sp.sparse.random(rows_used_for_sparsity[i],
N_x,
density=this_density).todense())
#TODO: Make sure there are no 'holes!' in W
# Build sparse adjacency matrix W:
W_unnormalized = sp.multiply(
sp.random.choice((-1, 1), size=(N_x, N_x)),
sp.vstack(W_sparsity_list))
# Normalize by largest eigenvalue and additional scaling factor
# to control decrease of spectral radius.
spectral_radius = sp.amax(abs(sp.linalg.eigvals(W_unnormalized)))
print("SPECTRAL RADIUS IS IS " + str(spectral_radius))
W = sp.multiply(scaling_W,
sp.divide(W_unnormalized, spectral_radius))
sp.savetxt('W_(adjacency)/W_' + str(N_x) + '_' + str(N_x) + '_' +
str(sparsity_tuples_list) + '.txt',
W,
fmt='%.4f')
return W
def load_graph_adj_matrix():
adj_list_in_ids = {}
tag_name_to_idx = {}
with open('graph.csv') as graph_file:
graph_reader = csv.DictReader(graph_file)
tag_names = set()
for row in graph_reader:
tag_name_1 = row['tag1']
tag_name_2 = row['tag2']
post_count = int(row['post_count'])
tag_names.add(tag_name_1)
tag_names.add(tag_name_2)
try:
adj_list_in_ids[tag_name_1].append((tag_name_2, post_count))
except KeyError:
adj_list_in_ids[tag_name_1] = [(tag_name_2, post_count)]
tag_name_to_idx = {
tag_name: idx
for idx, tag_name in enumerate(sorted(tag_names))
}
# initialize empty matrix
tags_count = len(adj_list_in_ids)
adj_matrix = scipy.zeros((tags_count, tags_count))
for tag_name, adj_row in adj_list_in_ids.items():
tag_namex = tag_name_to_idx[tag_name]
for adj_tag, post_count in adj_row:
adj_tag_namex = tag_name_to_idx[adj_tag]
adj_matrix[tag_namex, adj_tag_namex] = post_count
adj_matrix[adj_tag_namex, tag_namex] = post_count
# normalization
normalized_adj_matrix = scipy.divide(adj_matrix,
adj_matrix.sum(1)[:, scipy.newaxis])
#ordered_by_idx_tag_names = sorted(tag_name_to_idx.keys(), key=lambda tag_name: tag_name_to_idx[tag_name])
return scipy.sparse.coo_matrix(normalized_adj_matrix), tag_name_to_idx
def CalcBodesFromDataset(tddict, bodelist, description='', \
truncfreq=100, filto=2, wn=0.1,\
avefilt=True, jump=250):
# pdb.set_trace()
bodedict={}
bodedict['description']=description
tempfreq=makefreqvect(tddict['t'])
co=thresh_py(tempfreq,truncfreq)
bodedict['freq']=tempfreq[0:co]
bodedict['xname']='freq'
bodedict['bodes']=[]
avedict=copy.deepcopy(bodedict)
N=len(tddict['t'])
fncopy=tddict['filenames']
fnout=[]
for fn in fncopy:
folder,name=os.path.split(fn)
fnout.append(name)
bodedict['filenames']=fnout
avedict['filenames']=fnout
for i, curbode in enumerate(bodelist):
outbode=copy.deepcopy(curbode)
outbode.labels=bodedict['filenames']
curavebode=copy.deepcopy(curbode)
curavebode.averaged=True
curavebode.labels=outbode.labels
curin_t=tddict[curbode.input]
curout_t=tddict[curbode.output]
t1=time.time()
curin_fft=fft(curin_t,None,0)*2/N
curout_fft=fft(curout_t,None,0)*2/N
t2=time.time()
print('fft time='+str(t2-t1))
curin_fft=curin_fft[0:co]
curout_fft=curout_fft[0:co]
curGxx=norm2(curin_fft)
curGyy=norm2(curout_fft)
curGxy=scipy.multiply(scipy.conj(curin_fft),curout_fft)
H=scipy.divide(curGxy,curGxx)
Hmag=abs(H)
outbode.mag=Hmag
Gxyave=scipy.mean(curGxy,1)
Gxxave=scipy.mean(curGxx,1)
Gyyave=scipy.mean(curGyy,1)
cohnum=norm2(Gxyave)
cohden=scipy.multiply(Gxxave,Gyyave)
curavebode.coh=scipy.divide(cohnum,cohden)
Have=scipy.divide(Gxyave,Gxxave)
curavebode.mag=abs(Have)
Hphase=mat_atan2(scipy.imag(H),scipy.real(H))
Hphase_ave=mat_atan2(scipy.imag(Have),scipy.real(Have))
Hphase=Hphase*180/scipy.pi
Hphase_ave=Hphase_ave*180/scipy.pi
if curbode.seedfreq and curbode.seedphase:
# print('Massaging the phase')
Hphase=PhaseMassage(Hphase,bodedict['freq'],curbode.seedfreq,curbode.seedphase)
Hphase_ave=PhaseMassage(Hphase_ave,avedict['freq'],curbode.seedfreq,curbode.seedphase)
if avefilt:
Hphase=PhaseMassageFilter(Hphase,filto,wn,jump)
Hphase_ave=PhaseMassageFilter(Hphase_ave,filto,wn,jump)
# Hphase=AveMessage(Hphase,bodedict['freq'],curbode.seedfreq,curbode.seedphase,280.0,5)
# Hphase_ave=AveMessage(Hphase_ave,avedict['freq'],curbode.seedfreq,curbode.seedphase,280.0,5)
outbode.phase=Hphase
curavebode.phase=Hphase_ave
bodedict['bodes'].append(outbode)
avedict['bodes'].append(curavebode)
return bodedict,avedict
def findColorRegions(picture, res):
print "Counting Color Regions:", os.path.basename(picture) , '(', res, ')...',
struct = np.array([[0,1,0],
[1,1,1],
[0,1,0]])
##open image
im = Image.open(picture)
#im.show()
im = im.convert("L")
xsize, ysize = im.size
if (xsize*res < 60) or (ysize*res < 60):
print "Image to small for given resolution..."
res = 60.0 / min([xsize, ysize])
print "New resolution for this image:", res
im = im.resize((xsize*res, ysize*res),Image.ANTIALIAS)
xsize, ysize = im.size
im = fromimage(im)
im = scipy.transpose(im)
##reduce colors
im = scipy.divide(im, 10)
im = im *10
##make markers
mark = 0
markers = np.zeros_like(im).astype('int')
pd = 0
opd = 0
for x in range(xsize):
pd = int(x/xsize*.5)
if pd > opd: print '.',
opd = pd
for y in range(ysize):
if (x%(int(xsize/30)) == 0) and (y%(int(ysize/30)) == 0):
mark += 1
markers[x,y] = mark
##run watershed
water = ndimage.watershed_ift(im.astype('uint8'), markers, structure = struct)
##make some masks and count the size of each region
sizecount = []
marks = range(mark+1)
for index in range(len(marks)):
sizecount.append([])
pd = 0
opd = 0
for x in range(0,xsize):
for y in range(0,ysize):
sizecount[marks.index(water[x,y])].append((x,y))
##make markers based on large regions
mark = 0
shapes = 0
markers = np.zeros_like(im).astype('int')
for mark in marks:
if len(sizecount[marks.index(mark)]) >= (xsize/30 + ysize/30)/2: #should be a better ratio
shapes += 1
print shapes
return shapes
def waterPanelize(picture):
print "Water Panalizing:", os.path.basename(picture)
struct = np.array([[0,1,0],
[1,1,1],
[0,1,0]])
##open image
im = Image.open(picture)
imcopy = im
#im.show()
im = im.convert("L")
xsize, ysize = im.size
#prescaling
im = im.resize((xsize*ops.scaling, ysize*ops.scaling))
xsize, ysize = im.size
print "xSize:", xsize, "ySize:", ysize
print '!'
##reduce colors
im = scipy.divide(im, 30)
im = im *30
#transpose for scipy
im = scipy.transpose(im)
print "im shape:", im.shape
##make markers
mark = 0
markers = np.zeros_like(im).astype('int')
for x in range(xsize):
for y in range(ysize):
if (x%(ops.markRes) == 0) and (y%(ops.markRes) == 0):
mark += 1
markers[x,y] = mark
##run watershed
water = ndimage.watershed_ift(im.astype('uint8'), markers, structure = struct)
#water[xm, ym] = water[xm-1, ym-1] # remove the isolate seeds
#make diff mask for 'gutter'
bgwc = water[1,1] ##assumes that (1,1) is part of the gutter
blackbg = np.zeros_like(im).astype('uint8')
for x in range(xsize):
for y in range(ysize):
if not (water[x,y] == bgwc):
blackbg[x,y] = im[x,y]
#subtract balck bg mask
im = im - blackbg
##run watershed
water = ndimage.watershed_ift(im.astype('uint8'), markers, structure = struct)
##make some masks and count the size of each region
sizecount = []
masks = []
marks = range(mark+1)
for index in range(len(marks)):
sizecount.append(0)
masks.append([])
for x in range(0,xsize,ops.res):
print int(float(x)/xsize*100), '%'
for y in range(0,ysize,ops.res):
sizecount[marks.index(water[x,y])] += 1
masks[marks.index(water[x,y])].append((x,y))
##make markers based on large regions
mark = 0
markers = np.zeros_like(im).astype('int')
for mark in marks:
if sizecount[marks.index(mark)] >= 200*200/ops.res/ops.res*ops.scaling:
markers[masks[marks.index(mark)][int(200*200/ops.res/ops.res*ops.scaling)]] = mark
print 'panel found'
##run watershed
water = ndimage.watershed_ift(im.astype('uint8'), markers, structure = struct)
##retranspose and postscale
water = scipy.transpose(water)
water = water/ops.scaling
##save and view
if ops.view: toimage(water).resize((xsize/2,ysize/2)).show()
if ops.save:
print (os.path.join(ops.outDir,os.path.basename(picture)+'_mask.jpg'), "JPEG")
toimage(water).convert('RGB').save(os.path.join(ops.outDir,os.path.basename(picture)+'_mask.jpg'), "JPEG")
return os.path.join(ops.outDir,os.path.basename(picture)+'_mask.jpg'), "JPEG"
def findShapes(picture, res):
print "Counting Shapes:", os.path.basename(picture), '(', res, ')...',
struct = np.array([[0,1,0],
[1,1,1],
[0,1,0]])
##open image
im = Image.open(picture)
#im.show()
im = im.convert("L")
xsize, ysize = im.size
if (xsize*res < 60) or (ysize*res < 60):
print "Image to small for given resolution..."
res = 60.0 / min([xsize, ysize])
print "New resolution for this image:", res
im = im.resize((xsize*res, ysize*res), Image.ANTIALIAS)
xsize, ysize = im.size
im = im.filter(ImageFilter.FIND_EDGES)
im = fromimage(im)
im = scipy.transpose(im)
im = scipy.divide(im, 10)
im = im *10
##make markers
mark = 0
markers = np.zeros_like(im).astype('int')
for x in range(xsize):
for y in range(ysize):
if (x%(int(xsize/30)) == 0) and (y%(int(ysize/30)) == 0):
mark += 1
markers[x,y] = mark
##run watershed
water = ndimage.watershed_ift(im.astype('uint8'), markers, structure = struct)
#toimage(water).save("sw"+ os.path.basename(picture)) #debug output
##make some masks and count the size of each region
sizecount = []
marks = range(mark+1)
for index in range(len(marks)):
sizecount.append(0)
for x in range(0,xsize):
for y in range(0,ysize):
sizecount[marks.index(water[x,y])] += 1
##make markers based on large regions
mark = 0
shapes = 0
markers = np.zeros_like(im).astype('int')
for mark in marks:
if sizecount[marks.index(mark)] >= (xsize/30 + ysize/30)/2:
shapes += 1
print shapes
return shapes
def greentensor(Freq,EpsB,Cell,NX,NY,NZ):
"""Returns the Fourier transform GF of the
circular extension of the Green's tensor array
"""
c0=299792458.0 # speed of light in vacuum
Mu0=4.0*sci.pi*1.0e-7 # vacuum permeability
Eps0=1.0/(Mu0*c0*c0) # vacuum permittivity
Omega=2.0*sci.pi*Freq
EtaB=-1.0j*Omega*Eps0*EpsB
ZetaB=-1.0j*Omega*Mu0
KB=Omega*sci.sqrt(Eps0*EpsB*Mu0)
G=sci.zeros((NX,NY,NZ,3,3),complex)
GC=sci.zeros((NX*2,NY*2,NZ*2,3,3),complex)
GF=sci.zeros((NX*2,NY*2,NZ*2,3,3),complex)
# 3D arrays of x,y,z coordinates
xx,yy,zz=sci.mgrid[0:NX*Cell:Cell,0:NY*Cell:Cell,0:NZ*Cell:Cell]
dd=sci.zeros((NX,NY,NZ),complex)
alpha=sci.zeros((NX,NY,NZ),complex)
beta=sci.zeros((NX,NY,NZ),complex)
Q11=sci.zeros((NX,NY,NZ),complex)
Q12=sci.zeros((NX,NY,NZ),complex)
Q13=sci.zeros((NX,NY,NZ),complex)
Q21=sci.zeros((NX,NY,NZ),complex)
Q22=sci.zeros((NX,NY,NZ),complex)
Q23=sci.zeros((NX,NY,NZ),complex)
Q31=sci.zeros((NX,NY,NZ),complex)
Q32=sci.zeros((NX,NY,NZ),complex)
Q33=sci.zeros((NX,NY,NZ),complex)
# 3D arrays of distances
dd=sci.sqrt((xx)**2+(yy)**2+(zz)**2)
dd2=dd*dd
# 3D arrays of components of the Q-matrix
Q11=sci.divide(xx*xx,dd2)
Q12=sci.divide(xx*yy,dd2)
Q13=sci.divide(xx*zz,dd2)
Q21=Q12
Q22=sci.divide(yy*yy,dd2)
Q23=sci.divide(yy*zz,dd2)
Q31=Q13
Q32=Q23
Q33=sci.divide(zz*zz,dd2)
# alpha and beta scalar multipliers
alpha=sci.divide(sci.exp(1.0j*KB*dd),4.0*sci.pi*dd)*\
(-KB**2.0 - sci.divide(1.0j*3.0*KB,dd) + sci.divide(3.0,dd2))
beta=sci.divide(sci.exp(1.0j*KB*dd),4.0*sci.pi*dd)*\
(KB**2.0 + sci.divide(1.0j*KB,dd) - sci.divide(1.0,dd2))
print('All divisions by zero are done')
# Green's tensor without self-patch
G[:,:,:,0,0]=Q11*alpha+beta
G[:,:,:,0,1]=Q12*alpha
G[:,:,:,0,2]=Q13*alpha
G[:,:,:,1,0]=Q21*alpha
G[:,:,:,1,1]=Q22*alpha+beta
G[:,:,:,1,2]=Q23*alpha
G[:,:,:,2,0]=Q31*alpha
G[:,:,:,2,1]=Q32*alpha
G[:,:,:,2,2]=Q33*alpha+beta
G=G*(Cell**3) # multiplying by the elementary volume
# self-patch
G[0,0,0,0,0]=(2./3.)*(1.-1.j*KB*Cell*((3./(4.*sci.pi))**(1./3.)))*\
sci.exp(1.j*KB*Cell*((3./(4.*sci.pi))**(1./3.)))-1.0
G[0,0,0,0,1]=0.
G[0,0,0,0,2]=0.
G[0,0,0,1,0]=0.
G[0,0,0,1,1]=G[0,0,0,0,0]
G[0,0,0,1,2]=0.
G[0,0,0,2,0]=0.
G[0,0,0,2,1]=0.
G[0,0,0,2,2]=G[0,0,0,0,0]
#Circular extension of G
GC[0:NX,0:NY,0:NZ,:,:]=G
DeltaOp=sci.eye(3,3)
s=0
while s<=2:
ss=0
while ss<=2:
GC[NX+1:,0:NY,0:NZ,s,ss]=(1-2*DeltaOp[0,s])*(1-2*DeltaOp[0,ss])*G[:0:-1,:,:,s,ss]
GC[NX+1:,NY+1:,0:NZ,s,ss]=(1-2*DeltaOp[0,s])*(1-2*DeltaOp[0,ss])*\
(1-2*DeltaOp[1,s])*(1-2*DeltaOp[1,ss])*G[:0:-1,:0:-1,:,s,ss]
GC[NX+1:,NY+1:,NZ+1:,s,ss]=(1-2*DeltaOp[0,s])*(1-2*DeltaOp[0,ss])*\
(1-2*DeltaOp[1,s])*(1-2*DeltaOp[1,ss])*\
(1-2*DeltaOp[2,s])*(1-2*DeltaOp[2,ss])*G[:0:-1,:0:-1,:0:-1,s,ss]
GC[0:NX,NY+1:,0:NZ,s,ss]=(1-2*DeltaOp[1,s])*(1-2*DeltaOp[1,ss])*G[:,:0:-1,:,s,ss]
GC[0:NX,NY+1:,NZ+1:,s,ss]=(1-2*DeltaOp[1,s])*(1-2*DeltaOp[1,ss])*\
(1-2*DeltaOp[2,s])*(1-2*DeltaOp[2,ss])*G[:,:0:-1,:0:-1,s,ss]
GC[0:NX,0:NY,NZ+1:,s,ss]=(1-2*DeltaOp[2,s])*(1-2*DeltaOp[2,ss])*G[:,:,:0:-1,s,ss]
GC[NX+1:,0:NY,NZ+1:,s,ss]=(1-2*DeltaOp[0,s])*(1-2*DeltaOp[0,ss])*\
(1-2*DeltaOp[2,s])*(1-2*DeltaOp[2,ss])*G[:0:-1,:,:0:-1,s,ss]
ss=ss+1
s=s+1
# FFT of the Green's tensor array
s=0
while s<=2:
ss=0
while ss<=2:
GF[:,:,:,s,ss]=fft.fftn(sci.squeeze(GC[:,:,:,s,ss]))
ss=ss+1
s=s+1
return GF
def SingleReceiver(E,EpsArr,Freq,EpsB,Cell,NX,NY,NZ,Xr,Yr,Zr):
"""Returns the scattered field 3-vector Esc
at the location of the receiver (Xr,Yr,Zr)
"""
c0 = 299792458.0 # speed of light in vacuum
Mu0 = 4.0*sci.pi*1.0e-7 # vacuum permeability
Eps0 = 1.0/(Mu0*c0*c0) # vacuum permittivity
Omega = 2.0*sci.pi*Freq
EtaB = -1.0j*Omega*Eps0*EpsB
ZetaB = -1.0j*Omega*Mu0
KB = Omega*sci.sqrt(Eps0*EpsB*Mu0)
Esc = sci.zeros(3,complex)
J = sci.zeros((NX,NY,NZ,3),complex)
for s in range(3):
J[0:NX,0:NY,0:NZ,s]=E[0:NX,0:NY,0:NZ,s]*(EpsArr[0:NX,0:NY,0:NZ]-1.0)
G = sci.zeros((NX,NY,NZ,3,3),complex)
# 3D arrays of x,y,z coordinates
xx,yy,zz = sci.mgrid[0:NX*Cell:Cell,0:NY*Cell:Cell,0:NZ*Cell:Cell]
dd = sci.zeros((NX,NY,NZ),complex)
alpha = sci.zeros((NX,NY,NZ),complex)
beta = sci.zeros((NX,NY,NZ),complex)
Q11 = sci.zeros((NX,NY,NZ),complex)
Q12 = sci.zeros((NX,NY,NZ),complex)
Q13 = sci.zeros((NX,NY,NZ),complex)
Q21 = sci.zeros((NX,NY,NZ),complex)
Q22 = sci.zeros((NX,NY,NZ),complex)
Q23 = sci.zeros((NX,NY,NZ),complex)
Q31 = sci.zeros((NX,NY,NZ),complex)
Q32 = sci.zeros((NX,NY,NZ),complex)
Q33 = sci.zeros((NX,NY,NZ),complex)
# 3D arrays of distances
dd = sci.sqrt((Xr-xx)**2+(Yr-yy)**2+(Zr-zz)**2)
dd2 = dd*dd
# 3D arrays of components of the Q-matrix
Q11 = sci.divide((Xr-xx)*(Xr-xx),dd2)
Q12 = sci.divide((Xr-xx)*(Yr-yy),dd2)
Q13 = sci.divide((Xr-xx)*(Zr-zz),dd2)
Q21 = Q12
Q22 = sci.divide((Yr-yy)*(Yr-yy),dd2)
Q23 = sci.divide((Yr-yy)*(Zr-zz),dd2)
Q31 = Q13
Q32 = Q23
Q33 = sci.divide((Zr-zz)*(Zr-zz),dd2)
# alpha and beta scalar multipliers
alpha = sci.divide(sci.exp(1.0j*KB*dd),4.0*sci.pi*dd)*\
(-KB**2.0 - sci.divide(1.0j*3.0*KB,dd) + sci.divide(3.0,dd2))
beta = sci.divide(sci.exp(1.0j*KB*dd),4.0*sci.pi*dd)*\
(KB**2.0 + sci.divide(1.0j*KB,dd) - sci.divide(1.0,dd2))
# Green's tensor
G[:,:,:,0,0] = Q11*alpha+beta
G[:,:,:,0,1] = Q12*alpha
G[:,:,:,0,2] = Q13*alpha
G[:,:,:,1,0] = Q21*alpha
G[:,:,:,1,1] = Q22*alpha+beta
G[:,:,:,1,2] = Q23*alpha
G[:,:,:,2,0] = Q31*alpha
G[:,:,:,2,1] = Q32*alpha
G[:,:,:,2,2] = Q33*alpha+beta
G = G*(Cell**3) # multiplying by the elementary volume
Esc[0] = sci.sum(sci.squeeze(sci.multiply(G[:,:,:,0,0],J[:,:,:,0])+\
sci.multiply(G[:,:,:,0,1],J[:,:,:,1])+\
sci.multiply(G[:,:,:,0,2],J[:,:,:,2])))
Esc[1] = sci.sum(sci.squeeze(sci.multiply(G[:,:,:,1,0],J[:,:,:,0])+\
sci.multiply(G[:,:,:,1,1],J[:,:,:,1])+\
sci.multiply(G[:,:,:,1,2],J[:,:,:,2])))
Esc[2] = sci.sum(sci.squeeze(sci.multiply(G[:,:,:,2,0],J[:,:,:,0])+\
sci.multiply(G[:,:,:,2,1],J[:,:,:,1])+\
sci.multiply(G[:,:,:,2,2],J[:,:,:,2])))
return Esc