def set_K(self, fx=1, fy=1, cx=0, cy=0):
# K is the 3x3 Camera matrix
# fx, fy are focal lenghts expressed in pixel units
# cx, cy is a principal point usually at image center
self.fx = fx
self.fy = fy
self.cx = cx
self.cy = cy
self.K = np.mat([[fx, 0, cx], [0, fy, cy], [0, 0, 1.]],
dtype=np.float32)
self.set_P()
def ensemble_transfer_matrix_pi_half(NAtoms, g1d, gprime, gm, Delta1, Deltap,
Omega):
"""
NAtoms: The number of atoms
g1d: \Gamma_{1D}, the decay rate into the guided mode
gprime: \Gamma', the decay rate into all the other modes
gm: \Gamma_m, the decay rate from the meta-stable state
Delta1: The detuning of the carrier frequency \omega_L of the
quantum field from the atomic transition frequency \omega_{ab}.
Delta1 = \omega_L - \omega_{ab}
Deltap: The detuning of the classical drive frequency \omega_p from
the transition bc. Deltap = \omega_p - \omega_{bc}
"""
kd = 0.5 * np.pi
Mf = np.mat([[np.exp(1j * kd), 0], [0, np.exp(-1j * kd)]])
beta3 = Lambda_type_minus_r_over_t(g1d, gprime, gm, Delta1, Deltap, Omega)
M3 = np.mat([[1 - beta3, -beta3], [beta3, 1 + beta3]])
beta2 = two_level_minus_r_over_t(g1d, gprime, Delta1)
M2 = np.mat([[1 - beta2, -beta2], [beta2, 1 + beta2]])
Mcell = Mf * M2 * Mf * M3
NCells = NAtoms / 2
#diag, V = np.linalg.eig(Mcell)
#DN = np.diag(diag**(NCells))
#V_inv = np.linalg.inv(V)
#return V*DN*V_inv
theta = np.arccos(0.5 * np.trace(Mcell))
Id = np.mat([[1, 0], [0, 1]])
Mensemble\
= np.mat([[np.cos(NCells*theta)+1j*1j*np.sin(NCells*theta)/np.sin(theta)*(Mcell[1,1]-Mcell[0,0])/2,
-1j*1j*np.sin(NCells*theta)/np.sin(theta)*Mcell[0,1]],
[-1j*1j*np.sin(NCells*theta)/np.sin(theta)*Mcell[1,0],
np.cos(NCells*theta)-1j*1j*np.sin(NCells*theta)/np.sin(theta)*(Mcell[1,1]-Mcell[0,0])/2]])
return Mensemble
def set_R_axisAngle(self, x, y, z, alpha):
""" Creates a 3D [R|t] matrix for rotation
around the axis of the vector defined by (x,y,z)
and an alpha angle."""
#Normalize the rotation axis a
a = np.array([x, y, z])
a = a / np.linalg.norm(a)
#Build the skew symetric
a_skew = np.mat([[0, -a[2], a[1]], [a[2], 0, -a[0]], [-a[1], a[0], 0]])
R = np.eye(4)
R[:3, :3] = expm(a_skew * alpha)
self.R = R
self.update_Rt()
def ensemble_transfer_matrix(NAtoms, kd, g1d, gprime, gm, Delta1, Deltap,
Omega):
"""
NAtoms: The number of atoms
kd: The product of the wavevector k of the input quantum field
(and also approximately the wavevector of the classical drive)
and the distance between the atoms d. For example kd=pi means
that atoms are situated half a wavelength apart.
g1d: \Gamma_{1D}, the decay rate into the guided mode
gprime: \Gamma', the decay rate into all the other modes
gm: \Gamma_m, the decay rate from the meta-stable state
Delta1: The detuning of the carrier frequency \omega_L of the
quantum field from the atomic transition frequency \omega_{ab}.
Delta1 = \omega_L - \omega_{ab}
Deltap: The detuning of the classical drive frequency \omega_p from
the transition bc. Deltap = \omega_p - \omega_{bc}
"""
Mf = np.mat([[np.exp(1j * kd), 0], [0, np.exp(-1j * kd)]])
MensembleStandingWave = np.mat([[1, 0], [0, 1]])
xiConstant = Lambda_type_minus_r_over_t(g1d, gprime, gm, Delta1, Deltap,
Omega)
for n in range(NAtoms):
#This corresponds the the classical drive having the same
#frequency as the quantum transition. Thus the intensity
#of the classical drive oscillates with lambda/2
OmegaStandingWave = Omega * np.cos(kd * n)
xiStandingWave = Lambda_type_minus_r_over_t(g1d, gprime, gm, Delta1,
Deltap, OmegaStandingWave)
#Fill in the scattering matrices for the current atom
MatomStandingWave = np.mat([[1 - xiStandingWave, -xiStandingWave],
[xiStandingWave, 1 + xiStandingWave]])
#Multiply the scattering and free propagation matrices
#onto the ensemble matrices
MensembleStandingWave = Mf * MatomStandingWave * MensembleStandingWave
return MensembleStandingWave
def update_conic_matrix(self):
xo = self.center[0]
yo = self.center[1]
r = self.r
self.Aq = np.mat([[1, 0, -xo], [0, 1, -yo],
[-xo, -yo, xo**2 + yo**2 - r**2]])
self.a = self.Aq[0, 0]
self.c = self.Aq[1, 1]
self.f = self.Aq[2, 2]
self.b = self.Aq[0, 1] * 2.
self.d = self.Aq[0, 2] * 2.
self.e = self.Aq[1, 2] * 2.
return self.Aq
def impurity_unit_cell_pi_half(g1d, gprime, gm, Delta1, Deltap, Omega):
"""
NAtoms: The number of atoms
g1d: \Gamma_{1D}, the decay rate into the guided mode
gprime: \Gamma', the decay rate into all the other modes
gm: \Gamma_m, the decay rate from the meta-stable state
Delta1: The detuning of the carrier frequency \omega_L of the
quantum field from the atomic transition frequency \omega_{ab}.
Delta1 = \omega_L - \omega_{ab}
Deltap: The detuning of the classical drive frequency \omega_p from
the transition bc. Deltap = \omega_p - \omega_{bc}
"""
kd = 0.5 * np.pi
Mf = np.mat([[np.exp(1j * kd), 0], [0, np.exp(-1j * kd)]])
beta2_imp = two_level_minus_r_over_t(g1d, gprime, 0)
M2_imp = np.mat([[1 - beta2_imp, -beta2_imp], [beta2_imp, 1 + beta2_imp]])
beta2 = two_level_minus_r_over_t(g1d, gprime, Delta1)
M2 = np.mat([[1 - beta2, -beta2], [beta2, 1 + beta2]])
M_impurity_cell = Mf * M2 * Mf * M2_imp
return M_impurity_cell
def project(self, H):
H = np.mat(H)
Hinv = np.linalg.inv(H)
Q = (Hinv.T) * self.Aq * Hinv
projected_circle = Ellipse()
projected_circle.a = Q[0, 0]
projected_circle.c = Q[1, 1]
projected_circle.f = Q[2, 2]
projected_circle.b = Q[0, 1] * 2.
projected_circle.d = Q[0, 2] * 2.
projected_circle.e = Q[1, 2] * 2.
projected_circle.Aq = Q
projected_circle.r = self.r
return projected_circle
loss_temp_2_p = loss_temp_2_p + temp
loss_temp_2_q = -1.0 * n / 2 * np.log(2 * np.pi) - 1.0 / 2 * np.log(
np.linalg.det(np.dot(L_temp, np.transpose(
L_temp)))) - 1.0 / 2 * np.dot(np.transpose(epsilon), epsilon)
loss_temp = loss_temp_1 + loss_temp_2_p - loss_temp_2_q
return loss_temp
# load data
data = scio.loadmat(
"/Users/yawei/Documents/MATLAB/simulation based algorithm test library/simulation_based_machine_learning_library/dataset/heart/test_heart.mat"
)
data = data['yy']
label = data[:, 0]
[n, d] = np.shape(data)
training_data = np.mat(data[:, 1:d])
[n, d] = np.shape(training_data)
# initialize parameters
T = 10
alpha_0 = 1e-5 # learning rate for the primal update
beta_0 = 1e-5 # learning rate for the dual update
theta_sum_old = np.mat(np.zeros((n + n * n, 1)))
loss = np.mat(np.zeros((T, 1)))
theta = np.mat(np.ones((n + n * n, 1))) # primal variable, mu + L
y = np.mat(np.ones((2, 1))) # dual variable
pair_dist = np.mat(np.zeros((n * n, 1)))
for i in range(1, n):
for j in range(1, n):
if i == j:
continue
def project(self,H): H = np.mat(H) Hinv = np.linalg.inv(H) self.Q = (Hinv.T)*self.Aq*Hinv return Q
def update_conic_matrix(self):
self.Aq = np.mat([[self.a, self.b / 2., self.d / 2.],
[self.b / 2., self.c, self.e / 2.],
[self.d / 2., self.e / 2., self.f]])