def initialize_f(q1, q2, v1, v2, v3, params):
m_e = params.mass[0, 0]
m_p = params.mass[0, 1]
k = params.boltzmann_constant
n_b = params.density_background
T_b = params.temperature_background
k = params.boltzmann_constant
v1_bulk_electron = params.v1_bulk_electron
v1_bulk_positron = params.v1_bulk_positron
n = n_b + 0.01 * af.exp(-10 * (q1 - 5)**2)
f_e = n * (m_e / (2 * np.pi * k * T_b))**(1 / 2) \
* af.exp(-m_e * (v1[:, 0] - v1_bulk_electron)**2 / (2 * k * T_b)) \
f_p = n * (m_p / (2 * np.pi * k * T_b))**(1 / 2) \
* af.exp(-m_p * (v1[:, 1] - v1_bulk_positron)**2 / (2 * k * T_b)) \
f = af.join(1, f_e, f_p)
af.eval(f)
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
m_e = params.mass[0, 0]
m_i = params.mass[0, 1]
k = params.boltzmann_constant
n_b_e = params.n_background_e
T_b_e = params.temperature_background_e
n_b_i = params.n_background_i
T_b_i = params.temperature_background_i
n_e = n_b_e + params.alpha * af.cos(q1)
n_i = n_b_i + 0 * q1
T_e = T_b_e
T_i = T_b_i
f_e = n_e * np.sqrt(1 / (2 * np.pi)) * af.sqrt(m_e * T_i/m_i * T_e) \
* af.exp(-0.5 * (m_e * T_i/m_i * T_e) * (v1[:, 0])**2)
f_i = n_i * np.sqrt(1 / (2 * np.pi)) \
* af.exp(-0.5 * (v1[:, 1])**2)
f = af.join(1, f_e, f_i)
af.eval(f)
return (f)
def initialize_f(q1, q2, p1, p2, p3, params):
m = params.mass_particle
k = params.boltzmann_constant
rho_b = params.rho_background
T_b = params.temperature_background
p1_bulk = params.p1_bulk_background
p2_bulk = params.p2_bulk_background
p3_bulk = params.p3_bulk_background
pert_real = params.pert_real
pert_imag = params.pert_imag
k_q1 = params.k_q1
k_q2 = params.k_q2
# Calculating the perturbed density:
rho = rho_b + (pert_real * af.cos(k_q1 * q1 + k_q2 * q2) -
pert_imag * af.sin(k_q1 * q1 + k_q2 * q2))
f = rho * (m / (2 * np.pi * k * T_b))**(3 / 2) \
* af.exp(-m * (p1 - p1_bulk)**2 / (2 * k * T_b)) \
* af.exp(-m * (p2 - p2_bulk)**2 / (2 * k * T_b)) \
* af.exp(-m * (p3 - p3_bulk)**2 / (2 * k * T_b))
af.eval(f)
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
m = params.mass
k = params.boltzmann_constant
q2_minus = 0.5
q2_plus = 1.5
regulator = 20 # larger value makes the transition sharper
n = 1 + 0.5 * (af.tanh((q2 - q2_minus) * regulator) - af.tanh(
(q2 - q2_plus) * regulator))
v1_bulk = (af.tanh((q2 - q2_minus) * regulator) - af.tanh(
(q2 - q2_plus) * regulator) - 1)
v2_bulk = 0.01 * af.sin(2 * np.pi * q1) *\
( af.exp(-25 * (q2 - q2_minus)**2)
+ af.exp(-25 * (q2 - q2_plus )**2)
)
T = (10 / n)
f = n * (m / (2 * np.pi * k * T)) \
* af.exp(-m * (v1 - v1_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (v2 - v2_bulk)**2 / (2 * k * T))
af.eval(f)
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
m = params.mass
k = params.boltzmann_constant
n = af.select(af.abs(q2)>0.25, q1**0, 2)
# Random Numbers under to seed the instability:
seeding_velocities = 0.01 * (af.randu(1, 1, q1.shape[2], q1.shape[3],
dtype = af.Dtype.f64
) - 0.5
)
v1_bulk = af.select(af.abs(q2)>0.25,
-0.5 - seeding_velocities,
+0.5 + seeding_velocities
)
v2_bulk = seeding_velocities
T = (2.5 / n)
f = n * (m / (2 * np.pi * k * T))**(3 / 2) \
* af.exp(-m * (v1 - v1_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (v2 - v2_bulk)**2 / (2 * k * T)) \
* af.exp(-m * v3**2 / (2 * k * T))
af.eval(f)
return (f)
def initialize_f(q1, q2, p1, p2, p3, params):
m = params.mass
k = params.boltzmann_constant
q2_minus = 0.5
q2_plus = 1.5
regulator = 20 # larger value makes the transition sharper
rho = 1 + 0.5 * ( af.tanh(( q2 - q2_minus)*regulator)
- af.tanh(( q2 - q2_plus )*regulator)
)
p1_bulk = ( af.tanh(( q2 - q2_minus)*regulator)
- af.tanh(( q2 - q2_plus )*regulator) - 1
)
p2_bulk = 0.5 * af.sin(2*np.pi*q1) *\
( af.exp(-25 * (q2 - q2_minus)**2)
+ af.exp(-25 * (q2 - q2_plus )**2)
)
T = (10 / rho)
f = rho * (m / (2 * np.pi * k * T))**(3 / 2) \
* af.exp(-m * (p1 - p1_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (p2 - p2_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (p3)**2 / (2 * k * T))
af.eval(f)
return (f)
def initialize_f(q1, q2, p1, p2, p3, params):
m = params.mass_particle
k = params.boltzmann_constant
pert_real = params.pert_real
pert_imag = params.pert_imag
k_q1 = params.k_q1
k_q2 = params.k_q2
# Calculating the perturbed density:
rho = 1 + (pert_real * af.cos(k_q1 * q1 + k_q2 * q2) -
pert_imag * af.sin(k_q1 * q1 + k_q2 * q2))
n_p = 0.9 / np.sqrt(2 * np.pi)
n_b = 0.2 / np.sqrt(2 * np.pi)
f = rho \
* ( n_p * af.exp(-0.5*p1**2)
+ n_b * af.exp(-0.5*((p1 - 4.5)/0.5)**2)
)
af.eval(f)
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
m = params.mass
k = params.boltzmann_constant
n_b = params.density_background
T_b1 = params.temperature_background_1
T_b2 = params.temperature_background_2
T_b3 = params.temperature_background_3
k = params.boltzmann_constant
n = n_b + params.amplitude * af.cos(params.k_q1 * q1)
f1 = n * (m[0, 0] / (2 * np.pi * k * T_b1))**(1 / 2) \
* af.exp(-m[0, 0] * v1[:, 0]**2 / (2 * k * T_b1))
f2 = n * (m[0, 1] / (2 * np.pi * k * T_b2))**(1 / 2) \
* af.exp(-m[0, 1] * v1[:, 1]**2 / (2 * k * T_b2))
f3 = n * (m[0, 2] / (2 * np.pi * k * T_b3))**(1 / 2) \
* af.exp(-m[0, 2] * v1[:, 2]**2 / (2 * k * T_b3))
f = af.join(1, f1, f2, f3)
af.eval(f)
return (f)
def linear(self, signal_x, signal_y, Disper_cd):
signal_x_fft = af.fft(signal_x) * af.exp(Disper_cd / 2)
signal_x = af.ifft(signal_x_fft)
signal_y_fft = af.fft(signal_y) * af.exp(Disper_cd / 2)
signal_y = af.ifft(signal_y_fft)
return signal_x, signal_y
def initialize_f(q1, q2, p1, p2, p3, params):
m = params.mass_particle
k = params.boltzmann_constant
rho = af.select(af.abs(q2) > 0.25, q1**0, 2)
# Seeding the instability
p1_bulk = af.reorder(p1_bulk, 1, 2, 0, 3)
p1_bulk += af.to_array(
np.random.rand(1, q1.shape[1], q1.shape[2]) *
np.random.choice([-1, 1], size=(1, q1.shape[1], q1.shape[2]))) * 0.005
p2_bulk = af.to_array(
np.random.rand(1, q1.shape[1], q1.shape[2]) *
np.random.choice([-1, 1], size=(1, q1.shape[1], q1.shape[2]))) * 0.005
p1_bulk = af.reorder(p1_bulk, 2, 0, 1, 3)
p2_bulk = af.reorder(p2_bulk, 2, 0, 1, 3)
T = (2.5 / rho)
f = rho * (m / (2 * np.pi * k * T))**(3 / 2) \
* af.exp(-m * (p1 - p1_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (p2 - p2_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (p3)**2 / (2 * k * T))
af.eval(f)
return (f)
def f_left(f, t, q1, q2, p1, p2, p3, params):
k = params.boltzmann_constant
E_upper = params.E_band
T = params.initial_temperature
mu = params.initial_mu
t = params.current_time
omega = 2. * np.pi * params.AC_freq
vel_drift_x_in = params.vel_drift_x_in
if (params.p_space_grid == 'cartesian'):
p_x = p1
p_y = p2
elif (params.p_space_grid == 'polar2D'):
p_x = p1 * af.cos(p2)
p_y = p1 * af.sin(p2)
else:
raise NotImplementedError('Unsupported coordinate system in p_space')
fermi_dirac_in = (1. / (af.exp(
(E_upper - vel_drift_x_in * p_x - mu) / (k * T)) + 1.))
if params.zero_temperature:
fermi_dirac_in = fermi_dirac_in - 0.5
if (params.contact_geometry == "straight"):
# Contacts on either side of the device
q2_contact_start = params.contact_start
q2_contact_end = params.contact_end
cond = ((params.y >= q2_contact_start) & \
(params.y <= q2_contact_end) \
)
cond_2 = ((params.y >= 0.) & \
(params.y <= 1.) \
)
print("boundaries.py : ")
f_left = cond * fermi_dirac_in + (1 - cond) * f
elif (params.contact_geometry == "turn_around"):
# Contacts on the same side of the device
vel_drift_x_out = -params.vel_drift_x_in * np.sin(omega * t)
fermi_dirac_out = (1. / (af.exp(
(E_upper - vel_drift_x_out * p_x - mu) / (k * T)) + 1.))
# TODO: set these parameters in params.py
cond_in = ((q2 >= 3.5) & (q2 <= 4.5))
cond_out = ((q2 >= 5.5) & (q2 <= 6.5))
f_left = cond_in*fermi_dirac_in + cond_out*fermi_dirac_out \
+ (1 - cond_in)*(1 - cond_out)*f
af.eval(f_left)
return (f_left)
def initialize_f(q1, q2, p1, p2, p3, params):
m = params.mass_particle
k = params.boltzmann_constant
rho = af.select(af.abs(q2) > 0.25, q1**0, 2)
try:
p1_bulk = af.select(
af.abs(q2) > 0.25, -0.5 - 0.01 *
(af.randu(1, q1.shape[1], q2.shape[2], dtype=af.Dtype.f64) - 0.5),
+0.5 + 0.01 *
(af.randu(1, q1.shape[1], q2.shape[2], dtype=af.Dtype.f64) - 0.5))
p2_bulk = 0.01 * (
af.randu(1, q1.shape[1], q2.shape[2], dtype=af.Dtype.f64) - 0.5)
except:
p1_bulk = af.select(
af.abs(q2) > 0.25, -0.5 - 0.01 *
(af.randu(q1.shape[0], q2.shape[1], dtype=af.Dtype.f64) - 0.5),
+0.5 + 0.01 *
(af.randu(q1.shape[0], q2.shape[1], dtype=af.Dtype.f64) - 0.5))
p2_bulk = 0.01 * (
af.randu(q1.shape[0], q2.shape[1], dtype=af.Dtype.f64) - 0.5)
T = (2.5 / rho)
f = rho * (m / (2 * np.pi * k * T))**(3 / 2) \
* af.exp(-m * (p1 - p1_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (p2 - p2_bulk)**2 / (2 * k * T)) \
* af.exp(-m * p3**2 / (2 * k * T))
af.eval(f)
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
m = params.mass
k = params.boltzmann_constant
n_b = params.density_background
T_b = params.temperature_background
k = params.boltzmann_constant
v1_bulk = 0
# Assigning separate bulk velocities
v2_bulk = params.amplitude * -1.7450858652952794e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.5123323181646575 * af.sin(params.k_q1 * q1)
v3_bulk = params.amplitude * 0.5123323181646597 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f = n * (m / (2 * np.pi * k * T_b)) \
* af.exp(-m * (v2 - v2_bulk)**2 / (2 * k * T_b)) \
* af.exp(-m * (v3 - v3_bulk)**2 / (2 * k * T_b))
af.eval(f)
return (f)
def initialize_f(r, theta, rdot, thetadot, phidot, params):
# Using a transformation to get the coordinates in the form used in regular cartesian coordinates:
q1 = r * af.cos(theta)
q2 = r * af.sin(theta)
p1 = rdot * af.cos(theta) - r * af.sin(theta) * thetadot
p2 = rdot * af.sin(theta) + r * af.cos(theta) * thetadot
q10 = params.q10
q20 = params.q20
p10 = params.p10
p20 = params.p20
sigma_q = params.sigma_q
sigma_p = params.sigma_p
q_profile = (1 / sigma_q**2 / (2 * np.pi)) * \
af.exp(-0.5 * ((q1 - q10)**2 + (q2 - q20)**2) / sigma_q**2)
p_profile = (1 / sigma_p**2 / (2 * np.pi)) * \
af.exp(-0.5 * ((p1 - p10)**2 + (p2 - p20)**2) / sigma_p**2)
f = q_profile * p_profile
af.eval(f)
return (f)
def linear_prop_arrayfire(xpol, ypol, length, D):
xpol_fft = af.fft(xpol)
ypol_fft = af.fft(ypol)
xpol_fft = xpol_fft * af.exp(D * length)
ypol_fft = ypol_fft * af.exp(D * length)
xpol = af.ifft(xpol_fft)
ypol = af.ifft(ypol_fft)
return xpol, ypol
def initialize_E(q1, q2, params):
E1 = af.exp(-100 * (q2 - 0.5)**2)
E2 = af.exp(-100 * (q1 - 0.5)**2)
E3 = 0 * q1**0
af.eval(E1, E2, E3)
return (E1, E2, E3)
def maxwell_boltzmann(rho, T, p1_b, p2_b, p3_b, p1, p2, p3):
f = rho * (1 / (2 * np.pi * T))**(3 / 2) \
* af.exp(-1 * (p1 - p1_b)**2 / (2 * T)) \
* af.exp(-1 * (p2 - p2_b)**2 / (2 * T)) \
* af.exp(-1 * (p3 - p3_b)**2 / (2 * T))
af.eval(f)
return (f)
def test_initialize():
obj = test()
initialize(obj, params)
f_background_ana = (1 / (2 * np.pi))**(3 / 2) \
* af.exp(-0.5 * obj.p1**2) \
* af.exp(-0.5 * obj.p2**2) \
* af.exp(-0.5 * obj.p3**2)
assert (af.sum(af.abs(obj.f_background - f_background_ana)) < 1e-13)
def f_bottom(f, t, q1, q2, p1, p2, p3, params):
k = params.boltzmann_constant
E_upper = params.E_band
T = params.initial_temperature
mu = params.initial_mu
t = params.current_time
omega = 2. * np.pi * params.AC_freq
q1_contact_start = params.contact_start
q1_contact_end = params.contact_end
contact_width = q1_contact_end - q1_contact_start
q1_contact_start_2 = 0.
q1_contact_end_2 = 1.73 / 2
contact_width_2 = q1_contact_end_2 - q1_contact_start_2
vel_drift_y_out = -params.vel_drift_x_out / contact_width
vel_drift_y_out_2 = 10. * params.vel_drift_x_out / contact_width_2
if (params.p_space_grid == 'cartesian'):
p_x = p1
p_y = p2
elif (params.p_space_grid == 'polar2D'):
p_x = p1 * af.cos(p2)
p_y = p1 * af.sin(p2)
else:
raise NotImplementedError('Unsupported coordinate system in p_space')
fermi_dirac_out = (1. / (af.exp(
(E_upper - vel_drift_y_out * p_y - mu) / (k * T)) + 1.))
fermi_dirac_out_2 = (1. / (af.exp(
(E_upper - vel_drift_y_out_2 * p_y - mu) / (k * T)) + 1.))
if (params.contact_geometry == "straight"):
# Contacts on either side of the device
cond = ((q1 >= q1_contact_start) & \
(q1 <= q1_contact_end) \
)
cond_2 = ((q1 >= q1_contact_start_2) & \
(q1 <= q1_contact_end_2) \
)
f_right = cond * fermi_dirac_out + cond_2 * fermi_dirac_out_2 + (
1 - cond_2) * (1 - cond) * f
elif (params.contact_geometry == "turn_around"):
# Contacts on the same side of the device
f_right = f
af.eval(f_right)
return (f_right)
def initialize_f(q1, q2, v1, v2, v3, params):
m = params.mass
k = params.boltzmann_constant
n_b = params.density_background
T_b = params.temperature_background
v1_bulk_b = params.v1_bulk_background
v2_bulk_b = params.v2_bulk_background
v3_bulk_b = params.v3_bulk_background
pert_real_n = 1
pert_imag_n = 0
pert_real_v1 = -np.sqrt(params.gamma * T_b) / n_b \
* params.k_q1 / np.sqrt(params.k_q1**2 + params.k_q2**2) * 1j
pert_imag_v1 = 0
pert_real_v2 = -np.sqrt(params.gamma * T_b) / n_b \
* params.k_q2 / np.sqrt(params.k_q1**2 + params.k_q2**2) * 1j
pert_imag_v2 = 0
pert_real_T = T_b * (params.gamma - 1) / n_b
pert_imag_T = 0
k_q1 = params.k_q1
k_q2 = params.k_q2
amp = params.amplitude
# Introducing the perturbation amounts:
# This is obtained from the Sage Worksheet(https://goo.gl/Sh8Nqt):
# Plugging in the value from the Eigenvectors:
# Calculating the perturbed density:
n = n_b + amp * (pert_real_n * af.cos(k_q1 * q1 + k_q2 * q2) -
pert_imag_n * af.sin(k_q1 * q1 + k_q2 * q2))
# Calculating the perturbed bulk velocities:
v1_bulk = v1_bulk_b + amp * (pert_real_v1 * af.cos(k_q1 * q1 + k_q2 * q2) -
pert_imag_v1 * af.sin(k_q1 * q1 + k_q2 * q2))
v2_bulk = v2_bulk_b + amp * (pert_real_v2 * af.cos(k_q1 * q1 + k_q2 * q2) -
pert_imag_v2 * af.sin(k_q1 * q1 + k_q2 * q2))
v3_bulk = v3_bulk_b
# Calculating the perturbed temperature:
T = T_b + amp * (pert_real_T * af.cos(k_q1 * q1 + k_q2 * q2) -
pert_imag_T * af.sin(k_q1 * q1 + k_q2 * q2))
f = n * (m / (2 * np.pi * k * T))**(3 / 2) \
* af.exp(-m * (v1 - v1_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (v2 - v2_bulk)**2 / (2 * k * T)) \
* af.exp(-m * (v3 - v3_bulk)**2 / (2 * k * T))
af.eval(f)
return (f)
def initialize_B(q1, q2, params):
dt = params.dt
B1 = 0 * q1**0
B2 = 0 * q1**0
# B3 at n + 1/2
B3 = af.exp(-100 * (q2 - 0.5 - 0.5 * dt)**2) \
- af.exp(-100 * (q1 - 0.5 - 0.5 * dt)**2)
af.eval(B1, B2, B3)
return (B1, B2, B3)
def MB_dist(q1, q2, p1, p2, p3, params):
# Calculating the perturbed density:
rho = 1 + (0.01 * af.cos(2 * np.pi * q1 + 4 * np.pi * q2))
f = rho * (1 / (2 * np.pi))**(3 / 2) \
* af.exp(-0.5 * p1**2) \
* af.exp(-0.5 * p2**2) \
* af.exp(-0.5 * p3**2)
af.eval(f)
return (f)
def __init__(self):
self.physical_system = type('obj', (object, ), {
'moment_exponents': moment_exponents,
'moment_coeffs': moment_coeffs
})
self.p1_start = -10
self.p2_start = -10
self.p3_start = -10
self.N_p1 = 32
self.N_p2 = 32
self.N_p3 = 32
self.dp1 = (-2 * self.p1_start) / self.N_p1
self.dp2 = (-2 * self.p2_start) / self.N_p2
self.dp3 = (-2 * self.p3_start) / self.N_p3
self.N_q1 = 16
self.N_q2 = 16
self.N_ghost = 3
self.p1 = self.p1_start + (0.5 + np.arange(self.N_p1)) * self.dp1
self.p2 = self.p2_start + (0.5 + np.arange(self.N_p2)) * self.dp2
self.p3 = self.p3_start + (0.5 + np.arange(self.N_p3)) * self.dp3
self.p2, self.p1, self.p3 = np.meshgrid(self.p2, self.p1, self.p3)
self.p1 = af.flat(af.to_array(self.p1))
self.p2 = af.flat(af.to_array(self.p2))
self.p3 = af.flat(af.to_array(self.p3))
self.q1 = (-self.N_ghost + 0.5 +
np.arange(self.N_q1 + 2 * self.N_ghost)) / self.N_q1
self.q2 = (-self.N_ghost + 0.5 +
np.arange(self.N_q2 + 2 * self.N_ghost)) / self.N_q2
self.q2, self.q1 = np.meshgrid(self.q2, self.q1)
self.q1 = af.reorder(af.to_array(self.q1), 2, 0, 1)
self.q2 = af.reorder(af.to_array(self.q2), 2, 0, 1)
rho = (1 + 0.01 * af.sin(2 * np.pi * self.q1 + 4 * np.pi * self.q2))
T = (1 + 0.01 * af.cos(2 * np.pi * self.q1 + 4 * np.pi * self.q2))
p1_b = 0.01 * af.exp(-10 * self.q1**2 - 10 * self.q2**2)
p2_b = 0.01 * af.exp(-10 * self.q1**2 - 10 * self.q2**2)
p3_b = 0.01 * af.exp(-10 * self.q1**2 - 10 * self.q2**2)
self.f = maxwell_boltzmann(rho, T, p1_b, p2_b, p3_b, self.p1, self.p2,
self.p3)
def f_left(f, t, q1, q2, p1, p2, p3, params):
rho = 1 * q1**0
T = 1 * q1**0
m = params.mass
k = params.boltzmann_constant
f = rho * af.sqrt(m / (2 * np.pi * k * T))**3 \
* af.exp(-m * p1**2 / (2 * k * T)) \
* af.exp(-m * p2**2 / (2 * k * T)) \
* af.exp(-m * p3**2 / (2 * k * T))
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
k = params.boltzmann_constant
n_left = params.n_left
v1_bulk_left = params.v1_bulk_left
T_left = params.T_left
f = q1**0 * n_left * (params.mass / (2 * np.pi * k * T_left))**(3 / 2) \
* af.exp(-params.mass * (v1 - v1_bulk_left)**2 / (2 * k * T_left)) \
* af.exp(-params.mass * v2**2 / (2 * k * T_left)) \
* af.exp(-params.mass * v3**2 / (2 * k * T_left))
af.eval(f)
return (f)
def f_right(f, q1, q2, p1, p2, p3, params):
rho = 0.125 * q1**0
T = 0.8 * q1**0
m = params.mass_particle
k = params.boltzmann_constant
f = rho * af.sqrt(m / (2 * np.pi * k * T))**3 \
* af.exp(-m * p1**2 / (2 * k * T)) \
* af.exp(-m * p2**2 / (2 * k * T)) \
* af.exp(-m * p3**2 / (2 * k * T))
return (f)
def MB_dist(q1, q2, p1, p2, p3, p_dim):
# Calculating the perturbed density:
rho = 1 + 0.01 * af.cos(2 * np.pi * q1)
T = 1 + 0.01 * af.cos(2 * np.pi * q1)
p1b = 0.01 * af.cos(2 * np.pi * q1)
f = rho * (1 / (2 * np.pi * T))**(p_dim / 2) \
* af.exp(-0.5 * (p1-p1b)**2/T) \
* af.exp(-0.5 * p2**2/T) \
* af.exp(-0.5 * p3**2/T)
af.eval(f)
return (f)
def f_right(f, q1, q2, p1, p2, p3, params):
rho = 2 / 3 * q1**0
T = 1 / 4 * q1**0
p1_b = 1.5 * q1**0
m = params.mass_particle
k = params.boltzmann_constant
f = rho * af.sqrt(m / (2 * np.pi * k * T))**3 \
* af.exp(-m * (p1-p1_b)**2 / (2 * k * T)) \
* af.exp(-m * p2**2 / (2 * k * T)) \
* af.exp(-m * p3**2 / (2 * k * T))
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
m_e = params.mass[0, 0]
m_i = params.mass[0, 1]
k = params.boltzmann_constant
n = params.n_background * q1**0
u_be = params.u_be
u_bi = params.u_bi
T = params.T_background
f_e = n * (m_e / (2 * np.pi * k * T))**(3 / 2) \
* 0.5 * ( af.exp(-m_e * (v1[:, 0] - u_be)**2 / (2 * k * T))
+ af.exp(-m_e * (v1[:, 0] + u_be)**2 / (2 * k * T))
) \
* af.exp(-m_e * v2[:, 0]**2 / (2 * k * T)) \
* af.exp(-m_e * v3[:, 0]**2 / (2 * k * T))
f_i = n * (m_i / (2 * np.pi * k * T))**(3 / 2) \
* 0.5 * ( af.exp(-m_i * (v1[:, 1] - u_bi)**2 / (2 * k * T))
+ af.exp(-m_i * (v1[:, 1] + u_bi)**2 / (2 * k * T))
) \
* af.exp(-m_i * v2[:, 1]**2 / (2 * k * T)) \
* af.exp(-m_i * v3[:, 1]**2 / (2 * k * T))
f = af.join(1, f_e, f_i)
af.eval(f)
return (f)
def test_compute_moments():
obj = test()
rho_num = compute_moments(obj, 'density')
rho_ana = 1 + 0.01 * af.sin(2 * np.pi * obj.q1_center +
4 * np.pi * obj.q2_center)
error_rho = af.mean(af.abs(rho_num - rho_ana))
E_num = compute_moments(obj, 'energy')
E_ana = 3/2 * (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (1 + 0.01 * af.cos(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
+ 3/2 * (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))**2
error_E = af.mean(af.abs(E_num - E_ana))
mom_p1b_num = compute_moments(obj, 'mom_v1_bulk')
mom_p1b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))
error_p1b = af.mean(af.abs(mom_p1b_num - mom_p1b_ana))
mom_p2b_num = compute_moments(obj, 'mom_v2_bulk')
mom_p2b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))
error_p2b = af.mean(af.abs(mom_p2b_num - mom_p2b_ana))
mom_p3b_num = compute_moments(obj, 'mom_v3_bulk')
mom_p3b_ana = (1 + 0.01 * af.sin(2 * np.pi * obj.q1_center + 4 * np.pi * obj.q2_center)) \
* (0.01 * af.exp(-10 * obj.q1_center**2 - 10 * obj.q2_center**2))
error_p3b = af.mean(af.abs(mom_p3b_num - mom_p3b_ana))
print(error_rho)
print(error_E)
print(error_p1b)
print(error_p2b)
print(error_p3b)
# print((error_rho + error_E + error_p1b + error_p2b + error_p3b) / 5)
assert (error_rho < 1e-13)
assert (error_E < 1e-13)
assert (error_p1b < 1e-13)
assert (error_p2b < 1e-13)
assert (error_p3b < 1e-13)
def main():
T = 1
nT = 20 * T
R_first = 1000
R = 5000000
x0 = 0 # initial log stock price
v0 = 0.087**2 # initial volatility
r = math.log(1.0319) # risk-free rate
rho = -0.82 # instantaneous correlation between Brownian motions
sigmaV = 0.14 # variance of volatility
kappa = 3.46 # mean reversion speed
vBar = 0.008 # mean variance
k = math.log(0.95) # strike price
# first run
( x, v ) = simulateHestonModel( T, nT, R_first, r, kappa, vBar, sigmaV, rho, x0, v0 )
# Price plain vanilla call option
tic = time.time()
( x, v ) = simulateHestonModel( T, nT, R, r, kappa, vBar, sigmaV, rho, x0, v0 )
af.sync()
toc = time.time() - tic
K = math.exp(k)
zeroConstant = af.constant(0, R, dtype=af.Dtype.f32)
C_CPU = math.exp(-r * T) * af.mean(af.maxof(af.exp(x) - K, zeroConstant))
print("Time elapsed = {} secs".format(toc))
print("Call price = {}".format(C_CPU))
print(af.mean(v))
def black_scholes(S, X, R, V, T):
# S = Underlying stock price
# X = Strike Price
# R = Risk free rate of interest
# V = Volatility
# T = Time to maturity
d1 = af.log(S / X)
d1 = d1 + (R + (V * V) * 0.5) * T
d1 = d1 / (V * af.sqrt(T))
d2 = d1 - (V * af.sqrt(T))
cnd_d1 = cnd(d1)
cnd_d2 = cnd(d2)
C = S * cnd_d1 - (X * af.exp((-R) * T) * cnd_d2)
P = X * af.exp((-R) * T) * (1 - cnd_d2) - (S * (1 -cnd_d1))
return (C, P)
def monte_carlo_options(N, K, t, vol, r, strike, steps, use_barrier = True, B = None, ty = af.Dtype.f32):
payoff = af.constant(0, N, 1, dtype = ty)
dt = t / float(steps - 1)
s = af.constant(strike, N, 1, dtype = ty)
randmat = af.randn(N, steps - 1, dtype = ty)
randmat = af.exp((r - (vol * vol * 0.5)) * dt + vol * math.sqrt(dt) * randmat);
S = af.product(af.join(1, s, randmat), 1)
if (use_barrier):
S = S * af.all_true(S < B, 1)
payoff = af.maxof(0, S - K)
return af.mean(payoff) * math.exp(-r * t)
def sigtest(x): return 1 / (1 + af.exp(-x))
af.display(af.conjg(d)) af.display(af.sinh(a)) af.display(af.cosh(a)) af.display(af.tanh(a)) af.display(af.asinh(a)) af.display(af.acosh(a)) af.display(af.atanh(a)) a = af.abs(a) b = af.abs(b) af.display(af.root(a, b)) af.display(af.pow(a, b)) af.display(af.pow2(a)) af.display(af.exp(a)) af.display(af.expm1(a)) af.display(af.erf(a)) af.display(af.erfc(a)) af.display(af.log(a)) af.display(af.log1p(a)) af.display(af.log10(a)) af.display(af.log2(a)) af.display(af.sqrt(a)) af.display(af.cbrt(a)) a = af.round(5 * af.randu(3,3) - 1) b = af.round(5 * af.randu(3,3) - 1) af.display(af.factorial(a)) af.display(af.tgamma(a))
def simple_arith(verbose = False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(3,3,dtype=af.Dtype.u32)
b = af.constant(4, 3, 3, dtype=af.Dtype.u32)
display_func(a)
display_func(b)
c = a + b
d = a
d += b
display_func(c)
display_func(d)
display_func(a + 2)
display_func(3 + a)
c = a - b
d = a
d -= b
display_func(c)
display_func(d)
display_func(a - 2)
display_func(3 - a)
c = a * b
d = a
d *= b
display_func(c * 2)
display_func(3 * d)
display_func(a * 2)
display_func(3 * a)
c = a / b
d = a
d /= b
display_func(c / 2.0)
display_func(3.0 / d)
display_func(a / 2)
display_func(3 / a)
c = a % b
d = a
d %= b
display_func(c % 2.0)
display_func(3.0 % d)
display_func(a % 2)
display_func(3 % a)
c = a ** b
d = a
d **= b
display_func(c ** 2.0)
display_func(3.0 ** d)
display_func(a ** 2)
display_func(3 ** a)
display_func(a < b)
display_func(a < 0.5)
display_func(0.5 < a)
display_func(a <= b)
display_func(a <= 0.5)
display_func(0.5 <= a)
display_func(a > b)
display_func(a > 0.5)
display_func(0.5 > a)
display_func(a >= b)
display_func(a >= 0.5)
display_func(0.5 >= a)
display_func(a != b)
display_func(a != 0.5)
display_func(0.5 != a)
display_func(a == b)
display_func(a == 0.5)
display_func(0.5 == a)
display_func(a & b)
display_func(a & 2)
c = a
c &= 2
display_func(c)
display_func(a | b)
display_func(a | 2)
c = a
c |= 2
display_func(c)
display_func(a >> b)
display_func(a >> 2)
c = a
c >>= 2
display_func(c)
display_func(a << b)
display_func(a << 2)
c = a
c <<= 2
display_func(c)
display_func(-a)
display_func(+a)
display_func(~a)
display_func(a)
display_func(af.cast(a, af.Dtype.c32))
display_func(af.maxof(a,b))
display_func(af.minof(a,b))
display_func(af.rem(a,b))
a = af.randu(3,3) - 0.5
b = af.randu(3,3) - 0.5
display_func(af.abs(a))
display_func(af.arg(a))
display_func(af.sign(a))
display_func(af.round(a))
display_func(af.trunc(a))
display_func(af.floor(a))
display_func(af.ceil(a))
display_func(af.hypot(a, b))
display_func(af.sin(a))
display_func(af.cos(a))
display_func(af.tan(a))
display_func(af.asin(a))
display_func(af.acos(a))
display_func(af.atan(a))
display_func(af.atan2(a, b))
c = af.cplx(a)
d = af.cplx(a,b)
display_func(c)
display_func(d)
display_func(af.real(d))
display_func(af.imag(d))
display_func(af.conjg(d))
display_func(af.sinh(a))
display_func(af.cosh(a))
display_func(af.tanh(a))
display_func(af.asinh(a))
display_func(af.acosh(a))
display_func(af.atanh(a))
a = af.abs(a)
b = af.abs(b)
display_func(af.root(a, b))
display_func(af.pow(a, b))
display_func(af.pow2(a))
display_func(af.exp(a))
display_func(af.expm1(a))
display_func(af.erf(a))
display_func(af.erfc(a))
display_func(af.log(a))
display_func(af.log1p(a))
display_func(af.log10(a))
display_func(af.log2(a))
display_func(af.sqrt(a))
display_func(af.cbrt(a))
a = af.round(5 * af.randu(3,3) - 1)
b = af.round(5 * af.randu(3,3) - 1)
display_func(af.factorial(a))
display_func(af.tgamma(a))
display_func(af.lgamma(a))
display_func(af.iszero(a))
display_func(af.isinf(a/b))
display_func(af.isnan(a/a))
a = af.randu(5, 1)
b = af.randu(1, 5)
c = af.broadcast(lambda x,y: x+y, a, b)
display_func(a)
display_func(b)
display_func(c)
@af.broadcast
def test_add(aa, bb):
return aa + bb
display_func(test_add(a, b))
def _sigmoid(x): return 1 / (1 + af.exp(-x))
def exp(x):
if isinstance(x, afnumpy.ndarray):
s = arrayfire.exp(x.d_array)
return afnumpy.ndarray(x.shape, dtype=pu.typemap(s.dtype()), af_array=s)
else:
return numpy.exp(x)
