def calculate_p_center(p1_start, p2_start, p3_start,
N_p1, N_p2, N_p3,
dp1, dp2, dp3,
):
"""
Initializes the cannonical variables p1, p2 and p3 using a centered
formulation.
"""
p1_center = af.constant(0, N_p1 * N_p2 * N_p3, len(p1_start), dtype = af.Dtype.f64)
p2_center = af.constant(0, N_p1 * N_p2 * N_p3, len(p2_start), dtype = af.Dtype.f64)
p3_center = af.constant(0, N_p1 * N_p2 * N_p3, len(p3_start), dtype = af.Dtype.f64)
# Assigning for each species:
for i in range(len(p1_start)):
p1 = p1_start[i] + (0.5 + np.arange(N_p1)) * dp1[i]
p2 = p2_start[i] + (0.5 + np.arange(N_p2)) * dp2[i]
p3 = p3_start[i] + (0.5 + np.arange(N_p3)) * dp3[i]
p2_center[:, i] = af.flat(af.to_array(np.meshgrid(p2, p1, p3)[0]))
p1_center[:, i] = af.flat(af.to_array(np.meshgrid(p2, p1, p3)[1]))
p3_center[:, i] = af.flat(af.to_array(np.meshgrid(p2, p1, p3)[2]))
af.eval(p1_center, p2_center, p3_center)
return (p1_center, p2_center, p3_center)
def calculate_q(q1_start, q2_start, N_q1, N_q2, N_g1, N_g2, dq1, dq2):
i_q1 = np.arange(-N_g1, N_q1 + N_g1)
i_q2 = np.arange(-N_g2, N_q2 + N_g2)
q1_left_bot = q1_start + i_q1 * dq1
q2_left_bot = q2_start + i_q2 * dq2
q2_left_bot, q1_left_bot = np.meshgrid(q2_left_bot, q1_left_bot)
q2_left_bot, q1_left_bot = af.to_array(q2_left_bot), af.to_array(
q1_left_bot)
# To bring the data structure to the default form:(N_p, N_s, N_q1, N_q2)
q1_left_bot = af.reorder(q1_left_bot, 3, 2, 0, 1)
q2_left_bot = af.reorder(q2_left_bot, 3, 2, 0, 1)
q1_center_bot = q1_left_bot + 0.5 * dq1
q2_center_bot = q2_left_bot
q1_left_center = q1_left_bot
q2_left_center = q2_left_bot + 0.5 * dq2
q1_center = q1_left_bot + 0.5 * dq1
q2_center = q2_left_bot + 0.5 * dq2
ans = [[q1_left_bot, q2_left_bot], [q1_center_bot, q2_center_bot],
[q1_left_center, q2_center_bot], [q1_center, q2_center]]
return (ans)
def test_dump_moments():
test_obj = test()
N_g = test_obj.N_ghost
dump_moments(test_obj, 'test_file')
h5f = h5py.File('test_file.h5', 'r')
moments_read = h5f['moments'][:]
h5f.close()
moments_read = np.swapaxes(moments_read, 0, 1)
print(moments_read.shape)
print(compute_moments_imported(test_obj, 'density').shape)
assert(af.sum(af.to_array(moments_read[:, :, 0]) -
af.reorder(compute_moments_imported(test_obj, 'density'),
1, 2, 0
)[N_g:-N_g, N_g:-N_g]
)==0
)
assert(af.sum(af.to_array(moments_read[:, :, 1]) -
af.reorder(compute_moments_imported(test_obj, 'energy'),
1, 2, 0
)[N_g:-N_g, N_g:-N_g]
)==0
)
def _calculate_p_center(self):
"""
Initializes the cannonical variables p1, p2 and p3 using a centered
formulation. The size, and resolution are the same as declared
under domain of the physical system object.
"""
p1_center = self.p1_start + (0.5 + np.arange(
-self.N_ghost_p, self.N_p1 + self.N_ghost_p)) * self.dp1
p2_center = self.p2_start + (0.5 + np.arange(
-self.N_ghost_p, self.N_p2 + self.N_ghost_p)) * self.dp2
p3_center = self.p3_start + (0.5 + np.arange(
-self.N_ghost_p, self.N_p3 + self.N_ghost_p)) * self.dp3
p2_center, p1_center, p3_center = np.meshgrid(p2_center, p1_center,
p3_center)
# Flattening the arrays:
p1_center = af.flat(af.to_array(p1_center))
p2_center = af.flat(af.to_array(p2_center))
p3_center = af.flat(af.to_array(p3_center))
if (self.N_species > 1):
p1_center = af.tile(p1_center, 1, self.N_species)
p2_center = af.tile(p2_center, 1, self.N_species)
p3_center = af.tile(p3_center, 1, self.N_species)
af.eval(p1_center, p2_center, p3_center)
return (p1_center, p2_center, p3_center)
def _calculate_p_back(self):
p1_center = self.p1_start + (0.5 + np.arange(
-self.N_ghost_p, self.N_p1 + self.N_ghost_p)) * self.dp1
p2_center = self.p2_start + (0.5 + np.arange(
-self.N_ghost_p, self.N_p2 + self.N_ghost_p)) * self.dp2
p3_back = self.p3_start + np.arange(
-self.N_ghost_p, self.N_p3 + self.N_ghost_p) * self.dp3
p2_back, p1_back, p3_back = np.meshgrid(p2_center, p1_center,
p3_center)
# Flattening the arrays:
p1_back = af.flat(af.to_array(p1_back))
p2_back = af.flat(af.to_array(p2_back))
p3_back = af.flat(af.to_array(p3_back))
if (self.N_species > 1):
p1_back = af.tile(p1_back, 1, self.N_species)
p2_back = af.tile(p2_back, 1, self.N_species)
p3_back = af.tile(p3_back, 1, self.N_species)
af.eval(p1_back, p2_back, p3_back)
return (p1_back, p2_back, p3_back)
def _calculate_p_center(self):
"""
Initializes the cannonical variables p1, p2 and p3 using a centered
formulation. The size, and resolution are the same as declared
under domain of the physical system object.
"""
p1_center = \
self.p1_start + (0.5 + np.arange(0, self.N_p1, 1)) * self.dp1
p2_center = \
self.p2_start + (0.5 + np.arange(0, self.N_p2, 1)) * self.dp2
p3_center = \
self.p3_start + (0.5 + np.arange(0, self.N_p3, 1)) * self.dp3
p2_center, p1_center, p3_center = np.meshgrid(p2_center,
p1_center,
p3_center
)
# Flattening the obtained arrays:
p1_center = af.flat(af.to_array(p1_center))
p2_center = af.flat(af.to_array(p2_center))
p3_center = af.flat(af.to_array(p3_center))
# Reordering such that variation in velocity is along axis 2:
# This is done to be consistent with the positionsExpanded form:
p1_center = af.reorder(p1_center, 2, 3, 0, 1)
p2_center = af.reorder(p2_center, 2, 3, 0, 1)
p3_center = af.reorder(p3_center, 2, 3, 0, 1)
af.eval(p1_center, p2_center, p3_center)
return(p1_center, p2_center, p3_center)
def _calculate_q_center(self):
"""
Initializes the cannonical variables q1, q2 using a centered
formulation. The size, and resolution are the same as declared
under domain of the physical system object.
Returns in q_expanded form.
"""
# Obtaining start coordinates for the local zone
# Additionally, we also obtain the size of the local zone
((i_q1_start, i_q2_start), (N_q1_local,
N_q2_local)) = self._da_f.getCorners()
i_q1_center = i_q1_start + 0.5
i_q2_center = i_q2_start + 0.5
i_q1 = (i_q1_center +
np.arange(-self.N_ghost_q, N_q1_local + self.N_ghost_q))
i_q2 = (i_q2_center +
np.arange(-self.N_ghost_q, N_q2_local + self.N_ghost_q))
q1_center = self.q1_start + i_q1 * self.dq1
q2_center = self.q2_start + i_q2 * self.dq2
q2_center, q1_center = np.meshgrid(q2_center, q1_center)
q1_center, q2_center = af.to_array(q1_center), af.to_array(q2_center)
# To bring the data structure to the default form:(N_p, N_s, N_q1, N_q2)
q1_center = af.reorder(q1_center, 3, 2, 0, 1)
q2_center = af.reorder(q2_center, 3, 2, 0, 1)
af.eval(q1_center, q2_center)
return (q1_center, q2_center)
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 __init__(self):
self.f = af.to_array(np.array([0]))
self.cell_centered_EM_fields = af.to_array(np.array([0]))
self.yee_grid_EM_fields = af.to_array(np.array([0]))
self.performance_test_flag = False
def __init__(self):
self.physical_system = type('obj', (object, ),
{'params': type('obj', (object, ),
{'charge_electron': -1})
})
self.N_q1 = 32
self.N_q2 = 64
self.single_mode_evolution = False
self.N_p1 = 2
self.N_p2 = 3
self.N_p3 = 4
self.k_q1 = 2 * np.pi * fftfreq(self.N_q1, 1 / self.N_q1)
self.k_q2 = 2 * np.pi * fftfreq(self.N_q2, 1 / self.N_q2)
self.k_q2, self.k_q1 = np.meshgrid(self.k_q2, self.k_q1)
self.k_q2, self.k_q1 = af.to_array(self.k_q2), af.to_array(self.k_q1)
self.q1 = af.to_array((0.5 + np.arange(self.N_q1)) * (1 / self.N_q1))
self.q2 = af.to_array((0.5 + np.arange(self.N_q2)) * (1 / self.N_q2))
self.q1 = af.tile(self.q1, 1, self.N_q2)
self.q2 = af.tile(af.reorder(self.q2), self.N_q1, 1)
def __init__(self):
self.q1_start = np.random.randint(0, 5)
self.q2_start = np.random.randint(0, 5)
self.q1_end = np.random.randint(5, 10)
self.q2_end = np.random.randint(5, 10)
self.N_q1 = np.random.randint(16, 32)
self.N_q2 = np.random.randint(16, 32)
self.dq1 = (self.q1_end - self.q1_start) / self.N_q1
self.dq2 = (self.q2_end - self.q2_start) / self.N_q2
N_g = self.N_ghost = np.random.randint(1, 5)
self.q1 = self.q1_start \
* (0.5 + np.arange(-self.N_ghost,
self.N_q1 + self.N_ghost
)
) * self.dq1
self.q2 = self.q2_start \
* (0.5 + np.arange(-self.N_ghost,
self.N_q2 + self.N_ghost
)
) * self.dq2
self.q2, self.q1 = np.meshgrid(self.q2, self.q1)
self.q1, self.q2 = af.to_array(self.q1), af.to_array(self.q2)
self.q1 = af.reorder(self.q1, 2, 0, 1)
self.q2 = af.reorder(self.q2, 2, 0, 1)
self.q1 = af.tile(self.q1, 6)
self.q2 = af.tile(self.q2, 6)
self._da_fields = PETSc.DMDA().create([self.N_q1, self.N_q2],
dof=6,
stencil_width=self.N_ghost,
boundary_type=('periodic',
'periodic'),
stencil_type=1,
)
self._glob_fields = self._da_fields.createGlobalVec()
self._local_fields = self._da_fields.createLocalVec()
self._glob_fields_array = self._glob_fields.getArray()
self._local_fields_array = self._local_fields.getArray()
self.cell_centered_EM_fields = af.constant(0, 6, self.q1.shape[1],
self.q1.shape[2],
dtype=af.Dtype.f64
)
self.cell_centered_EM_fields[:, N_g:-N_g, N_g:-N_g] = \
af.sin(2 * np.pi * self.q1 + 4 * np.pi * self.q2)[:, N_g:-N_g,N_g:-N_g]
self.performance_test_flag = False
def test_calculate_p():
obj = test()
p1, p2, p3 = calculate_p(obj)
p1_expected = obj.p1_start + (0.5 + np.arange(obj.N_p1)) * obj.dp1
p2_expected = obj.p2_start + (0.5 + np.arange(obj.N_p2)) * obj.dp2
p3_expected = obj.p3_start + (0.5 + np.arange(obj.N_p3)) * obj.dp3
p2_expected, p1_expected, p3_expected = np.meshgrid(p2_expected,
p1_expected,
p3_expected
)
p1_expected = af.reorder(af.flat(af.to_array(p1_expected)),
2, 3, 0, 1
)
p2_expected = af.reorder(af.flat(af.to_array(p2_expected)),
2, 3, 0, 1
)
p3_expected = af.reorder(af.flat(af.to_array(p3_expected)),
2, 3, 0, 1
)
assert(af.sum(af.abs(p1_expected - p1)) == 0)
assert(af.sum(af.abs(p2_expected - p2)) == 0)
assert(af.sum(af.abs(p3_expected - p3)) == 0)
def test_fft_poisson():
"""
This function tests that the FFT solver works as intended.
We take an expression for density for which the fields can
be calculated analytically, and check that the numerical
solution as given by the FFT solver and the analytical
solution correspond well with each other.
"""
x_start = 0
y_start = 0
z_start = 0
x_end = 1
y_end = 2
z_end = 3
N_x = np.random.randint(16, 32)
N_y = np.random.randint(16, 32)
N_z = np.random.randint(16, 32)
dx = (x_end - x_start) / N_x
dy = (y_end - y_start) / N_y
dz = (z_end - z_start) / N_z
# Using a centered formulation for the grid points of x, y, z:
x = x_start + (np.arange(N_x) + 0.5) * dx
y = y_start + (np.arange(N_y) + 0.5) * dy
z = z_start + (np.arange(N_z) + 0.5) * dz
y, x, z = np.meshgrid(y, x, z)
x = af.to_array(x)
y = af.to_array(y)
z = af.to_array(z)
rho = af.sin(2 * np.pi * x + 4 * np.pi * y + 6 * np.pi * z)
Ex_analytic = -(2 * np.pi) / (56 * np.pi**2) * \
af.cos(2 * np.pi * x + 4 * np.pi * y + 6 * np.pi * z)
Ey_analytic = -(4 * np.pi) / (56 * np.pi**2) * \
af.cos(2 * np.pi * x + 4 * np.pi * y + 6 * np.pi * z)
Ez_analytic = -(6 * np.pi) / (56 * np.pi**2) * \
af.cos(2 * np.pi * x + 4 * np.pi * y + 6 * np.pi * z)
Ex_numerical, Ey_numerical, Ez_numerical = fft_poisson(rho, dx, dy, dz)
# Checking that the L1 norm of error is at machine precision:
Ex_err = af.sum(
af.abs(Ex_numerical - Ex_analytic)) / Ex_analytic.elements()
Ey_err = af.sum(
af.abs(Ey_numerical - Ey_analytic)) / Ey_analytic.elements()
Ez_err = af.sum(
af.abs(Ez_numerical - Ez_analytic)) / Ez_analytic.elements()
assert (Ex_err < 1e-14)
assert (Ey_err < 1e-14)
assert (Ez_err < 1e-14)
def communicate_fields(self, on_fdtd_grid=False):
"""
Used in communicating the values at the boundary zones for each of
the local vectors among all procs.This routine is called to take care
of communication(and periodic B.C's) procedures for the EM field
arrays. The function is used for communicating the EM field values
on the cell centered grid which is used by default. Additionally,it can
also be used to communicate the values on the Yee-grid which is used by the FDTD solver.
"""
if (self.performance_test_flag == True):
tic = af.time()
# Obtaining start coordinates for the local zone
# Additionally, we also obtain the size of the local zone
((i_q1_start, i_q2_start), (N_q1_local,
N_q2_local)) = self._da_fields.getCorners()
N_g = self.N_g
# Assigning the values of the af.Array
# fields quantities to the PETSc.Vec:
if (on_fdtd_grid is True):
flattened_global_EM_fields_array = \
af.flat(self.yee_grid_EM_fields[:, :, N_g:-N_g, N_g:-N_g])
flattened_global_EM_fields_array.to_ndarray(self._glob_fields_array)
else:
flattened_global_EM_fields_array = \
af.flat(self.cell_centered_EM_fields[:, :, N_g:-N_g, N_g:-N_g])
flattened_global_EM_fields_array.to_ndarray(self._glob_fields_array)
# Takes care of boundary conditions and interzonal communications:
self._da_fields.globalToLocal(self._glob_fields, self._local_fields)
# Converting back to af.Array
if (on_fdtd_grid is True):
self.yee_grid_EM_fields = af.moddims(
af.to_array(self._local_fields_array), 6, 1, N_q1_local + 2 * N_g,
N_q2_local + 2 * N_g)
af.eval(self.yee_grid_EM_fields)
else:
self.cell_centered_EM_fields = af.moddims(
af.to_array(self._local_fields_array), 6, 1, N_q1_local + 2 * N_g,
N_q2_local + 2 * N_g)
af.eval(self.cell_centered_EM_fields)
if (self.performance_test_flag == True):
af.sync()
toc = af.time()
self.time_communicate_fields += toc - tic
return
def Jx_Esirkepov_2D( charge_electron,\
number_of_electrons,\
positions_x ,positions_y,\
velocities_x, velocities_y,\
x_grid, y_grid,\
ghost_cells,\
length_domain_x, length_domain_y,\
dx, dy,\
dt\
):
elements = x_grid.elements() * y_grid.elements()
Jx_x_indices, Jx_y_indices,\
Jx_values_at_these_indices,\
Jy_x_indices, Jy_y_indices,\
Jy_values_at_these_indices = indices_and_currents_TSC_2D(charge_electron,\
positions_x, positions_y,\
velocities_x, velocities_y,\
x_grid, y_grid,\
ghost_cells,\
length_domain_x, length_domain_y,\
dt\
)
# Current deposition using numpy's histogram
input_indices = (Jx_x_indices*(y_grid.elements()) + Jx_y_indices)
# Computing Jx_Yee
Jx_Yee, temp = np.histogram( input_indices,\
bins=elements,\
range=(0, elements),\
weights=Jx_values_at_these_indices\
)
Jx_Yee = af.data.moddims(af.to_array(Jx_Yee), y_grid.elements(), x_grid.elements())
# Computing Jy_Yee
input_indices = (Jy_x_indices*(y_grid.elements()) + Jy_y_indices)
Jy_Yee, temp = np.histogram(input_indices,\
bins=elements,\
range=(0, elements),\
weights=Jy_values_at_these_indices\
)
Jy_Yee = af.data.moddims(af.to_array(Jy_Yee), y_grid.elements(), x_grid.elements())
af.eval(Jx_Yee, Jy_Yee)
return Jx_Yee, Jy_Yee
def __init__(self, N):
self.q1_start = 0
self.q2_start = 0
self.q1_end = 1
self.q2_end = 1
self.N_q1 = N
self.N_q2 = N
self.dq1 = (self.q1_end - self.q1_start) / self.N_q1
self.dq2 = (self.q2_end - self.q2_start) / self.N_q2
self.N_ghost = np.random.randint(3, 5)
self.q1 = self.q1_start \
+ (0.5 + np.arange(-self.N_ghost,self.N_q1 + self.N_ghost)) * self.dq1
self.q2 = self.q2_start \
+ (0.5 + np.arange(-self.N_ghost,self.N_q2 + self.N_ghost)) * self.dq2
self.q2, self.q1 = np.meshgrid(self.q2, self.q1)
self.q2, self.q1 = af.to_array(self.q2), af.to_array(self.q1)
self.q1 = af.reorder(self.q1, 2, 0, 1)
self.q2 = af.reorder(self.q2, 2, 0, 1)
self.yee_grid_EM_fields = af.constant(0,
6,
self.q1.shape[1],
self.q1.shape[2],
dtype=af.Dtype.f64)
self._da_fields = PETSc.DMDA().create(
[self.N_q1, self.N_q2],
dof=6,
stencil_width=self.N_ghost,
boundary_type=('periodic', 'periodic'),
stencil_type=1,
)
self._glob_fields = self._da_fields.createGlobalVec()
self._local_fields = self._da_fields.createLocalVec()
self._glob_fields_array = self._glob_fields.getArray()
self._local_fields_array = self._local_fields.getArray()
self.boundary_conditions = type('obj', (object, ), {
'in_q1': 'periodic',
'in_q2': 'periodic'
})
self.performance_test_flag = False
def fft_poisson(rho, dx, dy=None):
"""
FFT solver which returns the value of electric field. This will only work
when the system being solved for has periodic boundary conditions.
Parameters:
-----------
rho : The 1D/2D density array obtained from calculate_density() is passed to this
function.
dx : Step size in the x-grid
dy : Step size in the y-grid.Set to None by default to avoid conflict with the 1D case.
Output:
-------
E_x, E_y : Depending on the dimensionality of the system considered, either both E_x, and
E_y are returned or E_x is returned.
"""
k_x = af.to_array(fftfreq(rho.shape[1], dx))
k_x = af.Array.as_type(k_x, af.Dtype.c64)
k_y = af.to_array(fftfreq(rho.shape[0], dy))
k_x = af.tile(af.reorder(k_x), rho.shape[0], 1)
k_y = af.tile(k_y, 1, rho.shape[1])
k_y = af.Array.as_type(k_y, af.Dtype.c64)
rho = np.array(rho)
rho_hat = fft2(rho)
rho_hat = af.to_array(rho_hat)
potential_hat = af.constant(0,
rho.shape[0],
rho.shape[1],
dtype=af.Dtype.c64)
potential_hat = (1 / (4 * np.pi**2 * (k_x * k_x + k_y * k_y))) * rho_hat
potential_hat[0, 0] = 0
potential_hat = np.array(potential_hat)
E_x_hat = -1j * 2 * np.pi * np.array(k_x) * potential_hat
E_y_hat = -1j * 2 * np.pi * np.array(k_y) * potential_hat
E_x = (ifft2(E_x_hat)).real
E_y = (ifft2(E_y_hat)).real
E_x = af.to_array(E_x)
E_y = af.to_array(E_y)
af.eval(E_x, E_y)
return (E_x, E_y)
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 fft_poisson(self, f=None):
"""
Solves the Poisson Equation using the FFTs:
Used as a backup solver in case of low resolution runs
(ie. used on a single node) with periodic boundary
conditions.
"""
if (self.performance_test_flag == True):
tic = af.time()
if (self._comm.size != 1):
raise Exception('FFT solver can only be used when run in serial')
else:
N_g = self.N_ghost
rho = af.reorder( self.physical_system.params.charge_electron \
* self.compute_moments('density', f)[:, N_g:-N_g, N_g:-N_g],
1, 2, 0
)
k_q1 = fftfreq(rho.shape[0], self.dq1)
k_q2 = fftfreq(rho.shape[1], self.dq2)
k_q2, k_q1 = np.meshgrid(k_q2, k_q1)
k_q1 = af.to_array(k_q1)
k_q2 = af.to_array(k_q2)
rho_hat = af.fft2(rho)
potential_hat = rho_hat / (4 * np.pi**2 * (k_q1**2 + k_q2**2))
potential_hat[0, 0] = 0
E1_hat = -1j * 2 * np.pi * k_q1 * potential_hat
E2_hat = -1j * 2 * np.pi * k_q2 * potential_hat
# Non-inclusive of ghost-zones:
E1_physical = af.reorder(af.real(af.ifft2(E1_hat)), 2, 0, 1)
E2_physical = af.reorder(af.real(af.ifft2(E2_hat)), 2, 0, 1)
self.cell_centered_EM_fields[0, N_g:-N_g, N_g:-N_g] = E1_physical
self.cell_centered_EM_fields[1, N_g:-N_g, N_g:-N_g] = E2_physical
af.eval(self.cell_centered_EM_fields)
if (self.performance_test_flag == True):
af.sync()
toc = af.time()
self.time_fieldsolver += toc - tic
return
def _calculate_k(self):
"""
Initializes the wave numbers k_q1 and k_q2 which will be
used when solving in fourier space.
"""
k_q1 = 2 * np.pi * fftfreq(self.N_q1, self.dq1)
k_q2 = 2 * np.pi * fftfreq(self.N_q2, self.dq2)
k_q2, k_q1 = np.meshgrid(k_q2, k_q1)
k_q2 = af.to_array(k_q2)
k_q1 = af.to_array(k_q1)
af.eval(k_q1, k_q2)
return(k_q1, k_q2)
def cloud_charge_deposition(charge, no_of_particles, positions_x, positions_y,
x_center_grid, y_center_grid, shape_function,
ghost_cells, Lx, Ly, dx, dy):
elements = x_center_grid.elements() * y_center_grid.elements()
rho_x_indices, rho_y_indices, rho_values_at_these_indices = shape_function(
charge, positions_x, positions_y, x_center_grid, y_center_grid,
ghost_cells, Lx, Ly)
input_indices = (rho_x_indices * (y_center_grid.elements()) +
rho_y_indices)
rho, temp = np.histogram(input_indices,
bins=elements,
range=(0, elements),
weights=rho_values_at_these_indices)
rho = af.data.moddims(af.to_array(rho), y_center_grid.elements(),
x_center_grid.elements())
# Periodic BC's for charge deposition
rho[0, :] = rho[-1, :] + rho[0, :]
rho[-1, :] = rho[0, :].copy()
rho[:, 0] = rho[:, -1] + rho[:, 0]
rho[:, -1] = rho[:, 0].copy()
af.eval(rho)
return rho
def test_calculate_q():
obj = test()
q1, q2 = calculate_q_center(obj)
q1_expected = obj.q1_start + \
(0.5 + np.arange(-obj.N_ghost, obj.N_q1 + obj.N_ghost)) * obj.dq1
q2_expected = obj.q2_start + \
(0.5 + np.arange(-obj.N_ghost, obj.N_q2 + obj.N_ghost)) * obj.dq2
q2_expected, q1_expected = np.meshgrid(q2_expected, q1_expected)
q1_expected = af.reorder(af.to_array(q1_expected), 2, 0, 1)
q2_expected = af.reorder(af.to_array(q2_expected), 2, 0, 1)
assert (af.sum(af.abs(q1_expected - q1)) == 0)
assert (af.sum(af.abs(q2_expected - q2)) == 0)
def load_distribution_function(self, file_name):
"""
This function is used to load the distribution function from the
dump file that was created by dump_distribution_function.
Parameters
----------
file_name : The distribution_function array will be loaded from this
provided file name.
Examples
--------
>> solver.load_distribution_function('distribution_function')
The above statemant will load the distribution function data stored in the file
distribution_function.h5 into self.f
"""
viewer = PETSc.Viewer().createHDF5(file_name + '.h5', PETSc.Viewer.Mode.READ)
self._glob_f.load(viewer)
self.f_hat = 2 * fft2(af.to_array(self._glob_f_array.reshape(self.N_p1 * self.N_p2 * self.N_p3,
self.N_species, self.N_q1, self.N_q2
)
)
) / (self.N_q1 * self.N_q2)
return
def load_EM_fields(self, file_name):
"""
This function is used to load the EM fields from the
dump file that was created by dump_EM_fields.
Parameters
----------
file_name : The EM_fields array will be loaded from this
provided file name.
Examples
--------
>> solver.load_EM_fields('data_EM_fields')
"""
viewer = PETSc.Viewer().createHDF5(file_name + '.h5', PETSc.Viewer.Mode.READ)
self.fields_solver._glob_fields.load(viewer)
self.fields_solver.fields_hat = \
2 * fft2(af.to_array(self.fields_solver._glob_fields_array.reshape(6, 1,
self.N_q1,
self.N_q2
)
)
) / (self.N_q1 * self.N_q2)
def _calculate_q_center(self):
"""
Initializes the cannonical variables q1, q2 using a centered
formulation. The size, and resolution are the same as declared
under domain of the physical system object.
"""
q1_center = self.q1_start + (0.5 + np.arange(self.N_q1)) * self.dq1
q2_center = self.q2_start + (0.5 + np.arange(self.N_q2)) * self.dq2
q2_center, q1_center = np.meshgrid(q2_center, q1_center)
q2_center = af.to_array(q2_center)
q1_center = af.to_array(q1_center)
af.eval(q1_center, q2_center)
return(q1_center, q2_center)
def calculate_x(config):
"""
Returns the 2D array of x which is used in the computations of the Cheng-Knorr code.
Parameters:
-----------
config : Object config which is obtained by set() is passed to this file
Output:
-------
x : Array holding the values of x tiled along axis 1
"""
N_x = config.N_x
N_vel_x = config.N_vel_x
N_ghost_x = config.N_ghost_x
left_boundary = config.left_boundary
right_boundary = config.right_boundary
x = np.linspace(left_boundary, right_boundary, N_x)
dx = x[1] - x[0]
x_ghost_left = np.linspace(-(N_ghost_x)*dx + left_boundary, left_boundary - dx, N_ghost_x)
x_ghost_right = np.linspace(right_boundary + dx, right_boundary + N_ghost_x*dx , N_ghost_x)
x = np.concatenate([x_ghost_left, x, x_ghost_right])
x = af.Array.as_type(af.to_array(x), af.Dtype.f64)
x = af.tile(x, 1, N_vel_x)
af.eval(x)
return x
def load_distribution_function(self, file_name):
"""
This function is used to load the distribution function from the
dump file that was created by dump_distribution_function.
Parameters
----------
file_name : The distribution_function array will be loaded from this
provided file name.
Examples
--------
>> solver.load_distribution_function('distribution_function')
The above statemant will load the distribution function data stored in the file
distribution_function.h5 into self.f
"""
viewer = PETSc.Viewer().createHDF5(file_name + '.h5',
PETSc.Viewer.Mode.READ,
comm=self._comm
)
self._glob_f.load(viewer)
N_g = self.N_ghost
self.f[:, N_g:-N_g, N_g:-N_g] = af.moddims(af.to_array(self._glob_f_array),
self.N_p1 * self.N_p2 * self.N_p3,
self.N_q1, self.N_q2
)
return
def test_dump_moments():
test_obj = test()
dump_moments(test_obj, 'test_file')
h5f = h5py.File('test_file.h5', 'r')
moments_read = h5f['moments'][:]
h5f.close()
moments_read = np.swapaxes(moments_read, 0, 1)
assert (af.sum(
af.to_array(moments_read[:, :, 0]) -
compute_moments_imported(test_obj, 'density')) == 0)
assert (af.sum(
af.to_array(moments_read[:, :, 1]) -
compute_moments_imported(test_obj, 'energy')) == 0)
def calculate_k(N_q1, N_q2, dq1, dq2):
"""
Initializes the wave numbers k_q1 and k_q2 which will be
used when solving in fourier space.
"""
k_q1 = 2 * np.pi * np.fft.fftfreq(N_q1, dq1)
k_q2 = 2 * np.pi * np.fft.fftfreq(N_q2, dq2)
k_q2, k_q1 = np.meshgrid(k_q2, k_q1)
k_q1 = af.to_array(k_q1)
k_q2 = af.to_array(k_q2)
k_q1 = af.reorder(k_q1, 2, 3, 0, 1)
k_q2 = af.reorder(k_q2, 2, 3, 0, 1)
af.eval(k_q1, k_q2)
return (k_q1, k_q2)
def Umeda_2003(charge,\
no_of_particles,\
positions_x,\
velocities_x,\
x_center_grid,\
ghost_cells,\
Lx,\
dx,\
dt\
):
'''
function set_up_perturbation(positions_x, number_particles, N_divisions,\
amplitude , k, length_domain_x\
):
-----------------------------------------------------------------------
Input variables: positions_x, number_particles, N_divisions, amplitude, k,length_domain_x
positions_x: An one dimensional array of size equal to number of particles taken in the PIC code.
It contains the positions of particles.
number_particles: The number of electrons /macro particles
N_divisions: The number of divisions considered for placing the macro particles
amplitude: This is the amplitude of the density perturbation
k_x: The is the wave number of the cosine density pertubation
length_domain_x: This is the length of the domain in x direction
-----------------------------------------------------------------------
returns: Jx
This function returns a array positions_x such that there is a cosine density perturbation
of the given amplitude
'''
elements = x_center_grid.elements()
Jx_x_indices, Jx_values_at_these_indices = Umeda_b1_deposition(charge,\
positions_x,\
velocities_x,\
x_center_grid,\
ghost_cells,\
Lx,\
dt\
)
input_indices = (Jx_x_indices)
Jx, temp = np.histogram(input_indices,
bins=elements,
range=(0, elements),
weights=Jx_values_at_these_indices)
Jx = af.to_array(Jx)
af.eval(Jx)
return Jx
def simple_interop(verbose = False):
if af.AF_NUMPY_FOUND:
import numpy as np
n = np.random.random((5,))
a = af.to_array(n)
n2 = np.array(a)
assert((n==n2).all())
n2[:] = 0
a.to_ndarray(n2)
assert((n==n2).all())
n = np.random.random((5,3))
a = af.to_array(n)
n2 = np.array(a)
assert((n==n2).all())
n2[:] = 0
a.to_ndarray(n2)
assert((n==n2).all())
n = np.random.random((5,3,2))
a = af.to_array(n)
n2 = np.array(a)
assert((n==n2).all())
n2[:] = 0
a.to_ndarray(n2)
assert((n==n2).all())
n = np.random.random((5,3,2,2))
a = af.to_array(n)
n2 = np.array(a)
assert((n==n2).all())
n2[:] = 0
a.to_ndarray(n2)
assert((n==n2).all())
if af.AF_PYCUDA_FOUND and af.get_active_backend() == 'cuda':
import pycuda.autoinit
import pycuda.gpuarray as cudaArray
n = np.random.random((5,))
c = cudaArray.to_gpu(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())
n = np.random.random((5,3))
c = cudaArray.to_gpu(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())
n = np.random.random((5,3,2))
c = cudaArray.to_gpu(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())
n = np.random.random((5,3,2,2))
c = cudaArray.to_gpu(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())
if af.AF_PYOPENCL_FOUND and af.backend.name() == 'opencl':
# This needs fixing upstream
# https://github.com/arrayfire/arrayfire/issues/1728
# import pyopencl as cl
# import pyopencl.array as clArray
# ctx = cl.create_some_context()
# queue = cl.CommandQueue(ctx)
# n = np.random.random((5,))
# c = cl.array.to_device(queue, n)
# a = af.to_array(c)
# n2 = np.array(a)
# assert((n==n2).all())
# n = np.random.random((5,3))
# c = cl.array.to_device(queue, n)
# a = af.to_array(c)
# n2 = np.array(a)
# assert((n==n2).all())
# n = np.random.random((5,3,2))
# c = cl.array.to_device(queue, n)
# a = af.to_array(c)
# n2 = np.array(a)
# assert((n==n2).all())
# n = np.random.random((5,3,2,2))
# c = cl.array.to_device(queue, n)
# a = af.to_array(c)
# n2 = np.array(a)
# assert((n==n2).all())
pass
if af.AF_NUMBA_FOUND and af.get_active_backend() == 'cuda':
import numba
from numba import cuda
n = np.random.random((5,))
c = cuda.to_device(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())
n = np.random.random((5,3))
c = cuda.to_device(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())
n = np.random.random((5,3,2))
c = cuda.to_device(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())
n = np.random.random((5,3,2,2))
c = cuda.to_device(n)
a = af.to_array(c)
n2 = np.array(a)
assert((n==n2).all())