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_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_density(f, vel_x): deltav = af.sum(vel_x[0, 1]-vel_x[0, 0]) value_of_density = af.sum(f, 1)*deltav af.eval(value_of_density) return(value_of_density)
def center_of_mass(inarr):
arr = af.abs(inarr)
normalizer = af.sum(arr)
t_dims = list(arr.dims())
mod_dims = [None, None, None, None]
for i in range(len(t_dims)):
mod_dims[i] = 1
com = []
for dim in range(len(t_dims)):
# swap
mod_dims[dim] = t_dims[dim]
t_dims[dim] = 1
grid = af.iota(mod_dims[0],
mod_dims[1],
mod_dims[2],
mod_dims[3],
tile_dims=t_dims)
# print(grid)
com.append(af.sum(grid * arr) / normalizer)
# swap back
t_dims[dim] = mod_dims[dim]
mod_dims[dim] = 1
return com
def fraction_finder(positions_x, positions_y, x_grid, y_grid, dx, dy):
'''
function fraction_finder(positions_x, positions_y, x_grid, y_grid, dx, dy)
-----------------------------------------------------------------------
Input variables: positions_x and 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 in x direction.
positions_y: An one dimensional array of size equal to number of particles taken in the PIC code.
It contains the positions of particles in y direction.
x_grid, y_grid: This is an array denoting the position grid chosen in the PIC simulation in
x and y directions respectively
dx, dy: This is the distance between any two consecutive grid nodes of the position grid
in x and y directions respectively
-----------------------------------------------------------------------
returns: x_frac, y_frac
This function returns the fractions of grid cells needed to perform the 2D charge deposition
'''
x_frac = (positions_x - af.sum(x_grid[0])) / dx
y_frac = (positions_y - af.sum(y_grid[0])) / dy
af.eval(x_frac, y_frac)
return x_frac, y_frac
def polyval_2d(poly_2d, xi, eta):
'''
'''
poly_2d_shape = poly_2d.shape
poly_xy = af.tile(poly_2d, d0 = 1, d1 = 1, d2 = 1, d3 = xi.shape[0])
poly_xy_shape = poly_xy.shape
# print(poly_xy)
xi_power = af.flip(af.range(poly_xy_shape[1], dtype = af.Dtype.u32))
xi_power = af.tile(af.transpose(xi_power), d0 = poly_xy_shape[0])
xi_power = af.tile(xi_power, d0 = 1, d1 = 1, d2 = xi.shape[0])
eta_power = af.flip(af.range(poly_xy_shape[0], dtype = af.Dtype.u32))
eta_power = af.tile(eta_power, d0 = 1, d1 = poly_xy_shape[1])
eta_power = af.tile(eta_power, d0 = 1, d1 = 1, d2 = eta.shape[0])
Xi = af.reorder(xi, d0 = 2, d1 = 1, d2 = 0)
Xi = af.tile(Xi, d0 = poly_xy_shape[0], d1 = poly_xy_shape[1])
Xi = af.pow(Xi, xi_power)
Xi = af.reorder(Xi, d0 = 0, d1 = 1, d2 = 3, d3 = 2)
# print(Xi)
Eta = af.reorder(eta, d0 = 2, d1 = 1, d2 = 0)
Eta = af.tile(Eta, d0 = poly_xy_shape[0], d1 = poly_xy_shape[1])
Eta = af.pow(Eta, eta_power)
Eta = af.reorder(Eta, d0 = 0, d1 = 1, d2 = 3, d3 = 2)
# print(Eta)
Xi_Eta = Xi * Eta
poly_val = af.broadcast(multiply, poly_xy, Xi_Eta)
poly_val = af.sum(af.sum(poly_val, dim = 1), dim = 0)
poly_val = af.reorder(poly_val, d0 = 2, d1 = 3, d2 = 0, d3 = 1)
return poly_val
def integrate(integrand_coeffs):
'''
Performs integration according to the given quadrature method
by taking in the coefficients of the polynomial and the number of
quadrature points.
The number of quadrature points and the quadrature scheme are set
in params.py module.
Parameters
----------
integrand_coeffs : arrayfire.Array [M N 1 1]
The coefficients of M number of polynomials of order N
arranged in a 2D array.
Returns
-------
Integral : arrayfire.Array [M 1 1 1]
The value of the definite integration performed using the
specified quadrature method for M polynomials.
'''
integrand = integrand_coeffs
if (params.scheme == 'gauss_quadrature'):
#print('gauss_quad')
gaussian_nodes = params.gauss_points
Gauss_weights = params.gauss_weights
nodes_tile = af.transpose(
af.tile(gaussian_nodes, 1, integrand.shape[1]))
power = af.flip(af.range(integrand.shape[1]))
nodes_power = af.broadcast(utils.power, nodes_tile, power)
weights_tile = af.transpose(
af.tile(Gauss_weights, 1, integrand.shape[1]))
nodes_weight = nodes_power * weights_tile
value_at_gauss_nodes = af.matmul(integrand, nodes_weight)
integral = af.sum(value_at_gauss_nodes, 1)
if (params.scheme == 'lobatto_quadrature'):
#print('lob_quad')
lobatto_nodes = params.lobatto_quadrature_nodes
Lobatto_weights = params.lobatto_weights_quadrature
nodes_tile = af.transpose(af.tile(lobatto_nodes, 1,
integrand.shape[1]))
power = af.flip(af.range(integrand.shape[1]))
nodes_power = af.broadcast(utils.power, nodes_tile, power)
weights_tile = af.transpose(
af.tile(Lobatto_weights, 1, integrand.shape[1]))
nodes_weight = nodes_power * weights_tile
value_at_lobatto_nodes = af.matmul(integrand, nodes_weight)
integral = af.sum(value_at_lobatto_nodes, 1)
return integral
def cost(Weights, X, Y, lambda_param=1.0):
# Number of samples
m = Y.dims()[0]
dim0 = Weights.dims()[0]
dim1 = Weights.dims()[1] if len(Weights.dims()) > 1 else None
dim2 = Weights.dims()[2] if len(Weights.dims()) > 2 else None
dim3 = Weights.dims()[3] if len(Weights.dims()) > 3 else None
# Make the lambda corresponding to Weights(0) == 0
lambdat = af.constant(lambda_param, dim0, dim1, dim2, dim3)
# No regularization for bias weights
lambdat[0, :] = 0
# Get the prediction
H = predict_prob(X, Weights)
# Cost of misprediction
Jerr = -1 * af.sum(Y * af.log(H) + (1 - Y) * af.log(1 - H), dim=0)
# Regularization cost
Jreg = 0.5 * af.sum(lambdat * Weights * Weights, dim=0)
# Total cost
J = (Jerr + Jreg) / m
# Find the gradient of cost
D = (H - Y)
dJ = (af.matmulTN(X, D) + lambdat * Weights) / m
return J, dJ
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 calculate_vbulk(f, vel_x): deltav = af.sum(vel_x[0, 1]-vel_x[0, 0]) value_of_momentum = af.sum(f*vel_x, 1)*deltav value_of_vbulk = value_of_momentum/calculate_density(f, vel_x) af.eval(value_of_vbulk) return(value_of_vbulk)
def calculate_temperature(f, vel_x): deltav = af.sum(vel_x[0, 1]-vel_x[0, 0]) v_bulk = af.tile(calculate_vbulk(f, vel_x), 1, N_velocity) value_of_temperature = af.sum(f*(vel_x-v_bulk)**2, 1)*deltav value_of_temperature = value_of_temperature/calculate_density(f, vel_x) af.eval(value_of_temperature) return(value_of_temperature)
def integrate_1d(polynomials, order, scheme = 'gauss'):
'''
Integrates single variables using the Gauss-Legendre or Gauss-Lobatto
quadrature.
Parameters
----------
polynomials : af.Array [number_of_polynomials degree 1 1]
The polynomials to be integrated.
order : int
Order of the quadrature.
scheme : str
Possible options are
- ``gauss`` for using Gauss-Legendre quadrature
- ``lobatto`` for using Gauss-Lobatto quadrature
Returns
-------
integral : af.Array [number_of_polynomials 1 1 1]
The integral for the respective polynomials using the given
quadrature scheme.
'''
integral = 0.0
if scheme == 'gauss':
N_g = order
xi_gauss = af.np_to_af_array(lagrange.gauss_nodes(N_g))
gauss_weights = lagrange.gaussian_weights(N_g)
polyval_gauss = polyval_1d(polynomials, xi_gauss)
integral = af.sum(af.transpose(af.broadcast(multiply,
af.transpose(polyval_gauss),
gauss_weights)), dim = 1)
return integral
elif scheme == 'lobatto':
N_l = order
xi_lobatto = lagrange.LGL_points(N_l)
lobatto_weights = lagrange.lobatto_weights(N_l)
polyval_lobatto = polyval_1d(polynomials, xi_lobatto)
integral = af.sum(af.transpose(af.broadcast(multiply,
af.transpose(polyval_lobatto),
lobatto_weights)), dim = 1)
return integral
else:
return -1.
def test_fdtd_mode1():
error_B1 = np.zeros(3)
error_B2 = np.zeros(3)
error_E3 = np.zeros(3)
N = 2**np.arange(5, 8)
for i in range(N.size):
obj = test(N[i])
N_g = obj.N_ghost
B1_fdtd = gauss1D(obj.q2[:, N_g:-N_g, N_g:-N_g], 0.1)
B2_fdtd = gauss1D(obj.q1[:, N_g:-N_g, N_g:-N_g], 0.1)
obj.yee_grid_EM_fields[3, N_g:-N_g, N_g:-N_g] = B1_fdtd
obj.yee_grid_EM_fields[4, N_g:-N_g, N_g:-N_g] = B2_fdtd
dt = obj.dq1 / 2
time = np.arange(dt, 1 + dt, dt)
E3_initial = obj.yee_grid_EM_fields[2].copy()
B1_initial = obj.yee_grid_EM_fields[3].copy()
B2_initial = obj.yee_grid_EM_fields[4].copy()
obj.J1, obj.J2, obj.J3 = 0, 0, 0
for time_index, t0 in enumerate(time):
fdtd(obj, dt)
error_B1[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[3, N_g:-N_g, N_g:-N_g] -
B1_initial[0, N_g:-N_g, N_g:-N_g])) / (
B1_initial.elements())
error_B2[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[4, N_g:-N_g, N_g:-N_g] -
B2_initial[0, N_g:-N_g, N_g:-N_g])) / (
B2_initial.elements())
error_E3[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[2, N_g:-N_g, N_g:-N_g] -
E3_initial[0, N_g:-N_g, N_g:-N_g])) / (
E3_initial.elements())
poly_B1 = np.polyfit(np.log10(N), np.log10(error_B1), 1)
poly_B2 = np.polyfit(np.log10(N), np.log10(error_B2), 1)
poly_E3 = np.polyfit(np.log10(N), np.log10(error_E3), 1)
assert (abs(poly_B1[0] + 3) < 0.6)
assert (abs(poly_B2[0] + 3) < 0.6)
assert (abs(poly_E3[0] + 2) < 0.6)
def evolve_electrodynamic_fields(self, J1, J2, J3, dt):
"""
Evolve the fields using FDTD.
Parameters
----------
J1 : af.Array
Array which contains the J1 current for each species.
J2 : af.Array
Array which contains the J2 current for each species.
J3 : af.Array
Array which contains the J3 current for each species.
dt: double
Timestep size
"""
self.J1 = af.sum(J1, 1)
self.J2 = af.sum(J2, 1)
self.J3 = af.sum(J3, 1)
self.current_values_to_yee_grid()
# Here:
# cell_centered_EM_fields[:3] is at n
# cell_centered_EM_fields[3:] is at n+1/2
# cell_centered_EM_fields_at_n_plus_half[3:] is at n-1/2
self.cell_centered_EM_fields_at_n[:3] = self.cell_centered_EM_fields[:
3]
self.cell_centered_EM_fields_at_n[3:] = \
0.5 * ( self.cell_centered_EM_fields_at_n_plus_half[3:]
+ self.cell_centered_EM_fields[3:]
)
self.cell_centered_EM_fields_at_n_plus_half[
3:] = self.cell_centered_EM_fields[3:]
fdtd(self, dt)
self.yee_grid_to_cell_centered_grid()
# Here
# cell_centered_EM_fields[:3] is at n+1
# cell_centered_EM_fields[3:] is at n+3/2
self.cell_centered_EM_fields_at_n_plus_half[:3] = \
0.5 * ( self.cell_centered_EM_fields_at_n[:3]
+ self.cell_centered_EM_fields[:3]
)
return
def check_error(params):
error = np.zeros(N.size)
for i in range(N.size):
domain.N_p1 = int(N[i])
domain.N_p2 = int(N[i])
domain.N_p3 = int(N[i])
# Defining the physical system to be solved:
system = physical_system(domain, boundary_conditions, params,
initialize, advection_terms,
collision_operator.BGK, moments)
# Declaring a linear system object which will evolve the defined physical system:
nls = nonlinear_solver(system)
# Time parameters:
dt = 0.0001 * 32 / nls.N_p1
t_final = 0.2
time_array = np.arange(dt, t_final + dt, dt)
if (time_array[-1] > t_final):
time_array = np.delete(time_array, -1)
# Finding final resting point of the blob:
E1 = nls.fields_solver.cell_centered_EM_fields[0]
E2 = nls.fields_solver.cell_centered_EM_fields[1]
E3 = nls.fields_solver.cell_centered_EM_fields[2]
B1 = nls.fields_solver.cell_centered_EM_fields[3]
B2 = nls.fields_solver.cell_centered_EM_fields[4]
B3 = nls.fields_solver.cell_centered_EM_fields[5]
sol = odeint(dp_dt,
np.array([0, 0, 0]),
time_array,
args=(af.mean(E1), af.mean(E2), af.mean(E3), af.mean(B1),
af.mean(B2), af.mean(B3), af.sum(params.charge[0]),
af.sum(params.mass[0])),
atol=1e-12,
rtol=1e-12)
f_reference = af.broadcast(initialize.initialize_f, nls.q1_center,
nls.q2_center, nls.p1_center - sol[-1, 0],
nls.p2_center - sol[-1, 1],
nls.p3_center - sol[-1, 2], params)
for time_index, t0 in enumerate(time_array):
nls.strang_timestep(dt)
error[i] = af.mean(af.abs(nls.f - f_reference))
return (error)
def fraction_finder(x, y, x_grid, y_grid, dx_frac_finder, dy_frac_finder):
# print('x_grid[0] is ', x_grid[0])
x_frac = (x - af.sum(x_grid[0])) / dx_frac_finder
# print('y_grid[0] is ', y_grid[0])
# print(' (y - (y_grid[0])) / dy_frac_finder is ', (y - (y_grid[0])) / dy_frac_finder)
y_frac = (y - af.sum(y_grid[0])) / dy_frac_finder
af.eval(x_frac, y_frac)
return x_frac, y_frac
def test_fdtd_mode2():
error_E1 = np.zeros(3)
error_E2 = np.zeros(3)
error_B3 = np.zeros(3)
N = 2**np.arange(5, 8)
for i in range(N.size):
obj = test(N[i])
N_g = obj.N_ghost
obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] = gauss1D(
obj.q2[:, N_g:-N_g, N_g:-N_g], 0.1)
obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] = gauss1D(
obj.q1[:, N_g:-N_g, N_g:-N_g], 0.1)
dt = obj.dq1 / 2
time = np.arange(dt, 1 + dt, dt)
B3_initial = obj.yee_grid_EM_fields[5].copy()
E1_initial = obj.yee_grid_EM_fields[0].copy()
E2_initial = obj.yee_grid_EM_fields[1].copy()
obj.J1, obj.J2, obj.J3 = 0, 0, 0
for time_index, t0 in enumerate(time):
fdtd(obj, dt)
error_E1[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[0, N_g:-N_g, N_g:-N_g] -
E1_initial[:, N_g:-N_g, N_g:-N_g])) / (
E1_initial.elements())
error_E2[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[1, N_g:-N_g, N_g:-N_g] -
E2_initial[:, N_g:-N_g, N_g:-N_g])) / (
E2_initial.elements())
error_B3[i] = af.sum(
af.abs(obj.yee_grid_EM_fields[5, N_g:-N_g, N_g:-N_g] -
B3_initial[:, N_g:-N_g, N_g:-N_g])) / (
B3_initial.elements())
poly_E1 = np.polyfit(np.log10(N), np.log10(error_E1), 1)
poly_E2 = np.polyfit(np.log10(N), np.log10(error_E2), 1)
poly_B3 = np.polyfit(np.log10(N), np.log10(error_B3), 1)
assert (abs(poly_E1[0] + 3) < 0.4)
assert (abs(poly_E2[0] + 3) < 0.4)
assert (abs(poly_B3[0] + 2) < 0.4)
def gaussian(dims, sigmas, **kwargs):
alpha = 1.0
grid = af.constant(1.0, dims[0], dims[1], dims[2])
for i in range(len(sigmas)):
multiplier = -0.5 * alpha / pow(sigmas[i], 2)
exponent = af.pow((af.range(dims[0], dims[1], dims[2], dim=i) -
(dims[i] - 1) / 2.0), 2) * multiplier
grid = grid * af.arith.exp(exponent)
grid_tot = af.sum(af.sum(af.sum(grid, dim=0), dim=1), dim=2)
grid_total = af.tile(grid_tot, dims[0], dims[1], dims[2])
grid = grid / grid_total
return grid
def func(x0):
fields = self._scattering_obj.forward(x0, fx_illu, fy_illu)
field_scattered = self._defocus_obj.forward(field_scattered, self.prop_distances)
field_measure = self._crop_obj.forward(field_scattered)
residual = af.abs(field_measure) - amplitude
function_value = af.sum(residual*af.conjg(residual)).real
return function_value
def lagrange_interpolation(fn_i):
'''
Finds the general interpolation of a function.
Parameters
----------
fn_i : af.Array [N N_LGL 1 1]
Value of :math:`N` functions at the LGL points.
Returns
-------
lagrange_interpolation : af.Array [N N_LGL 1 1]
:math:`N` interpolated polynomials for
:math:`N` functions.
'''
fn_i = af.transpose(af.reorder(fn_i, d0=2, d1=1, d2=0))
lagrange_interpolation = af.broadcast(utils.multiply,
params.lagrange_coeffs, fn_i)
lagrange_interpolation = af.reorder(af.sum(lagrange_interpolation, dim=0),
d0=2,
d1=1,
d2=0)
return lagrange_interpolation
def input_info(A, Asp):
m, n = A.dims()
nnz = af.sum((A != 0))
print(" matrix size: %i x %i" %(m, n))
print(" matrix sparsity: %2.2f %%" %(100*nnz/n**2,))
print(" dense matrix memory usage: ")
print(" sparse matrix memory usage: ")
def _binObject(self, obj, adjoint=False):
"""
function to bin the object by factor of slice_binning_factor
"""
if self.slice_binning_factor == 1:
return obj
assert self.shape[2] >= 1
if adjoint:
obj_out = af.constant(0.0,
self._shape_full[0],
self._shape_full[1],
self._shape_full[2],
dtype=af_complex_datatype)
for idx in range((self.shape[2] - 1) * self.slice_binning_factor,
-1, -self.slice_binning_factor):
idx_slice = slice(
idx,
np.min([obj_out.shape[2],
idx + self.slice_binning_factor]))
obj_out[:, :, idx_slice] = af.broadcast(
self.assign_broadcast, obj_out[:, :, idx_slice],
obj[:, :, idx // self.slice_binning_factor])
else:
obj_out = af.constant(0.0,
self.shape[0],
self.shape[1],
self.shape[2],
dtype=af_complex_datatype)
for idx in range(0, obj.shape[2], self.slice_binning_factor):
idx_slice = slice(
idx,
np.min([obj.shape[2], idx + self.slice_binning_factor]))
obj_out[:, :, idx // self.slice_binning_factor] = af.sum(
obj[:, :, idx_slice], 2)
return obj_out
def lobatto_quad_multivar_poly(poly_xi_eta, N_quad, advec_var):
'''
'''
shape_poly_2d = shape(poly_xi_eta)
xi_LGL = lagrange.LGL_points(N_quad)
eta_LGL = lagrange.LGL_points(N_quad)
Xi, Eta = af_meshgrid(xi_LGL, eta_LGL)
Xi = af.flat(Xi)
Eta = af.flat(Eta)
w_i = lagrange.lobatto_weights(N_quad)
w_j = lagrange.lobatto_weights(N_quad)
W_i, W_j = af_meshgrid(w_i, w_j)
W_i = af.tile(af.flat(W_i), d0 = 1, d1 = shape_poly_2d[2])
W_j = af.tile(af.flat(W_j), d0 = 1, d1 = shape_poly_2d[2])
P_xi_eta_quad_val = af.transpose(polyval_2d(poly_xi_eta, Xi, Eta))
integral = af.sum(W_i * W_j * P_xi_eta_quad_val, dim = 0)
return af.transpose(integral)
def log_loss(y_true, y_prob):
"""Compute Logistic loss for classification.
Parameters
----------
y_true : array-like or label indicator matrix
Ground truth (correct) labels.
y_prob : array-like of float, shape = (n_samples, n_classes)
Predicted probabilities, as returned by a classifier's
predict_proba method.
Returns
-------
loss : float
The degree to which the samples are correctly predicted.
"""
# eps = np.finfo(y_prob.dtype).eps
# y_prob = np.clip(y_prob, eps, 1 - eps)
# if y_prob.shape[1] == 1:
# y_prob = np.append(1 - y_prob, y_prob, axis=1)
#
# if y_true.shape[1] == 1:
# y_true = np.append(1 - y_true, y_true, axis=1)
#
# return - xlogy(y_true, y_prob).sum() / y_prob.shape[0]
eps = numpy.finfo(typemap(y_prob.dtype())).eps
y_prob[y_prob < eps] = eps
y_prob[y_prob > (1.0 - eps)] = 1.0 - eps
if y_prob.numdims() == 1:
y_prob = af.join(1, (1.0 - y_prob).as_type(y_prob.dtype()), y_prob)
if y_true.numdims() == 1:
y_true = af.join(1, (1.0 - y_true).as_type(y_true.dtype()), y_true)
return - af.sum(af.flat(xlogy(y_true, y_prob))) / y_prob.shape[0]
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 sum(a: ndarray, axis: tp.Optional[int] = None) \
-> tp.Union[numbers.Number, ndarray]:
"""
Sum of array elements over a given axis.
"""
return _wrap_af_array(af.sum(a._af_array, dim=axis))
def compute_electrostatic_fields(self, rho_hat):
"""
Computes the electrostatic fields by making use of FFTs by solving
the Poisson equation: div^2 phi = rho to return the FT of the
fields.
Parameters
----------
rho_hat : af.Array
FT for the charge density for each of the species.
shape:(1, N_s, N_q1, N_q2)
"""
# Summing over all the species:
phi_hat = multiply(af.sum(rho_hat, 1), 1 / (self.k_q1**2 + self.k_q2**2)) # (1, 1, N_q1, N_q2)
# Setting the background electric potential to zero:
phi_hat[: , :, 0, 0] = 0
self.E1_hat = -phi_hat * 1j * self.k_q1 / self.params.eps
self.E2_hat = -phi_hat * 1j * self.k_q2 / self.params.eps
self.E3_hat = 0 * self.E1_hat
self.B1_hat = 0 * self.E1_hat
self.B2_hat = 0 * self.E1_hat
self.B3_hat = 0 * self.E1_hat
af.eval(self.E1_hat, self.E2_hat, self.E3_hat,
self.B1_hat, self.B2_hat, self.B3_hat
)
return
def lagrange_interpolation_u(u, gv):
'''
Calculates the coefficients of the Lagrange interpolation using
the value of u at the mapped LGL points in the domain.
The interpolation using the Lagrange basis polynomials is given by
:math:`L_i(\\xi) u_i(\\xi)`
Where L_i are the Lagrange basis polynomials and u_i is the value
of u at the LGL points.
Parameters
----------
u : arrayfire.Array [N_LGL N_Elements 1 1]
The value of u at the mapped LGL points.
Returns
-------
lagrange_interpolated_coeffs : arrayfire.Array[1 N_LGL N_Elements 1]
The coefficients of the polynomials obtained
by Lagrange interpolation. Each polynomial
is of order N_LGL - 1.
'''
lagrange_coeffs_tile = af.tile(gv.lagrange_coeffs, 1, 1,\
params.N_Elements)
reordered_u = af.reorder(u, 0, 2, 1)
lagrange_interpolated_coeffs = af.sum(af.broadcast(utils.multiply,\
reordered_u, lagrange_coeffs_tile), 0)
return lagrange_interpolated_coeffs
def input_info(A, Asp):
m, n = A.dims()
nnz = af.sum((A != 0))
print(" matrix size: %i x %i" % (m, n))
print(" matrix sparsity: %2.2f %%" % (100 * nnz / n**2, ))
print(" dense matrix memory usage: ")
print(" sparse matrix memory usage: ")
def matmul_3D(a, b):
'''
Finds the matrix multiplication of :math:`Q` pairs of matrices ``a`` and
``b``.
Parameters
----------
a : af.Array [M N Q 1]
First set of :math:`Q` 2D arrays :math:`N \\neq 1` and :math:`M \\neq 1`.
b : af.Array [N P Q 1]
Second set of :math:`Q` 2D arrays :math:`P \\neq 1`.
Returns
-------
matmul : af.Array [M P Q 1]
Matrix multiplication of :math:`Q` sets of 2D arrays.
'''
shape_a = shape(a)
shape_b = shape(b)
P = shape_b[1]
a = af.transpose(a)
a = af.reorder(a, d0=0, d1=3, d2=2, d3=1)
a = af.tile(a, d0=1, d1=P)
b = af.tile(b, d0=1, d1=1, d2=1, d3=a.shape[3])
matmul = af.sum(a * b, dim=0)
matmul = af.reorder(matmul, d0=3, d1=1, d2=2, d3=0)
return matmul
def compute_electrostatic_fields(self, rho):
# Summing for all species:
rho = af.sum(rho, 1)
if (self.params.fields_solver == 'fft'):
fft_poisson(self, rho)
communicate.communicate_fields(self)
apply_bcs_fields(self)
def __index_shape__(A_shape, idx, del_singleton=True):
shape = []
for i in range(0,len(idx)):
if(idx[i] is None):
shape.append(0)
elif(isinstance(idx[i],numbers.Number)):
if del_singleton:
# Remove dimensions indexed with a scalar
continue
else:
shape.append(1)
elif(isinstance(idx[i],arrayfire.index.Seq)):
if(idx[i].s == arrayfire.af_span):
shape.append(A_shape[i])
else:
shape.append(idx[i].size)
elif(isinstance(idx[i],slice)):
shape.append(__slice_len__(idx[i], pu.c2f(A_shape), i))
elif(isinstance(idx[i], arrayfire.Array)):
if idx[i].dtype() is arrayfire.Dtype.b8:
shape.append(int(arrayfire.sum(idx[i])))
else:
shape.append(idx[i].elements())
elif(isinstance(idx[i],arrayfire.index)):
if(idx[i].isspan()):
shape.append(A_shape[i])
else:
af_idx = idx[i].get()
if(af_idx.isBatch):
raise ValueError
if(af_idx.isSeq):
shape.append(arrayfire.seq(af_idx.seq()).size)
else:
shape.append(af_idx.arr_elements())
else:
raise ValueError
return pu.c2f(shape)
def test():
print("\nTesting benchmark functions...")
A, b, x0 = setup_input(n=50, sparsity=7) # dense A
Asp = to_sparse(A)
x1, _ = calc_arrayfire(A, b, x0)
x2, _ = calc_arrayfire(Asp, b, x0)
if af.sum(af.abs(x1 - x2)/x2 > 1e-5):
raise ValueError("arrayfire test failed")
if np:
An = to_numpy(A)
bn = to_numpy(b)
x0n = to_numpy(x0)
x3, _ = calc_numpy(An, bn, x0n)
if not np.allclose(x3, x1.to_list()):
raise ValueError("numpy test failed")
if sp:
Asc = to_scipy_sparse(Asp)
x4, _ = calc_scipy_sparse(Asc, bn, x0n)
if not np.allclose(x4, x1.to_list()):
raise ValueError("scipy.sparse test failed")
x5, _ = calc_scipy_sparse_linalg_cg(Asc, bn, x0n)
if not np.allclose(x5, x1.to_list()):
raise ValueError("scipy.sparse.linalg.cg test failed")
print(" all tests passed...")
def calc_pi_device(samples):
x = randu(samples)
y = randu(samples)
return 4 * af.sum((x * x + y * y) < 1) / samples
def sum(self, s, axis):
if self.dtype == numpy.bool:
s = arrayfire.cast(s, pu.typemap(numpy.int64))
# s = s.astype(pu.typemap(numpy.int64))
return arrayfire.sum(s, dim=axis)
def simple_algorithm(verbose = False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(3, 3)
print_func(af.sum(a), af.product(a), af.min(a), af.max(a),
af.count(a), af.any_true(a), af.all_true(a))
display_func(af.sum(a, 0))
display_func(af.sum(a, 1))
display_func(af.product(a, 0))
display_func(af.product(a, 1))
display_func(af.min(a, 0))
display_func(af.min(a, 1))
display_func(af.max(a, 0))
display_func(af.max(a, 1))
display_func(af.count(a, 0))
display_func(af.count(a, 1))
display_func(af.any_true(a, 0))
display_func(af.any_true(a, 1))
display_func(af.all_true(a, 0))
display_func(af.all_true(a, 1))
display_func(af.accum(a, 0))
display_func(af.accum(a, 1))
display_func(af.sort(a, is_ascending=True))
display_func(af.sort(a, is_ascending=False))
b = (a > 0.1) * a
c = (a > 0.4) * a
d = b / c
print_func(af.sum(d));
print_func(af.sum(d, nan_val=0.0));
display_func(af.sum(d, dim=0, nan_val=0.0));
val,idx = af.sort_index(a, is_ascending=True)
display_func(val)
display_func(idx)
val,idx = af.sort_index(a, is_ascending=False)
display_func(val)
display_func(idx)
b = af.randu(3,3)
keys,vals = af.sort_by_key(a, b, is_ascending=True)
display_func(keys)
display_func(vals)
keys,vals = af.sort_by_key(a, b, is_ascending=False)
display_func(keys)
display_func(vals)
c = af.randu(5,1)
d = af.randu(5,1)
cc = af.set_unique(c, is_sorted=False)
dd = af.set_unique(af.sort(d), is_sorted=True)
display_func(cc)
display_func(dd)
display_func(af.set_union(cc, dd, is_unique=True))
display_func(af.set_union(cc, dd, is_unique=False))
display_func(af.set_intersect(cc, cc, is_unique=True))
display_func(af.set_intersect(cc, cc, is_unique=False))
#!/usr/bin/python import arrayfire as arr a = arr.random.rand(4,3) b = arr.random.randn(3,5) c = arr.dot(a,b) d = arr.sum(c) d0 = arr.sum(c, 0) d1 = arr.sum(c, 1) print(a) print(b) print(c) print(d) print(d0) print(d1)
A[1,:] = B[2,:]
af.display(A)
print("\n---- Bitwise operations\n")
af.display(A & B)
af.display(A | B)
af.display(A ^ B)
print("\n---- Transpose\n")
af.display(A)
af.display(af.transpose(A))
print("\n---- Flip Vertically / Horizontally\n")
af.display(A)
af.display(af.flip(A, 0))
af.display(af.flip(A, 1))
print("\n---- Sum, Min, Max along row / columns\n")
af.display(A)
af.display(af.sum(A, 0))
af.display(af.min(A, 0))
af.display(af.max(A, 0))
af.display(af.sum(A, 1))
af.display(af.min(A, 1))
af.display(af.max(A, 1))
print("\n---- Get minimum with index\n")
(min_val, min_idx) = af.imin(A, 0)
af.display(min_val)
af.display(min_idx)
#!/usr/bin/python import arrayfire as af a = af.randu(3, 3) print(af.sum(a), af.product(a), af.min(a), af.max(a), af.count(a), af.any_true(a), af.all_true(a)) af.print_array(af.sum(a, 0)) af.print_array(af.sum(a, 1)) af.print_array(af.product(a, 0)) af.print_array(af.product(a, 1)) af.print_array(af.min(a, 0)) af.print_array(af.min(a, 1)) af.print_array(af.max(a, 0)) af.print_array(af.max(a, 1)) af.print_array(af.count(a, 0)) af.print_array(af.count(a, 1)) af.print_array(af.any_true(a, 0)) af.print_array(af.any_true(a, 1)) af.print_array(af.all_true(a, 0)) af.print_array(af.all_true(a, 1)) af.print_array(af.accum(a, 0)) af.print_array(af.accum(a, 1))