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 calculate_dfdp_background(self):
"""
Calculates the derivative of the background distribution
with respect to the variables p1, p2, p3. This is used to
solve for the contribution from the fields
"""
f_b = af.moddims(self.f_background, self.N_p1, self.N_p2, self.N_p3)
# Using a 4th order central difference stencil:
dfdp1_background = (-af.shift(f_b, -2) + 8 * af.shift(f_b, -1) + af.shift(
f_b, 2) - 8 * af.shift(f_b, 1)) / (12 * self.dp1)
dfdp2_background = (-af.shift(f_b, 0, -2) + 8 * af.shift(f_b, 0, -1) +
af.shift(f_b, 0, 2) -
8 * af.shift(f_b, 0, 1)) / (12 * self.dp2)
dfdp3_background = (-af.shift(f_b, 0, 0, -2) +
8 * af.shift(f_b, 0, 0, -1) + af.shift(f_b, 0, 0, 2) -
8 * af.shift(f_b, 0, 0, 1)) / (12 * self.dp3)
# Reordering such that the variations in velocity are along axis 2
self.dfdp1_background = af.reorder(af.flat(dfdp1_background), 2, 3, 0, 1)
self.dfdp2_background = af.reorder(af.flat(dfdp2_background), 2, 3, 0, 1)
self.dfdp3_background = af.reorder(af.flat(dfdp3_background), 2, 3, 0, 1)
af.eval(self.dfdp1_background, self.dfdp2_background,
self.dfdp3_background)
return
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 A_matrix():
'''
Calculates A matrix whose elements :math:`A_{p i}` are given by
:math:`A_{pi} = \\int^1_{-1} L_p(\\xi)L_i(\\xi) \\frac{dx}{d\\xi}`
The integrals are computed using the integrate() function.
Since elements are taken to be of equal size, :math:`\\frac {dx}{d\\xi}`
is same everywhere
Returns
-------
A_matrix : arrayfire.Array [N_LGL N_LGL 1 1]
The value of integral of product of lagrange basis functions
obtained by LGL points, using the integrate() function
'''
# Coefficients of Lagrange basis polynomials.
lagrange_coeffs = params.lagrange_coeffs
lagrange_coeffs = af.reorder(lagrange_coeffs, 1, 2, 0)
# Coefficients of product of Lagrange basis polynomials.
lag_prod_coeffs = af.convolve1(lagrange_coeffs,\
af.reorder(lagrange_coeffs, 0, 2, 1),\
conv_mode=af.CONV_MODE.EXPAND)
lag_prod_coeffs = af.reorder(lag_prod_coeffs, 1, 2, 0)
lag_prod_coeffs = af.moddims(lag_prod_coeffs, params.N_LGL**2,
2 * params.N_LGL - 1)
dx_dxi = params.dx_dxi
A_matrix = dx_dxi * af.moddims(lagrange.integrate(lag_prod_coeffs),\
params.N_LGL, params.N_LGL)
return A_matrix
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 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_polynomial_product_coeffs():
'''
'''
threshold = 1e-12
poly1 = af.reorder(
af.transpose(
af.np_to_af_array(np.array([[1, 2, 3., 4], [5, -2, -4.7211, 2]]))),
0, 2, 1)
poly2 = af.reorder(
af.transpose(
af.np_to_af_array(np.array([[-2, 4, 7., 9], [1, 0, -9.1124, 7]]))),
0, 2, 1)
numerical_product_coeffs = utils.polynomial_product_coeffs(poly1, poly2)
analytical_product_coeffs_1 = af.np_to_af_array(
np.array([[-2, -4, -6, -8], [4, 8, 12, 16], [7, 14, 21, 28],
[9, 18, 27, 36]]))
analytical_product_coeffs_2 = af.np_to_af_array(
np.array([[5, -2, -4.7211, 2], [0, 0, 0, 0],
[-45.562, 18.2248, 43.02055164, -18.2248],
[35, -14, -33.0477, 14]]))
print(numerical_product_coeffs)
assert af.max(af.abs(numerical_product_coeffs[:, :, 0] - analytical_product_coeffs_1 + \
numerical_product_coeffs[:, :, 1] - analytical_product_coeffs_2)) < threshold
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 _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 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 __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 _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 Get_Linear_Equation_Gpu(x,
weight,
bin_data_num,
bin_data_y,
r,
dtype='f4'):
n, p = x.shape
d = p - 1
if dtype is 'f4':
dtype = af.Dtype.f32
elif dtype is 'f8':
dtype = af.Dtype.f64
xw = af.constant(0, n, p, dtype=dtype)
for ii in af.ParallelRange(p):
xw[:, ii] = x[:, ii] * weight
s = af.constant(0, p, p, np.prod(bin_data_num.shape), dtype=dtype)
t = af.constant(0, p, np.prod(bin_data_num.shape), dtype=dtype)
ker_d = np.ones(4, dtype='int')
ker_d[:d] = 2 * r + 1
if d is 4:
for i in range(p):
for j in range(i, p):
if i is 0:
kernel = af.moddims(xw[:, j], ker_d[0], ker_d[1], ker_d[2],
ker_d[3])
t[j] = af.flat(
af.reorder(Convolve4(bin_data_y, kernel), 3, 2, 1, 0))
else:
kernel = af.moddims(xw[:, i] * x[:, j], ker_d[0], ker_d[1],
ker_d[2], ker_d[3])
s[i, j] = af.flat(
af.reorder(Convolve4(bin_data_num, kernel), 3, 2, 1, 0))
s[j, i] = s[i, j]
elif d < 4:
for i in range(p):
for j in range(i, p):
if i is 0:
kernel = af.moddims(xw[:, j], ker_d[0], ker_d[1], ker_d[2],
ker_d[3])
if kernel.elements() is 1:
t[j] = af.flat((bin_data_y * kernel.to_list()[0]).T)
else:
t[j] = af.flat(af.fft_convolve(bin_data_y, kernel).T)
else:
kernel = af.moddims(xw[:, i] * x[:, j], ker_d[0], ker_d[1],
ker_d[2], ker_d[3])
if kernel.elements() is 1:
s[i, j] = af.flat((bin_data_num * kernel.to_list()[0]).T)
else:
s[i, j] = af.flat(af.fft_convolve(bin_data_num, kernel).T)
s[j, i] = s[i, j]
for i in range(1, p):
s[i, i] += 1e-12
return ([
np.array(s).reshape(p**2, -1).T.reshape(-1, p, p),
np.array(af.flat(t))
])
def fft2(array):
# Reorder from (N_p, N_s, N_q1, N_q2) --> (N_q1, N_q2, N_p, N_s)
array = af.reorder(array, 2, 3, 0, 1)
array = af.fft2(array)
# Reorder back from (N_q1, N_q2, N_p, N_s) --> (N_p, N_s, N_q1, N_q2)
array = af.reorder(array, 2, 3, 0, 1)
af.eval(array)
return(array)
def ifft2(array):
# Reorder from (N_p, N_s, N_q1, N_q2) --> (N_q1, N_q2, N_p, N_s)
array = af.reorder(array, 2, 3, 0, 1)
array = af.ifft2(array, scale=1)/(array.shape[0] * array.shape[1]) # fix for https://github.com/arrayfire/arrayfire/issues/2050
# Reorder back from (N_q1, N_q2, N_p, N_s) --> (N_p, N_s, N_q1, N_q2)
array = af.reorder(array, 2, 3, 0, 1)
af.eval(array)
return(array)
def pool(image, w, s):
#TODO: Remove assumption of image.dims()[3] == 1
d0, d1, d2 = image.dims()
#TODO: remove reorder and moddims call
image = af.moddims(af.reorder(image, 2, 0, 1), 1, d2, d0, d1)
d0, d1, d2, d3 = image.dims()
h_o = (d2 - w)/s + 1
w_o = (d3 - w)/s + 1
tiles = af.unwrap(af.reorder(image, 2, 3, 1, 0), w, w, s, s)
return af.reorder(af.reorder(af.moddims(af.max(tiles, 0), d0, h_o, w_o,
d1), 0, 3, 1, 2), 2, 3, 1, 0)
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 __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 conv(weights, biases, image, wx, wy, sx = 1, sy = 1, px = 0, py = 0, groups = 1):
image = __pad(image, px, py)
batch = util.num_input(image)
n_filters = util.num_filters(weights)
n_channel = util.num_channels(weights)
w_i = image.dims()[0]
h_i = image.dims()[1]
w_o = (w_i - wx) / sx + 1
h_o = (h_i - wy) / sy + 1
tiles = af.unwrap(image, wx, wy, sx, sy)
weights = af.moddims(weights, wx*wy, n_channel, n_filters)
out = af.constant(0, batch, n_filters, w_o, h_o)
if groups > 1:
out = af.constant(0, w_o, h_o, n_filters, batch)
split_in = util.num_channels(image) / groups
s_i = split_in
split_out = n_filters / groups
s_o = split_out
for i in xrange(groups):
weights_slice = af.moddims(weights[:,:,i*s_o:(i+1)*s_o],
wx, wy, n_channel, split_out)
biases_slice = biases[i*s_o:(i+1)*s_o]
image_slice = image[:,:,i*s_i:(i+1)*s_i]
out[:,:,i*s_o:(i+1)*s_o] = conv(weights_slice,
biases_slice,
image_slice,
wx, wy, sx, sy, 0, 0, 1)
# out[:,i*s_o:(i+1)*s_o] = conv(weights_slice,
# biases_slice,
# image_slice,
# wx, wy, sx, sy, 0, 0, 1)
return out
#TODO: Speedup this section
for f in xrange(n_filters):
for d in xrange(n_channel):
tile_d = af.reorder(tiles[:,:,d],1,0)
weight_d = weights[:,d,f]
out[0,f] += af.moddims(af.matmul(tile_d, weight_d), 1,1, w_o, h_o)
out[0,f] += biases[f].to_list()[0]
return af.reorder(out, 2, 3, 1, 0)
def lax_friedrichs_flux(u, gv):
'''
'''
u = af.reorder(af.moddims(u, params.N_LGL**2, 10, 10), 2, 1, 0)
diff_u_boundary = af.np_to_af_array(np.zeros([10, 10, params.N_LGL**2]))
u_xi_minus1_boundary_right = u[:, :, :params.N_LGL]
u_xi_minus1_boundary_left = af.shift(u[:, :, -params.N_LGL:], d0=0, d1=1)
u[:, :, :params.N_LGL] = (u_xi_minus1_boundary_right +
u_xi_minus1_boundary_left) / 2
diff_u_boundary[:, :, :params.N_LGL] = (u_xi_minus1_boundary_right -
u_xi_minus1_boundary_left)
u_xi_1_boundary_left = u[:, :, -params.N_LGL:]
u_xi_1_boundary_right = af.shift(u[:, :, :params.N_LGL], d0=0, d1=-1)
u[:, :, :params.N_LGL] = (u_xi_minus1_boundary_left +
u_xi_minus1_boundary_right) / 2
diff_u_boundary[:, :, -params.N_LGL:] = (u_xi_minus1_boundary_right -
u_xi_minus1_boundary_left)
u_eta_minus1_boundary_down = af.shift(u[:, :, params.N_LGL -
1:params.N_LGL**2:params.N_LGL],
d0=-1)
u_eta_minus1_boundary_up = u[:, :, 0:-params.N_LGL + 1:params.N_LGL]
u[:, :, 0:-params.N_LGL + 1:params.N_LGL] = (u_eta_minus1_boundary_down\
+ u_eta_minus1_boundary_up) / 2
diff_u_boundary[:, :, 0:-params.N_LGL + 1:params.N_LGL] = (u_eta_minus1_boundary_up\
-u_eta_minus1_boundary_down)
u_eta_1_boundary_down = u[:, :,
params.N_LGL - 1:params.N_LGL**2:params.N_LGL]
u_eta_1_boundary_up = af.shift(u[:, :, 0:-params.N_LGL + 1:params.N_LGL],
d0=1)
u[:, :, params.N_LGL - 1:params.N_LGL ** 2:params.N_LGL] = (u_eta_1_boundary_up\
+u_eta_1_boundary_down) / 2
diff_u_boundary[:, :, params.N_LGL - 1:params.N_LGL ** 2:params.N_LGL] = (u_eta_1_boundary_up\
-u_eta_1_boundary_down)
u = af.moddims(af.reorder(u, 2, 1, 0), params.N_LGL**2, 100)
diff_u_boundary = af.moddims(af.reorder(diff_u_boundary, 2, 1, 0),
params.N_LGL**2, 100)
F_xi_e_ij = F_xi(u, gv) - params.c_x * diff_u_boundary
F_eta_e_ij = F_eta(u, gv) - params.c_y * diff_u_boundary
return F_xi_e_ij, F_eta_e_ij
def Li_Lj_coeffs(N_LGL):
'''
'''
xi_LGL = lagrange.LGL_points(N_LGL)
lagrange_coeffs = af.np_to_af_array(
lagrange.lagrange_polynomials(xi_LGL)[1])
Li_xi = af.moddims(af.tile(af.reorder(lagrange_coeffs, 1, 2, 0), 1, N_LGL),
N_LGL, 1, N_LGL**2)
Lj_eta = af.tile(af.reorder(lagrange_coeffs, 1, 2, 0), 1, 1, N_LGL)
Li_Lj_coeffs = utils.polynomial_product_coeffs(Li_xi, Lj_eta)
return Li_Lj_coeffs
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 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 __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 simple_data(verbose=False):
display_func = _util.display_func(verbose)
display_func(af.constant(100, 3, 3, dtype=af.Dtype.f32))
display_func(af.constant(25, 3, 3, dtype=af.Dtype.c32))
display_func(af.constant(2**50, 3, 3, dtype=af.Dtype.s64))
display_func(af.constant(2+3j, 3, 3))
display_func(af.constant(3+5j, 3, 3, dtype=af.Dtype.c32))
display_func(af.range(3, 3))
display_func(af.iota(3, 3, tile_dims=(2, 2)))
display_func(af.identity(3, 3, 1, 2, af.Dtype.b8))
display_func(af.identity(3, 3, dtype=af.Dtype.c32))
a = af.randu(3, 4)
b = af.diag(a, extract=True)
c = af.diag(a, 1, extract=True)
display_func(a)
display_func(b)
display_func(c)
display_func(af.diag(b, extract=False))
display_func(af.diag(c, 1, extract=False))
display_func(af.join(0, a, a))
display_func(af.join(1, a, a, a))
display_func(af.tile(a, 2, 2))
display_func(af.reorder(a, 1, 0))
display_func(af.shift(a, -1, 1))
display_func(af.moddims(a, 6, 2))
display_func(af.flat(a))
display_func(af.flip(a, 0))
display_func(af.flip(a, 1))
display_func(af.lower(a, False))
display_func(af.lower(a, True))
display_func(af.upper(a, False))
display_func(af.upper(a, True))
a = af.randu(5, 5)
display_func(af.transpose(a))
af.transpose_inplace(a)
display_func(a)
display_func(af.select(a > 0.3, a, -0.3))
af.replace(a, a > 0.3, -0.3)
display_func(a)
display_func(af.pad(a, (1, 1, 0, 0), (2, 2, 0, 0)))
def simple_data(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
display_func(af.constant(100, 3,3, dtype=af.Dtype.f32))
display_func(af.constant(25, 3,3, dtype=af.Dtype.c32))
display_func(af.constant(2**50, 3,3, dtype=af.Dtype.s64))
display_func(af.constant(2+3j, 3,3))
display_func(af.constant(3+5j, 3,3, dtype=af.Dtype.c32))
display_func(af.range(3, 3))
display_func(af.iota(3, 3, tile_dims=(2,2)))
display_func(af.identity(3, 3, 1, 2, af.Dtype.b8))
display_func(af.identity(3, 3, dtype=af.Dtype.c32))
a = af.randu(3, 4)
b = af.diag(a, extract=True)
c = af.diag(a, 1, extract=True)
display_func(a)
display_func(b)
display_func(c)
display_func(af.diag(b, extract = False))
display_func(af.diag(c, 1, extract = False))
display_func(af.join(0, a, a))
display_func(af.join(1, a, a, a))
display_func(af.tile(a, 2, 2))
display_func(af.reorder(a, 1, 0))
display_func(af.shift(a, -1, 1))
display_func(af.moddims(a, 6, 2))
display_func(af.flat(a))
display_func(af.flip(a, 0))
display_func(af.flip(a, 1))
display_func(af.lower(a, False))
display_func(af.lower(a, True))
display_func(af.upper(a, False))
display_func(af.upper(a, True))
a = af.randu(5,5)
display_func(af.transpose(a))
af.transpose_inplace(a)
display_func(a)
display_func(af.select(a > 0.3, a, -0.3))
af.replace(a, a > 0.3, -0.3)
display_func(a)
def test_1V():
obj = test()
obj.single_mode_evolution = False
f_generalized = MB_dist(obj.q1_center, obj.q2_center, obj.p1, obj.p2,
obj.p3, 1)
C_f_hat_generalized = 2 * af.fft2(
collision_operator.BGK(
f_generalized, obj.q1_center, obj.q2_center, obj.p1, obj.p2,
obj.p3, obj.compute_moments,
obj.physical_system.params)) / (obj.N_q2 * obj.N_q1)
# Background
C_f_hat_generalized[0, 0, :] = 0
# Finding the indices of the mode excited:
i_q1_max = np.unravel_index(
af.imax(af.abs(C_f_hat_generalized))[1],
(obj.N_q1, obj.N_q2, obj.N_p1 * obj.N_p2 * obj.N_p3),
order='F')[0]
i_q2_max = np.unravel_index(
af.imax(af.abs(C_f_hat_generalized))[1],
(obj.N_q1, obj.N_q2, obj.N_p1 * obj.N_p2 * obj.N_p3),
order='F')[1]
obj.p1 = np.array(af.reorder(obj.p1, 1, 2, 3, 0))
obj.p2 = np.array(af.reorder(obj.p2, 1, 2, 3, 0))
obj.p3 = np.array(af.reorder(obj.p3, 1, 2, 3, 0))
delta_f_hat = 0.01 * (1 / (2 * np.pi))**(1 / 2) \
* np.exp(-0.5 * obj.p1**2)
obj.single_mode_evolution = True
C_f_hat_single_mode = collision_operator.linearized_BGK(
delta_f_hat, obj.p1, obj.p2, obj.p3, obj.compute_moments,
obj.physical_system.params)
assert (af.mean(
af.abs(
af.flat(C_f_hat_generalized[i_q1_max, i_q2_max]) -
af.to_array(C_f_hat_single_mode.flatten()))) < 1e-14)
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 reorder(a: ndarray, new_order: tp.Tuple[int, ...]):
if len(new_order) > 4:
raise ValueError(
f'Cocos does not support arrays with more than 4 axes.')
d0, d1, d2, d3 = _pad_shape_tuple_axis(new_order)
# print(f'd0={d0}, d1={d1}, d2={d2}, d3={d3}')
output_array = af.reorder(a._af_array, d0, d1, d2, d3)
return ndarray(output_array)
def transpose(self, *axes):
if(self.ndim == 1):
return self
if len(axes) == 0 and self.ndim == 2:
s = arrayfire.transpose(self.d_array)
else:
order = [0,1,2,3]
if len(axes) == 0 or axes[0] is None:
order[:self.ndim] = order[:self.ndim][::-1]
else:
if isinstance(axes[0], collections.Iterable):
axes = axes[0]
for i,ax in enumerate(axes):
order[i] = pu.c2f(self.shape, ax)
# We have to do this gymnastic due to the fact that arrayfire
# uses Fortran order
order[:len(axes)] = order[:len(axes)][::-1]
#print order
s = arrayfire.reorder(self.d_array, order[0],order[1],order[2],order[3])
return ndarray(pu.af_shape(s), dtype=self.dtype, af_array=s)
af.display(af.identity(3, 3, dtype=af.c32)) a = af.randu(3, 4) b = af.diag(a, extract=True) c = af.diag(a, 1, extract=True) af.display(a) af.display(b) af.display(c) af.display(af.diag(b, extract = False)) af.display(af.diag(c, 1, extract = False)) af.display(af.tile(a, 2, 2)) af.display(af.reorder(a, 1, 0)) af.display(af.shift(a, -1, 1)) af.display(af.moddims(a, 6, 2)) af.display(af.flat(a)) af.display(af.flip(a, 0)) af.display(af.flip(a, 1)) af.display(af.lower(a, False)) af.display(af.lower(a, True)) af.display(af.upper(a, False)) af.display(af.upper(a, True))
af.print_array(af.identity(3, 3, dtype=af.c32)) a = af.randu(3, 4) b = af.diag(a, extract=True) c = af.diag(a, 1, extract=True) af.print_array(a) af.print_array(b) af.print_array(c) af.print_array(af.diag(b, extract = False)) af.print_array(af.diag(c, 1, extract = False)) af.print_array(af.tile(a, 2, 2)) af.print_array(af.reorder(a, 1, 0)) af.print_array(af.shift(a, -1, 1)) af.print_array(af.moddims(a, 6, 2)) af.print_array(af.flat(a)) af.print_array(af.flip(a, 0)) af.print_array(af.flip(a, 1)) af.print_array(af.lower(a, False)) af.print_array(af.lower(a, True)) af.print_array(af.upper(a, False)) af.print_array(af.upper(a, True))