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 _initialize(self, rho_initial):
# If option is given as user-defined:
if (self.params.fields_initialize == 'user-defined'):
E1, E2, E3 = self.initialize_E(self.q1, self.q2, self.params)
B1, B2, B3 = self.initialize_B(self.q1, self.q2, self.params)
# Scaling Appropriately
self.E1_hat = 2 * fft2(E1) / (self.N_q1 * self.N_q2)
self.E2_hat = 2 * fft2(E2) / (self.N_q1 * self.N_q2)
self.E3_hat = 2 * fft2(E3) / (self.N_q1 * self.N_q2)
self.B1_hat = 2 * fft2(B1) / (self.N_q1 * self.N_q2)
self.B2_hat = 2 * fft2(B2) / (self.N_q1 * self.N_q2)
self.B3_hat = 2 * fft2(B3) / (self.N_q1 * self.N_q2)
# Initializing EM fields using Poisson Equation:
else:
compute_electrostatic_fields(self, rho_initial)
self.fields_hat = af.join(
0, af.join(0, self.E1_hat, self.E2_hat, self.E3_hat), self.B1_hat,
self.B2_hat, self.B3_hat)
af.eval(self.fields_hat)
return
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 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 arrayfire_perceptron_demo(dataset, num_classes=None):
# Determine number of classes if not provided
if num_classes is None:
num_classes = np.amax(dataset[1] + 1)
# Convert numpy array to af array (and convert labels/targets from ints to
# one-hot encodings)
train_feats = af.from_ndarray(dataset[0])
train_targets = af.from_ndarray(ints_to_onehots(dataset[1], num_classes))
test_feats = af.from_ndarray(dataset[2])
test_targets = af.from_ndarray(ints_to_onehots(dataset[3], num_classes))
num_train = train_feats.dims()[0]
num_test = test_feats.dims()[0]
# Add bias
train_bias = af.constant(1, num_train, 1)
test_bias = af.constant(1, num_test, 1)
train_feats = af.join(1, train_bias, train_feats)
test_feats = af.join(1, test_bias, test_feats)
print('arrayfire perceptron classifier implementation')
clf = AfPerceptron(alpha=0.1, maxerr=0.01, maxiter=1000, verbose=False)
# Initial run to avoid overhead in training
clf.train(train_feats, train_targets)
clf.init_weights(train_feats, train_targets)
# Benchmark training
t0 = time.time()
clf.train(train_feats, train_targets)
clf.eval()
t1 = time.time()
dt_train = t1 - t0
print('Training time: {0:4.4f} s'.format(dt_train))
# Benchmark prediction
iters = 100
test_outputs = None
t0 = time.time()
for i in range(iters):
test_outputs = clf.predict_proba(test_feats)
af.eval(test_outputs)
af.sync()
t1 = time.time()
dt = t1 - t0
print('Prediction time: {0:4.4f} s'.format(dt / iters))
print('Accuracy (test data): {0:2.2f}'.format(
accuracy(test_outputs, test_targets)))
# print('Accuracy on training data: {0:2.2f}'.format(accuracy(train_outputs, train_targets)))
# print('Accuracy on testing data: {0:2.2f}'.format(accuracy(test_outputs, test_targets)))
# print('Maximum error on testing data: {0:2.2f}'.format(abserr(test_outputs, test_targets)))
return clf, dt_train
def _train(self, X: af.Array, Y: af.Array, alpha: float,
lambda_param: float, penalty: str, maxerr: float,
maxiter: int) -> af.Array:
# Add bias feature
bias = af.constant(1, X.dims()[0], 1)
X_biased = af.join(1, bias, X)
# Initialize parameters to 0
Weights = af.constant(0, X_biased.dims()[1], Y.dims()[1])
for i in range(maxiter):
# Get the cost and gradient
J, dJ = self._cost(Weights, X_biased, Y, lambda_param, penalty)
err = af.max(af.abs(J))
if err < maxerr:
Weights = Weights[1:] # Remove bias weights
return Weights
# Update the weights via gradient descent
Weights = Weights - alpha * dJ
# Remove bias weights
Weights = Weights[1:]
return Weights
def dump_coordinate_info(self, arrays, name, file_name):
self._da_coord_arrays = PETSc.DMDA().create(
[self.N_q1, self.N_q2],
dof=len(arrays),
proc_sizes=(self._nproc_in_q1, self._nproc_in_q2),
ownership_ranges=self._ownership_ranges,
comm=self._comm)
self._glob_coord = self._da_coord_arrays.createGlobalVec()
self._glob_coord_array = self._glob_coord.getArray()
N_g = self.N_ghost
for i in range(len(arrays)):
if (i == 0):
array_to_dump = arrays[0][:, :, N_g:-N_g, N_g:-N_g]
else:
array_to_dump = af.join(0, array_to_dump, arrays[i][:, :, N_g:-N_g,
N_g:-N_g])
af.flat(array_to_dump).to_ndarray(self._glob_coord_array)
PETSc.Object.setName(self._glob_coord, name)
viewer = PETSc.Viewer().createBinary(file_name + '.bin',
'w',
comm=self._comm)
viewer(self._glob_coord)
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 = 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 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 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 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 histogram_deposition(current_indices_flat, currents_flat, grid_elements):
'''
function: histogram_deposition(current_indices_flat, currents_flat, grid)
inputs: current_indices_flat, currents_flat, grid_elements
current_indices_flat, currents_flat: They denote the indices and the currents
to be deposited on the flattened current vector.
grid_elements: The number of elements present the matrix/vector representing the
currents.
'''
# setting default indices and current for histogram deposition
indices_fix = af.data.range(grid_elements + 1, dtype=af.Dtype.s64)
currents_fix = 0 * af.data.range(grid_elements + 1, dtype=af.Dtype.f64)
# Concatenating the indices and currents in a single vector
combined_indices_flat = af.join(0, indices_fix, current_indices_flat)
combined_currents_flat = af.join(0, currents_fix, currents_flat)
# Sort by key operation
indices, currents = af.sort_by_key(combined_indices_flat,
combined_currents_flat,
dim=0)
# scan by key operation with default binary addition operation which sums up currents
# for the respective indices
Histogram_scan = af.scan_by_key(indices, currents)
# diff1 operation to determine the uniques indices in the current
diff1_op = af.diff1(indices, dim=0)
# Determining the uniques indices for current deposition
indices_unique = af.where(diff1_op > 0)
# Determining the current vector
J_flat = Histogram_scan[indices_unique]
af.eval(J_flat)
return J_flat
def initialize_electric_fields(self):
if('initialize_E' in dir(self.initialize)):
E1 = self.initialize.initialize_E(self.q1_left_center,
self.q2_left_center,
self.params
)[0]
E2 = self.initialize.initialize_E(self.q1_center_bot,
self.q2_center_bot,
self.params
)[1]
E3 = self.initialize.initialize_E(self.q1_center,
self.q2_center,
self.params
)[2]
elif('initialize_A_phi' in dir(self.initialize)):
A1 = self.initialize.initialize_A_phi(self.q1_center_bot,
self.q2_center_bot,
self.params
)[0]
A2 = self.initialize.initialize_A_phi(self.q1_left_center,
self.q2_left_center,
self.params
)[1]
A3 = self.initialize.initialize_A_phi(self.q1_left_bot,
self.q2_left_bot,
self.params
)[2]
phi = self.initialize.initialize_A_phi(self.q1_center,
self.q2_center,
self.params
)[3]
dA3_dq2 = (af.shift(A3, 0, 0, 0, -1) - A3) / self.dq2
dA3_dq1 = (af.shift(A3, 0, 0, -1, 0) - A3) / self.dq1
dA2_dq1 = (af.shift(A2, 0, 0, -1, 0) - A2) / self.dq1
dA1_dq2 = (af.shift(A1, 0, 0, 0, -1) - A1) / self.dq2
dphi_dq1 = -(af.shift(phi, 0, 0, 1, 0) - phi) / self.dq1
dphi_dq2 = -(af.shift(phi, 0, 0, 0, 1) - phi) / self.dq2
E1 = dA3_dq2 - dphi_dq1
E2 = -dA3_dq1 - dphi_dq2
E3 = dA2_dq1 - dA1_dq2
else:
raise NotImplementedError('Initialization method for electric fields not valid/found')
self.yee_grid_EM_fields[:3] = af.join(0, E1, E2, E3)
af.eval(self.yee_grid_EM_fields)
return
def concatenate(arrays, axis=0):
arrays = tuple(arrays)
if len(arrays) == 0:
raise ValueError('need at least one array to concatenate')
base = arrays[0]
if len(arrays) == 1:
return base.copy()
# arrayfire accepts at most 4 arrays to concatenate at once so we'll have
# to chunk the arrays
# The first case is special as we don't want to create unnecessary copies
i = 0
a = arrays[i].d_array
if i+1 < len(arrays):
b = arrays[i+1].d_array
else:
b = None
if i+2 < len(arrays):
c = arrays[i+2].d_array
else:
c = None
if i+3 < len(arrays):
d = arrays[i+3].d_array
else:
d = None
ret = arrayfire.join(pu.c2f(arrays[0].shape, axis), a, b, c, d)
for i in range(4,len(arrays),4):
a = ret.d_array
if i < len(arrays):
b = arrays[i].d_array
else:
b = None
if i+1 < len(arrays):
c = arrays[i+1].d_array
else:
c = None
if i+2 < len(arrays):
d = arrays[i+2].d_array
else:
d = None
ret = arrayfire.join(pu.c2f(arrays[0].shape, axis), a, b, c, d)
return ret
def dump_moments(self, file_name):
"""
This function is used to dump variables to a file for later usage.
Parameters
----------
file_name : str
The variables will be dumped to this provided file name.
Returns
-------
This function returns None. However it creates a file 'file_name.h5',
containing all the moments that were defined under moments_defs in
physical_system.
Examples
--------
>> solver.dump_variables('boltzmann_moments_dump')
The above set of statements will create a HDF5 file which contains the
all the moments which have been defined in the physical_system object.
The data is always stored with the key 'moments' inside the HDF5 file.
Suppose 'density' and 'energy' are two these moments, and are declared
the first and second in the moment_exponents object:
These variables can then be accessed from the file using
>> import h5py
>> h5f = h5py.File('boltzmann_moments_dump.h5', 'r')
>> rho = h5f['moments'][:][:, :, 0]
>> E = h5f['moments'][:][:, :, 1]
>> h5f.close()
"""
N_g = self.N_ghost
i = 0
for key in self.physical_system.moment_exponents:
if (i == 0):
array_to_dump = self.compute_moments(key)[:, N_g:-N_g, N_g:-N_g]
else:
array_to_dump = af.join(
0, array_to_dump,
self.compute_moments(key)[:, N_g:-N_g, N_g:-N_g])
i += 1
af.flat(array_to_dump).to_ndarray(self._glob_moments_array)
PETSc.Object.setName(self._glob_moments, 'moments')
viewer = PETSc.Viewer().createHDF5(file_name + '.h5', 'w', comm=self._comm)
viewer(self._glob_moments)
def concatenate(arrays, axis=0):
if(len(arrays) < 1):
raise ValueError('need at least one array to concatenate')
if(axis > 3):
raise NotImplementedError('only up to 4 axis as currently supported')
arr = arrays[0].d_array.copy()
axis = pu.c2f(arrays[0].shape, axis)
for a in arrays[1:]:
arr = arrayfire.join(axis, arr, a.d_array)
return afnumpy.ndarray(pu.af_shape(arr), dtype=arrays[0].dtype, af_array=arr)
def dct1(arr, norm=None):
N = arr.dims()[0]
out = 2 * af.real(
af.exp(-0.5j * np.pi / N *
af.range(*arr.dims(), dim=0, dtype=arr.dtype())) *
af.fft(af.join(0, arr[0:N:2], af.flip(arr[1:N:2]))))
if norm == 'ortho':
out /= np.sqrt(2 * N)
out[0] /= np.sqrt(2)
return out
def update_user_defined_fields(self, time_elapsed):
"""
Updates the cell-centered EM fields value using the value that is
returned by the user defined function at that particular time.
Parameters
----------
time_elapsed : double
Time at which the field values are to be evaluated.
"""
E1, E2, E3 = self.params.user_defined_E(self.q1, self.q2, time_elapsed)
B1, B2, B3 = self.params.user_defined_B(self.q1, self.q2, time_elapsed)
self.cell_centered_EM_fields = af.join(0, E1, E2, E3,
af.join(0, B1, B2, B3))
return
def concatenate(arrays, axis=0):
if (len(arrays) < 1):
raise ValueError('need at least one array to concatenate')
if (axis > 3):
raise NotImplementedError('only up to 4 axis as currently supported')
arr = arrays[0].d_array.copy()
axis = pu.c2f(arrays[0].shape, axis)
for a in arrays[1:]:
arr = arrayfire.join(axis, arr, a.d_array)
return afnumpy.ndarray(pu.af_shape(arr),
dtype=arrays[0].dtype,
af_array=arr)
def Verlet(initial_conditions,dt): x = initial_conditions[0:no_of_particles] y = initial_conditions[no_of_particles:2*no_of_particles] v_x = initial_conditions[2*no_of_particles:3*no_of_particles] v_y = initial_conditions[3*no_of_particles:4*no_of_particles] x_new = x + v_x*dt v_x_new = v_x y_new = y + v_y*dt v_y_new = v_y nextstep = af.join(0,x_new,y_new,v_x,v_y) return(nextstep)
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 concatenate(arrays: tp.Tuple[ndarray, ...], axis: int = 0) -> ndarray:
if len(arrays) < 2 or len(arrays) > 4:
raise ValueError("the number of arrays to be concatenated is supposed "
"to be between two and four")
first = arrays[0]._af_array
second = arrays[1]._af_array
third = None
fourth = None
if len(arrays) > 2:
third = arrays[2]._af_array
if len(arrays) > 3:
fourth = arrays[3]._af_array
af_array = af.join(axis, first, second, third, fourth)
return ndarray(af_array)
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_i = params.amplitude * -5.745404152435185e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.45462729344290764 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * -5.88418203051333e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.2722586144213775 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0.4546272934429093 * af.cos(params.k_q1 * q1) \
- params.amplitude * 2.220446049250313e-16 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0.2722586144213809 * af.cos(params.k_q1 * q1) \
- params.amplitude * -2.7755575615628914e-16 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
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_i = params.amplitude * -2.7044279698172115e-17 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.5272181185265511 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * -1.2414728973845785e-16 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.21327009745028128 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0.5272181185265513 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0.21327009745028208 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
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_i = params.amplitude * -8.677632316054021e-16 * af.cos(params.k_q1 * q1) \
- params.amplitude * - 0.2853625652083089 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * -1.0205323999062932e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * - 0.3876714549109159 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0.28536256520831227 * af.cos(params.k_q1 * q1) \
- params.amplitude * 1.71364929624912e-16 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0.3876714549109187 * af.cos(params.k_q1 * q1) \
- params.amplitude * -2.7755575615628914e-16 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
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_i = params.amplitude * 0.07845711202586898 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * 0.5583486611611699 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.07845711202586896 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.5583486611611693 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
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_i = params.amplitude * -5.745404152435185e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * - 0.16281859014475286 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * -5.88418203051333e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * - 0.47061042449268503 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0.16281859014475358 * af.cos(params.k_q1 * q1) \
- params.amplitude * 2.220446049250313e-16 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0.4706104244926854 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
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_i = params.amplitude * 0.18699852141220014 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * 0.4525906297083754 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.18699852141220033 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.4525906297083753 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
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_i = params.amplitude * 0.6504875697582941 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * 0.08496465162562208 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * -0.6504875697582938 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * -0.08496465162562145 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
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_i = params.amplitude * 0.5807459530914606 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * 0.1633005468170238 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * - 0.5807459530914602 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0 * af.cos(params.k_q1 * q1) \
- params.amplitude * - 0.16330054681702416 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
af.eval(f)
return (f)
def initialize_f(q1, q2, v1, v2, v3, params):
m1 = params.mass[0, 0]
m2 = params.mass[0, 1]
k = params.boltzmann_constant
n1 = 1 + 0.01 * af.cos(2 * np.pi * q1)
n2 = 1 + 0.02 * af.cos(4 * np.pi * q1)
T1 = 1 + 0.02 * af.sin(2 * np.pi * q1)
T2 = 100 + 0.01 * af.sin(4 * np.pi * q1)
f1 = n1 * (1 / (2 * np.pi * k * T1))**(1 / 2) \
* af.exp(-m1 * v1[:, 0]**2 / (2 * k * T1)) \
f2 = n2 * (1 / (2 * np.pi * k * T2))**(1 / 2) \
* af.exp(-m2 * v1[:, 1]**2 / (2 * k * T2)) \
f = af.join(1, f1, f2)
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_i = params.amplitude * -4.801714581503802e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.6363571202013185 * af.sin(params.k_q1 * q1)
v2_bulk_e = params.amplitude * -4.85722573273506e-15 * af.cos(params.k_q1 * q1) \
- params.amplitude * 0.10249033165518363 * af.sin(params.k_q1 * q1)
v3_bulk_i = params.amplitude * 0.6363571202013188 * af.cos(params.k_q1 * q1) \
- params.amplitude * 1.8041124150158794e-16 * af.sin(params.k_q1 * q1)
v3_bulk_e = params.amplitude * 0.10249033165518295 * af.cos(params.k_q1 * q1) \
- params.amplitude * -3.885780586188048e-16 * af.sin(params.k_q1 * q1)
n = n_b + 0 * q1**0
f_e = n * (m[0, 0] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 0] * (v2[:, 0] - v2_bulk_e)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 0] * (v3[:, 0] - v3_bulk_e)**2 / (2 * k * T_b))
f_i = n * (m[0, 1] / (2 * np.pi * k * T_b)) \
* af.exp(-m[0, 1] * (v2[:, 1] - v2_bulk_i)**2 / (2 * k * T_b)) \
* af.exp(-m[0, 1] * (v3[:, 1] - v3_bulk_i)**2 / (2 * k * T_b))
f = af.join(1, f_e, f_i)
af.eval(f)
return (f)
while (not simple_win.close()) and (not pretty_win.close()):
delay = time()
if (not simple_win.close()): simple_win.image(state)
if (not pretty_win.close()): pretty_win.image(display)
frame_count += 1
if (frame_count % reset == 0):
state = (af.randu(game_h, game_w) > 0.4).as_type(af.Dtype.f32)
neighborhood = af.convolve(state, kernel)
# state == 1 && neighborhood < 2 --> state = 0
# state == 1 && neighborhood > 3 --> state = 0
# state == 0 && neighborhood == 3 --> state = 1
# else state remains un changed
C0 = neighborhood == 2
C1 = neighborhood == 3
A0 = (state == 1) & (neighborhood < 2)
A1 = (state != 0) & (C0 | C1)
A2 = (state == 0) & C1
A3 = (state == 1) & (neighborhood > 3)
display = af.join(2, A0 + A1, A1 + A2, A3).as_type(af.Dtype.f32)
state = state * C0 + C1
while(time() - delay < (1.0 / fps)):
pass
# Copyright (c) 2015, ArrayFire
# All rights reserved.
#
# This file is distributed under 3-clause BSD license.
# The complete license agreement can be obtained at:
# http://arrayfire.com/licenses/BSD-3-Clause
########################################################
import arrayfire as af
af.info()
ITERATIONS = 200
POINTS = int(10.0 * ITERATIONS)
Z = 1 + af.range(POINTS) / ITERATIONS
win = af.Window(800, 800, "3D Plot example using ArrayFire")
t = 0.1
while not win.close():
X = af.cos(Z * t + t) / Z
Y = af.sin(Z * t + t) / Z
X = af.maxof(af.minof(X, 1), -1)
Y = af.maxof(af.minof(Y, 1), -1)
Pts = af.join(1, X, Y, Z)
win.plot3(Pts)
t = t + 0.01
