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 RK4_timestepping(A_inverse, u, delta_t, gv):
'''
Implementing the Runge-Kutta (RK4) method to evolve the wave.
Parameters
----------
A_inverse : arrayfire.Array[N_LGL N_LGL 1 1]
The inverse of the A matrix which was calculated
using A_matrix() function.
u : arrayfire.Array[N_LGL N_Elements 1 1]
u at the mapped LGL points
delta_t : float64
The time-step by which u is to be evolved.
Returns
-------
delta_u : arrayfire.Array [N_LGL N_Elements 1 1]
The change in u at the mapped LGL points.
'''
k1 = af.matmul(A_inverse, b_vector(u, gv))
k2 = af.matmul(A_inverse, b_vector(u + k1 * delta_t / 2, gv))
k3 = af.matmul(A_inverse, b_vector(u + k2 * delta_t / 2, gv))
k4 = af.matmul(A_inverse, b_vector(u + k3 * delta_t, gv))
delta_u = delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6
return delta_u
def simple_blas(verbose=False):
display_func = _util.display_func(verbose)
a = af.randu(5, 5)
b = af.randu(5, 5)
display_func(af.matmul(a, b))
display_func(af.matmul(a, b, af.MATPROP.TRANS))
display_func(af.matmul(a, b, af.MATPROP.NONE, af.MATPROP.TRANS))
b = af.randu(5, 1)
display_func(af.dot(b, b))
def simple_blas(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5,5)
b = af.randu(5,5)
display_func(af.matmul(a,b))
display_func(af.matmul(a,b,af.MATPROP.TRANS))
display_func(af.matmul(a,b,af.MATPROP.NONE, af.MATPROP.TRANS))
b = af.randu(5,1)
display_func(af.dot(b,b))
def diffusion_step(u, v, Lambda, A_diffusion_inverse):
'''
The diffusion step. Lambda = visc * delta_t / (delta_x ** 2)
The matlab code uses -lambda
'''
length = int(u.shape[0]**0.5)
u[:length] -= Lambda
u_new = af.matmul(A_diffusion_inverse, u)
v_new = af.matmul(A_diffusion_inverse, v)
return u_new, v_new
def calc_arrayfire(A, b, x0, maxiter=10):
x = af.constant(0, b.dims()[0], dtype=af.Dtype.f32)
r = b - af.matmul(A, x)
p = r
for i in range(maxiter):
Ap = af.matmul(A, p)
alpha_num = af.dot(r, r)
alpha_den = af.dot(p, Ap)
alpha = alpha_num / alpha_den
r -= af.tile(alpha, Ap.dims()[0]) * Ap
x += af.tile(alpha, Ap.dims()[0]) * p
beta_num = af.dot(r, r)
beta = beta_num / alpha_num
p = r + af.tile(beta, p.dims()[0]) * p
res = x0 - x
return x, af.dot(res, res)
def simulateHestonModel( T, N, R, mu, kappa, vBar, sigmaV, rho, x0, v0 ) :
deltaT = T / (float)(N - 1)
x = [af.constant(x0, R, dtype=af.Dtype.f32), af.constant(0, R, dtype=af.Dtype.f32)]
v = [af.constant(v0, R, dtype=af.Dtype.f32), af.constant(0, R, dtype=af.Dtype.f32)]
sqrtDeltaT = math.sqrt(deltaT)
sqrtOneMinusRhoSquare = math.sqrt(1-rho**2)
m = af.constant(0, 2, dtype=af.Dtype.f32)
m[0] = rho
m[1] = sqrtOneMinusRhoSquare
zeroArray = af.constant(0, R, 1, dtype=af.Dtype.f32)
for t in range(1, N) :
tPrevious = (t + 1) % 2
tCurrent = t % 2
dBt = af.randn(R, 2, dtype=af.Dtype.f32) * sqrtDeltaT
vLag = af.maxof(v[tPrevious], zeroArray)
sqrtVLag = af.sqrt(vLag)
x[tCurrent] = x[tPrevious] + (mu - 0.5 * vLag) * deltaT + sqrtVLag * dBt[:, 0]
v[tCurrent] = vLag + kappa * (vBar - vLag) * deltaT + sigmaV * (sqrtVLag * af.matmul(dBt, m))
return (x[tCurrent], af.maxof(v[tCurrent], zeroArray))
def gradient(nn, delta):
nabla_b = []
nabla_w = []
# output
dact = nn['nonlin'][-1][1]
t = nn['zs'][-1]
asdf = dact(2)
#This is d_relu. It is a binary output
dW = average_gradient(delta * af.sign(1e-5 - nn['zs'][-1]),
nn['activations'][-2])
nabla_b.append(af.mean(delta))
nabla_w.append(dW)
for i in range(len(nn['weights']) - 2, -1, -1):
dact = delta * af.max(nn['zs'][i + 1])
trans = nn['weights'][i + 1].T
delta = af.matmul(trans, dact)
dW = average_gradient(delta, nn['activations'][i])
nabla_b.append(af.mean(delta * af.max(nn['zs'][i])))
nabla_w.append(dW)
return nabla_w, nabla_b
def gradient(nn, delta):
nabla_b = []
nabla_w = []
# output
dact = nn['nonlin'][-1][1]
t = nn['zs'][-1]
asdf = dact(2)
#This is d_relu. It is a binary output
dW = average_gradient(delta*af.sign(1e-5 - nn['zs'][-1]), nn['activations'][-2])
nabla_b.append(af.mean(delta))
nabla_w.append(dW)
for i in range(len(nn['weights']) - 2, -1, -1):
dact = delta * af.max(nn['zs'][i+1])
trans = nn['weights'][i+1].T
delta = af.matmul(trans, dact)
dW = average_gradient(delta,nn['activations'][i])
nabla_b.append(af.mean(delta*af.max(nn['zs'][i])))
nabla_w.append(dW)
return nabla_w, nabla_b
def polyval_1d(polynomials, xi):
'''
Finds the value of the polynomials at the given :math:`\\xi` coordinates.
Parameters
----------
polynomials : af.Array [number_of_polynomials N 1 1]
``number_of_polynomials`` :math:`2D` polynomials of degree
:math:`N - 1` of the form
.. math:: P(x) = a_0x^0 + a_1x^1 + ... \\
a_{N - 1}x^{N - 1} + a_Nx^N
xi : af.Array [N 1 1 1]
:math:`\\xi` coordinates at which the :math:`i^{th}` Lagrange
basis polynomial is to be evaluated.
Returns
-------
af.Array [i.shape[0] xi.shape[0] 1 1]
Evaluated polynomials at given :math:`\\xi` coordinates
'''
N = int(polynomials.shape[1])
xi_ = af.tile(af.transpose(xi), d0=N)
power = af.tile(af.flip(af.range(N), dim=0), d0=1, d1=xi.shape[0])
xi_power = xi_**power
return af.matmul(polynomials, xi_power)
def matmul(a: ndarray,
b: ndarray) \
-> ndarray:
"""
Matrix product of two arrays.
"""
return ndarray(af.matmul(a._af_array, b._af_array))
def calc_arrayfire(A, b, x0, maxiter=10):
x = af.constant(0, b.dims()[0], dtype=af.Dtype.f32)
r = b - af.matmul(A, x)
p = r
for i in range(maxiter):
Ap = af.matmul(A, p)
alpha_num = af.dot(r, r)
alpha_den = af.dot(p, Ap)
alpha = alpha_num/alpha_den
r -= af.tile(alpha, Ap.dims()[0]) * Ap
x += af.tile(alpha, Ap.dims()[0]) * p
beta_num = af.dot(r, r)
beta = beta_num/alpha_num
p = r + af.tile(beta, p.dims()[0]) * p
af.eval(x)
res = x0 - x
return x, af.dot(res, res)
def projection_step_poisson(u, v, A_projection_inv):
'''
Solve the poisson equation to obtain q for the projection step.
'''
A_inverse = A_projection_inv
divergence_velocity = div_velocity(u, v)
q = af.matmul(A_inverse, divergence_velocity)
return q
def forward(nn_np, data):
"""
Given a dictionary representing a feed forward neural net and an input data matrix compute the network's output and store it within the dictionary
:param nn: neural network dictionary
:param data: a numpy n by m matrix where m in the number of input units in nn
:return: the output layer activations
"""
nn = nn_np
nn['activations'] = []
#prct = []
#prct.append(data[0][0])
#prct.append(data[1][0])
#src = data.astype(float)
nsrc = data#af.Array(prct)
nn['activations'].append(nsrc)
#(af.Array(src.ctypes.data, src.shape, src.dtype.char))
nn['zs'] = []
for w, s, b in map(None, nn['weights'], nn['nonlin'], nn['biases']):
#:wq
#print af.transpose(nn['activations'][-1])
#print(type(nn['activations'][0]))
#print(nn['activations'][0])
z = af.matmul(w, nn['activations'][-1])
#for i in range(w.shape[1]-1):
# newB = af.join(1,newB,b)
p = z.T + b
nn['zs'].append(p.T)
if len(p.shape) == 2:
maxVal = af.constant(1e-5,p.shape[0],p.shape[1]).T
else:
maxVal = af.constant(1e-5,p.shape[0]).T
q = af.maxof(p.T,1e-5)#p(i) = 1e-5
nn['activations'].append(q)
return nn['activations'][-1]
def setup_input(n, sparsity=7):
T = af.randu(n, n, dtype=af.Dtype.f32)
A = af.floor(T*1000)
A = A * ((A % sparsity) == 0) / 1000
A = A.T + A + n*af.identity(n, n, dtype=af.Dtype.f32)
x0 = af.randu(n, dtype=af.Dtype.f32)
b = af.matmul(A, x0)
# printing
# nnz = af.sum((A != 0))
# print "Sparsity of A: %2.2f %%" %(100*nnz/n**2,)
return A, b, x0
def dot(a, b):
# Arrayfire requires that the types match for dot and matmul
res_dtype = numpy.result_type(a, b)
a = a.astype(res_dtype, copy=False)
b = b.astype(res_dtype, copy=False)
if a.ndim == 1 and b.ndim == 1:
s = arrayfire.dot(a.d_array, b.d_array)
return afnumpy.ndarray((), dtype=a.dtype, af_array=s)[()]
a_shape = a.shape
b_shape = b.shape
if a.ndim == 1:
a = a.reshape((a.shape[0], 1))
if b.ndim == 1:
b = b.reshape((b.shape[0], 1))
if a.ndim == 2 and b.ndim == 2:
# Notice the order of the arguments to matmul. It's not a bug!
s = arrayfire.matmul(b.d_array, a.d_array)
return afnumpy.ndarray(pu.af_shape(s),
dtype=pu.typemap(s.dtype()),
af_array=s)
# Multidimensional dot is done with loops
# Calculate the shape of the result array
a_shape = list(a_shape)
a_shape.pop(-1)
b_shape = list(b_shape)
b_shape.pop(-2)
res_shape = a_shape + b_shape
# Make sure the arrays are at least 3D
if a.ndim < 3:
a = a.reshape((1, ) + a.shape)
if b.ndim < 3:
b = b.reshape((1, ) + b.shape)
# We're going to flatten the regions over which we're going to loop over
# to make our life easier and reduce the amount of indexing code
a = a.reshape((-1, a.shape[-2], a.shape[-1]))
b = b.reshape((-1, b.shape[-2], b.shape[-1]))
# Initialize the output array. The shape matches the reshape a and b.
res = afnumpy.empty((a.shape[0], a.shape[-2], b.shape[0], b.shape[-1]),
dtype=a.dtype)
# Loop through the flattened indices and calculate the matmuls
for i in range(0, a.shape[0]):
for j in range(0, b.shape[0]):
res[i, :, j, :] = afnumpy.dot(a[i], b[j])
# Finally appropriately reshape the result array
return res.reshape(res_shape)
def setup_input(n, sparsity=7):
T = af.randu(n, n, dtype=af.Dtype.f32)
A = af.floor(T * 1000)
A = A * ((A % sparsity) == 0) / 1000
A = A.T + A + n * af.identity(n, n, dtype=af.Dtype.f32)
x0 = af.randu(n, dtype=af.Dtype.f32)
b = af.matmul(A, x0)
# printing
# nnz = af.sum((A != 0))
# print "Sparsity of A: %2.2f %%" %(100*nnz/n**2,)
return A, b, x0
def dot(a, b):
# Arrayfire requires that the types match for dot and matmul
res_dtype = numpy.result_type(a,b)
a = a.astype(res_dtype, copy=False)
b = b.astype(res_dtype, copy=False)
if a.ndim == 1 and b.ndim == 1:
s = arrayfire.dot(a.d_array, b.d_array)
return afnumpy.ndarray((), dtype=a.dtype, af_array=s)[()]
a_shape = a.shape
b_shape = b.shape
if a.ndim == 1:
a = a.reshape((a.shape[0],1))
if b.ndim == 1:
b = b.reshape((b.shape[0],1))
if a.ndim == 2 and b.ndim == 2:
# Notice the order of the arguments to matmul. It's not a bug!
s = arrayfire.matmul(b.d_array, a.d_array)
return afnumpy.ndarray(pu.af_shape(s), dtype=pu.typemap(s.dtype()),
af_array=s)
# Multidimensional dot is done with loops
# Calculate the shape of the result array
a_shape = list(a_shape)
a_shape.pop(-1)
b_shape = list(b_shape)
b_shape.pop(-2)
res_shape = a_shape + b_shape
# Make sure the arrays are at least 3D
if a.ndim < 3:
a = a.reshape((1,)+a.shape)
if b.ndim < 3:
b = b.reshape((1,)+b.shape)
# We're going to flatten the regions over which we're going to loop over
# to make our life easier and reduce the amount of indexing code
a = a.reshape((-1,a.shape[-2],a.shape[-1]))
b = b.reshape((-1,b.shape[-2],b.shape[-1]))
# Initialize the output array. The shape matches the reshape a and b.
res = afnumpy.empty((a.shape[0], a.shape[-2], b.shape[0],
b.shape[-1]), dtype=a.dtype)
# Loop through the flattened indices and calculate the matmuls
for i in range(0,a.shape[0]):
for j in range(0,b.shape[0]):
res[i,:,j,:] = afnumpy.dot(a[i],b[j])
# Finally appropriately reshape the result array
return res.reshape(res_shape)
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 fc(weights, biases, image):
#TODO: fix shape of fc weights
#TODO: fix handling 1d vs 3d image
#TODO: remove assumption of only 1 input
s = image.dims()[0]
if len(image.dims()) is 3:
in0, in1, in2 = image.dims()
image = af.reorder(image, 1, 0, 2)
s = in0*in1*in2
image = af.moddims(image, 1, s)
d0, d1, d2, d3 = weights.dims()
weights = af.moddims(weights, d2, d3)
out = af.moddims(af.matmul(image, weights), d3) + biases
return out
def multivariable_poly_value(poly_2d, x, y):
'''
'''
polynomial_coeffs = af.transpose(af.moddims(poly_2d, poly_2d.shape[0] ** 2, poly_2d.shape[2]))
power_index = af.flip(af.np_to_af_array(np.arange(poly_2d.shape[0])))
x_power_indices = af.flat(af.transpose(af.tile(power_index, 1, poly_2d.shape[0])))
y_power_indices = af.tile(power_index, poly_2d.shape[0])
x_power = af.broadcast(power, af.transpose(x), x_power_indices)
y_power = af.broadcast(power, af.transpose(y), y_power_indices)
polynomial_value = af.matmul(polynomial_coeffs, x_power * y_power)
return polynomial_value
def forward(nn_np, data):
"""
Given a dictionary representing a feed forward neural net and an input data matrix compute the network's output and store it within the dictionary
:param nn: neural network dictionary
:param data: a numpy n by m matrix where m in the number of input units in nn
:return: the output layer activations
"""
nn = nn_np
nn['activations'] = []
#prct = []
#prct.append(data[0][0])
#prct.append(data[1][0])
#src = data.astype(float)
nsrc = data #af.Array(prct)
nn['activations'].append(nsrc)
#(af.Array(src.ctypes.data, src.shape, src.dtype.char))
nn['zs'] = []
for w, s, b in map(None, nn['weights'], nn['nonlin'], nn['biases']):
#:wq
#print af.transpose(nn['activations'][-1])
#print(type(nn['activations'][0]))
#print(nn['activations'][0])
z = af.matmul(w, nn['activations'][-1])
#for i in range(w.shape[1]-1):
# newB = af.join(1,newB,b)
p = z.T + b
nn['zs'].append(p.T)
if len(p.shape) == 2:
maxVal = af.constant(1e-5, p.shape[0], p.shape[1]).T
else:
maxVal = af.constant(1e-5, p.shape[0]).T
q = af.maxof(p.T, 1e-5) #p(i) = 1e-5
nn['activations'].append(q)
return nn['activations'][-1]
def af_gauss(data,kernels):
d_kernels = []
for k in kernels:
d_k = af.np_to_af_array(k)
d_kernels.append(af.matmul(d_k,af.transpose(d_k)))
##d_k = af.matmul(af.transpose(d_k),d_k)
out = []
for d in data:
d_img = af.np_to_af_array(d)
for d_k in d_kernels:
#res = af.convolve2_separable(d_k, af.transpose(d_k), d_img)
res = af.convolve2(d_img, d_k)
# create numpy array
out.append(res.__array__())
return out
def simulateHestonModel(T, N, R, mu, kappa, vBar, sigmaV, rho, x0, v0):
deltaT = T / (float)(N - 1)
x = [
af.constant(x0, R, dtype=af.Dtype.f32),
af.constant(0, R, dtype=af.Dtype.f32)
]
v = [
af.constant(v0, R, dtype=af.Dtype.f32),
af.constant(0, R, dtype=af.Dtype.f32)
]
sqrtDeltaT = math.sqrt(deltaT)
sqrtOneMinusRhoSquare = math.sqrt(1 - rho**2)
m = af.constant(0, 2, dtype=af.Dtype.f32)
m[0] = rho
m[1] = sqrtOneMinusRhoSquare
zeroArray = af.constant(0, R, 1, dtype=af.Dtype.f32)
for t in range(1, N):
tPrevious = (t + 1) % 2
tCurrent = t % 2
dBt = af.randn(R, 2, dtype=af.Dtype.f32) * sqrtDeltaT
vLag = af.maxof(v[tPrevious], zeroArray)
sqrtVLag = af.sqrt(vLag)
x[tCurrent] = x[tPrevious] + (
mu - 0.5 * vLag) * deltaT + sqrtVLag * dBt[:, 0]
v[tCurrent] = vLag + kappa * (vBar - vLag) * deltaT + sigmaV * (
sqrtVLag * af.matmul(dBt, m))
return (x[tCurrent], af.maxof(v[tCurrent], zeroArray))
def simple_lapack(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5, 5)
l, u, p = af.lu(a)
display_func(l)
display_func(u)
display_func(p)
p = af.lu_inplace(a, "full")
display_func(a)
display_func(p)
a = af.randu(5, 3)
q, r, t = af.qr(a)
display_func(q)
display_func(r)
display_func(t)
af.qr_inplace(a)
display_func(a)
a = af.randu(5, 5)
a = af.matmulTN(a, a.copy()) + 10 * af.identity(5, 5)
R, info = af.cholesky(a)
display_func(R)
print_func(info)
af.cholesky_inplace(a)
display_func(a)
a = af.randu(5, 5)
ai = af.inverse(a)
display_func(a)
display_func(ai)
x0 = af.randu(5, 3)
b = af.matmul(a, x0)
x1 = af.solve(a, b)
display_func(x0)
display_func(x1)
p = af.lu_inplace(a)
x2 = af.solve_lu(a, p, b)
display_func(x2)
print_func(af.rank(a))
print_func(af.det(a))
print_func(af.norm(a, af.NORM.EUCLID))
print_func(af.norm(a, af.NORM.MATRIX_1))
print_func(af.norm(a, af.NORM.MATRIX_INF))
print_func(af.norm(a, af.NORM.MATRIX_L_PQ, 1, 1))
a = af.randu(10, 10)
display_func(a)
u, s, vt = af.svd(a)
display_func(af.matmul(af.matmul(u, af.diag(s, 0, False)), vt))
u, s, vt = af.svd_inplace(a)
display_func(af.matmul(af.matmul(u, af.diag(s, 0, False)), vt))
def predict_proba(self, X):
Z = af.matmul(X, self.__weights)
return af.sigmoid(Z)
import sys
from array import array
def af_assert(left, right, eps=1E-6):
if (af.max(af.abs(left -right)) > eps):
raise ValueError("Arrays not within dictated precision")
return
if __name__ == "__main__":
if (len(sys.argv) > 1):
af.set_device(int(sys.argv[1]))
af.info()
h_dx = array('f', (1.0/12, -8.0/12, 0, 8.0/12, 1.0/12))
h_spread = array('f', (1.0/5, 1.0/5, 1.0/5, 1.0/5, 1.0/5))
img = af.randu(640, 480)
dx = af.Array(h_dx, (5,1))
spread = af.Array(h_spread, (1, 5))
kernel = af.matmul(dx, spread)
full_res = af.convolve2(img, kernel)
sep_res = af.convolve2_separable(dx, spread, img)
af_assert(full_res, sep_res)
print("full 2D convolution time: %.5f ms" %
(1000 * af.timeit(af.convolve2, img, kernel)))
print("separable 2D convolution time: %.5f ms" %
(1000 * af.timeit(af.convolve2_separable, dx, spread, img)))
def simple_lapack(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5,5)
l,u,p = af.lu(a)
display_func(l)
display_func(u)
display_func(p)
p = af.lu_inplace(a, "full")
display_func(a)
display_func(p)
a = af.randu(5,3)
q,r,t = af.qr(a)
display_func(q)
display_func(r)
display_func(t)
af.qr_inplace(a)
display_func(a)
a = af.randu(5, 5)
a = af.matmulTN(a, a) + 10 * af.identity(5,5)
R,info = af.cholesky(a)
display_func(R)
print_func(info)
af.cholesky_inplace(a)
display_func(a)
a = af.randu(5,5)
ai = af.inverse(a)
display_func(a)
display_func(ai)
x0 = af.randu(5, 3)
b = af.matmul(a, x0)
x1 = af.solve(a, b)
display_func(x0)
display_func(x1)
p = af.lu_inplace(a)
x2 = af.solve_lu(a, p, b)
display_func(x2)
print_func(af.rank(a))
print_func(af.det(a))
print_func(af.norm(a, af.NORM.EUCLID))
print_func(af.norm(a, af.NORM.MATRIX_1))
print_func(af.norm(a, af.NORM.MATRIX_INF))
print_func(af.norm(a, af.NORM.MATRIX_L_PQ, 1, 1))
def bench(A, iters=100):
start = time()
for t in range(iters):
B = af.matmul(A, A)
af.sync()
return (time() - start) / iters
R, info = af.cholesky(a) af.display(R) print(info) af.cholesky_inplace(a) af.display(a) a = af.randu(5, 5) ai = af.inverse(a) af.display(a) af.display(ai) x0 = af.randu(5, 3) b = af.matmul(a, x0) x1 = af.solve(a, b) af.display(x0) af.display(x1) p = af.lu_inplace(a) x2 = af.solve_lu(a, p, b) af.display(x2) print(af.rank(a)) print(af.det(a)) print(af.norm(a, af.AF_NORM_EUCLID)) print(af.norm(a, af.AF_NORM_MATRIX_1))
#!/usr/bin/python ####################################################### # 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 a = af.randu(5, 5) b = af.randu(5, 5) af.display(af.matmul(a, b)) af.display(af.matmul(a, b, af.AF_MAT_TRANS)) af.display(af.matmul(a, b, af.AF_MAT_NONE, af.AF_MAT_TRANS)) b = af.randu(5, 1) af.display(af.dot(b, b))
def af_assert(left, right, eps=1E-6):
if (af.max(af.abs(left - right)) > eps):
raise ValueError("Arrays not within dictated precision")
return
if __name__ == "__main__":
if (len(sys.argv) > 1):
af.set_device(int(sys.argv[1]))
af.info()
h_dx = array('f', (1.0 / 12, -8.0 / 12, 0, 8.0 / 12, 1.0 / 12))
h_spread = array('f', (1.0 / 5, 1.0 / 5, 1.0 / 5, 1.0 / 5, 1.0 / 5))
img = af.randu(3072, 3072)
dx = af.Array(h_dx, (5, 1))
spread = af.Array(h_spread, (1, 5))
kernel = af.matmul(dx, spread)
full_res = af.convolve2(img, kernel)
sep_res = af.convolve2_separable(dx, spread, img)
af_assert(full_res, sep_res)
print("full 2D convolution time: %.5f ms" %
(1000 * af.timeit(af.convolve2, img, kernel)))
print("separable 2D convolution time: %.5f ms" %
(1000 * af.timeit(af.convolve2_separable, dx, spread, img)))
def bench(A, iters = 100):
start = time()
for t in range(iters):
B = af.matmul(A, A)
af.sync()
return (time() - start) / iters
def predict_prob(X, Weights):
Z = af.matmul(X, Weights)
return af.sigmoid(Z)
def run(iters):
for t in range(iters):
B = af.matmul(A, A)
af.sync()
def volume_integral_flux(u_n):
'''
Calculates the volume integral of flux in the wave equation.
:math:`\\int_{-1}^1 f(u) \\frac{d L_p}{d\\xi} d\\xi`
This will give N values of flux integral as p varies from 0 to N - 1.
This integral is carried out using the analytical form of the integrand
obtained as a linear combination of Lagrange basis polynomials.
This integrand is the used in the integrate() function.
Calculation of volume integral flux using N_LGL Lobatto quadrature points
can be vectorized and is much faster.
Parameters
----------
u : arrayfire.Array [N_LGL N_Elements M 1]
Amplitude of the wave at the mapped LGL nodes of each element. This
function can computer flux for :math:`M` :math:`u`.
Returns
-------
flux_integral : arrayfire.Array [N_LGL N_Elements M 1]
Value of the volume integral flux. It contains the integral
of all N_LGL * N_Element integrands.
'''
shape_u_n = utils.shape(u_n)
# The coefficients of dLp / d\xi
diff_lag_coeff = params.dl_dxi_coeffs
lobatto_nodes = params.lobatto_quadrature_nodes
Lobatto_weights = params.lobatto_weights_quadrature
nodes_tile = af.transpose(
af.tile(lobatto_nodes, 1, diff_lag_coeff.shape[1]))
power = af.flip(af.range(diff_lag_coeff.shape[1]))
power_tile = af.tile(power, 1, params.N_quad)
nodes_power = nodes_tile**power_tile
weights_tile = af.transpose(
af.tile(Lobatto_weights, 1, diff_lag_coeff.shape[1]))
nodes_weight = nodes_power * weights_tile
dLp_dxi = af.matmul(diff_lag_coeff, nodes_weight)
# The first option to calculate the volume integral term, directly uses
# the Lobatto quadrature instead of using the integrate() function by
# passing the coefficients of the Lagrange interpolated polynomial.
if(params.volume_integral_scheme == 'lobatto_quadrature' \
and params.N_quad == params.N_LGL):
# Flux using u_n, reordered to 1 X N_LGL X N_Elements array.
F_u_n = af.reorder(flux_x(u_n), 3, 0, 1, 2)
F_u_n = af.tile(F_u_n, d0=params.N_LGL)
# Multiplying with dLp / d\xi
integral_expansion = af.broadcast(utils.multiply, dLp_dxi, F_u_n)
# # Using the quadrature rule.
flux_integral = af.sum(integral_expansion, 1)
flux_integral = af.reorder(flux_integral, 0, 2, 3, 1)
# Using the integrate() function to calculate the volume integral term
# by passing the Lagrange interpolated polynomial.
else:
#print('option3')
analytical_flux_coeffs = af.transpose(af.moddims(u_n,
d0 = params.N_LGL,
d1 = params.N_Elements \
* shape_u_n[2]))
analytical_flux_coeffs = flux_x(
lagrange.lagrange_interpolation(analytical_flux_coeffs))
analytical_flux_coeffs = af.transpose(
af.moddims(af.transpose(analytical_flux_coeffs),
d0=params.N_LGL,
d1=params.N_Elements,
d2=shape_u_n[2]))
analytical_flux_coeffs = af.reorder(analytical_flux_coeffs,
d0=3,
d1=1,
d2=0,
d3=2)
analytical_flux_coeffs = af.tile(analytical_flux_coeffs,
d0=params.N_LGL)
analytical_flux_coeffs = af.moddims(
af.transpose(analytical_flux_coeffs),
d0=params.N_LGL,
d1=params.N_LGL * params.N_Elements,
d2=1,
d3=shape_u_n[2])
analytical_flux_coeffs = af.moddims(analytical_flux_coeffs,
d0=params.N_LGL,
d1=params.N_LGL *
params.N_Elements * shape_u_n[2],
d2=1,
d3=1)
analytical_flux_coeffs = af.transpose(analytical_flux_coeffs)
dl_dxi_coefficients = af.tile(af.tile(params.dl_dxi_coeffs,
d0 = params.N_Elements), \
d0 = shape_u_n[2])
volume_int_coeffs = utils.poly1d_product(dl_dxi_coefficients,
analytical_flux_coeffs)
flux_integral = lagrange.integrate(volume_int_coeffs)
flux_integral = af.moddims(af.transpose(flux_integral),
d0=params.N_LGL,
d1=params.N_Elements,
d2=shape_u_n[2])
return flux_integral
def __mul__(self, other):
other = afnp.asarray(other).astype(self.dtype)
s = arrayfire.matmul(self.d_array, other.d_array)
a = afnp.ndarray(pu.af_shape(s), dtype=pu.typemap(s.dtype()), af_array=s)
a._eval()
return a
def _predict_proba(self, X: af.Array, Weights: af.Array) -> af.Array:
Z = af.matmul(X, Weights)
return af.sigmoid(Z)
