def test_poly1d_prod():
'''
Checks the product of the polynomials of different degrees using the
poly1d_product function and compares it to the analytically calculated
product coefficients.
'''
N = 3
N_a = 3
poly_a = af.range(N * N_a, dtype=af.Dtype.u32)
poly_a = af.moddims(poly_a, d0=N, d1=N_a)
N_b = 2
poly_b = af.range(N * N_b, dtype=af.Dtype.u32)
poly_b = af.moddims(poly_b, d0=N, d1=N_b)
ref_poly = af.np_to_af_array(
np.array([[0., 0., 9., 18.], [1., 8., 23., 28.], [4., 20., 41., 40.]]))
test_poly1d_prod = utils.poly1d_product(poly_a, poly_b)
test_poly1d_prod_commutative = utils.poly1d_product(poly_b, poly_a)
diff = af.abs(test_poly1d_prod - ref_poly)
diff_commutative = af.abs(test_poly1d_prod_commutative - ref_poly)
assert af.all_true(diff == 0.) and af.all_true(diff_commutative == 0.)
def test_Li_basis_value():
'''
This test compares the output of the lagrange basis value calculated by the
function ``Li_basis_value`` to the analytical value of the lagrange
polynomials created using the same LGL points.
The analytical values were calculated in this sage worksheet_
.. _worksheet: https://goo.gl/ADyA3U
'''
threshold = 1e-11
Li_value_ref = af.np_to_af_array(utils.csv_to_numpy(
'dg_maxwell/tests/lagrange/files/Li_value.csv'))
N_LGL = 8
xi_LGL = lagrange.LGL_points(N_LGL)
L_basis_poly1d, L_basis_af = lagrange.lagrange_polynomials(xi_LGL)
L_basis_af = af.np_to_af_array(L_basis_af)
Li_indexes = af.np_to_af_array(np.arange(3, dtype = np.int32))
xi = af.np_to_af_array(np.linspace(-1., 1, 10))
Li_value = lagrange.Li_basis_value(L_basis_af, Li_indexes, xi)
assert af.all_true(af.abs(Li_value - Li_value_ref) < threshold)
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 test_dy_dxi():
'''
This test checks the derivative :math:`\\frac{\\partial y}{\\partial \\xi}`
calculated using the function :math:`dg_maxwell.wave_equation_2d.dy_dxi`
for the :math:`0^{th}` element of a mesh for a circular ring. You may
download the file from this
:download:`link <../dg_maxwell/tests/wave_equation_2d/files/circle.msh>`.
'''
threshold = 1e-7
dy_dxi_reference = af.np_to_af_array(
utils.csv_to_numpy(
'dg_maxwell/tests/wave_equation_2d/files/dy_dxi_data.csv'))
nodes, elements = msh_parser.read_order_2_msh(
'dg_maxwell/tests/wave_equation_2d/files/circle.msh')
N_LGL = 16
xi_LGL = lagrange.LGL_points(N_LGL)
eta_LGL = lagrange.LGL_points(N_LGL)
Xi = af.data.tile(af.array.transpose(xi_LGL), d0=N_LGL)
Eta = af.data.tile(eta_LGL, d0=1, d1=N_LGL)
dy_dxi = wave_equation_2d.dy_dxi(nodes[elements[0]][:, 1], Xi, Eta)
check = af.abs(dy_dxi - dy_dxi_reference) < threshold
assert af.all_true(check)
def test_integrate_1d():
'''
Tests the ``integrate_1d`` by comparing the integral agains the
analytically calculated integral. The polynomials to be integrated
are all the Lagrange polynomials obtained for the LGL points.
The analytical integral is calculated in this `sage worksheet`_
.. _sage worksheet: https://goo.gl/1uYyNJ
'''
threshold = 1e-12
N_LGL = 8
xi_LGL = lagrange.LGL_points(N_LGL)
eta_LGL = lagrange.LGL_points(N_LGL)
_, Li_xi = lagrange.lagrange_polynomials(xi_LGL)
_, Lj_eta = lagrange.lagrange_polynomials(eta_LGL)
Li_xi = af.np_to_af_array(Li_xi)
Lp_xi = Li_xi.copy()
Li_Lp = utils.poly1d_product(Li_xi, Lp_xi)
test_integral_gauss = utils.integrate_1d(Li_Lp, order=9, scheme='gauss')
test_integral_lobatto = utils.integrate_1d(Li_Lp,
order=N_LGL + 1,
scheme='lobatto')
ref_integral = af.np_to_af_array(
np.array([
0.0333333333333, 0.196657278667, 0.318381179651, 0.384961541681,
0.384961541681, 0.318381179651, 0.196657278667, 0.0333333333333
]))
diff_gauss = af.abs(ref_integral - test_integral_gauss)
diff_lobatto = af.abs(ref_integral - test_integral_lobatto)
assert af.all_true(diff_gauss < threshold) and af.all_true(
diff_lobatto < threshold)
def all(a: ndarray,
axis: tp.Optional[int] = None,
out: tp.Optional[ndarray] = None,
keepdims: bool = False) \
-> tp.Union[bool, ndarray]:
"""
Returns True if all elements evaluate to True.
"""
if out:
raise ValueError('out != None is not supported')
return _wrap_af_array(af.all_true(a._af_array, dim=axis))
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 test_polyval_2d():
'''
Tests the ``utils.polyval_2d`` function by evaluating the polynomial
.. math:: P_0(\\xi) P_1(\\eta)
here,
.. math:: P_0(\\xi) = 3 \, \\xi^{2} + 2 \, \\xi + 1
.. math:: P_1(\\eta) = 3 \, \\eta^{2} + 2 \, \\eta + 1
at corresponding ``linspace`` points in :math:`\\xi \\in [-1, 1]` and
:math:`\\eta \\in [-1, 1]`.
This value is then compared with the reference value calculated analytically.
The reference values are calculated in
`polynomial_product_two_variables.sagews`_
.. _polynomial_product_two_variables.sagews: https://goo.gl/KwG7k9
'''
threshold = 1e-12
poly_xi_degree = 4
poly_xi = af.flip(af.np_to_af_array(np.arange(1, poly_xi_degree)))
poly_eta_degree = 4
poly_eta = af.flip(af.np_to_af_array(np.arange(1, poly_eta_degree)))
poly_xi_eta = utils.polynomial_product_coeffs(poly_xi, poly_eta)
xi = utils.linspace(-1, 1, 8)
eta = utils.linspace(-1, 1, 8)
polyval_xi_eta = af.transpose(utils.polyval_2d(poly_xi_eta, xi, eta))
polyval_xi_eta_ref = af.np_to_af_array(
np.array([
4.00000000000000, 1.21449396084962, 0.481466055810080,
0.601416076634741, 1.81424406497291, 5.79925031236988,
15.6751353602663, 36.0000000000000
]))
diff = af.abs(polyval_xi_eta - polyval_xi_eta_ref)
assert af.all_true(diff < threshold)
def all(self, s, axis):
return arrayfire.all_true(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))
def all(self, s, axis):
return arrayfire.all_true(s, dim=axis)
#!/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(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.display(af.sum(a, 0))
af.display(af.sum(a, 1))
af.display(af.product(a, 0))
af.display(af.product(a, 1))
af.display(af.min(a, 0))
af.display(af.min(a, 1))
af.display(af.max(a, 0))
af.display(af.max(a, 1))
af.display(af.count(a, 0))
af.display(af.count(a, 1))
#!/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))
def simple_algorithm(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(3, 3)
k = af.constant(1, 3, 3, dtype=af.Dtype.u32)
af.eval(k)
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))
rk = af.constant(1, 3, dtype=af.Dtype.u32)
rk[2] = 0
af.eval(rk)
display_func(af.sumByKey(rk, a, dim=0))
display_func(af.sumByKey(rk, a, dim=1))
display_func(af.productByKey(rk, a, dim=0))
display_func(af.productByKey(rk, a, dim=1))
display_func(af.minByKey(rk, a, dim=0))
display_func(af.minByKey(rk, a, dim=1))
display_func(af.maxByKey(rk, a, dim=0))
display_func(af.maxByKey(rk, a, dim=1))
display_func(af.anyTrueByKey(rk, a, dim=0))
display_func(af.anyTrueByKey(rk, a, dim=1))
display_func(af.allTrueByKey(rk, a, dim=0))
display_func(af.allTrueByKey(rk, a, dim=1))
display_func(af.countByKey(rk, a, dim=0))
display_func(af.countByKey(rk, a, dim=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.scan(a, 0, af.BINARYOP.ADD))
display_func(af.scan(a, 1, af.BINARYOP.MAX))
display_func(af.scan_by_key(k, a, 0, af.BINARYOP.ADD))
display_func(af.scan_by_key(k, a, 1, af.BINARYOP.MAX))
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))