def test_jacobi_intergrate(N, a, b, k, dtype):
c = coords.Coordinate('x')
d = distributor.Distributor((c,))
b = basis.Jacobi(c, size=N, a0=a, b0=b, a=a+k, b=b+k, bounds=(0, 1))
x = b.local_grid(1)
f = field.Field(dist=d, bases=(b,), dtype=dtype)
f['g'] = x**5
fi = operators.Integrate(f, c).evaluate()
assert np.allclose(fi['g'], 1/6)
def add_property(self, property, name, precompute_integral=False):
"""Add a property."""
self.properties.add_task(property, layout='g', name=name)
if precompute_integral:
# Add integral under slightly obscured name
task_op = self.properties.tasks[-1]['operator']
integral_op = operators.Integrate(task_op)
integral_name = '_{}_integral'.format(name)
self.properties.add_task(integral_op,
layout='g',
name=integral_name)
def test_integrate_scalar(Nphi, Nr, k, dealias, dtype, basis, n):
c, d, b, phi, r, x, y = basis(Nphi, Nr, k, dealias, dtype)
f = field.Field(dist=d, bases=(b, ), dtype=dtype)
f.preset_scales(b.domain.dealias)
f['g'] = r**(2 * n)
h = operators.Integrate(f, c).evaluate()
if isinstance(b, DiskBasis):
r_inner, r_outer = 0, b.radius
else:
r_inner, r_outer = b.radii
hg = 2 * np.pi * (r_outer**(2 + 2 * n) - r_inner**(2 + 2 * n)) / (2 +
2 * n)
assert np.allclose(h['g'], hg)
def test_fourier_integrate(N, bounds, dtype):
c = coords.Coordinate('x')
d = distributor.Distributor((c, ))
if dtype == np.float64:
b = basis.RealFourier(c, size=N, bounds=bounds)
elif dtype == np.complex128:
b = basis.ComplexFourier(c, size=N, bounds=bounds)
x = b.local_grid(1)
f = field.Field(dist=d, bases=(b, ), dtype=dtype)
k = 4 * np.pi / (bounds[1] - bounds[0])
f['g'] = 1 + np.sin(k * x + 0.1)
fi = operators.Integrate(f, c).evaluate()
assert np.allclose(fi['g'], bounds[1] - bounds[0])
def volume_integral(self, name):
"""Compute volume integral of a property."""
# Check for precomputed integral
try:
integral_name = '_{}_integral'.format(name)
integral_field = self.properties[integral_name]
except KeyError:
# Compute volume integral
field = self.properties[name]
integral_op = operators.Integrate(field)
integral_field = integral_op.evaluate()
# Communicate integral value to all processes
integral_value = self.reducer.global_max(integral_field['g'])
return integral_value