def test_invalid_acc_raises_exception(self):
with self.assertRaises(ValueError):
coefficients(deriv=1, acc=3)
with self.assertRaises(ValueError):
coefficients(deriv=1, acc=0)
with self.assertRaises(ValueError):
coefficients_non_uni(1, 3, None, None)
with self.assertRaises(ValueError):
coefficients_non_uni(1, 0, None, None)
def diff_non_uni(self, y, coords, **kwargs):
"""The core function to take a partial derivative on a non-uniform grid"""
if "acc" in kwargs:
acc = kwargs["acc"]
elif self.acc is not None:
acc = self.acc
else:
acc = 2
order, dim = self.order, self.axis
coef_list = []
for i in range(len(coords)):
coef_list.append(coefficients_non_uni(order, acc, coords, i))
yd = np.zeros_like(y)
ndims = len(y.shape)
multi_slice = [slice(None, None)] * ndims
ref_multi_slice = [slice(None, None)] * ndims
for i, x in enumerate(coords):
coefs = coef_list[i]
weights = coefs["coefficients"]
offsets = coefs["offsets"]
ref_multi_slice[dim] = i
for off, w in zip(offsets, weights):
multi_slice[dim] = i + off
yd[tuple(ref_multi_slice)] += w * y[tuple(multi_slice)]
return yd
def _matrix_nonuniform(self, shape, coords, acc):
coords = coords[self.axis]
siz = np.prod(shape)
long_inds = np.arange(siz).reshape(shape)
short_inds = [np.arange(shape[k]) for k in range(len(shape))]
short_inds = list(itertools.product(*short_inds))
coef_dicts = []
for i in range(len(coords)):
coef_dicts.append(coefficients_non_uni(self.order, acc, coords, i))
mat = sparse.lil_matrix((siz, siz))
for base_ind_long, base_ind_short in enumerate(short_inds):
cd = coef_dicts[base_ind_short[self.axis]]
cs, os = cd['coefficients'], cd['offsets']
for c, o in zip(cs, os):
off_short = np.zeros(len(shape), dtype=np.int)
off_short[self.axis] = int(o)
off_ind_short = np.array(base_ind_short,
dtype=np.int) + off_short
off_long = long_inds[tuple(off_ind_short)]
mat[base_ind_long, off_long] += c
return mat
def _determine_coefs(self):
"""Calculates the finite difference coefficients for the requested partial derivatives"""
for axis, deriv in self.derivs.items():
coefs = []
for i in range(len(deriv["coords"])):
coefs.append(coefficients_non_uni(deriv["order"], self.acc, deriv["coords"], i))
self.derivs[axis]["coefs"] = coefs
def apply(self, fd, u):
for axis, order in self.derivs.items():
if self.spac:
u = fd.diff(u, self.spac[axis], order, axis, coefficients(order, fd.acc))
else:
coefs = []
for i in range(len(self.coords[axis])):
coefs.append(coefficients_non_uni(order, fd.acc, self.coords[axis], i))
u = fd.diff_non_uni(u, self.coords[axis], axis, coefs)
return u
def test_non_uniform(self):
x = np.linspace(0, 10, 100)
dx = x[1] - x[0]
c_uni = coefficients(deriv=2, acc=2)
coefs_uni = c_uni["center"]["coefficients"] / dx**2
c_non_uni = coefficients_non_uni(deriv=2, acc=2, coords=x, idx=5)
coefs_non_uni = c_non_uni["coefficients"]
np.testing.assert_array_almost_equal(coefs_non_uni, coefs_uni)
def test_invalid_deriv_raises_exception(self):
with self.assertRaises(ValueError):
coefficients(-1, 2)
with self.assertRaises(ValueError):
coefficients_non_uni(-1, 2, None, None)