Commit f9e88655 authored by Martin Bauer's avatar Martin Bauer
Browse files

Merge branch 'fvm' into 'master'

FiniteDifferenceStaggeredStencilDerivation must be applied to field access

See merge request !109
parents 29ad4e74 1e02ab8f
......@@ -340,11 +340,5 @@ class FiniteDifferenceStaggeredStencilDerivation:
from pystencils.stencil import plot
plot(pts, data=ws)
def apply(self, field):
if field.index_dimensions == 0:
return sum([field.__getitem__(point) * weight for point, weight in zip(self.points, self.weights)])
else:
total = field.neighbor_vector(self.points[0]) * self.weights[0]
for point, weight in zip(self.points[1:], self.weights[1:]):
total += field.neighbor_vector(point) * weight
return total
def apply(self, access: Field.Access):
return sum([access.get_shifted(*point) * weight for point, weight in zip(self.points, self.weights)])
......@@ -845,7 +845,7 @@ class Field(AbstractField):
assert FieldType.is_staggered(self._field)
neighbor = self._field.staggered_stencil[index]
neighbor = direction_string_to_offset(neighbor, self._field.spatial_dimensions)
return [(o - sp.Rational(int(neighbor[i]), 2)) for i, o in enumerate(offsets)]
return [(o + sp.Rational(int(neighbor[i]), 2)) for i, o in enumerate(offsets)]
def _latex(self, _):
n = self._field.latex_name if self._field.latex_name else self._field.name
......
%% Cell type:code id: tags:
``` python
from pystencils.session import *
from pystencils.fd.derivation import *
```
%% Cell type:markdown id: tags:
# 2D standard stencils
%% Cell type:code id: tags:
``` python
stencil = [(-1, 0), (1, 0), (0, -1), (0, 1), (0, 0)]
standard_2d_00 = FiniteDifferenceStencilDerivation((0,0), stencil)
f = ps.fields("f: [2D]")
standard_2d_00_res = standard_2d_00.get_stencil()
res = standard_2d_00_res.apply(f.center)
expected = f[-1, 0] - 2 * f[0, 0] + f[1, 0]
assert res == expected
```
%% Cell type:code id: tags:
``` python
assert standard_2d_00_res.accuracy == 2
assert not standard_2d_00_res.is_isotropic
standard_2d_00_res
```
%%%% Output: execute_result
Finite difference stencil of accuracy 2, isotropic error: False
%% Cell type:code id: tags:
``` python
standard_2d_00.get_stencil().as_matrix()
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$$\left[\begin{matrix}0 & 0 & 0\\1 & -2 & 1\\0 & 0 & 0\end{matrix}\right]$$
⎡0 0 0⎤
⎢ ⎥
⎢1 -2 1⎥
⎢ ⎥
⎣0 0 0⎦
%% Cell type:markdown id: tags:
# 2D isotropic stencils
## second x-derivative
%% Cell type:code id: tags:
``` python
stencil = [(i, j) for i in (-1, 0, 1) for j in (-1, 0, 1)]
isotropic_2d_00 = FiniteDifferenceStencilDerivation((0,0), stencil)
isotropic_2d_00_res = isotropic_2d_00.get_stencil(isotropic=True)
assert isotropic_2d_00_res.is_isotropic
assert isotropic_2d_00_res.accuracy == 2
isotropic_2d_00_res
```
%%%% Output: execute_result
Finite difference stencil of accuracy 2, isotropic error: True
%% Cell type:code id: tags:
``` python
isotropic_2d_00_res.as_matrix()
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$$\left[\begin{matrix}\frac{1}{12} & - \frac{1}{6} & \frac{1}{12}\\\frac{5}{6} & - \frac{5}{3} & \frac{5}{6}\\\frac{1}{12} & - \frac{1}{6} & \frac{1}{12}\end{matrix}\right]$$
⎡1/12 -1/6 1/12⎤
⎢ ⎥
⎢5/6 -5/3 5/6 ⎥
⎢ ⎥
⎣1/12 -1/6 1/12⎦
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(2,2))
isotropic_2d_00_res.visualize()
```
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
expected_result = sp.Matrix([[1, -2, 1], [10, -20, 10], [1, -2, 1]]) / 12
assert expected_result == isotropic_2d_00_res.as_matrix()
```
%% Cell type:code id: tags:
``` python
type(isotropic_2d_00_res.as_matrix())
```
%%%% Output: execute_result
sympy.matrices.dense.MutableDenseMatrix
%% Cell type:code id: tags:
``` python
type(expected_result)
```
%%%% Output: execute_result
sympy.matrices.dense.MutableDenseMatrix
%% Cell type:markdown id: tags:
## Isotropic laplacian
%% Cell type:code id: tags:
``` python
isotropic_2d_11 = FiniteDifferenceStencilDerivation((1,1), stencil)
isotropic_2d_11_res = isotropic_2d_11.get_stencil(isotropic=True)
iso_laplacian = isotropic_2d_00_res.as_matrix() + isotropic_2d_11_res.as_matrix()
iso_laplacian
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$$\left[\begin{matrix}\frac{1}{6} & \frac{2}{3} & \frac{1}{6}\\\frac{2}{3} & - \frac{10}{3} & \frac{2}{3}\\\frac{1}{6} & \frac{2}{3} & \frac{1}{6}\end{matrix}\right]$$
⎡1/6 2/3 1/6⎤
⎢ ⎥
⎢2/3 -10/3 2/3⎥
⎢ ⎥
⎣1/6 2/3 1/6⎦
%% Cell type:code id: tags:
``` python
expected_result = sp.Matrix([[1, 4, 1], [4, -20, 4], [1, 4, 1]]) / 6
assert iso_laplacian == expected_result
```
%% Cell type:markdown id: tags:
# stencils for staggered fields
%% Cell type:code id: tags:
``` python
half = sp.Rational(1, 2)
fd_points_ex = (
(half, 0),
(-half, 0),
(half, 1),
(half, -1),
(-half, 1),
(-half, -1)
)
assert set(fd_points_ex) == set(FiniteDifferenceStaggeredStencilDerivation("E", 2).stencil)
fd_points_ey = (
(0, half),
(0, -half),
(-1,-half),
(-1, half),
(1, -half),
(1, half)
)
assert set(fd_points_ey) == set(FiniteDifferenceStaggeredStencilDerivation("N",2).stencil)
fd_points_c = (
(half, half),
(-half, -half),
(half, -half),
(-half, half)
)
assert set(fd_points_c) == set(FiniteDifferenceStaggeredStencilDerivation("NE",2).stencil)
assert len(FiniteDifferenceStaggeredStencilDerivation("E",3).points) == 10
assert len(FiniteDifferenceStaggeredStencilDerivation("NE",3).points) == 12
assert len(FiniteDifferenceStaggeredStencilDerivation("TNE",3).points) == 8
```
%% Cell type:code id: tags:
``` python
c = ps.fields("c: [2D]")
c3 = ps.fields("c3: [3D]")
assert FiniteDifferenceStaggeredStencilDerivation("E", 2, (0,)).apply(c) == c[1, 0] - c[0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("W", 2, (0,)).apply(c) == c[0, 0] - c[-1, 0]
assert FiniteDifferenceStaggeredStencilDerivation("N", 2, (1,)).apply(c) == c[0, 1] - c[0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("S", 2, (1,)).apply(c) == c[0, 0] - c[0, -1]
assert FiniteDifferenceStaggeredStencilDerivation("E", 3, (0,)).apply(c3) == c3[1, 0, 0] - c3[0, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("W", 3, (0,)).apply(c3) == c3[0, 0, 0] - c3[-1, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("N", 3, (1,)).apply(c3) == c3[0, 1, 0] - c3[0, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("S", 3, (1,)).apply(c3) == c3[0, 0, 0] - c3[0, -1, 0]
assert FiniteDifferenceStaggeredStencilDerivation("T", 3, (2,)).apply(c3) == c3[0, 0, 1] - c3[0, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("B", 3, (2,)).apply(c3) == c3[0, 0, 0] - c3[0, 0, -1]
assert FiniteDifferenceStaggeredStencilDerivation("E", 2, (0,)).apply(c.center) == c[1, 0] - c[0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("W", 2, (0,)).apply(c.center) == c[0, 0] - c[-1, 0]
assert FiniteDifferenceStaggeredStencilDerivation("N", 2, (1,)).apply(c.center) == c[0, 1] - c[0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("S", 2, (1,)).apply(c.center) == c[0, 0] - c[0, -1]
assert FiniteDifferenceStaggeredStencilDerivation("E", 3, (0,)).apply(c3.center) == c3[1, 0, 0] - c3[0, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("W", 3, (0,)).apply(c3.center) == c3[0, 0, 0] - c3[-1, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("N", 3, (1,)).apply(c3.center) == c3[0, 1, 0] - c3[0, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("S", 3, (1,)).apply(c3.center) == c3[0, 0, 0] - c3[0, -1, 0]
assert FiniteDifferenceStaggeredStencilDerivation("T", 3, (2,)).apply(c3.center) == c3[0, 0, 1] - c3[0, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("B", 3, (2,)).apply(c3.center) == c3[0, 0, 0] - c3[0, 0, -1]
assert FiniteDifferenceStaggeredStencilDerivation("S", 2, (0,)).apply(c) == \
assert FiniteDifferenceStaggeredStencilDerivation("S", 2, (0,)).apply(c.center) == \
(c[1, 0] + c[1, -1] - c[-1, 0] - c[-1, -1])/4
assert FiniteDifferenceStaggeredStencilDerivation("NE", 2, (0,)).apply(c) + \
FiniteDifferenceStaggeredStencilDerivation("NE", 2, (1,)).apply(c) == c[1, 1] - c[0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("NE", 3, (0,)).apply(c3) + \
FiniteDifferenceStaggeredStencilDerivation("NE", 3, (1,)).apply(c3) == c3[1, 1, 0] - c3[0, 0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("NE", 2, (0,)).apply(c.center) + \
FiniteDifferenceStaggeredStencilDerivation("NE", 2, (1,)).apply(c.center) == c[1, 1] - c[0, 0]
assert FiniteDifferenceStaggeredStencilDerivation("NE", 3, (0,)).apply(c3.center) + \
FiniteDifferenceStaggeredStencilDerivation("NE", 3, (1,)).apply(c3.center) == c3[1, 1, 0] - c3[0, 0, 0]
```
%% Cell type:code id: tags:
``` python
d = FiniteDifferenceStaggeredStencilDerivation("NE", 2, (0, 1))
assert d.apply(c) == c[0,0] + c[1,1] - c[1,0] - c[0,1]
assert d.apply(c.center) == c[0,0] + c[1,1] - c[1,0] - c[0,1]
d.visualize()
```
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
v3 = ps.fields("v(3): [3D]")
assert FiniteDifferenceStaggeredStencilDerivation("E", 3, (0,)).apply(v3) == \
sp.Matrix([v3[1,0,0](i) - v3[0,0,0](i) for i in range(*v3.index_shape)])
for i in range(*v3.index_shape):
assert FiniteDifferenceStaggeredStencilDerivation("E", 3, (0,)).apply(v3.center_vector[i]) == \
v3[1,0,0](i) - v3[0,0,0](i)
```
%% Cell type:code id: tags:
``` python
```
......
......@@ -154,12 +154,18 @@ def test_staggered():
for j in range(2)] for i in range(2)])
# D2Q9
k = ps.fields('k(4) : double[2D]', field_type=FieldType.STAGGERED)
assert k[1, 1](2) == k.staggered_access("NE")
assert k[0, 0](2) == k.staggered_access("SW")
assert k[0, 0](3) == k.staggered_access("NW")
k1, k2 = ps.fields('k1(4), k2(2) : double[2D]', field_type=FieldType.STAGGERED)
assert k1[1, 1](2) == k1.staggered_access("NE")
assert k1[0, 0](2) == k1.staggered_access("SW")
assert k1[0, 0](3) == k1.staggered_access("NW")
a = k1.staggered_access("NE")
assert a._staggered_offset(a.offsets, a.index[0]) == [sp.Rational(1, 2), sp.Rational(1, 2)]
a = k1.staggered_access("SW")
assert a._staggered_offset(a.offsets, a.index[0]) == [sp.Rational(-1, 2), sp.Rational(-1, 2)]
a = k1.staggered_access("NW")
assert a._staggered_offset(a.offsets, a.index[0]) == [sp.Rational(-1, 2), sp.Rational(1, 2)]
# sign reversed when using as flux field
r = ps.fields('r(2) : double[2D]', field_type=FieldType.STAGGERED_FLUX)
......
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