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Tom Harke
pystencils
Commits
2d7485a8
Commit
2d7485a8
authored
Dec 03, 2019
by
Michael Kuron
Browse files
FiniteDifferenceStaggeredStencilDerivation
parent
e1b452f7
Changes
2
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pystencils/fd/derivation.py
View file @
2d7485a8
import
warnings
from
collections
import
defaultdict
import
itertools
import
numpy
as
np
import
sympy
as
sp
from
pystencils.field
import
Field
from
pystencils.stencil
import
direction_string_to_offset
from
pystencils.sympyextensions
import
multidimensional_sum
,
prod
from
pystencils.utils
import
LinearEquationSystem
,
fully_contains
...
...
@@ 228,3 +230,114 @@ class FiniteDifferenceStencilDerivation:
def
__repr__
(
self
):
return
"Finite difference stencil of accuracy {}, isotropic error: {}"
.
format
(
self
.
accuracy
,
self
.
is_isotropic
)
class
FiniteDifferenceStaggeredStencilDerivation
:
"""Derives a finite difference stencil for application at a staggered position
Args:
neighbor: the neighbor direction string or vector at whose staggered position to calculate the derivative
dim: how many dimensions (2 or 3)
derivative: a tuple of directions over which to perform derivatives
"""
def
__init__
(
self
,
neighbor
,
dim
,
derivative
=
tuple
()):
if
type
(
neighbor
)
is
str
:
neighbor
=
direction_string_to_offset
(
neighbor
)
if
dim
==
2
:
assert
neighbor
[
dim
:]
==
0
assert
derivative
is
tuple
()
or
max
(
derivative
)
<
dim
neighbor
=
sp
.
Matrix
(
neighbor
[:
dim
])
pos
=
neighbor
/
2
def
unitvec
(
i
):
"""return the `i`th unit vector in three dimensions"""
a
=
np
.
zeros
(
dim
,
dtype
=
int
)
a
[
i
]
=
1
return
a
def
flipped
(
a
,
i
):
"""return `a` with its `i`th element's sign flipped"""
a
=
a
.
copy
()
a
[
i
]
*=

1
return
a
# determine the points to use, coordinates are relative to position
points
=
[]
if
np
.
linalg
.
norm
(
neighbor
,
1
)
==
1
:
main_points
=
[
neighbor
/
2
,
neighbor
/

2
]
elif
np
.
linalg
.
norm
(
neighbor
,
1
)
==
2
:
nonzero_indices
=
[
i
for
i
,
v
in
enumerate
(
neighbor
)
if
v
!=
0
and
i
<
dim
]
main_points
=
[
neighbor
/
2
,
neighbor
/

2
,
flipped
(
neighbor
/
2
,
nonzero_indices
[
0
]),
flipped
(
neighbor
/

2
,
nonzero_indices
[
0
])]
else
:
main_points
=
[
neighbor
.
multiply_elementwise
(
sp
.
Matrix
(
c
)
/
2
)
for
c
in
itertools
.
product
([

1
,
1
],
repeat
=
3
)]
points
+=
main_points
zero_indices
=
[
i
for
i
,
v
in
enumerate
(
neighbor
)
if
v
==
0
and
i
<
dim
]
for
i
in
zero_indices
:
points
+=
[
point
+
sp
.
Matrix
(
unitvec
(
i
))
for
point
in
main_points
]
points
+=
[
point

sp
.
Matrix
(
unitvec
(
i
))
for
point
in
main_points
]
points_tuple
=
tuple
([
tuple
(
p
)
for
p
in
points
])
self
.
_stencil
=
points_tuple
# determine the stencil weights
if
len
(
derivative
)
==
0
:
weights
=
None
else
:
derivation
=
FiniteDifferenceStencilDerivation
(
derivative
,
points_tuple
).
get_stencil
()
if
not
derivation
.
accuracy
:
raise
Exception
(
'the requested derivative cannot be performed with the available neighbors'
)
weights
=
derivation
.
weights
# if the weights are underdefined, we can choose the free symbols to find the sparsest stencil
free_weights
=
set
(
itertools
.
chain
(
*
[
w
.
free_symbols
for
w
in
weights
]))
if
len
(
free_weights
)
>
0
:
zero_counts
=
defaultdict
(
list
)
for
values
in
itertools
.
product
([

1
,

sp
.
Rational
(
1
,
2
),
0
,
1
,
sp
.
Rational
(
1
,
2
)],
repeat
=
len
(
free_weights
)):
subs
=
{
free_weight
:
value
for
free_weight
,
value
in
zip
(
free_weights
,
values
)}
weights
=
[
w
.
subs
(
subs
)
for
w
in
derivation
.
weights
]
if
not
all
(
a
==
0
for
a
in
weights
):
zero_count
=
sum
([
1
for
w
in
weights
if
w
==
0
])
zero_counts
[
zero_count
].
append
(
weights
)
best
=
zero_counts
[
max
(
zero_counts
.
keys
())]
if
len
(
best
)
>
1
:
# if there are multiple, pick the one that contains a nonzero center weight
center
=
[
tuple
(
p
+
pos
)
for
p
in
points
].
index
((
0
,
0
,
0
))
best
=
[
b
for
b
in
best
if
b
[
center
]
!=
0
]
if
len
(
best
)
>
1
:
raise
NotImplementedError
(
"more than one suitable set of weights found, don't know how to proceed"
)
weights
=
best
[
0
]
assert
weights
points_tuple
=
tuple
([
tuple
(
p
+
pos
)
for
p
in
points
])
self
.
_points
=
points_tuple
self
.
_weights
=
weights
@
property
def
points
(
self
):
"""return the points of the stencil"""
return
self
.
_points
@
property
def
stencil
(
self
):
"""return the points of the stencil relative to the staggered position specified by neighbor"""
return
self
.
_stencil
@
property
def
weights
(
self
):
"""return the weights of the stencil"""
assert
self
.
_weights
is
not
None
return
self
.
_weights
def
visualize
(
self
):
if
self
.
_weights
is
None
:
ws
=
None
else
:
ws
=
np
.
array
([
w
for
w
in
self
.
weights
if
w
!=
0
],
dtype
=
float
)
pts
=
np
.
array
([
p
for
i
,
p
in
enumerate
(
self
.
points
)
if
self
.
weights
[
i
]
!=
0
],
dtype
=
int
)
from
pystencils.stencil
import
plot
plot
(
pts
,
data
=
ws
)
def
apply
(
self
,
field
):
return
sum
([
field
.
__getitem__
(
point
)
*
weight
for
point
,
weight
in
zip
(
self
.
points
,
self
.
weights
)])
pystencils_tests/test_fd_derivation.ipynb
View file @
2d7485a8
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