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Frederik Hennig
pystencils
Commits
8c53c16a
Commit
8c53c16a
authored
Mar 16, 2022
by
Frederik Hennig
Committed by
Markus Holzer
Mar 16, 2022
Browse files
Added simplify_by_equality
parent
825be1df
Changes
2
Hide whitespace changes
Inline
Sidebyside
pystencils/sympyextensions.py
View file @
8c53c16a
...
...
@@ 453,6 +453,72 @@ def recursive_collect(expr, symbols, order_by_occurences=False):
return
rec_sum
def
summands
(
expr
):
return
set
(
expr
.
args
)
if
isinstance
(
expr
,
sp
.
Add
)
else
{
expr
}
def
simplify_by_equality
(
expr
,
a
,
b
,
c
):
"""
Uses the equality a = b + c, where a and b must be symbols, to simplify expr
by attempting to express additive combinations of two quantities by the third.
This works on expressions that are reducible to the form
:math:`a * (...) + b * (...) + c * (...)`,
without any mixed terms of a, b and c.
"""
if
not
isinstance
(
a
,
sp
.
Symbol
)
or
not
isinstance
(
b
,
sp
.
Symbol
):
raise
ValueError
(
"a and b must be symbols."
)
c
=
sp
.
sympify
(
c
)
if
not
(
isinstance
(
c
,
sp
.
Symbol
)
or
is_constant
(
c
)):
raise
ValueError
(
"c must be either a symbol or a constant!"
)
expr
=
sp
.
sympify
(
expr
)
expr_expanded
=
sp
.
expand
(
expr
)
a_coeff
=
expr_expanded
.
coeff
(
a
,
1
)
expr_expanded
=
(
a
*
a_coeff
).
expand
()
b_coeff
=
expr_expanded
.
coeff
(
b
,
1
)
expr_expanded
=
(
b
*
b_coeff
).
expand
()
if
isinstance
(
c
,
sp
.
Symbol
):
c_coeff
=
expr_expanded
.
coeff
(
c
,
1
)
rest
=
expr_expanded

(
c
*
c_coeff
).
expand
()
else
:
c_coeff
=
expr_expanded
/
c
rest
=
0
a_summands
=
summands
(
a_coeff
)
b_summands
=
summands
(
b_coeff
)
c_summands
=
summands
(
c_coeff
)
# replace b + c by a
b_plus_c_coeffs
=
b_summands
&
c_summands
for
coeff
in
b_plus_c_coeffs
:
rest
+=
a
*
coeff
b_summands
=
b_plus_c_coeffs
c_summands
=
b_plus_c_coeffs
# replace a  b by c
neg_b_summands
=
{

x
for
x
in
b_summands
}
a_minus_b_coeffs
=
a_summands
&
neg_b_summands
for
coeff
in
a_minus_b_coeffs
:
rest
+=
c
*
coeff
a_summands
=
a_minus_b_coeffs
b_summands
=
{

x
for
x
in
a_minus_b_coeffs
}
# replace a  c by b
neg_c_summands
=
{

x
for
x
in
c_summands
}
a_minus_c_coeffs
=
a_summands
&
neg_c_summands
for
coeff
in
a_minus_c_coeffs
:
rest
+=
b
*
coeff
a_summands
=
a_minus_c_coeffs
c_summands
=
{

x
for
x
in
a_minus_c_coeffs
}
# put it back together
return
(
rest
+
a
*
sum
(
a_summands
)
+
b
*
sum
(
b_summands
)
+
c
*
sum
(
c_summands
)).
expand
()
def
count_operations
(
term
:
Union
[
sp
.
Expr
,
List
[
sp
.
Expr
],
List
[
Assignment
]],
only_type
:
Optional
[
str
]
=
'real'
)
>
Dict
[
str
,
int
]:
"""Counts the number of additions, multiplications and division.
...
...
pystencils_tests/test_sympyextensions.py
View file @
8c53c16a
import
sympy
import
numpy
as
np
import
sympy
as
sp
import
pystencils
from
pystencils.sympyextensions
import
replace_second_order_products
from
pystencils.sympyextensions
import
remove_higher_order_terms
from
pystencils.sympyextensions
import
complete_the_squares_in_exp
from
pystencils.sympyextensions
import
extract_most_common_factor
from
pystencils.sympyextensions
import
simplify_by_equality
from
pystencils.sympyextensions
import
count_operations
from
pystencils.sympyextensions
import
common_denominator
from
pystencils.sympyextensions
import
get_symmetric_part
...
...
@@ 176,3 +178,26 @@ def test_get_symmetric_part():
sym_part
=
get_symmetric_part
(
expr
,
sympy
.
symbols
(
f
'y z'
))
assert
sym_part
==
expected_result
def
test_simplify_by_equality
():
x
,
y
,
z
=
sp
.
symbols
(
'x, y, z'
)
p
,
q
=
sp
.
symbols
(
'p, q'
)
# Let x = y + z
expr
=
x
*
p

y
*
p
+
z
*
q
expr
=
simplify_by_equality
(
expr
,
x
,
y
,
z
)
assert
expr
==
z
*
p
+
z
*
q
expr
=
x
*
(
p

2
*
q
)
+
2
*
q
*
z
expr
=
simplify_by_equality
(
expr
,
x
,
y
,
z
)
assert
expr
==
x
*
p

2
*
q
*
y
expr
=
x
*
(
y
+
z
)

y
*
z
expr
=
simplify_by_equality
(
expr
,
x
,
y
,
z
)
assert
expr
==
x
*
y
+
z
**
2
# Let x = y + 2
expr
=
x
*
p

2
*
p
expr
=
simplify_by_equality
(
expr
,
x
,
y
,
2
)
assert
expr
==
y
*
p
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