# -*- coding: utf-8 -*-
"""
Several methods to simplify expressions involving unit objects.
"""
from __future__ import division
from sympy.utilities.exceptions import SymPyDeprecationWarning
from sympy import Add, Function, Mul, Pow, Rational, Tuple, sympify
from sympy.core.compatibility import reduce, Iterable, ordered
from sympy.physics.units.dimensions import Dimension, dimsys_default
from sympy.physics.units.quantities import Quantity
from sympy.physics.units.prefixes import Prefix
from sympy.utilities.iterables import sift
def dim_simplify(expr):
"""
NOTE: this function could be deprecated in the future.
Simplify expression by recursively evaluating the dimension arguments.
This function proceeds to a very rough dimensional analysis. It tries to
simplify expression with dimensions, and it deletes all what multiplies a
dimension without being a dimension. This is necessary to avoid strange
behavior when Add(L, L) be transformed into Mul(2, L).
"""
SymPyDeprecationWarning(
deprecated_since_version="1.2",
feature="dimensional simplification function",
issue=13336,
useinstead="don't use",
).warn()
_, expr = Quantity._collect_factor_and_dimension(expr)
return expr
def _get_conversion_matrix_for_expr(expr, target_units):
from sympy import Matrix
expr_dim = Dimension(Quantity.get_dimensional_expr(expr))
dim_dependencies = dimsys_default.get_dimensional_dependencies(expr_dim, mark_dimensionless=True)
target_dims = [Dimension(Quantity.get_dimensional_expr(x)) for x in target_units]
canon_dim_units = {i for x in target_dims for i in dimsys_default.get_dimensional_dependencies(x, mark_dimensionless=True)}
canon_expr_units = {i for i in dim_dependencies}
if not canon_expr_units.issubset(canon_dim_units):
return None
canon_dim_units = sorted(canon_dim_units)
camat = Matrix([[dimsys_default.get_dimensional_dependencies(i, mark_dimensionless=True).get(j, 0) for i in target_dims] for j in canon_dim_units])
exprmat = Matrix([dim_dependencies.get(k, 0) for k in canon_dim_units])
res_exponents = camat.solve_least_squares(exprmat, method=None)
return res_exponents
[docs]def convert_to(expr, target_units):
"""
Convert ``expr`` to the same expression with all of its units and quantities
represented as factors of ``target_units``, whenever the dimension is compatible.
``target_units`` may be a single unit/quantity, or a collection of
units/quantities.
Examples
========
>>> from sympy.physics.units import speed_of_light, meter, gram, second, day
>>> from sympy.physics.units import mile, newton, kilogram, atomic_mass_constant
>>> from sympy.physics.units import kilometer, centimeter
>>> from sympy.physics.units import convert_to
>>> convert_to(mile, kilometer)
25146*kilometer/15625
>>> convert_to(mile, kilometer).n()
1.609344*kilometer
>>> convert_to(speed_of_light, meter/second)
299792458*meter/second
>>> convert_to(day, second)
86400*second
>>> 3*newton
3*newton
>>> convert_to(3*newton, kilogram*meter/second**2)
3*kilogram*meter/second**2
>>> convert_to(atomic_mass_constant, gram)
1.66053904e-24*gram
Conversion to multiple units:
>>> convert_to(speed_of_light, [meter, second])
299792458*meter/second
>>> convert_to(3*newton, [centimeter, gram, second])
300000*centimeter*gram/second**2
Conversion to Planck units:
>>> from sympy.physics.units import gravitational_constant, hbar
>>> convert_to(atomic_mass_constant, [gravitational_constant, speed_of_light, hbar]).n()
7.62950196312651e-20*gravitational_constant**(-0.5)*hbar**0.5*speed_of_light**0.5
"""
if not isinstance(target_units, (Iterable, Tuple)):
target_units = [target_units]
if isinstance(expr, Add):
return Add.fromiter(convert_to(i, target_units) for i in expr.args)
expr = sympify(expr)
if not isinstance(expr, Quantity) and expr.has(Quantity):
expr = expr.replace(lambda x: isinstance(x, Quantity), lambda x: x.convert_to(target_units))
def get_total_scale_factor(expr):
if isinstance(expr, Mul):
return reduce(lambda x, y: x * y, [get_total_scale_factor(i) for i in expr.args])
elif isinstance(expr, Pow):
return get_total_scale_factor(expr.base) ** expr.exp
elif isinstance(expr, Quantity):
return expr.scale_factor
return expr
depmat = _get_conversion_matrix_for_expr(expr, target_units)
if depmat is None:
return expr
expr_scale_factor = get_total_scale_factor(expr)
return expr_scale_factor * Mul.fromiter((1/get_total_scale_factor(u) * u) ** p for u, p in zip(target_units, depmat))
def quantity_simplify(expr):
"""Return an equivalent expression in which prefixes are replaced
with numerical values and all units of a given dimension are the
unified in a canonical manner.
Examples
========
>>> from sympy.physics.units.util import quantity_simplify
>>> from sympy.physics.units.prefixes import kilo
>>> from sympy.physics.units import foot, inch
>>> quantity_simplify(kilo*foot*inch)
250*foot**2/3
>>> quantity_simplify(foot - 6*inch)
foot/2
"""
if expr.is_Atom or not expr.has(Prefix, Quantity):
return expr
# replace all prefixes with numerical values
p = expr.atoms(Prefix)
expr = expr.xreplace({p: p.scale_factor for p in p})
# replace all quantities of given dimension with a canonical
# quantity, chosen from those in the expression
d = sift(expr.atoms(Quantity), lambda i: i.dimension)
for k in d:
if len(d[k]) == 1:
continue
v = list(ordered(d[k]))
ref = v[0]/v[0].scale_factor
expr = expr.xreplace({vi: ref*vi.scale_factor for vi in v[1:]})
return expr
def check_dimensions(expr):
"""Return expr if there are not unitless values added to
dimensional quantities, else raise a ValueError."""
from sympy.solvers.solveset import _term_factors
# the case of adding a number to a dimensional quantity
# is ignored for the sake of SymPy core routines, so this
# function will raise an error now if such an addend is
# found.
# Also, when doing substitutions, multiplicative constants
# might be introduced, so remove those now
adds = expr.atoms(Add)
DIM_OF = dimsys_default.get_dimensional_dependencies
for a in adds:
deset = set()
for ai in a.args:
if ai.is_number:
deset.add(())
continue
dims = []
skip = False
for i in Mul.make_args(ai):
if i.has(Quantity):
i = Dimension(Quantity.get_dimensional_expr(i))
if i.has(Dimension):
dims.extend(DIM_OF(i).items())
elif i.free_symbols:
skip = True
break
if not skip:
deset.add(tuple(sorted(dims)))
if len(deset) > 1:
raise ValueError(
"addends have incompatible dimensions")
# clear multiplicative constants on Dimensions which may be
# left after substitution
reps = {}
for m in expr.atoms(Mul):
if any(isinstance(i, Dimension) for i in m.args):
reps[m] = m.func(*[
i for i in m.args if not i.is_number])
return expr.xreplace(reps)
