# -*- 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
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):
if expr.is_Atom:
return expr
if not expr.is_Mul:
return expr.func(*map(quantity_simplify, expr.args))
if expr.has(Prefix):
coeff, args = expr.as_coeff_mul(Prefix)
args = list(args)
for arg in args:
if isinstance(arg, Pow):
coeff = coeff * (arg.base.scale_factor ** arg.exp)
else:
coeff = coeff * arg.scale_factor
expr = coeff
coeff, args = expr.as_coeff_mul(Quantity)
args_pow = [arg.as_base_exp() for arg in args]
quantity_pow, other_pow = sift(args_pow, lambda x: isinstance(x[0], Quantity), binary=True)
quantity_pow_by_dim = sift(quantity_pow, lambda x: x[0].dimension)
# Just pick the first quantity:
ref_quantities = [i[0][0] for i in quantity_pow_by_dim.values()]
new_quantities = [
Mul.fromiter(
(quantity*i.scale_factor/quantity.scale_factor)**p for i, p in v)
if len(v) > 1 else v[0][0]**v[0][1]
for quantity, (k, v) in zip(ref_quantities, quantity_pow_by_dim.items())]
return coeff*Mul.fromiter(other_pow)*Mul.fromiter(new_quantities)
