Source code for sympy.physics.units.util

# -*- 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).
        feature="dimensional simplification function",
        useinstead="don't use",
    _, 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)