Source code for sympy.physics.units.util

# -*- coding: utf-8 -*-

Several methods to simplify expressions involving unit objects.

from __future__ import division

import collections

from sympy.physics.units.quantities import Quantity
from sympy import Add, Mul, Pow, Function, Rational, Tuple, sympify
from sympy.core.compatibility import reduce
from sympy.physics.units.dimensions import Dimension

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).

    if isinstance(expr, Dimension):
        return expr

    if isinstance(expr, Pow):
        return dim_simplify(expr.base)**dim_simplify(expr.exp)
    elif isinstance(expr, Function):
        return dim_simplify(expr.args[0])
    elif isinstance(expr, Add):
        if (all(isinstance(arg, Dimension) for arg in expr.args) or
            all(arg.is_dimensionless for arg in expr.args if isinstance(arg, Dimension))):
            return reduce(lambda x, y: x.add(y), expr.args)
            raise ValueError("Dimensions cannot be added: %s" % expr)
    elif isinstance(expr, Mul):
        return Dimension(Mul(*[dim_simplify(i).name for i in expr.args if isinstance(i, Dimension)]))

    raise ValueError("Cannot be simplifed: %s", expr)

def _get_conversion_matrix_for_expr(expr, target_units):
    from sympy import Matrix

    expr_dim = Dimension(Quantity.get_dimensional_expr(expr))
    dim_dependencies = expr_dim.get_dimensional_dependencies(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 x.get_dimensional_dependencies(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([[i.get_dimensional_dependencies(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, (collections.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))