591 lines
20 KiB
Python
591 lines
20 KiB
Python
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"""
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Definition of physical dimensions.
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Unit systems will be constructed on top of these dimensions.
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Most of the examples in the doc use MKS system and are presented from the
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computer point of view: from a human point, adding length to time is not legal
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in MKS but it is in natural system; for a computer in natural system there is
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no time dimension (but a velocity dimension instead) - in the basis - so the
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question of adding time to length has no meaning.
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"""
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from __future__ import annotations
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import collections
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from functools import reduce
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from sympy.core.basic import Basic
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from sympy.core.containers import (Dict, Tuple)
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from sympy.core.singleton import S
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from sympy.core.sorting import default_sort_key
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from sympy.core.symbol import Symbol
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from sympy.core.sympify import sympify
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from sympy.matrices.dense import Matrix
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from sympy.functions.elementary.trigonometric import TrigonometricFunction
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from sympy.core.expr import Expr
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from sympy.core.power import Pow
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class _QuantityMapper:
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_quantity_scale_factors_global: dict[Expr, Expr] = {}
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_quantity_dimensional_equivalence_map_global: dict[Expr, Expr] = {}
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_quantity_dimension_global: dict[Expr, Expr] = {}
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def __init__(self, *args, **kwargs):
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self._quantity_dimension_map = {}
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self._quantity_scale_factors = {}
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def set_quantity_dimension(self, quantity, dimension):
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"""
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Set the dimension for the quantity in a unit system.
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If this relation is valid in every unit system, use
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``quantity.set_global_dimension(dimension)`` instead.
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"""
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from sympy.physics.units import Quantity
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dimension = sympify(dimension)
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if not isinstance(dimension, Dimension):
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if dimension == 1:
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dimension = Dimension(1)
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else:
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raise ValueError("expected dimension or 1")
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elif isinstance(dimension, Quantity):
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dimension = self.get_quantity_dimension(dimension)
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self._quantity_dimension_map[quantity] = dimension
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def set_quantity_scale_factor(self, quantity, scale_factor):
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"""
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Set the scale factor of a quantity relative to another quantity.
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It should be used only once per quantity to just one other quantity,
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the algorithm will then be able to compute the scale factors to all
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other quantities.
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In case the scale factor is valid in every unit system, please use
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``quantity.set_global_relative_scale_factor(scale_factor)`` instead.
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"""
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from sympy.physics.units import Quantity
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from sympy.physics.units.prefixes import Prefix
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scale_factor = sympify(scale_factor)
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# replace all prefixes by their ratio to canonical units:
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scale_factor = scale_factor.replace(
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lambda x: isinstance(x, Prefix),
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lambda x: x.scale_factor
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)
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# replace all quantities by their ratio to canonical units:
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scale_factor = scale_factor.replace(
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lambda x: isinstance(x, Quantity),
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lambda x: self.get_quantity_scale_factor(x)
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)
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self._quantity_scale_factors[quantity] = scale_factor
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def get_quantity_dimension(self, unit):
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from sympy.physics.units import Quantity
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# First look-up the local dimension map, then the global one:
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if unit in self._quantity_dimension_map:
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return self._quantity_dimension_map[unit]
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if unit in self._quantity_dimension_global:
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return self._quantity_dimension_global[unit]
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if unit in self._quantity_dimensional_equivalence_map_global:
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dep_unit = self._quantity_dimensional_equivalence_map_global[unit]
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if isinstance(dep_unit, Quantity):
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return self.get_quantity_dimension(dep_unit)
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else:
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return Dimension(self.get_dimensional_expr(dep_unit))
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if isinstance(unit, Quantity):
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return Dimension(unit.name)
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else:
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return Dimension(1)
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def get_quantity_scale_factor(self, unit):
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if unit in self._quantity_scale_factors:
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return self._quantity_scale_factors[unit]
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if unit in self._quantity_scale_factors_global:
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mul_factor, other_unit = self._quantity_scale_factors_global[unit]
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return mul_factor*self.get_quantity_scale_factor(other_unit)
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return S.One
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class Dimension(Expr):
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"""
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This class represent the dimension of a physical quantities.
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The ``Dimension`` constructor takes as parameters a name and an optional
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symbol.
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For example, in classical mechanics we know that time is different from
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temperature and dimensions make this difference (but they do not provide
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any measure of these quantites.
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>>> from sympy.physics.units import Dimension
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>>> length = Dimension('length')
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>>> length
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Dimension(length)
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>>> time = Dimension('time')
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>>> time
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Dimension(time)
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Dimensions can be composed using multiplication, division and
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exponentiation (by a number) to give new dimensions. Addition and
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subtraction is defined only when the two objects are the same dimension.
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>>> velocity = length / time
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>>> velocity
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Dimension(length/time)
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It is possible to use a dimension system object to get the dimensionsal
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dependencies of a dimension, for example the dimension system used by the
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SI units convention can be used:
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>>> from sympy.physics.units.systems.si import dimsys_SI
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>>> dimsys_SI.get_dimensional_dependencies(velocity)
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{Dimension(length, L): 1, Dimension(time, T): -1}
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>>> length + length
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Dimension(length)
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>>> l2 = length**2
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>>> l2
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Dimension(length**2)
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>>> dimsys_SI.get_dimensional_dependencies(l2)
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{Dimension(length, L): 2}
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"""
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_op_priority = 13.0
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# XXX: This doesn't seem to be used anywhere...
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_dimensional_dependencies = {} # type: ignore
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is_commutative = True
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is_number = False
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# make sqrt(M**2) --> M
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is_positive = True
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is_real = True
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def __new__(cls, name, symbol=None):
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if isinstance(name, str):
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name = Symbol(name)
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else:
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name = sympify(name)
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if not isinstance(name, Expr):
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raise TypeError("Dimension name needs to be a valid math expression")
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if isinstance(symbol, str):
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symbol = Symbol(symbol)
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elif symbol is not None:
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assert isinstance(symbol, Symbol)
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obj = Expr.__new__(cls, name)
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obj._name = name
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obj._symbol = symbol
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return obj
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@property
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def name(self):
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return self._name
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@property
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def symbol(self):
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return self._symbol
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def __str__(self):
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"""
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Display the string representation of the dimension.
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"""
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if self.symbol is None:
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return "Dimension(%s)" % (self.name)
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else:
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return "Dimension(%s, %s)" % (self.name, self.symbol)
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def __repr__(self):
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return self.__str__()
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def __neg__(self):
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return self
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def __add__(self, other):
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from sympy.physics.units.quantities import Quantity
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other = sympify(other)
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if isinstance(other, Basic):
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if other.has(Quantity):
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raise TypeError("cannot sum dimension and quantity")
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if isinstance(other, Dimension) and self == other:
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return self
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return super().__add__(other)
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return self
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def __radd__(self, other):
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return self.__add__(other)
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def __sub__(self, other):
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# there is no notion of ordering (or magnitude) among dimension,
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# subtraction is equivalent to addition when the operation is legal
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return self + other
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def __rsub__(self, other):
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# there is no notion of ordering (or magnitude) among dimension,
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# subtraction is equivalent to addition when the operation is legal
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return self + other
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def __pow__(self, other):
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return self._eval_power(other)
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def _eval_power(self, other):
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other = sympify(other)
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return Dimension(self.name**other)
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def __mul__(self, other):
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from sympy.physics.units.quantities import Quantity
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if isinstance(other, Basic):
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if other.has(Quantity):
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raise TypeError("cannot sum dimension and quantity")
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if isinstance(other, Dimension):
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return Dimension(self.name*other.name)
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if not other.free_symbols: # other.is_number cannot be used
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return self
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return super().__mul__(other)
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return self
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def __rmul__(self, other):
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return self.__mul__(other)
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def __truediv__(self, other):
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return self*Pow(other, -1)
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def __rtruediv__(self, other):
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return other * pow(self, -1)
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@classmethod
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def _from_dimensional_dependencies(cls, dependencies):
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return reduce(lambda x, y: x * y, (
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d**e for d, e in dependencies.items()
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), 1)
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def has_integer_powers(self, dim_sys):
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"""
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Check if the dimension object has only integer powers.
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All the dimension powers should be integers, but rational powers may
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appear in intermediate steps. This method may be used to check that the
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final result is well-defined.
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"""
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return all(dpow.is_Integer for dpow in dim_sys.get_dimensional_dependencies(self).values())
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# Create dimensions according to the base units in MKSA.
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# For other unit systems, they can be derived by transforming the base
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# dimensional dependency dictionary.
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class DimensionSystem(Basic, _QuantityMapper):
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r"""
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DimensionSystem represents a coherent set of dimensions.
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The constructor takes three parameters:
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- base dimensions;
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- derived dimensions: these are defined in terms of the base dimensions
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(for example velocity is defined from the division of length by time);
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- dependency of dimensions: how the derived dimensions depend
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on the base dimensions.
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Optionally either the ``derived_dims`` or the ``dimensional_dependencies``
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may be omitted.
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"""
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def __new__(cls, base_dims, derived_dims=(), dimensional_dependencies={}):
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dimensional_dependencies = dict(dimensional_dependencies)
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def parse_dim(dim):
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if isinstance(dim, str):
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dim = Dimension(Symbol(dim))
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elif isinstance(dim, Dimension):
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pass
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elif isinstance(dim, Symbol):
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dim = Dimension(dim)
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else:
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raise TypeError("%s wrong type" % dim)
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return dim
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base_dims = [parse_dim(i) for i in base_dims]
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derived_dims = [parse_dim(i) for i in derived_dims]
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for dim in base_dims:
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if (dim in dimensional_dependencies
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and (len(dimensional_dependencies[dim]) != 1 or
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dimensional_dependencies[dim].get(dim, None) != 1)):
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raise IndexError("Repeated value in base dimensions")
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dimensional_dependencies[dim] = Dict({dim: 1})
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def parse_dim_name(dim):
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if isinstance(dim, Dimension):
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return dim
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elif isinstance(dim, str):
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return Dimension(Symbol(dim))
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elif isinstance(dim, Symbol):
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return Dimension(dim)
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else:
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raise TypeError("unrecognized type %s for %s" % (type(dim), dim))
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for dim in dimensional_dependencies.keys():
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dim = parse_dim(dim)
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if (dim not in derived_dims) and (dim not in base_dims):
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derived_dims.append(dim)
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def parse_dict(d):
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return Dict({parse_dim_name(i): j for i, j in d.items()})
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# Make sure everything is a SymPy type:
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dimensional_dependencies = {parse_dim_name(i): parse_dict(j) for i, j in
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dimensional_dependencies.items()}
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for dim in derived_dims:
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if dim in base_dims:
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raise ValueError("Dimension %s both in base and derived" % dim)
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if dim not in dimensional_dependencies:
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# TODO: should this raise a warning?
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dimensional_dependencies[dim] = Dict({dim: 1})
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base_dims.sort(key=default_sort_key)
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derived_dims.sort(key=default_sort_key)
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base_dims = Tuple(*base_dims)
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derived_dims = Tuple(*derived_dims)
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dimensional_dependencies = Dict({i: Dict(j) for i, j in dimensional_dependencies.items()})
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obj = Basic.__new__(cls, base_dims, derived_dims, dimensional_dependencies)
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return obj
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@property
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def base_dims(self):
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return self.args[0]
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@property
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def derived_dims(self):
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return self.args[1]
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@property
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def dimensional_dependencies(self):
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return self.args[2]
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def _get_dimensional_dependencies_for_name(self, dimension):
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if isinstance(dimension, str):
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dimension = Dimension(Symbol(dimension))
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elif not isinstance(dimension, Dimension):
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dimension = Dimension(dimension)
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if dimension.name.is_Symbol:
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# Dimensions not included in the dependencies are considered
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# as base dimensions:
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return dict(self.dimensional_dependencies.get(dimension, {dimension: 1}))
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if dimension.name.is_number or dimension.name.is_NumberSymbol:
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return {}
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get_for_name = self._get_dimensional_dependencies_for_name
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||
|
|
|
||
|
|
if dimension.name.is_Mul:
|
||
|
|
ret = collections.defaultdict(int)
|
||
|
|
dicts = [get_for_name(i) for i in dimension.name.args]
|
||
|
|
for d in dicts:
|
||
|
|
for k, v in d.items():
|
||
|
|
ret[k] += v
|
||
|
|
return {k: v for (k, v) in ret.items() if v != 0}
|
||
|
|
|
||
|
|
if dimension.name.is_Add:
|
||
|
|
dicts = [get_for_name(i) for i in dimension.name.args]
|
||
|
|
if all(d == dicts[0] for d in dicts[1:]):
|
||
|
|
return dicts[0]
|
||
|
|
raise TypeError("Only equivalent dimensions can be added or subtracted.")
|
||
|
|
|
||
|
|
if dimension.name.is_Pow:
|
||
|
|
dim_base = get_for_name(dimension.name.base)
|
||
|
|
dim_exp = get_for_name(dimension.name.exp)
|
||
|
|
if dim_exp == {} or dimension.name.exp.is_Symbol:
|
||
|
|
return {k: v * dimension.name.exp for (k, v) in dim_base.items()}
|
||
|
|
else:
|
||
|
|
raise TypeError("The exponent for the power operator must be a Symbol or dimensionless.")
|
||
|
|
|
||
|
|
if dimension.name.is_Function:
|
||
|
|
args = (Dimension._from_dimensional_dependencies(
|
||
|
|
get_for_name(arg)) for arg in dimension.name.args)
|
||
|
|
result = dimension.name.func(*args)
|
||
|
|
|
||
|
|
dicts = [get_for_name(i) for i in dimension.name.args]
|
||
|
|
|
||
|
|
if isinstance(result, Dimension):
|
||
|
|
return self.get_dimensional_dependencies(result)
|
||
|
|
elif result.func == dimension.name.func:
|
||
|
|
if isinstance(dimension.name, TrigonometricFunction):
|
||
|
|
if dicts[0] in ({}, {Dimension('angle'): 1}):
|
||
|
|
return {}
|
||
|
|
else:
|
||
|
|
raise TypeError("The input argument for the function {} must be dimensionless or have dimensions of angle.".format(dimension.func))
|
||
|
|
else:
|
||
|
|
if all(item == {} for item in dicts):
|
||
|
|
return {}
|
||
|
|
else:
|
||
|
|
raise TypeError("The input arguments for the function {} must be dimensionless.".format(dimension.func))
|
||
|
|
else:
|
||
|
|
return get_for_name(result)
|
||
|
|
|
||
|
|
raise TypeError("Type {} not implemented for get_dimensional_dependencies".format(type(dimension.name)))
|
||
|
|
|
||
|
|
def get_dimensional_dependencies(self, name, mark_dimensionless=False):
|
||
|
|
dimdep = self._get_dimensional_dependencies_for_name(name)
|
||
|
|
if mark_dimensionless and dimdep == {}:
|
||
|
|
return {Dimension(1): 1}
|
||
|
|
return {k: v for k, v in dimdep.items()}
|
||
|
|
|
||
|
|
def equivalent_dims(self, dim1, dim2):
|
||
|
|
deps1 = self.get_dimensional_dependencies(dim1)
|
||
|
|
deps2 = self.get_dimensional_dependencies(dim2)
|
||
|
|
return deps1 == deps2
|
||
|
|
|
||
|
|
def extend(self, new_base_dims, new_derived_dims=(), new_dim_deps=None):
|
||
|
|
deps = dict(self.dimensional_dependencies)
|
||
|
|
if new_dim_deps:
|
||
|
|
deps.update(new_dim_deps)
|
||
|
|
|
||
|
|
new_dim_sys = DimensionSystem(
|
||
|
|
tuple(self.base_dims) + tuple(new_base_dims),
|
||
|
|
tuple(self.derived_dims) + tuple(new_derived_dims),
|
||
|
|
deps
|
||
|
|
)
|
||
|
|
new_dim_sys._quantity_dimension_map.update(self._quantity_dimension_map)
|
||
|
|
new_dim_sys._quantity_scale_factors.update(self._quantity_scale_factors)
|
||
|
|
return new_dim_sys
|
||
|
|
|
||
|
|
def is_dimensionless(self, dimension):
|
||
|
|
"""
|
||
|
|
Check if the dimension object really has a dimension.
|
||
|
|
|
||
|
|
A dimension should have at least one component with non-zero power.
|
||
|
|
"""
|
||
|
|
if dimension.name == 1:
|
||
|
|
return True
|
||
|
|
return self.get_dimensional_dependencies(dimension) == {}
|
||
|
|
|
||
|
|
@property
|
||
|
|
def list_can_dims(self):
|
||
|
|
"""
|
||
|
|
Useless method, kept for compatibility with previous versions.
|
||
|
|
|
||
|
|
DO NOT USE.
|
||
|
|
|
||
|
|
List all canonical dimension names.
|
||
|
|
"""
|
||
|
|
dimset = set()
|
||
|
|
for i in self.base_dims:
|
||
|
|
dimset.update(set(self.get_dimensional_dependencies(i).keys()))
|
||
|
|
return tuple(sorted(dimset, key=str))
|
||
|
|
|
||
|
|
@property
|
||
|
|
def inv_can_transf_matrix(self):
|
||
|
|
"""
|
||
|
|
Useless method, kept for compatibility with previous versions.
|
||
|
|
|
||
|
|
DO NOT USE.
|
||
|
|
|
||
|
|
Compute the inverse transformation matrix from the base to the
|
||
|
|
canonical dimension basis.
|
||
|
|
|
||
|
|
It corresponds to the matrix where columns are the vector of base
|
||
|
|
dimensions in canonical basis.
|
||
|
|
|
||
|
|
This matrix will almost never be used because dimensions are always
|
||
|
|
defined with respect to the canonical basis, so no work has to be done
|
||
|
|
to get them in this basis. Nonetheless if this matrix is not square
|
||
|
|
(or not invertible) it means that we have chosen a bad basis.
|
||
|
|
"""
|
||
|
|
matrix = reduce(lambda x, y: x.row_join(y),
|
||
|
|
[self.dim_can_vector(d) for d in self.base_dims])
|
||
|
|
return matrix
|
||
|
|
|
||
|
|
@property
|
||
|
|
def can_transf_matrix(self):
|
||
|
|
"""
|
||
|
|
Useless method, kept for compatibility with previous versions.
|
||
|
|
|
||
|
|
DO NOT USE.
|
||
|
|
|
||
|
|
Return the canonical transformation matrix from the canonical to the
|
||
|
|
base dimension basis.
|
||
|
|
|
||
|
|
It is the inverse of the matrix computed with inv_can_transf_matrix().
|
||
|
|
"""
|
||
|
|
|
||
|
|
#TODO: the inversion will fail if the system is inconsistent, for
|
||
|
|
# example if the matrix is not a square
|
||
|
|
return reduce(lambda x, y: x.row_join(y),
|
||
|
|
[self.dim_can_vector(d) for d in sorted(self.base_dims, key=str)]
|
||
|
|
).inv()
|
||
|
|
|
||
|
|
def dim_can_vector(self, dim):
|
||
|
|
"""
|
||
|
|
Useless method, kept for compatibility with previous versions.
|
||
|
|
|
||
|
|
DO NOT USE.
|
||
|
|
|
||
|
|
Dimensional representation in terms of the canonical base dimensions.
|
||
|
|
"""
|
||
|
|
|
||
|
|
vec = []
|
||
|
|
for d in self.list_can_dims:
|
||
|
|
vec.append(self.get_dimensional_dependencies(dim).get(d, 0))
|
||
|
|
return Matrix(vec)
|
||
|
|
|
||
|
|
def dim_vector(self, dim):
|
||
|
|
"""
|
||
|
|
Useless method, kept for compatibility with previous versions.
|
||
|
|
|
||
|
|
DO NOT USE.
|
||
|
|
|
||
|
|
|
||
|
|
Vector representation in terms of the base dimensions.
|
||
|
|
"""
|
||
|
|
return self.can_transf_matrix * Matrix(self.dim_can_vector(dim))
|
||
|
|
|
||
|
|
def print_dim_base(self, dim):
|
||
|
|
"""
|
||
|
|
Give the string expression of a dimension in term of the basis symbols.
|
||
|
|
"""
|
||
|
|
dims = self.dim_vector(dim)
|
||
|
|
symbols = [i.symbol if i.symbol is not None else i.name for i in self.base_dims]
|
||
|
|
res = S.One
|
||
|
|
for (s, p) in zip(symbols, dims):
|
||
|
|
res *= s**p
|
||
|
|
return res
|
||
|
|
|
||
|
|
@property
|
||
|
|
def dim(self):
|
||
|
|
"""
|
||
|
|
Useless method, kept for compatibility with previous versions.
|
||
|
|
|
||
|
|
DO NOT USE.
|
||
|
|
|
||
|
|
Give the dimension of the system.
|
||
|
|
|
||
|
|
That is return the number of dimensions forming the basis.
|
||
|
|
"""
|
||
|
|
return len(self.base_dims)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def is_consistent(self):
|
||
|
|
"""
|
||
|
|
Useless method, kept for compatibility with previous versions.
|
||
|
|
|
||
|
|
DO NOT USE.
|
||
|
|
|
||
|
|
Check if the system is well defined.
|
||
|
|
"""
|
||
|
|
|
||
|
|
# not enough or too many base dimensions compared to independent
|
||
|
|
# dimensions
|
||
|
|
# in vector language: the set of vectors do not form a basis
|
||
|
|
return self.inv_can_transf_matrix.is_square
|