Source code for simtk.unit.quantity

#!/bin/env python
"""
Module simtk.unit.quantity

Physical quantities with units, intended to produce similar functionality
to Boost.Units package in C++ (but with a runtime cost).
Uses similar API as Scientific.Physics.PhysicalQuantities
but different internals to satisfy our local requirements.
In particular, there is no underlying set of 'canonical' base
units, whereas in Scientific.Physics.PhysicalQuantities all
units are secretly in terms of SI units.  Also, it is easier
to add new fundamental dimensions to simtk.dimensions.  You
might want to make new dimensions for, say, "currency" or
"information".

Some features of this implementation:
  * Quantities are a combination of a value and a unit.  The value
    part can be any python type, including numbers, lists, numpy
    arrays, and anything else.  The unit part must be a simtk.unit.Unit.
  * Operations like adding incompatible units raises an error.
  * Multiplying or dividing units/quantities creates new units.
  * Users can create new Units and Dimensions, but most of the useful
    ones are predefined.
  * Conversion factors between units are applied transitively, so all
    possible conversions are available.
  * I want dimensioned Quantities that are compatible with numpy arrays,
    but do not necessarily require the python numpy package. In other
    words, Quantities can be based on either numpy arrays or on built in
    python types.
  * Units are NOT necessarily stored in terms of SI units internally.
    This is very important for me, because one important application
    area for us is at the molecular scale. Using SI units internally
    can lead to exponent overflow in commonly used molecular force
    calculations. Internally, all unit systems are equally fundamental
    in SimTK.

Two possible enhancements that have not been implemented are
  1) Include uncertainties with propagation of errors
  2) Incorporate offsets for celsius <-> kelvin conversion



This is part of the OpenMM molecular simulation toolkit originating from
Simbios, the NIH National Center for Physics-Based Simulation of
Biological Structures at Stanford, funded under the NIH Roadmap for
Medical Research, grant U54 GM072970. See https://simtk.org.

Portions copyright (c) 2012 Stanford University and the Authors.
Authors: Christopher M. Bruns
Contributors: Peter Eastman

Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the "Software"),
to deal in the Software without restriction, including without limitation
the rights to use, copy, modify, merge, publish, distribute, sublicense,
and/or sell copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
THE AUTHORS, CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
USE OR OTHER DEALINGS IN THE SOFTWARE.
"""
from __future__ import division, print_function, absolute_import

__author__ = "Christopher M. Bruns"
__version__ = "0.5"


import math
import copy
from .standard_dimensions import *
from .unit import Unit, is_unit, dimensionless

[docs]class Quantity(object): """Physical quantity, such as 1.3 meters per second. Quantities contain both a value, such as 1.3; and a unit, such as 'meters per second'. Supported value types include: 1 - numbers (float, int, long) 2 - lists of numbers, e.g. [1,2,3] 3 - tuples of numbers, e.g. (1,2,3) Note - unit conversions will cause tuples to be converted to lists 4 - lists of tuples of numbers, lists of lists of ... etc. of numbers 5 - numpy.arrays """ __array_priority__ = 99
[docs] def __init__(self, value=None, unit=None): """ Create a new Quantity from a value and a unit. Parameters - value: (any type, usually a number) Measure of this quantity - unit: (Unit) the physical unit, e.g. simtk.unit.meters. """ # When no unit is specified, bend over backwards to handle all one-argument possibilities if unit is None: # one argument version, copied from UList if is_unit(value): # Unit argument creates an empty list with that unit attached unit = value value = [] elif is_quantity(value): # Ulist of a Quantity is just the Quantity itself unit = value.unit value = value._value elif _is_string(value): unit = dimensionless else: # Is value a container? is_container = True try: i = iter(value) except TypeError: is_container = False if is_container: if len(value) < 1: unit = dimensionless else: first_item = next(iter(value)) # Avoid infinite recursion for string, because a one-character # string is its own first element try: isstr = bool(value == first_item) except ValueError: # For numpy, value == first_item returns a numpy # array of booleans, which cannot be evaluated for # truthiness (a ValueError is raised). So in this # case, we don't have a string isstr = False if isstr: unit = dimensionless else: unit = Quantity(first_item).unit # Notice that tuples, lists, and numpy.arrays can all be initialized with a list new_container = Quantity([], unit) for item in value: new_container.append(Quantity(item)) # Strips off units into list new_container._value # __class__ trick does not work for numpy.arrays try: import numpy if isinstance(value, numpy.ndarray): value = numpy.array(new_container._value) else: # delegate contruction to container class from list value = value.__class__(new_container._value) except ImportError: # delegate contruction to container class from list value = value.__class__(new_container._value) else: # Non-Quantity, non container # Wrap in a dimensionless Quantity unit = dimensionless # Accept simple scalar quantities as units if is_quantity(unit): value = value * unit._value unit = unit.unit # Use empty list for unspecified values if value is None: value = [] self._value = value self.unit = unit
def __getstate__(self): state = dict() state['_value'] = self._value state['unit'] = self.unit return state def __setstate__(self, state): self._value = state['_value'] self.unit = state['unit'] return def __copy__(self): """ Shallow copy produces a new Quantity with the shallow copy of value and the same unit. Because we want copy operations to work just the same way they would on the underlying value. """ return Quantity(copy.copy(self._value), self.unit) def __deepcopy__(self, memo): """ Deep copy produces a new Quantity with a deep copy of the value, and the same unit. Because we want copy operations to work just the same way they would on the underlying value. """ return Quantity(copy.deepcopy(self._value, memo), self.unit) def __getattr__(self, attribute): """ Delegate unrecognized attribute calls to the underlying value type. """ ret_val = getattr(self._value, attribute) return ret_val def __str__(self): """Printable string version of this Quantity. Returns a string consisting of quantity number followed by unit abbreviation. """ return str(self._value) + ' ' + str(self.unit.get_symbol()) def __repr__(self): """ """ return (Quantity.__name__ + '(value=' + repr(self._value) + ', unit=' + str(self.unit) + ')') def format(self, format_spec): return format_spec % self._value + ' ' + str(self.unit.get_symbol()) def __add__(self, other): """Add two Quantities. Only Quantities with the same dimensions (e.g. length) can be added. Raises TypeError otherwise. Parameters - self: left hand member of sum - other: right hand member of sum Returns a new Quantity that is the sum of the two arguments. """ # can only add using like units if not self.unit.is_compatible(other.unit): raise TypeError('Cannot add two quantities with incompatible units "%s" and "%s".' % (self.unit, other.unit)) value = self._value + other.value_in_unit(self.unit) unit = self.unit return Quantity(value, unit) def __sub__(self, other): """Subtract two Quantities. Only Quantities with the same dimensions (e.g. length) can be subtracted. Raises TypeError otherwise. Parameters - self: left hand member (a) of a - b. - other: right hand member (b) of a - b. Returns a new Quantity that is the difference of the two arguments. """ if not self.unit.is_compatible(other.unit): raise TypeError('Cannot subtract two quantities with incompatible units "%s" and "%s".' % (self.unit, other.unit)) value = self._value - other.value_in_unit(self.unit) unit = self.unit return Quantity(value, unit) def __eq__(self, other): """ """ if not is_quantity(other): return False if not self.unit.is_compatible(other.unit): return False return self.value_in_unit(other.unit) == other._value def __ne__(self, other): """ """ return not self.__eq__(other) def __lt__(self, other): """Compares two quantities. Raises TypeError if the Quantities are of different dimension (e.g. length vs. mass) Returns True if self < other, False otherwise. """ return self._value < other.value_in_unit(self.unit) def __ge__(self, other): return self._value >= (other.value_in_unit(self.unit)) def __gt__(self, other): return self._value > (other.value_in_unit(self.unit)) def __le__(self, other): return self._value <= (other.value_in_unit(self.unit)) def __lt__(self, other): return self._value < (other.value_in_unit(self.unit)) _reduce_cache = {}
[docs] def reduce_unit(self, guide_unit=None): """ Combine similar component units and scale, to form an equal Quantity in simpler units. Returns underlying value type if unit is dimensionless. """ key = (self.unit, guide_unit) if key in Quantity._reduce_cache: (unit, value_factor) = Quantity._reduce_cache[key] else: value_factor = 1.0 canonical_units = {} # dict of dimensionTuple: (Base/ScaledUnit, exponent) # Bias result toward guide units if guide_unit is not None: for u, exponent in guide_unit.iter_base_or_scaled_units(): d = u.get_dimension_tuple() if d not in canonical_units: canonical_units[d] = [u, 0] for u, exponent in self.unit.iter_base_or_scaled_units(): d = u.get_dimension_tuple() # Take first unit found in a dimension as canonical if d not in canonical_units: canonical_units[d] = [u, exponent] else: value_factor *= (u.conversion_factor_to(canonical_units[d][0])**exponent) canonical_units[d][1] += exponent new_base_units = {} for d in canonical_units: u, exponent = canonical_units[d] if exponent != 0: assert u not in new_base_units new_base_units[u] = exponent # Create new unit if len(new_base_units) == 0: unit = dimensionless else: unit = Unit(new_base_units) # There might be a factor due to unit conversion, even though unit is dimensionless # e.g. suppose unit is meter/centimeter if unit.is_dimensionless(): unit_factor = unit.conversion_factor_to(dimensionless) if unit_factor != 1.0: value_factor *= unit_factor # print "value_factor = %s" % value_factor unit = dimensionless Quantity._reduce_cache[key] = (unit, value_factor) # Create Quantity, then scale (in case value is a container) # That's why we don't just scale the value. result = Quantity(self._value, unit) if value_factor != 1.0: # __mul__ strips off dimensionless, if appropriate result = result * value_factor if unit.is_dimensionless(): assert unit is dimensionless # should have been set earlier in this method if is_quantity(result): result = copy.deepcopy(result._value) return result
def __mul__(self, other): """Multiply a quantity by another object Returns a new Quantity that is the product of the self * other, unless the resulting unit is dimensionless, in which case the underlying value type is returned, instead of a Quantity. """ if is_unit(other): # print "quantity * unit" # Many other mul/div operations delegate to here because I was debugging # a dimensionless unit conversion problem, which I ended up fixing within # the reduce_unit() method. unit = self.unit * other return Quantity(self._value, unit).reduce_unit(self.unit) elif is_quantity(other): # print "quantity * quantity" # Situations where the units cancel can result in scale factors from the unit cancellation. # To simplify things, delegate Quantity * Quantity to (Quantity * scalar) * unit return (self * other._value) * other.unit else: # print "quantity * scalar" return self._change_units_with_factor(self.unit, other, post_multiply=False) # value type might not be commutative for multiplication def __rmul__(self, other): """Multiply a scalar by a Quantity Returns a new Quantity with the same units as self, but with the value multiplied by other. """ if is_unit(other): raise NotImplementedError('programmer is surprised __rmul__ was called instead of __mul__') # print "R unit * quantity" elif is_quantity(other): # print "R quantity * quantity" raise NotImplementedError('programmer is surprised __rmul__ was called instead of __mul__') else: # print "scalar * quantity" return self._change_units_with_factor(self.unit, other, post_multiply=True) # return Quantity(other * self._value, self.unit) def __truediv__(self, other): """Divide a Quantity by another object Returns a new Quantity, unless the resulting unit type is dimensionless, in which case the underlying value type is returned. """ if is_unit(other): # print "quantity / unit" return self * pow(other, -1.0) # unit = self.unit / other # return Quantity(self._value, unit).reduce_unit(self.unit) elif is_quantity(other): # print "quantity / quantity" # Delegate quantity/quantity to (quantity/scalar)/unit return (self/other._value) / other.unit else: # print "quantity / scalar" return self * pow(other, -1.0) # return Quantity(self._value / other, self.unit) __div__ = __truediv__ def __rtruediv__(self, other): """Divide a scalar by a quantity. Returns a new Quantity. The resulting units are the inverse of the self argument units. """ if is_unit(other): # print "R unit / quantity" raise NotImplementedError('programmer is surprised __rtruediv__ was called instead of __truediv__') elif is_quantity(other): raise NotImplementedError('programmer is surprised __rtruediv__ was called instead of __truediv__') else: # print "R scalar / quantity" return other * pow(self, -1.0) # return Quantity(other / self._value, pow(self.unit, -1.0)) __rdiv__ = __rtruediv__ def __pow__(self, exponent): """Raise a Quantity to a power. Generally both the value and the unit of the Quantity are affected by this operation. Returns a new Quantity equal to self**exponent. """ return Quantity(pow(self._value, exponent), pow(self.unit, exponent))
[docs] def sqrt(self): """ Returns square root of a Quantity. Raises ArithmeticError if component exponents are not even. This behavior can be changed if you present a reasonable real life case to me. """ # There might be a conversion factor from taking the square root of the unit new_value = math.sqrt(self._value) new_unit = self.unit.sqrt() unit_factor = self.unit.conversion_factor_to(new_unit*new_unit) if unit_factor != 1.0: new_value *= math.sqrt(unit_factor) return Quantity(value=new_value, unit=new_unit)
[docs] def sum(self, *args, **kwargs): """ Computes the sum of a sequence, with the result having the same unit as the current sequence. If the value is not iterable, it raises a TypeError (same behavior as if you tried to iterate over, for instance, an integer). This function can take as arguments any arguments recognized by `numpy.sum`. If arguments are passed to a non-numpy array, a TypeError is raised """ try: # This will be much faster for numpy arrays mysum = self._value.sum(*args, **kwargs) except AttributeError: if args or kwargs: raise TypeError('Unsupported arguments for Quantity.sum') if len(self._value) == 0: mysum = 0 else: mysum = self._value[0] for i in range(1, len(self._value)): mysum += self._value[i] return Quantity(mysum, self.unit)
[docs] def mean(self, *args, **kwargs): """ Computes the mean of a sequence, with the result having the same unit as the current sequence. If the value is not iterable, it raises a TypeError This function can take as arguments any arguments recognized by `numpy.mean`. If arguments are passed to a non-numpy array, a TypeError is raised """ try: # Faster for numpy arrays mean = self._value.mean(*args, **kwargs) except AttributeError: if args or kwargs: raise TypeError('Unsupported arguments for Quantity.mean') mean = (self.sum() / len(self._value))._value return Quantity(mean, self.unit)
[docs] def std(self, *args, **kwargs): """ Computes the square root of the variance of a sequence, with the result having the same unit as the current sequence. If the value is not iterable, it raises a TypeError This function can take as arguments any arguments recognized by `numpy.std`. If arguments are passed to a non-numpy array, a TypeError is raised """ try: # Faster for numpy arrays std = self._value.std(*args, **kwargs) except AttributeError: if args or kwargs: raise TypeError('Unsupported arguments for Quantity.std') mean = self.mean()._value var = 0 for val in self._value: res = mean - val var += res * res var /= len(self._value) std = math.sqrt(var) return Quantity(std, self.unit)
[docs] def max(self, *args, **kwargs): """ Computes the maximum value of the sequence, with the result having the same unit as the current sequence. If the value is not iterable, it raises a TypeError This function can take as arguments any arguments recognized by `numpy.max`. If arguments are passed to a non-numpy array, a TypeError is raised """ try: # Faster for numpy arrays mymax = self._value.max(*args, **kwargs) except AttributeError: if args or kwargs: raise TypeError('Unsupported arguments for Quantity.max') mymax = max(self._value) return Quantity(mymax, self.unit)
[docs] def min(self, *args, **kwargs): """ Computes the minimum value of the sequence, with the result having the same unit as the current sequence. If the value is not iterable, it raises a TypeError This function can take as arguments any arguments recognized by `numpy.min`. If arguments are passed to a non-numpy array, a TypeError is raised """ try: # Faster for numpy arrays mymin = self._value.min(*args, **kwargs) except AttributeError: if args or kwargs: raise TypeError('Unsupported arguments for Quantity.min') mymin = min(self._value) return Quantity(mymin, self.unit)
[docs] def reshape(self, shape, order='C'): """ Same as numpy.ndarray.reshape, except the result is a Quantity with the same units as the current object rather than a plain numpy.ndarray """ try: return Quantity(self._value.reshape(shape, order=order), self.unit) except AttributeError: raise AttributeError('Only numpy array Quantity objects can be ' 'reshaped')
def __abs__(self): """ Return absolute value of a Quantity. The unit is unchanged. A negative value of self will result in a positive value in the result. """ return Quantity(abs(self._value), self.unit) def __pos__(self): """ Returns a reference to self. """ return Quantity(+(self._value), self.unit) def __neg__(self): """Negate a Quantity. Returns a new Quantity with a different sign on the value. """ return Quantity(-(self._value), self.unit) def __nonzero__(self): """Returns True if value underlying Quantity is zero, False otherwise. """ return bool(self._value) def __bool__(self): return bool(self._value) def __complex__(self): return Quantity(complex(self._value), self.unit) def __float__(self): return Quantity(float(self._value), self.unit) def __int__(self): return Quantity(int(self._value), self.unit) def __long__(self): return Quantity(int(self._value), self.unit)
[docs] def value_in_unit(self, unit): """ Returns underlying value, in the specified units. """ val = self.in_units_of(unit) if is_quantity(val): return val._value else: # naked dimensionless return val
[docs] def value_in_unit_system(self, system): """ Returns the underlying value type, after conversion to a particular unit system. """ result = self.in_unit_system(system) if is_quantity(result): return result._value else: return result # dimensionless
[docs] def in_unit_system(self, system): """ Returns a new Quantity equal to this one, expressed in a particular unit system. """ new_units = system.express_unit(self.unit) f = self.unit.conversion_factor_to(new_units) return self._change_units_with_factor(new_units, f)
[docs] def in_units_of(self, other_unit): """ Returns an equal Quantity expressed in different units. If the units are the same as those in self, a reference to self is returned. Raises a TypeError if the new unit is not compatible with the original unit. The post_multiply argument is used in case the multiplication operation is not commutative. i.e. result = factor * value when post_multiply is False and result = value * factor when post_multiply is True """ if not self.unit.is_compatible(other_unit): raise TypeError('Unit "%s" is not compatible with Unit "%s".' % (self.unit, other_unit)) f = self.unit.conversion_factor_to(other_unit) return self._change_units_with_factor(other_unit, f)
def _change_units_with_factor(self, new_unit, factor, post_multiply=True): # numpy arrays cannot be compared with 1.0, so just "try" factor_is_identity = False try: if (factor == 1.0): factor_is_identity = True except ValueError: pass if factor_is_identity: # No multiplication required result = Quantity(copy.deepcopy(self._value), new_unit) else: try: # multiply operator, if it exists, is preferred if post_multiply: value = self._value * factor # works for number, numpy.array, or vec3, e.g. else: value = factor * self._value # works for number, numpy.array, or vec3, e.g. result = Quantity(value, new_unit) except TypeError: value = copy.deepcopy(self._value) result = Quantity(self._scale_sequence(value, factor, post_multiply), new_unit) if (new_unit.is_dimensionless()): return result._value else: return result def _scale_sequence(self, value, factor, post_multiply): try: if post_multiply: value = value*factor else: value = factor*value except TypeError: try: if post_multiply: if isinstance(value, tuple): value = tuple([x*factor for x in value]) else: for i in range(len(value)): value[i] = value[i]*factor else: if isinstance(value, tuple): value = tuple([factor*x for x in value]) else: for i in range(len(value)): value[i] = factor*value[i] except TypeError: if isinstance(value, tuple): value = tuple([self._scale_sequence(x, factor, post_multiply) for x in value]) else: for i in range(len(value)): value[i] = self._scale_sequence(value[i], factor, post_multiply) return value #################################### ### Sequence methods of Quantity ### ### in case value is a sequence ### #################################### def __len__(self): """ Return size of internal value type. """ return len(self._value) def __getitem__(self, key): """ Keep the same units on contained elements. """ assert not is_quantity(self._value[key]) return Quantity(self._value[key], self.unit) def __setitem__(self, key, value): # Delegate slices to one-at-a time ___setitem___ if isinstance(key, slice): # slice indices = key.indices(len(self)) for i in range(*indices): self[i] = value[i] else: # single index # Check unit compatibility if self.unit.is_dimensionless() and is_dimensionless(value): pass # OK elif not self.unit.is_compatible(value.unit): raise TypeError('Unit "%s" is not compatible with Unit "%s".' % (self.unit, value.unit)) self._value[key] = value / self.unit assert not is_quantity(self._value[key]) def __delitem__(self, key): del(self._value[key]) def __contains__(self, item): return self._value.__contains__(item.value_in_unit(self.unit)) def __iter__(self): for item in self._value: yield Quantity(item, self.unit) def count(self, item): return self._value.count(item.value_in_unit(self.unit)) def index(self, item): return self._value.index(item.value_in_unit(self.unit)) def append(self, item): if is_quantity(item): return self._value.append(item.value_in_unit(self.unit)) elif is_dimensionless(self.unit): return self._value.append(item) else: raise TypeError("Cannot append item without units into list with units") def extend(self, rhs): self._value.extend(rhs.value_in_unit(self.unit)) def insert(self, index, item): self._value.insert(index, item.value_in_unit(self.unit)) def remove(self, item): self._value.remove(item) def pop(self, *args): return self._value.pop(*args) * self.unit
# list.reverse will automatically delegate correctly # list.sort with no arguments will delegate correctly # list.sort with a comparison function cannot be done correctly
[docs]def is_quantity(x): """ Returns True if x is a Quantity, False otherwise. """ return isinstance(x, Quantity)
def is_dimensionless(x): """ """ if is_unit(x): return x.is_dimensionless() elif is_quantity(x): return x.unit.is_dimensionless() else: # everything else in the universe is dimensionless return True # Strings can cause trouble # as can any container that has infinite levels of containment def _is_string(x): # step 1) String is always a container # and its contents are themselves containers. if isinstance(x, str): return True try: first_item = next(iter(x)) inner_item = next(iter(first_item)) if first_item is inner_item: return True else: return False except TypeError: return False except StopIteration: return False # run module directly for testing if __name__=='__main__': # Test the examples in the docstrings import doctest, sys doctest.testmod(sys.modules[__name__])