#!/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 """ from __future__ import division __author__ = "Christopher M. Bruns" __version__ = "0.5" import math import copy from standard_dimensions import * from unit import Unit, is_unit, dimensionless 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 Create numpy.arrays with units using the Quantity constructor, not the multiply operator. e.g. Quantity(numpy.array([1,2,3]), centimeters) # correct *NOT* numpy.array([1,2,3]) * centimeters # won't work because numpy.arrays already overload the multiply operator for EVERYTHING. """ 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 == 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 = iter(value).next() # Avoid infinite recursion for string, because a one-character # string is its own first element if value == first_item: 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 == 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 = {} 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 != 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 = 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)) 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) 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 __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) 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 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 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) 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 if (self.unit is new_unit): result = self else: result = Quantity(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: # list * float fails with TypeError # Presumably a list type # deep copy value = self._value[:] # deep copy # convert tuple to list try: value[0] = value[0] # tuple is immutable except TypeError: # convert immutable tuple to list value = [] for i in self._value: value.append(i) 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: if isinstance(self._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(self._value, tuple): value = tuple([factor*x for x in value]) else: for i in range(len(value)): value[i] = factor*value[i] except TypeError as ex: 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 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 = iter(x).next() inner_item = iter(first_item).next() 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__])