2. Quantity¶
Unit-safe computations with quantities.
2.1. Usage¶
2.1.1. Defining a quantity class¶
A basic type of quantity is declared just by sub-classing
Quantity
:
>>> class Length(Quantity):
... pass
...
But, as long as there is no unit defined for that class, you can not create any instance for the new quantity class:
>>> l = Length(1)
Traceback (most recent call last):
ValueError: A unit must be given.
If there is a reference unit, the simplest way to define it is giving a name
and a symbol for it as keywords. The meta-class of Quantity
will
then create a unit automatically:
>>> class Mass(Quantity,
... ref_unit_name='Kilogram',
... ref_unit_symbol='kg'):
... pass
...
>>> Mass.ref_unit
Unit('kg')
>>> class Length(Quantity,
... ref_unit_name='Metre',
... ref_unit_symbol='m'):
... pass
...
>>> Length.ref_unit
Unit('m')
Now, this unit can be given to create a quantity:
>>> METRE = Length.ref_unit
>>> print(Length(15, METRE))
15 m
If no unit is given, the reference unit is used:
>>> print(Length(15))
15 m
Other units can be derived from the reference unit (or another unit), giving a definition by multiplying a scaling factor with that unit:
>>> a_thousandth = Decimal("0.001")
>>> KILOGRAM = Mass.ref_unit
>>> GRAM = Mass.new_unit('g', 'Gram', a_thousandth * KILOGRAM)
>>> MILLIMETRE = Length.new_unit('mm', 'Millimetre', a_thousandth * METRE)
>>> MILLIMETRE
Unit('mm')
>>> KILOMETRE = Length.new_unit('km', 'Kilometre', 1000 * METRE)
>>> KILOMETRE
Unit('km')
>>> CENTIMETRE = Length.new_unit('cm', 'Centimetre', 10 * MILLIMETRE)
>>> CENTIMETRE
Unit('cm')
Instead of a number a SI prefix can be used as scaling factor. SI prefixes are provided in a sub-module:
>>> from quantity.si_prefixes import *
>>> NANO.abbr, NANO.name, NANO.factor
('n', 'Nano', Decimal('0.000000001'))
>>> NANOMETRE = Length.new_unit('nm', 'Nanometre', NANO * METRE)
>>> NANOMETRE
Unit('nm')
Using one unit as a reference and defining all other units by giving a scaling factor is only possible if the units have the same scale. Otherwise, units can just be instantiated without giving a definition:
>>> class Temperature(Quantity):
... pass
...
>>> CELSIUS = Temperature.new_unit('°C', 'Degree Celsius')
>>> FAHRENHEIT = Temperature.new_unit('°F', 'Degree Fahrenheit')
>>> KELVIN = Temperature.new_unit('K', 'Kelvin')
Derived types of quantities are declared by giving a definition based on more basic types of quantities:
>>> class Volume(Quantity,
... define_as=Length ** 3,
... ref_unit_name='Cubic Metre'):
... pass
...
>>> class Duration(Quantity,
... ref_unit_name='Second',
... ref_unit_symbol='s'):
... pass
...
>>> class Velocity(Quantity,
... define_as=Length / Duration,
... ref_unit_name='Metre per Second'):
... pass
...
If no symbol for the reference unit is given with the class declaration, a symbol is generated from the definition, as long as all types of quantities in that definition have a reference unit.
>>> Volume.ref_unit.symbol
'm³'
>>> Velocity.ref_unit.symbol
'm/s'
Other units have to be defined explicitly. This can be done either as shown above or by deriving them from units of the base quantities:
>>> CUBIC_CENTIMETRE = Volume.derive_unit_from(CENTIMETRE,
... name='Cubic Centimetre')
>>> CUBIC_CENTIMETRE
Unit('cm³')
>>> HOUR = Duration.new_unit('h', 'Hour', 3600 * Duration.ref_unit)
>>> KILOMETRE_PER_HOUR = Velocity.derive_unit_from(KILOMETRE, HOUR)
>>> KILOMETRE_PER_HOUR
Unit('km/h')
In order to define a quantized quantity, the smallest possible fraction (in terms of the reference unit) can be given as quantum:
>>> class DataVolume(Quantity,
... ref_unit_name='Byte',
... ref_unit_symbol='B',
... quantum=Decimal('0.125')):
... pass
...
>>> DataVolume.quantum
Decimal('0.125')
The method quantum can then be used to retrieve the smallest amount for a unit:
>>> BYTE = DataVolume.ref_unit
>>> BYTE.quantum
Decimal('0.125')
>>> KILOBYTE = DataVolume.new_unit('kB', 'Kilobyte', KILO * BYTE)
>>> KILOBYTE.quantum
Decimal('0.000125')
2.1.2. Instantiating quantities¶
The simplest way to create an instance of a Quantity
subclass is to
call the class giving an amount and a unit. If the unit is omitted, the
quantity’s reference unit is used (if one is defined):
>>> Length(15, MILLIMETRE)
Length(Decimal(15), Unit('mm'))
>>> Length(15)
Length(Decimal(15))
Alternatively, an amount and a unit can be multiplied:
>>> 17.5 * KILOMETRE
Length(Decimal('17.5'), Unit('km'))
Also, it’s possible to create a Quantity
instance from a string
representation:
>>> Length('17.5 km')
Length(Decimal('17.5'), Unit('km'))
If a unit is given in addition, the resulting quantity is converted accordingly:
>>> Length('17 m', KILOMETRE)
Length(Decimal('0.017'), Unit('km'))
Instead of calling a subclass, the class Quantity
can be used as a
factory function …:
>>> Quantity(15, MILLIMETRE)
Length(Decimal(15), Unit('mm'))
>>> Quantity('17.5 km')
Length(Decimal('17.5'), Unit('km'))
… as long as a unit is given:
>>> Quantity(17.5)
Traceback (most recent call last):
QuantityError: A unit must be given.
If the Quantity
subclass defines a quantum, the amount of each
instance is automatically rounded to this quantum:
>>> DataVolume('1/7', KILOBYTE)
DataVolume(Decimal('0.142875'), Unit('kB'))
2.1.3. Converting between units¶
A quantity can be converted to a quantity using a different unit by calling
the method Quantity.convert()
:
>>> l5cm = Length(Decimal(5), CENTIMETRE)
>>> l5cm.convert(MILLIMETRE)
Length(Decimal(50), Unit('mm'))
>>> l5cm.convert(KILOMETRE)
Length(Decimal('0.00005'), Unit('km'))
These kinds of conversion are automatically enabled for types of quantities with reference units. For other types of quantities there is no default way of converting between units.
>>> t27c = Temperature(Decimal(27), CELSIUS)
>>> t27c.convert(FAHRENHEIT)
Traceback (most recent call last):
UnitConversionError: Can't convert '°C' to '°F'.
2.1.3.1. Converters¶
For types of quantities that do not have a reference unit, one or more callables can be registered as converters:
>>> def fahrenheit2celsius(qty, to_unit):
... if qty.unit is FAHRENHEIT and to_unit is CELSIUS:
... return (qty.amount - 32) / Decimal('1.8')
... return None
...
>>> def celsius2fahrenheit(qty, to_unit):
... if qty.unit is CELSIUS and to_unit is FAHRENHEIT:
... return qty.amount * Decimal('1.8') + 32
... return None
...
>>> Temperature.register_converter(fahrenheit2celsius)
>>> Temperature.register_converter(celsius2fahrenheit)
>>> assert list(Temperature.registered_converters()) == \
... [celsius2fahrenheit, fahrenheit2celsius]
...
For the signature of the callables used as converters see Converter
.
>>> t27c.convert(FAHRENHEIT)
Temperature(Decimal('80.6'), Unit('°F'))
>>> t27c.convert(FAHRENHEIT).convert(CELSIUS)
Temperature(Decimal(27), Unit('°C'))
Alternatively, an instance of TableConverter
can be created and
registered as converter.
The example given above can be implemented as follows:
>>> tconv = TableConverter({(CELSIUS, FAHRENHEIT): (Decimal('1.8'), 32)})
>>> Temperature.register_converter(tconv)
>>> t27c = Temperature(Decimal(27), CELSIUS)
>>> t27c.convert(FAHRENHEIT)
Temperature(Decimal('80.6'), Unit('°F'))
It is suffient to define the conversion in one direction, because a reversed conversion is used automatically:
>>> t27c.convert(FAHRENHEIT).convert(CELSIUS)
Temperature(Decimal(27), Unit('°C'))
2.1.4. Unit-safe computations¶
2.1.4.1. Comparison¶
Quantities can be compared to other quantities using all comparison operators defined for numbers:
>>> Length(27) > Length(9)
True
>>> Length(27) >= Length(91)
False
>>> Length(27) < Length(9)
False
>>> Length(27) <= Length(91)
True
>>> Length(27) == Length(27)
True
>>> Length(27) != Length(91)
True
Different units are taken in to account automatically, as long as they are compatible, that means a conversion is available:
>>> Length(27, METRE) <= Length(91, CENTIMETRE)
False
>>> Temperature(20, CELSIUS) > Temperature(20, FAHRENHEIT)
True
>>> Temperature(20, CELSIUS) > Temperature(20, KELVIN)
Traceback (most recent call last):
UnitConversionError: Can't convert 'K' to '°C'.
Testing instances of different quantity types for equality always returns false:
>>> Length(20) == Duration(20)
False
>>> Length(20) != Duration(20)
True
All other comparison operators raise an IncompatibleUnitsError in this case.
2.1.4.2. Addition and subtraction¶
Quantities can be added to or subtracted from other quantities …:
>>> Length(27) + Length(9)
Length(Decimal(36))
>>> Length(27) - Length(91)
Length(Decimal(-64))
… as long as they are instances of the same quantity type:
>>> Length(27) + Duration(9)
Traceback (most recent call last):
IncompatibleUnitsError: Can't add a 'Length' and a 'Duration'
When quantities with different units are added or subtracted, the values are converted to the unit of the first, if possible …:
>>> Length(27) + Length(12, CENTIMETRE)
Length(Decimal('27.12'))
>>> Length(12, CENTIMETRE) + Length(17, METRE)
Length(Decimal(1712), Unit('cm'))
>>> Temperature(20, CELSIUS) - Temperature(50, FAHRENHEIT)
Temperature(Decimal(10), Unit('°C'))
… but an exception is raised, if not:
>>> Temperature(20, CELSIUS) - Temperature(281, KELVIN)
Traceback (most recent call last):
UnitConversionError: Can't convert 'K' to '°C'.
2.1.4.3. Multiplication and division¶
Quantities can be multiplied or divided by scalars, preserving the unit:
>>> 7.5 * Length(3, CENTIMETRE)
Length(Decimal('22.5'), Unit('cm'))
>>> SECOND = Duration.ref_unit
>>> MINUTE = Duration.new_unit('min', 'Minute', Decimal(60) * SECOND)
>>> Duration(66, MINUTE) / 11
Duration(Decimal(6), Unit('min'))
Quantities can be multiplied or divided by other quantities …:
>>> Length(15, METRE) / Duration(3, SECOND)
Velocity(Decimal(5))
… as long as the resulting type of quantity is defined …:
>>> Duration(4, SECOND) * Length(7)
Traceback (most recent call last):
UndefinedResultError: Undefined result: Duration * Length
>>> Length(12, KILOMETRE) / Duration(2, MINUTE) / Duration(50, SECOND)
Traceback (most recent call last):
UndefinedResultError: Undefined result: Velocity / Duration
>>> class Acceleration(Quantity,
... define_as=Length / Duration ** 2,
... ref_unit_name='Metre per Second squared'):
... pass
...
>>> Length(12, KILOMETRE) / Duration(2, MINUTE) / Duration(50, SECOND)
Acceleration(Decimal(2))
… or the result is a scalar:
>>> Duration(2, MINUTE) / Duration(50, SECOND)
Decimal('2.4')
When cascading operations, all intermediate results have to be defined:
>>> Length(6, KILOMETRE) * Length(13, METRE) * Length(250, METRE)
Traceback (most recent call last):
UndefinedResultError: Undefined result: Length * Length
>>> class Area(Quantity,
... define_as=Length ** 2,
... ref_unit_name='Square Metre'):
... pass
...
>>> Length(6, KILOMETRE) * Length(13, METRE) * Length(250, METRE)
Volume(Decimal(19500000))
2.1.4.4. Exponentiation¶
Quantities can be raised by an exponent, as long as the exponent is an Integral number and the resulting quantity is defined:
>>> (5 * METRE) ** 2
Area(Decimal(25))
>>> (5 * METRE) ** 2.5
Traceback (most recent call last):
TypeError: unsupported operand type(s) for ** or pow(): 'Length' and
'float'
>>> (5 * METRE) ** -2
Traceback (most recent call last):
UndefinedResultError: Undefined result: Length ** -2
2.1.5. Rounding¶
The amount of a quantity can be rounded by using the standard round function. It returns a copy of the quanitity, with its amount rounded accordingly:
>>> round(Length(Decimal('17.375'), MILLIMETRE), 1)
Length(Decimal('17.4'), Unit('mm'))
In any case the unit of the resulting quantity will be the same as the unit of the called quantity.
For more advanced cases of rounding the method Quantity.quantize()
can
round a quantity to any quantum according to any rounding mode:
>>> l = Length('1.7296 km')
>>> l.quantize(Length(1))
Length(Decimal('1.73', 3), Unit('km'))
>>> l.quantize(25 * METRE)
Length(Decimal('1.725'), Unit('km'))
>>> l.quantize(25 * METRE, ROUNDING.ROUND_UP)
Length(Decimal('1.75', 3), Unit('km'))
2.1.6. Apportioning¶
The method Quantity.allocate()
can be used to apportion a quantity
according to a sequence of ratios:
>>> m = Mass('10 kg')
>>> ratios = [38, 5, 2, 15]
>>> portions, remainder = m.allocate(ratios)
>>> portions
[Mass(Fraction(19, 3)),
Mass(Fraction(5, 6)),
Mass(Fraction(1, 3)),
Mass(Decimal('2.5', 2))]
>>> remainder
Mass(Decimal(0, 2))
If the quantity is quantized, there can be rounding errors causing a remainder with an amount other than 0:
>>> b = 10 * KILOBYTE
>>> portions, remainder = b.allocate(ratios, disperse_rounding_error=False)
>>> portions
[DataVolume(Decimal('6.333375'), Unit('kB')),
DataVolume(Decimal('0.833375'), Unit('kB')),
DataVolume(Decimal('0.333375'), Unit('kB')),
DataVolume(Decimal('2.5', 6), Unit('kB'))]
>>> remainder
DataVolume(Decimal('-0.000125'), Unit('kB'))
By default the remainder will be dispersed:
>>> portions, remainder = b.allocate(ratios)
>>> portions
[DataVolume(Decimal('6.333375'), Unit('kB')),
DataVolume(Decimal('0.833375'), Unit('kB')),
DataVolume(Decimal('0.33325', 6), Unit('kB')),
DataVolume(Decimal('2.5', 6), Unit('kB'))]
>>> remainder
DataVolume(Decimal(0), Unit('kB'))
As well as of numbers, quantities can be used as ratios (as long as they have compatible units):
>>> CUBIC_METRE = Volume.ref_unit
>>> LITRE = Volume.new_unit('l', 'Litre', MILLI * CUBIC_METRE)
>>> l = 10 * LITRE
>>> ratios = [350 * GRAM, 500 * GRAM, 3 * KILOGRAM, 150 * GRAM]
>>> l.allocate(ratios)
([Volume(Decimal('0.875', 4), Unit('l')),
Volume(Decimal('1.25', 3), Unit('l')),
Volume(Decimal('7.5', 2), Unit('l')),
Volume(Decimal('0.375', 4), Unit('l'))],
Volume(Decimal(0, 4), Unit('l')))
2.1.7. Formatting as string¶
Quantity
supports the standard str function. It returns a string
representation of the quantity’s amount followed by a blank and the
quantity’s units symbol.
In addition, Quantity
supports the standard format function. The
format specifier should use two keys: ‘a’ for the amount and ‘u’ for the unit,
where ‘a’ can be followed by a valid format spec for numbers and ‘u’ by a
valid format spec for strings. If no format specifier is given, ‘{a} {u}’ is
used:
>>> v = Volume('19.36')
>>> format(v)
'19.36 m³'
>>> format(v, '{a:*>10.2f} {u:<3}')
'*****19.36 m³ '
2.2. Types¶
- QuantityClsDefT¶
Defintion of derived Quantity sub-classes.
alias of
Term
[QuantityMeta
]
- BinOpResT¶
Result of binary operations on quantities / units
alias of
Union
[Quantity
,Rational
,Tuple
[Rational
,Optional
[Unit
]]]
- ConverterT¶
Type of converters
alias of
Callable
[[…],Optional
[Rational
]]
- ConvMapT¶
The central part of internal API.
This represents a generic version of type ‘origin’ with type arguments ‘params’. There are two kind of these aliases: user defined and special. The special ones are wrappers around builtin collections and ABCs in collections.abc. These must have ‘name’ always set. If ‘inst’ is False, then the alias can’t be instantiated, this is used by e.g. typing.List and typing.Dict.
alias of
Mapping
[Tuple
[Unit
,Unit
],Tuple
[Rational
,Rational
]]
- ConvSpecIterableT¶
The central part of internal API.
This represents a generic version of type ‘origin’ with type arguments ‘params’. There are two kind of these aliases: user defined and special. The special ones are wrappers around builtin collections and ABCs in collections.abc. These must have ‘name’ always set. If ‘inst’ is False, then the alias can’t be instantiated, this is used by e.g. typing.List and typing.Dict.
2.3. Classes¶
- class Unit¶
Unit of measure.
Note
New instances of Unit can not be created directly by calling Unit. Instead, use <Quantity sub-class>.new_unit.
- __eq__(other: Any) bool ¶
self == other
- __format__(fmt_spec: str = '') str ¶
Convert to string (according to fmt_spec).
fmt_spec must be a valid format spec for strings.
- __ge__(other: Any) bool ¶
self >= other
- __gt__(other: Any) bool ¶
self > other
- __hash__() int ¶
hash(self)
- __le__(other: Any) bool ¶
self <= other
- __lt__(other: Any) bool ¶
self < other
- __mul__(other: int) Quantity ¶
- __mul__(other: float) Quantity
- __mul__(other: Real) Quantity
- __mul__(other: SIPrefix) Quantity
- __mul__(other: Unit) AmountUnitTupleT
- __mul__(other: Quantity) BinOpResT
self * other
- __repr__() str ¶
repr(self)
- __rmul__(other: int) Quantity ¶
- __rmul__(other: float) Quantity
- __rmul__(other: Real) Quantity
- __rmul__(other: SIPrefix) Quantity
- __rmul__(other: Unit) AmountUnitTupleT
- __rmul__(other: Quantity) BinOpResT
other * self
- __str__() str ¶
str(self)
- __truediv__(other: int) Quantity ¶
- __truediv__(other: float) Quantity
- __truediv__(other: Real) Quantity
- __truediv__(other: Unit) AmountUnitTupleT
- __truediv__(other: Quantity) BinOpResT
self / other
- is_base_unit() bool ¶
Return True if the unit is not derived from another unit.
- is_derived_unit() bool ¶
Return True if the unit is derived from another unit.
- is_ref_unit() bool ¶
Return True if the unit is a reference unit.
- property definition: UnitDefT¶
Return the units definition.
- property name: str¶
Return the units name.
If the unit was not given a name, its symbol is returned.
- property normalized_definition: UnitDefT¶
Return the units normalized definition.
- property qty_cls: QuantityMeta¶
Return the Quantity subclass related to the unit.
- property quantum: Rational | None¶
Return the minimum amount of a quantity with the unit as unit.
Returns None if the quantity class related to the unit does not define a quantum.
- property symbol: str¶
Return the units symbol.
The symbol is a unique string representation of the unit.
- class QuantityMeta¶
Meta class allowing to construct Quantity subclasses.
- Parameters:
name – name of the new quantity type
define_as (Optional[QuantityClsDefT]) – definition of the new derived quantity type
ref_unit_symbol (Optional[str]) – symbol of the reference unit to be created
ref_unit_name (Optional[str]) – name of the reference unit
quantum (Optional[Rational]) – minimum absolute amount for an instance of the new quantity type
- __init__(name: str, bases: Tuple[type, ...] = (), clsdict=MappingProxyType({}), **kwds: Any)¶
- __mul__(other: QuantityMeta | Term[ClassWithDefinitionMeta]) Term[ClassWithDefinitionMeta] ¶
Return class definition: cls * other.
- static __new__(mcs, name: str, bases: Tuple[type, ...] = (), clsdict=MappingProxyType({}), **kwds: Any) QuantityMeta ¶
Create new Quantity (sub-)class.
- __rmul__(other: Term[ClassWithDefinitionMeta]) Term[ClassWithDefinitionMeta] ¶
Return class definition: other * cls.
- __truediv__(other: QuantityMeta | Term[ClassWithDefinitionMeta]) Term[ClassWithDefinitionMeta] ¶
Return class definition: cls / other.
- derive_unit_from(*args: Unit, symbol: str | None = None, name: str | None = None) Unit ¶
Derive a new unit for cls from units of its base quantities.
- Parameters:
args – iterable of units of the base quantities of the quantity type
symbol – symbol of the new unit, generated based on args if not given
name – name of the new unit, defaults to symbol if not given
- Raises:
TypeError – ‘derive_unit_from’ called on a base quantity
TypeError – not all members of args are instances of Unit
ValueError – number of given base units doesn’t match number of base quantities of cls
ValueError – given base units don’t match base quantities
TypeError – symbol is not a string or None
ValueError – symbol is empty
- get_unit_by_symbol(symbol: str) Unit ¶
Return the unit with symbol symbol.
- Parameters:
symbol – symbol to look-up
- Returns:
unit with given symbol
- Raises:
ValueError – a unit with given symbol is not registered with cls
- is_base_cls() bool ¶
Return True if cls is not derived from other class(es).
- is_derived_cls() bool ¶
Return True if cls is derived from other class(es).
- new_unit(symbol: str, name: str | None = None, define_as: Quantity | UnitDefT | None = None) Unit ¶
Create, register and return a new unit for cls.
- Parameters:
symbol – symbol of the new unit
name – name of the new unit, defaults to symbol if not given
define_as – equivalent of the new unit in terms of another unit (usually given by multiplying a scalar or a SI scale and a unit) or a term defining the new unit in terms of other units
- Raises:
TypeError – symbol is not a string or None
ValueError – symbol is empty
ValueError – a unit with the given symbol is already registered
TypeError – define_as does not match the quantity type
ValueError – term given as define_as does not define a unit
- register_converter(conv: ConverterT) None ¶
Add converter conv to the list of converters registered in cls.
Does nothing if converter is already registered.
- registered_converters() Iterator[ConverterT] ¶
Return an iterator over the converters registered in ‘cls’.
The converts are returned in reversed order of registration.
- remove_converter(conv: ConverterT) None ¶
Remove converter conv from the converters registered in cls.
Raises ValueError if the converter is not present.
- property definition: Term[ClassWithDefinitionMeta]¶
Definition of cls.
- property normalized_definition: Term[ClassWithDefinitionMeta]¶
Normalized definition of cls.
- property quantum: Rational | None¶
Return the minimum absolute amount for an instance of cls.
The quantum is the minimum amount (in terms of the reference unit) an instance of cls can take (None if no quantum is defined).
- class Quantity¶
Base class for all types of quantities.
- __eq__(other: Any) bool ¶
self == other
- __format__(fmt_spec: str = '') str ¶
Convert to string (according to format specifier).
The specifier must be a standard format specifier in the form described in PEP 3101. It should use two keys: ‘a’ for self.amount and ‘u’ for self.unit, where ‘a’ can be followed by a valid format spec for numbers and ‘u’ by a valid format spec for strings.
- __ge__(other: Any) bool ¶
self >= other
- __gt__(other: Any) bool ¶
self > other
- __hash__() int ¶
hash(self)
- __le__(other: Any) bool ¶
self <= other
- __lt__(other: Any) bool ¶
self < other
- __mul__(other: int) Quantity ¶
- __mul__(other: float) Quantity
- __mul__(other: Real) Quantity
- __mul__(other: Quantity) BinOpResT
- __mul__(other: Unit) BinOpResT
self * other
- __repr__() str ¶
repr(self)
- __rmul__(other: Any) BinOpResT ¶
self * other
- __round__(n_digits: int = 0) Quantity ¶
Return copy of self with its amount rounded to n_digits.
- Parameters:
n_digits – number of fractional digits to be rounded to
- Returns:
round(self.amount, n_digits) * self.unit
- __str__() str ¶
str(self)
- __truediv__(other: int) Quantity ¶
- __truediv__(other: float) Quantity
- __truediv__(other: Real) Quantity
- __truediv__(other: Quantity) BinOpResT
- __truediv__(other: Unit) BinOpResT
self / other
- allocate(ratios: Collection[Rational | Quantity], disperse_rounding_error: bool = True) Tuple[List[Quantity], Quantity] ¶
Apportion self according to ratios.
- Parameters:
ratios – sequence of values defining the relative amount of the requested portions
disperse_rounding_error – determines whether a rounding error (if there is one due to quantization) shall be dispersed
- Returns:
- (portions of self according to ratios,
remainder = self - sum(portions))
- Raises:
TypeError – ratios contains elements that can not be added
IncompatibleUnitsError – ratios contains quantities that can not be added
- convert(to_unit: Unit) Quantity ¶
Return quantity q where q == self and q.unit is to_unit.
- Parameters:
to_unit – unit to be converted to
- Returns:
quantity equivalent to self, having unit to_unit
- Raises:
IncompatibleUnitsError – self can’t be converted to to_unit.
- quantize(quant: Quantity, rounding: ROUNDING | None = None) Quantity ¶
Return integer multiple of quant closest to self.
- Parameters:
quant – quantum to get a multiple from
rounding – rounding mode (default: None)
If no rounding mode is given, the current default mode from module decimalfp is used.
- Returns:
- integer multiple of quant closest to self (according to
rounding mode)
- Raises:
IncompatibleUnitsError – quant can not be converted to self.unit
TypeError – quant is not an instance of type(self)
TypeError – type(self) has no reference unit
- property amount: Rational¶
Return the numerical part of the quantity.
- class Converter¶
Convert a quantity’s amount to the equivalent amount for another unit.
A quantity converter can be any callable with a signature like conv(qty, to_unit) -> number f so that type(qty)(f, to_unit) == qty.
- __call__(qty: Quantity, to_unit: Unit) Rational | None ¶
Convert qty’s amount to the equivalent amount for to_unit.
- Parameters:
qty – quantity to be converted
to_unit – unit for equivalent amount
- Returns:
factor f so that f * to_unit == qty, or None if no such factor is available
- Raises:
IncompatibleUnitsError – qty and to_unit are incompatible
UnitConversionError – conversion factor not available
- __init__()¶
- __new__(**kwargs)¶
- class TableConverter¶
Bases:
Converter
Converter using a conversion table.
- Parameters:
conv_table (Mapping or list) – the mapping used to initialize the conversion table
Each item of the conversion table defines a conversion from one unit to another unit and consists of four elements:
from_unit (Unit): unit of the quantity to be converted
to_unit (Unit): target unit of the conversion
factor (Rational): factor to be applied to the quantity’s amount
offset (Rational): an amount added after applying the factor
When a Mapping is given as convTable, each key / value pair must map a tuple (from_unit, to_unit) to a tuple (factor, offset).
When a list is given as convTable, each item must be a tuple (from_unit, to_unit, factor, offset).
factor and offset must be set so that for an amount in terms of from_unit the eqivalent amount in terms of to_unit is:
result = amount * factor + offset
An instance of TableConverter can be called with a
Quantity
sub-class’ instance qty and aUnit
sub-class’ instance to_unit as parameters. It looks-up the pair (qty.unit, to_unit) for a factor and an offset and returns the resulting amount according to the formula given above.If there is no item for the pair (qty.unit, to_unit), it tries to find a reverse mapping by looking-up the pair (to_unit, qty.unit), and, if it finds one, it returns a result by applying a reversed formula:
result = (amount - offset) / factor
That means, for each pair of units it is sufficient to define a conversion in one direction.
An instance of TableConverter can be directly registered as a converter by calling the method Quantity.register_converter.
- __init__(conv_table: ConvMapT | ConvSpecIterableT)¶
- __new__(**kwargs)¶
2.4. Functions¶
- sum(items: Iterable[Any], start: Any | None = None) Any ¶
Return the sum of start (if not None) plus all items in items.
- Parameters:
items – iterable of numbers or number-like objects (NOT strings)
start – starting value to be added (default: None)
- Returns:
sum of all elements in items plus the value of start (if not None). When items is empty, returns start, if not None, otherwise 0.
In contrast to the built-in function ‘sum’ this function allows to sum sequences of number-like objects (like quantities) without having to provide a start value.
2.5. Exceptions¶
- exception QuantityError¶
Raised when a quantity can not be instanciated.
- __init__(*args, **kwargs)¶
- __new__(**kwargs)¶
- exception IncompatibleUnitsError¶
Raised when operands do not have compatible units.
- __init__(msg: str, operand1: Any, operand2: Any)¶
- __new__(**kwargs)¶