saiunit.UNITLESS

saiunit.UNITLESS#

saiunit.UNITLESS = Unit("1")#

A physical unit.

Basically, a unit is just a number with given dimensions, e.g. mvolt = 0.001 with the dimensions of voltage. The units module defines a large number of standard units, and you can also define your own (see below).

Mathematically, a unit represents:

\[\text{{factor}} \times \text{{base}}^{\text{{scale}}} \times \text{{dimension}}\]

where the factor is the conversion factor of the unit (e.g. 1 calorie = 4.18400 Joule, so the factor is 4.18400), the base is the base of the exponent (e.g. 10 for the kilo prefix), the scale is the exponent of the base (e.g. 3 for the kilo prefix), and the dimension is the physical dimensions of the unit (e.g. joule for energy).

The unit class also keeps track of various things that were used to define it so as to generate a nice string representation of it. See below.

Parameters:

dim (Dimension, optional) – The physical dimensions of the unit. Defaults to DIMENSIONLESS.
scale (array_like, optional) – The scale exponent, e.g. 3 for a “k” (kilo) prefix. Defaults to 0.
base (array_like, optional) – The base of the exponent, e.g. 10 for SI prefixes. Defaults to 10.
factor (array_like, optional) – The conversion factor of the unit. Defaults to 1.
name (str, optional) – The full name of the unit, e.g. 'volt'.
dispname (str, optional) – The display name, e.g. 'V'.
is_fullname (bool, optional) – Whether name is the canonical full name. Defaults to True.
display_parts (list of tuple, optional) – Canonical display components for compound units.

Notes

When creating scaled units, you can use the following prefixes:

Factor	Name	Prefix
10^24	yotta	Y
10^21	zetta	Z
10^18	exa	E
10^15	peta	P
10^12	tera	T
10^9	giga	G
10^6	mega	M
10^3	kilo	k
10^2	hecto	h
10^1	deka	da
1
10^-1	deci	d
10^-2	centi	c
10^-3	milli	m
10^-6	micro	u (mu in SI)
10^-9	nano	n
10^-12	pico	p
10^-15	femto	f
10^-18	atto	a
10^-21	zepto	z
10^-24	yocto	y

Defining your own

It can be useful to define your own units for printing purposes. So for example, to define the newton metre, you write:

>>> import saiunit as u
>>> Nm = u.newton * u.metre

You can then do:

>>> (1 * Nm).in_unit(Nm)
'1. N m'

New “compound units”, i.e. units that are composed of other units will be automatically registered and from then on used for display. For example, imagine you define total conductance for a membrane, and the total area of that membrane:

>>> import saiunit as u
>>> conductance = 10. * u.nS
>>> area = 20000 * u.um ** 2

If you now ask for the conductance density, you will get an “ugly” display in basic SI dimensions, as saiunit does not know of a corresponding unit:

>>> conductance / area
0.5 * metre ** -4 * kilogram ** -1 * second ** 3 * amp ** 2

By using an appropriate unit once, it will be registered and from then on used for display when appropriate:

>>> u.usiemens / u.cm ** 2
usiemens / (cmetre ** 2)
>>> conductance / area  # same as before, but now knows about uS/cm^2
50. * usiemens / (cmetre ** 2)

Note that user-defined units cannot override the standard units (volt, second, etc.) that are predefined. For example, the unit Nm has the dimensions “length^2 * mass / time^2”, and therefore the same dimensions as the standard unit joule. The latter will be used for display purposes:

>>> 3 * u.joule
3. * joule
>>> 3 * Nm
3. * joule

Examples

Create a simple unit:

>>> import saiunit as u
>>> u.volt
Unit("V")
>>> u.mvolt
Unit("mV")

Combine units:

>>> import saiunit as u
>>> u.volt / u.amp
Unit("V / A")

saiunit.UNITLESS

Contents

saiunit.UNITLESS#