# Physical units¶

Brian includes a system for defining physical units. These are defined by their standard SI unit names: amp, kilogram, second, metre/meter and the derived units coulomb, farad, gram/gramme, hertz, joule, pascal, ohm, siemens, volt, watt, together with prefixed versions (e.g. msiemens = 0.001*siemens) using the prefixes p, n, u, m, k, M, G, T (two exceptions: kilogram is not imported with any prefixes, metre and meter are additionaly defined with the “centi” prefix, i.e. cmetre/cmeter). In addition a couple of useful standard abbreviations like “cm” (instead of cmetre/cmeter), “nS” (instead of nsiemens), “ms” (instead of msecond), “Hz” (instead of hertz), etc. are included.

## Using units¶

You can generate a physical quantity by multiplying a scalar or vector value with its physical unit:

>>> tau = 20*ms
>>> print tau
20. ms
>>> rates = [10, 20, 30] * Hz
>>> print rates
[ 10.  20.  30.] Hz


Brian will check the consistency of operations on units and raise an error for dimensionality mismatches:

>>> tau += 1  # ms? second?
Traceback (most recent call last):
...
DimensionMismatchError: Addition, dimensions were (s) (1)
>>> 3*gram + 3*amp
Traceback (most recent call last):
...
DimensionMismatchError: Addition, dimensions were (kg) (A)


Most Brian functions will also complain about non-specified or incorrect units:

>>> G = NeuronGroup(10, 'dv/dt = -v/tau: volt', dt=0.5)
Traceback (most recent call last):
...
DimensionMismatchError: Function "__init__" variable "dt" has wrong dimensions, dimensions were (1) (s)


Numpy functions have been overwritten to correctly work with units (see the developer documentation for more details):

>>> print mean(rates)
20. Hz
>>> print rates.repeat(2)
[ 10.  10.  20.  20.  30.  30.] Hz


## Removing units¶

There are various options to remove the units from a value (e.g. to use it with analysis functions that do not correctly work with units)

• Divide the value by its unit (most of the time the recommended option because it is clear about the scale)
• Transform it to a pure numpy array in the base unit by calling asarray() (no copy) or array (copy)
• Directly get the unitless value of a state variable by appending an underscore to the name
>>> tau/ms
20.0
>> asarray(rates)
array([ 10.,  20.,  30.])
>>> G = NeuronGroup(5, 'dv/dt = -v/tau: volt')
>>> print G.v_[:]
[ 0.,  0.,  0.,  0.,  0.]


## Importing units¶

Brian generates standard names for units, combining the unit name (e.g. “siemens”) with a prefixes (e.g. “m”), and also generates squared and cubed versions by appending a number. For example, the units “msiemens”, “siemens2”, “usiemens3” are all predefined. You can import these units from the package brian2.units.allunits – accordingly, an from brian2.units.allunits import * will result in everything from Ylumen3 (cubed yotta lumen) to ymol (yocto mole) being imported.

A better choice is normally to do an from brian2.units import * or import everything from brian2 import *, this imports only the base units amp, kilogram, second, metre/meter and the derived units coulomb, farad, gram/gramme, hertz, joule, pascal, ohm, siemens, volt, watt, together with the prefixes p, n, u, m, k, M, G, T (two exceptions: kilogram is not imported with any prefixes, metre and meter are additionaly defined with the “centi” prefix, i.e. cmetre/cmeter).

In addition a couple of useful standard abbreviations like “cm” (instead of cmetre/cmeter), “nS” (instead of nsiemens), “ms” (instead of msecond), “Hz” (instead of hertz), etc. are added (they can be individually imported from brian2.units.stdunits).

## In-place operations on quantities¶

In-place operations on quantity arrays change the underlying array, in the same way as for standard numpy arrays. This means, that any other variables referencing the same object will be affected as well:

>>> q = [1, 2] * mV
>>> r = q
>>> q += 1*mV
>>> q
array([ 2.,  3.]) * mvolt
>>> r
array([ 2.,  3.]) * mvolt


In contrast, scalar quantities will never change the underlying value but instead return a new value (in the same way as standard Python scalars):

>>> x = 1*mV
>>> y = x
>>> x *= 2
>>> x
2. * mvolt
>>> y
1. * mvolt


## Comparison with Brian 1¶

Brian 1 did only support scalar quantities, units were not stored for arrays. Some expressions therefore have different values in Brian 1 and Brian 2:

Expression Brian 1 Brian 2
1 * mV 1.0 * mvolt 1.0 * mvolt
np.array(1) * mV 0.001 1.0 * mvolt
np.array([1]) * mV array([ 0.001]) array([1.]) * mvolt
np.mean(np.arange(5) * mV) 0.002 2.0 * mvolt
np.arange(2) * mV array([ 0. , 0.001]) array([ 0., 1.]) * mvolt
(np.arange(2) * mV) >= 1 * mV array([False, True], dtype=bool) array([False, True], dtype=bool)
(np.arange(2) * mV)[0] >= 1 * mV False False
(np.arange(2) * mV)[1] >= 1 * mV DimensionMismatchError True