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Examples

How it works: values and units

A quantity consists of two parts: a value and a unit. Internally, a unit is represented by a list of seven integers, one for each SI base unit:

unit: list[int] # [meter, kilogram, second, ampere, mol, kelvin, candela]

Each value in this list corresponds to the exponent of the respective unit. While it is possible to construct a SIObject by providing a value and a unit, it is not recommendend because it is not very readable and prone to error: 

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import si_units as si
mass = si.SIObject(125.0, [0, 1, 0, 0, 0, 0, 0])
print(mass)

125 kg

Instead, we can use one of the "units" (a SIObject with value one) defined in the package and multiply it by the value. Here we use KILOGRAM to yield the same result as above:

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import si_units as si
mass = 125.0 * si.KILOGRAM
print(mass)

125 kg

For convenience and readability, si_units also defines prefixes. The following again yields the same result using the KILO prefix together with GRAM:

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import si_units as si
mass = 125.0 * si.KILO * si.GRAM
print(mass)

125 kg

Prefixes and units can be used to define new types that you may want to reuse across your code: 

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import si_units as si
MPA = si.MEGA * si.PASCAL
KG_M3 = si.KILOGRAM / si.METER**3
FS = si.FEMTO * si.SECOND
...

Unit conversion

Consider the pressure of an ideal gas:

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from si_units import *
temperature = 298.15 * KELVIN
volume = 1.5 * METER**3
moles = 75.0 * MOL
pressure = moles * RGAS * temperature / volume
print(pressure)

123.94785148011941 kPa

Internally, all SIObjects are represented in base SI units. Dividing by a unit (including prefixes) yields the value which can be a scalar or an array or tensor. This can be used to "convert" a quantity into a value of the desired unit:

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import si_units as si
temperature = 298.15 * si.KELVIN
volume = 1.5 * si.METER**3
moles = 75.0 * si.MOL
pressure = moles * si.RGAS * temperature / volume
print('pressure / bar:   ', pressure / si.BAR)
print('pressure / mN/A^2:', pressure / (si.MILLI * si.NEWTON / si.ANGSTROM**2))
print('volume / l:       ', volume / si.LITER)

pressure / bar:    1.2394785148011942
pressure / mN/A^2: 1.239478514801194e-12
volume / l:        1500.0

One-dimensional array constructors

There are several ways to construct a SIObject where the value is a one-dimensional array.

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import si_units as si
# from a list of SIObjects
temperatures = si.array([298.15 * si.KELVIN, 313.15 * si.KELVIN])
# linearly spaced
heights = si.linspace(15 * si.CENTI * si.METER, 15 * si.METER, 1000)
# log-spaced
pressures = si.logspace(100 * si.KILO * si.PASCAL, 50 * si.BAR, 100)

For multi-dimensional arrays, first construct a numpy.ndarray of the desired shape and multiply it by an unit.

Gravitational pull of the moon on the earth

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import si_units as si
mass_earth = 5.9724e24 * si.KILOGRAM
mass_moon = 7.346e22 * si.KILOGRAM
distance = 383.398 * si.KILO * si.METER
force = si.G * mass_earth * mass_moon / distance**2
print(force)

1.992075748302325e26  N

Pressure distribution in the atmosphere

Using the barometric formula. This example demonstrates how dimensioned arrays can be constructed using numpy.ndarrays. 

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import si_units as si
import numpy as np

z = np.linspace(1.0, 70.0e3, 10) * si.METER
g = 9.81 * si.METER / si.SECOND**2
m = 28.949 * si.GRAM / si.MOL
t = 283.15 * si.KELVIN
p0 = si.BAR
pressure = p0 * np.exp((-z * m * g) / (si.RGAS * t))

# dividing with the unit of an SIObject returns a numpy.ndarray
# iteration is currently not implemented.
for zi, pi in zip(z / si.METER, pressure / (si.KILO * si.PASCAL)):
    print(f'z = {zi:16.10f}   p = {pi:16.10f}')
Output
z =     1.0000000000   p =    99.9879378249
z =  7778.6666666667   p =    39.1279560236
z = 15556.3333333333   p =    15.3118163640
z = 23334.0000000000   p =     5.9919235296
z = 31111.6666666667   p =     2.3448000375
z = 38889.3333333333   p =     0.9175830080
z = 46667.0000000000   p =     0.3590747881
z = 54444.6666666667   p =     0.1405155744
z = 62222.3333333333   p =     0.0549875048
z = 70000.0000000000   p =     0.0215180823

Alternatively, we could have used si_units.linspace instead of numpy: 

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import si_units as si
# instead of this
z = np.linspace(1.0, 70.0e3, 10) * si.METER
# we can also use this
z = si.linspace(1.0 * si.METER, 70.0e3 * si.METER, 10)

Using numpy or torch functions

Some functions work with methods or the equivalent numpy functions.

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import si_units as si
import numpy as np

sqm = si.METER**2
print(np.sqrt(sqm))
print(sqm.sqrt())   # this is equivalent

1  m
1  m

Some behaviour is not as you would expect. For example, when we change the above to an array, numpy will throw an exception: 

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import si_units as si
import numpy as np
sqm = np.array([1.0, 2.0]) * si.METER**2
print(np.sqrt(sqm))
print(sqm.sqrt())  # both calls raise an exception

AttributeError: 'numpy.ndarray' object has no attribute 'sqrt'

In such a case, we can divide by the unit to return the inner data type, perform the operation to the value and the unit separately, and finally multiply by the unit to get back a SIObject.

For torch.tensor's this is not an issue and the following works just fine:

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import si_units as si
import torch
ms = torch.tensor([2.0, 3.0, 4.0]) * si.METER
sqms = ms**2
print(sqms)
print(sqms.sqrt())

tensor([ 4.,  9., 16.]) m²
tensor([2., 3., 4.]) m