How to use mdpy.unit package

import mdpy as md
import numpy as np
from mdpy.unit import *
from mdpy.unit.unit_definition import *
from mdpy.error import *

Overview

mdpy.unit package contains three classes:

• mdpy.unit.BaseDimension class

• mdpy.unit.Unit class

• mdpy.unit.Quantity class

BaseDimension

mdpy.unit.BaseDimension defines the basic dimension of a unit.

The __str__ method displays the reference dimension used in mdpy.

In MDPy, the reference dimensions are consistent with SI unit system.

print(constant, end='; ')
print(length, end='; ')
print(mass, end='; ')
print(time, end='; ')
print(temperature, end='; ')
print(charge, end='; ')
print(mol_dimension, end='; ')

; m; kg; s; k; c; mol;

The multiplication and division of BaseDimension gives new BaseDimension object:

acceleration = length / time**2
force = mass * acceleration

print(acceleration, force)

m/s^2 kg*m/s^2

Unit

mdpy.unit.Unit class, consisting of the relative_value and BaseDimension, defines a specific physical unit.

The relative_value defines the relative scale to the reference unit, which is shown above.

The __str__ method displays the relative value and reference unit.

meter = Unit(length, 1)
nanometer = Unit(length, 1e-9)
print(meter, nanometer)

1.00e+00 m 1.00e-09 m

The multiplication and division of Unit creates a new Unit object:

meter = Unit(length, 1)
microsecond = Unit(time, 1e-6)
meter_per_microsecond = meter / microsecond
print(meter_per_microsecond)

1.00e+06 m/s

Quantity

mdpy.unit.Quantity class, consisting of value and Unit, defines a physical quantity.

The __str__ method displays the value and unit.

nanometer = Unit(length, 1e-9)
print(Quantity(1, nanometer))
print(Quantity(np.array([1, 2, 3, 4]), nanometer))

[1.] (1.00e-09 m)
[1. 2. 3. 4.] (1.00e-09 m)

Basic operations, including addition, subtraction, multiplication, division, and power, are closed for Quantity

Notice:

• All operations can only be performed between Quantity objects.

• Addition and subtraction can only be performed between Quantity objects with the same Unit.

f = Quantity(1, meter) * Quantity(1, kilogram) / Quantity(1, second)**2
print(f, f + Quantity(2) * f)

[1.] (1.00e+00 kg*m/s^2) [3.] (1.00e+00 kg*m/s^2)

2 * f

NotImplementedError("* between <class 'int'> and mdpy.unit.Quantity is not implemented")

try:
    f + Quantity(1, meter)
except UnitDimensionMismatchedError as e:
    print(e)

kg*m/s^2 and m can't be added together

Physical constant

mdpy.unit package also defines frequently used physical constants, including:

• KB: The Boltzmann constant

• EPSILON0: The permeability of vacuum

• NA: The Avogadro constant

print(Quantity(300, kelvin) * KB)
print(Quantity(1, elementary_charge**2/nanometer) / EPSILON0)
print(Quantity(1, mol) * NA)

[4.1419458e-21] (1.00e+00 m^2*kg/s^2)
[1.745916] (1.66e-18 m^2*kg/s^2)
[6.0221e+23] (1.00e+00 )

Unit conversion

The mdpy.unit package has two main jobs:

• To convert all kinds of unit systems to the default unit system used in MDPy.

• To convert the result from MDPy in the default unit system to frequently used unit systems.

To achieve this, Quantity class provides a convert_to method:

kbt = Quantity(300, kelvin) * KB
print('Origin: ', kbt)

kbt_default = kbt.convert_to(default_energy_unit)
print('Default unit: ', kbt_default)

kbt_kj_per_mol = kbt.convert_to(kilojoule_permol)
print('kj/mol: ', kbt_kj_per_mol)

print('Check consistence: ', kbt/kbt_default, kbt/kbt_kj_per_mol)

Origin:  [4.1419458e-21] (1.00e+00 m^2*kg/s^2)
Default unit:  [0.00024943] (1.66e-17 m^2*kg/s^2)
kj/mol:  [2.494321] (1.66e-21 m^2*kg/s^2)
Check consistence:  [1.] (1.00e+00 ) [1.] (1.00e+00 )