|
|
|
|
|
""" |
|
|
Dimensional analysis and unit systems. |
|
|
|
|
|
This module defines dimension/unit systems and physical quantities. It is |
|
|
based on a group-theoretical construction where dimensions are represented as |
|
|
vectors (coefficients being the exponents), and units are defined as a dimension |
|
|
to which we added a scale. |
|
|
|
|
|
Quantities are built from a factor and a unit, and are the basic objects that |
|
|
one will use when doing computations. |
|
|
|
|
|
All objects except systems and prefixes can be used in SymPy expressions. |
|
|
Note that as part of a CAS, various objects do not combine automatically |
|
|
under operations. |
|
|
|
|
|
Details about the implementation can be found in the documentation, and we |
|
|
will not repeat all the explanations we gave there concerning our approach. |
|
|
Ideas about future developments can be found on the `Github wiki |
|
|
<https://github.com/sympy/sympy/wiki/Unit-systems>`_, and you should consult |
|
|
this page if you are willing to help. |
|
|
|
|
|
Useful functions: |
|
|
|
|
|
- ``find_unit``: easily lookup pre-defined units. |
|
|
- ``convert_to(expr, newunit)``: converts an expression into the same |
|
|
expression expressed in another unit. |
|
|
|
|
|
""" |
|
|
|
|
|
from .dimensions import Dimension, DimensionSystem |
|
|
from .unitsystem import UnitSystem |
|
|
from .util import convert_to |
|
|
from .quantities import Quantity |
|
|
|
|
|
from .definitions.dimension_definitions import ( |
|
|
amount_of_substance, acceleration, action, area, |
|
|
capacitance, charge, conductance, current, energy, |
|
|
force, frequency, impedance, inductance, length, |
|
|
luminous_intensity, magnetic_density, |
|
|
magnetic_flux, mass, momentum, power, pressure, temperature, time, |
|
|
velocity, voltage, volume |
|
|
) |
|
|
|
|
|
Unit = Quantity |
|
|
|
|
|
speed = velocity |
|
|
luminosity = luminous_intensity |
|
|
magnetic_flux_density = magnetic_density |
|
|
amount = amount_of_substance |
|
|
|
|
|
from .prefixes import ( |
|
|
|
|
|
yotta, |
|
|
zetta, |
|
|
exa, |
|
|
peta, |
|
|
tera, |
|
|
giga, |
|
|
mega, |
|
|
kilo, |
|
|
hecto, |
|
|
deca, |
|
|
deci, |
|
|
centi, |
|
|
milli, |
|
|
micro, |
|
|
nano, |
|
|
pico, |
|
|
femto, |
|
|
atto, |
|
|
zepto, |
|
|
yocto, |
|
|
|
|
|
kibi, |
|
|
mebi, |
|
|
gibi, |
|
|
tebi, |
|
|
pebi, |
|
|
exbi, |
|
|
) |
|
|
|
|
|
from .definitions import ( |
|
|
percent, percents, |
|
|
permille, |
|
|
rad, radian, radians, |
|
|
deg, degree, degrees, |
|
|
sr, steradian, steradians, |
|
|
mil, angular_mil, angular_mils, |
|
|
m, meter, meters, |
|
|
kg, kilogram, kilograms, |
|
|
s, second, seconds, |
|
|
A, ampere, amperes, |
|
|
K, kelvin, kelvins, |
|
|
mol, mole, moles, |
|
|
cd, candela, candelas, |
|
|
g, gram, grams, |
|
|
mg, milligram, milligrams, |
|
|
ug, microgram, micrograms, |
|
|
t, tonne, metric_ton, |
|
|
newton, newtons, N, |
|
|
joule, joules, J, |
|
|
watt, watts, W, |
|
|
pascal, pascals, Pa, pa, |
|
|
hertz, hz, Hz, |
|
|
coulomb, coulombs, C, |
|
|
volt, volts, v, V, |
|
|
ohm, ohms, |
|
|
siemens, S, mho, mhos, |
|
|
farad, farads, F, |
|
|
henry, henrys, H, |
|
|
tesla, teslas, T, |
|
|
weber, webers, Wb, wb, |
|
|
optical_power, dioptre, D, |
|
|
lux, lx, |
|
|
katal, kat, |
|
|
gray, Gy, |
|
|
becquerel, Bq, |
|
|
km, kilometer, kilometers, |
|
|
dm, decimeter, decimeters, |
|
|
cm, centimeter, centimeters, |
|
|
mm, millimeter, millimeters, |
|
|
um, micrometer, micrometers, micron, microns, |
|
|
nm, nanometer, nanometers, |
|
|
pm, picometer, picometers, |
|
|
ft, foot, feet, |
|
|
inch, inches, |
|
|
yd, yard, yards, |
|
|
mi, mile, miles, |
|
|
nmi, nautical_mile, nautical_miles, |
|
|
angstrom, angstroms, |
|
|
ha, hectare, |
|
|
l, L, liter, liters, |
|
|
dl, dL, deciliter, deciliters, |
|
|
cl, cL, centiliter, centiliters, |
|
|
ml, mL, milliliter, milliliters, |
|
|
ms, millisecond, milliseconds, |
|
|
us, microsecond, microseconds, |
|
|
ns, nanosecond, nanoseconds, |
|
|
ps, picosecond, picoseconds, |
|
|
minute, minutes, |
|
|
h, hour, hours, |
|
|
day, days, |
|
|
anomalistic_year, anomalistic_years, |
|
|
sidereal_year, sidereal_years, |
|
|
tropical_year, tropical_years, |
|
|
common_year, common_years, |
|
|
julian_year, julian_years, |
|
|
draconic_year, draconic_years, |
|
|
gaussian_year, gaussian_years, |
|
|
full_moon_cycle, full_moon_cycles, |
|
|
year, years, |
|
|
G, gravitational_constant, |
|
|
c, speed_of_light, |
|
|
elementary_charge, |
|
|
hbar, |
|
|
planck, |
|
|
eV, electronvolt, electronvolts, |
|
|
avogadro_number, |
|
|
avogadro, avogadro_constant, |
|
|
boltzmann, boltzmann_constant, |
|
|
stefan, stefan_boltzmann_constant, |
|
|
R, molar_gas_constant, |
|
|
faraday_constant, |
|
|
josephson_constant, |
|
|
von_klitzing_constant, |
|
|
Da, dalton, amu, amus, atomic_mass_unit, atomic_mass_constant, |
|
|
me, electron_rest_mass, |
|
|
gee, gees, acceleration_due_to_gravity, |
|
|
u0, magnetic_constant, vacuum_permeability, |
|
|
e0, electric_constant, vacuum_permittivity, |
|
|
Z0, vacuum_impedance, |
|
|
coulomb_constant, electric_force_constant, |
|
|
atmosphere, atmospheres, atm, |
|
|
kPa, |
|
|
bar, bars, |
|
|
pound, pounds, |
|
|
psi, |
|
|
dHg0, |
|
|
mmHg, torr, |
|
|
mmu, mmus, milli_mass_unit, |
|
|
quart, quarts, |
|
|
ly, lightyear, lightyears, |
|
|
au, astronomical_unit, astronomical_units, |
|
|
planck_mass, |
|
|
planck_time, |
|
|
planck_temperature, |
|
|
planck_length, |
|
|
planck_charge, |
|
|
planck_area, |
|
|
planck_volume, |
|
|
planck_momentum, |
|
|
planck_energy, |
|
|
planck_force, |
|
|
planck_power, |
|
|
planck_density, |
|
|
planck_energy_density, |
|
|
planck_intensity, |
|
|
planck_angular_frequency, |
|
|
planck_pressure, |
|
|
planck_current, |
|
|
planck_voltage, |
|
|
planck_impedance, |
|
|
planck_acceleration, |
|
|
bit, bits, |
|
|
byte, |
|
|
kibibyte, kibibytes, |
|
|
mebibyte, mebibytes, |
|
|
gibibyte, gibibytes, |
|
|
tebibyte, tebibytes, |
|
|
pebibyte, pebibytes, |
|
|
exbibyte, exbibytes, |
|
|
) |
|
|
|
|
|
from .systems import ( |
|
|
mks, mksa, si |
|
|
) |
|
|
|
|
|
|
|
|
def find_unit(quantity, unit_system="SI"): |
|
|
""" |
|
|
Return a list of matching units or dimension names. |
|
|
|
|
|
- If ``quantity`` is a string -- units/dimensions containing the string |
|
|
`quantity`. |
|
|
- If ``quantity`` is a unit or dimension -- units having matching base |
|
|
units or dimensions. |
|
|
|
|
|
Examples |
|
|
======== |
|
|
|
|
|
>>> from sympy.physics import units as u |
|
|
>>> u.find_unit('charge') |
|
|
['C', 'coulomb', 'coulombs', 'planck_charge', 'elementary_charge'] |
|
|
>>> u.find_unit(u.charge) |
|
|
['C', 'coulomb', 'coulombs', 'planck_charge', 'elementary_charge'] |
|
|
>>> u.find_unit("ampere") |
|
|
['ampere', 'amperes'] |
|
|
>>> u.find_unit('angstrom') |
|
|
['angstrom', 'angstroms'] |
|
|
>>> u.find_unit('volt') |
|
|
['volt', 'volts', 'electronvolt', 'electronvolts', 'planck_voltage'] |
|
|
>>> u.find_unit(u.inch**3)[:9] |
|
|
['L', 'l', 'cL', 'cl', 'dL', 'dl', 'mL', 'ml', 'liter'] |
|
|
""" |
|
|
unit_system = UnitSystem.get_unit_system(unit_system) |
|
|
|
|
|
import sympy.physics.units as u |
|
|
rv = [] |
|
|
if isinstance(quantity, str): |
|
|
rv = [i for i in dir(u) if quantity in i and isinstance(getattr(u, i), Quantity)] |
|
|
dim = getattr(u, quantity) |
|
|
if isinstance(dim, Dimension): |
|
|
rv.extend(find_unit(dim)) |
|
|
else: |
|
|
for i in sorted(dir(u)): |
|
|
other = getattr(u, i) |
|
|
if not isinstance(other, Quantity): |
|
|
continue |
|
|
if isinstance(quantity, Quantity): |
|
|
if quantity.dimension == other.dimension: |
|
|
rv.append(str(i)) |
|
|
elif isinstance(quantity, Dimension): |
|
|
if other.dimension == quantity: |
|
|
rv.append(str(i)) |
|
|
elif other.dimension == Dimension(unit_system.get_dimensional_expr(quantity)): |
|
|
rv.append(str(i)) |
|
|
return sorted(set(rv), key=lambda x: (len(x), x)) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
__all__ = [ |
|
|
'Dimension', 'DimensionSystem', |
|
|
'UnitSystem', |
|
|
'convert_to', |
|
|
'Quantity', |
|
|
|
|
|
'amount_of_substance', 'acceleration', 'action', 'area', |
|
|
'capacitance', 'charge', 'conductance', 'current', 'energy', |
|
|
'force', 'frequency', 'impedance', 'inductance', 'length', |
|
|
'luminous_intensity', 'magnetic_density', |
|
|
'magnetic_flux', 'mass', 'momentum', 'power', 'pressure', 'temperature', 'time', |
|
|
'velocity', 'voltage', 'volume', |
|
|
|
|
|
'Unit', |
|
|
|
|
|
'speed', |
|
|
'luminosity', |
|
|
'magnetic_flux_density', |
|
|
'amount', |
|
|
|
|
|
'yotta', |
|
|
'zetta', |
|
|
'exa', |
|
|
'peta', |
|
|
'tera', |
|
|
'giga', |
|
|
'mega', |
|
|
'kilo', |
|
|
'hecto', |
|
|
'deca', |
|
|
'deci', |
|
|
'centi', |
|
|
'milli', |
|
|
'micro', |
|
|
'nano', |
|
|
'pico', |
|
|
'femto', |
|
|
'atto', |
|
|
'zepto', |
|
|
'yocto', |
|
|
|
|
|
'kibi', |
|
|
'mebi', |
|
|
'gibi', |
|
|
'tebi', |
|
|
'pebi', |
|
|
'exbi', |
|
|
|
|
|
'percent', 'percents', |
|
|
'permille', |
|
|
'rad', 'radian', 'radians', |
|
|
'deg', 'degree', 'degrees', |
|
|
'sr', 'steradian', 'steradians', |
|
|
'mil', 'angular_mil', 'angular_mils', |
|
|
'm', 'meter', 'meters', |
|
|
'kg', 'kilogram', 'kilograms', |
|
|
's', 'second', 'seconds', |
|
|
'A', 'ampere', 'amperes', |
|
|
'K', 'kelvin', 'kelvins', |
|
|
'mol', 'mole', 'moles', |
|
|
'cd', 'candela', 'candelas', |
|
|
'g', 'gram', 'grams', |
|
|
'mg', 'milligram', 'milligrams', |
|
|
'ug', 'microgram', 'micrograms', |
|
|
't', 'tonne', 'metric_ton', |
|
|
'newton', 'newtons', 'N', |
|
|
'joule', 'joules', 'J', |
|
|
'watt', 'watts', 'W', |
|
|
'pascal', 'pascals', 'Pa', 'pa', |
|
|
'hertz', 'hz', 'Hz', |
|
|
'coulomb', 'coulombs', 'C', |
|
|
'volt', 'volts', 'v', 'V', |
|
|
'ohm', 'ohms', |
|
|
'siemens', 'S', 'mho', 'mhos', |
|
|
'farad', 'farads', 'F', |
|
|
'henry', 'henrys', 'H', |
|
|
'tesla', 'teslas', 'T', |
|
|
'weber', 'webers', 'Wb', 'wb', |
|
|
'optical_power', 'dioptre', 'D', |
|
|
'lux', 'lx', |
|
|
'katal', 'kat', |
|
|
'gray', 'Gy', |
|
|
'becquerel', 'Bq', |
|
|
'km', 'kilometer', 'kilometers', |
|
|
'dm', 'decimeter', 'decimeters', |
|
|
'cm', 'centimeter', 'centimeters', |
|
|
'mm', 'millimeter', 'millimeters', |
|
|
'um', 'micrometer', 'micrometers', 'micron', 'microns', |
|
|
'nm', 'nanometer', 'nanometers', |
|
|
'pm', 'picometer', 'picometers', |
|
|
'ft', 'foot', 'feet', |
|
|
'inch', 'inches', |
|
|
'yd', 'yard', 'yards', |
|
|
'mi', 'mile', 'miles', |
|
|
'nmi', 'nautical_mile', 'nautical_miles', |
|
|
'angstrom', 'angstroms', |
|
|
'ha', 'hectare', |
|
|
'l', 'L', 'liter', 'liters', |
|
|
'dl', 'dL', 'deciliter', 'deciliters', |
|
|
'cl', 'cL', 'centiliter', 'centiliters', |
|
|
'ml', 'mL', 'milliliter', 'milliliters', |
|
|
'ms', 'millisecond', 'milliseconds', |
|
|
'us', 'microsecond', 'microseconds', |
|
|
'ns', 'nanosecond', 'nanoseconds', |
|
|
'ps', 'picosecond', 'picoseconds', |
|
|
'minute', 'minutes', |
|
|
'h', 'hour', 'hours', |
|
|
'day', 'days', |
|
|
'anomalistic_year', 'anomalistic_years', |
|
|
'sidereal_year', 'sidereal_years', |
|
|
'tropical_year', 'tropical_years', |
|
|
'common_year', 'common_years', |
|
|
'julian_year', 'julian_years', |
|
|
'draconic_year', 'draconic_years', |
|
|
'gaussian_year', 'gaussian_years', |
|
|
'full_moon_cycle', 'full_moon_cycles', |
|
|
'year', 'years', |
|
|
'G', 'gravitational_constant', |
|
|
'c', 'speed_of_light', |
|
|
'elementary_charge', |
|
|
'hbar', |
|
|
'planck', |
|
|
'eV', 'electronvolt', 'electronvolts', |
|
|
'avogadro_number', |
|
|
'avogadro', 'avogadro_constant', |
|
|
'boltzmann', 'boltzmann_constant', |
|
|
'stefan', 'stefan_boltzmann_constant', |
|
|
'R', 'molar_gas_constant', |
|
|
'faraday_constant', |
|
|
'josephson_constant', |
|
|
'von_klitzing_constant', |
|
|
'Da', 'dalton', 'amu', 'amus', 'atomic_mass_unit', 'atomic_mass_constant', |
|
|
'me', 'electron_rest_mass', |
|
|
'gee', 'gees', 'acceleration_due_to_gravity', |
|
|
'u0', 'magnetic_constant', 'vacuum_permeability', |
|
|
'e0', 'electric_constant', 'vacuum_permittivity', |
|
|
'Z0', 'vacuum_impedance', |
|
|
'coulomb_constant', 'electric_force_constant', |
|
|
'atmosphere', 'atmospheres', 'atm', |
|
|
'kPa', |
|
|
'bar', 'bars', |
|
|
'pound', 'pounds', |
|
|
'psi', |
|
|
'dHg0', |
|
|
'mmHg', 'torr', |
|
|
'mmu', 'mmus', 'milli_mass_unit', |
|
|
'quart', 'quarts', |
|
|
'ly', 'lightyear', 'lightyears', |
|
|
'au', 'astronomical_unit', 'astronomical_units', |
|
|
'planck_mass', |
|
|
'planck_time', |
|
|
'planck_temperature', |
|
|
'planck_length', |
|
|
'planck_charge', |
|
|
'planck_area', |
|
|
'planck_volume', |
|
|
'planck_momentum', |
|
|
'planck_energy', |
|
|
'planck_force', |
|
|
'planck_power', |
|
|
'planck_density', |
|
|
'planck_energy_density', |
|
|
'planck_intensity', |
|
|
'planck_angular_frequency', |
|
|
'planck_pressure', |
|
|
'planck_current', |
|
|
'planck_voltage', |
|
|
'planck_impedance', |
|
|
'planck_acceleration', |
|
|
'bit', 'bits', |
|
|
'byte', |
|
|
'kibibyte', 'kibibytes', |
|
|
'mebibyte', 'mebibytes', |
|
|
'gibibyte', 'gibibytes', |
|
|
'tebibyte', 'tebibytes', |
|
|
'pebibyte', 'pebibytes', |
|
|
'exbibyte', 'exbibytes', |
|
|
|
|
|
'mks', 'mksa', 'si', |
|
|
] |
|
|
|
