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