358 lines
10 KiB
Python
358 lines
10 KiB
Python
|
"""
|
||
|
|
Collection of physical constants and conversion factors.
|
||
|
|
|
||
|
|
Most constants are in SI units, so you can do
|
||
|
|
print '10 mile per minute is', 10*mile/minute, 'm/s or', 10*mile/(minute*knot), 'knots'
|
||
|
|
|
||
|
|
The list is not meant to be comprehensive, but just convenient for everyday use.
|
||
|
|
"""
|
||
|
|
|
||
|
|
from __future__ import annotations
|
||
|
|
|
||
|
|
import math as _math
|
||
|
|
from typing import TYPE_CHECKING, Any
|
||
|
|
|
||
|
|
from ._codata import value as _cd
|
||
|
|
import numpy as _np
|
||
|
|
|
||
|
|
if TYPE_CHECKING:
|
||
|
|
import numpy.typing as npt
|
||
|
|
|
||
|
|
"""
|
||
|
|
BasSw 2006
|
||
|
|
physical constants: imported from CODATA
|
||
|
|
unit conversion: see e.g., NIST special publication 811
|
||
|
|
Use at own risk: double-check values before calculating your Mars orbit-insertion burn.
|
||
|
|
Some constants exist in a few variants, which are marked with suffixes.
|
||
|
|
The ones without any suffix should be the most common ones.
|
||
|
|
"""
|
||
|
|
|
||
|
|
__all__ = [
|
||
|
|
'Avogadro', 'Boltzmann', 'Btu', 'Btu_IT', 'Btu_th', 'G',
|
||
|
|
'Julian_year', 'N_A', 'Planck', 'R', 'Rydberg',
|
||
|
|
'Stefan_Boltzmann', 'Wien', 'acre', 'alpha',
|
||
|
|
'angstrom', 'arcmin', 'arcminute', 'arcsec',
|
||
|
|
'arcsecond', 'astronomical_unit', 'atm',
|
||
|
|
'atmosphere', 'atomic_mass', 'atto', 'au', 'bar',
|
||
|
|
'barrel', 'bbl', 'blob', 'c', 'calorie',
|
||
|
|
'calorie_IT', 'calorie_th', 'carat', 'centi',
|
||
|
|
'convert_temperature', 'day', 'deci', 'degree',
|
||
|
|
'degree_Fahrenheit', 'deka', 'dyn', 'dyne', 'e',
|
||
|
|
'eV', 'electron_mass', 'electron_volt',
|
||
|
|
'elementary_charge', 'epsilon_0', 'erg',
|
||
|
|
'exa', 'exbi', 'femto', 'fermi', 'fine_structure',
|
||
|
|
'fluid_ounce', 'fluid_ounce_US', 'fluid_ounce_imp',
|
||
|
|
'foot', 'g', 'gallon', 'gallon_US', 'gallon_imp',
|
||
|
|
'gas_constant', 'gibi', 'giga', 'golden', 'golden_ratio',
|
||
|
|
'grain', 'gram', 'gravitational_constant', 'h', 'hbar',
|
||
|
|
'hectare', 'hecto', 'horsepower', 'hour', 'hp',
|
||
|
|
'inch', 'k', 'kgf', 'kibi', 'kilo', 'kilogram_force',
|
||
|
|
'kmh', 'knot', 'lambda2nu', 'lb', 'lbf',
|
||
|
|
'light_year', 'liter', 'litre', 'long_ton', 'm_e',
|
||
|
|
'm_n', 'm_p', 'm_u', 'mach', 'mebi', 'mega',
|
||
|
|
'metric_ton', 'micro', 'micron', 'mil', 'mile',
|
||
|
|
'milli', 'minute', 'mmHg', 'mph', 'mu_0', 'nano',
|
||
|
|
'nautical_mile', 'neutron_mass', 'nu2lambda',
|
||
|
|
'ounce', 'oz', 'parsec', 'pebi', 'peta',
|
||
|
|
'pi', 'pico', 'point', 'pound', 'pound_force',
|
||
|
|
'proton_mass', 'psi', 'pt', 'short_ton',
|
||
|
|
'sigma', 'slinch', 'slug', 'speed_of_light',
|
||
|
|
'speed_of_sound', 'stone', 'survey_foot',
|
||
|
|
'survey_mile', 'tebi', 'tera', 'ton_TNT',
|
||
|
|
'torr', 'troy_ounce', 'troy_pound', 'u',
|
||
|
|
'week', 'yard', 'year', 'yobi', 'yocto',
|
||
|
|
'yotta', 'zebi', 'zepto', 'zero_Celsius', 'zetta'
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
# mathematical constants
|
||
|
|
pi = _math.pi
|
||
|
|
golden = golden_ratio = (1 + _math.sqrt(5)) / 2
|
||
|
|
|
||
|
|
# SI prefixes
|
||
|
|
yotta = 1e24
|
||
|
|
zetta = 1e21
|
||
|
|
exa = 1e18
|
||
|
|
peta = 1e15
|
||
|
|
tera = 1e12
|
||
|
|
giga = 1e9
|
||
|
|
mega = 1e6
|
||
|
|
kilo = 1e3
|
||
|
|
hecto = 1e2
|
||
|
|
deka = 1e1
|
||
|
|
deci = 1e-1
|
||
|
|
centi = 1e-2
|
||
|
|
milli = 1e-3
|
||
|
|
micro = 1e-6
|
||
|
|
nano = 1e-9
|
||
|
|
pico = 1e-12
|
||
|
|
femto = 1e-15
|
||
|
|
atto = 1e-18
|
||
|
|
zepto = 1e-21
|
||
|
|
yocto = 1e-24
|
||
|
|
|
||
|
|
# binary prefixes
|
||
|
|
kibi = 2**10
|
||
|
|
mebi = 2**20
|
||
|
|
gibi = 2**30
|
||
|
|
tebi = 2**40
|
||
|
|
pebi = 2**50
|
||
|
|
exbi = 2**60
|
||
|
|
zebi = 2**70
|
||
|
|
yobi = 2**80
|
||
|
|
|
||
|
|
# physical constants
|
||
|
|
c = speed_of_light = _cd('speed of light in vacuum')
|
||
|
|
mu_0 = _cd('vacuum mag. permeability')
|
||
|
|
epsilon_0 = _cd('vacuum electric permittivity')
|
||
|
|
h = Planck = _cd('Planck constant')
|
||
|
|
hbar = h / (2 * pi)
|
||
|
|
G = gravitational_constant = _cd('Newtonian constant of gravitation')
|
||
|
|
g = _cd('standard acceleration of gravity')
|
||
|
|
e = elementary_charge = _cd('elementary charge')
|
||
|
|
R = gas_constant = _cd('molar gas constant')
|
||
|
|
alpha = fine_structure = _cd('fine-structure constant')
|
||
|
|
N_A = Avogadro = _cd('Avogadro constant')
|
||
|
|
k = Boltzmann = _cd('Boltzmann constant')
|
||
|
|
sigma = Stefan_Boltzmann = _cd('Stefan-Boltzmann constant')
|
||
|
|
Wien = _cd('Wien wavelength displacement law constant')
|
||
|
|
Rydberg = _cd('Rydberg constant')
|
||
|
|
|
||
|
|
# mass in kg
|
||
|
|
gram = 1e-3
|
||
|
|
metric_ton = 1e3
|
||
|
|
grain = 64.79891e-6
|
||
|
|
lb = pound = 7000 * grain # avoirdupois
|
||
|
|
blob = slinch = pound * g / 0.0254 # lbf*s**2/in (added in 1.0.0)
|
||
|
|
slug = blob / 12 # lbf*s**2/foot (added in 1.0.0)
|
||
|
|
oz = ounce = pound / 16
|
||
|
|
stone = 14 * pound
|
||
|
|
long_ton = 2240 * pound
|
||
|
|
short_ton = 2000 * pound
|
||
|
|
|
||
|
|
troy_ounce = 480 * grain # only for metals / gems
|
||
|
|
troy_pound = 12 * troy_ounce
|
||
|
|
carat = 200e-6
|
||
|
|
|
||
|
|
m_e = electron_mass = _cd('electron mass')
|
||
|
|
m_p = proton_mass = _cd('proton mass')
|
||
|
|
m_n = neutron_mass = _cd('neutron mass')
|
||
|
|
m_u = u = atomic_mass = _cd('atomic mass constant')
|
||
|
|
|
||
|
|
# angle in rad
|
||
|
|
degree = pi / 180
|
||
|
|
arcmin = arcminute = degree / 60
|
||
|
|
arcsec = arcsecond = arcmin / 60
|
||
|
|
|
||
|
|
# time in second
|
||
|
|
minute = 60.0
|
||
|
|
hour = 60 * minute
|
||
|
|
day = 24 * hour
|
||
|
|
week = 7 * day
|
||
|
|
year = 365 * day
|
||
|
|
Julian_year = 365.25 * day
|
||
|
|
|
||
|
|
# length in meter
|
||
|
|
inch = 0.0254
|
||
|
|
foot = 12 * inch
|
||
|
|
yard = 3 * foot
|
||
|
|
mile = 1760 * yard
|
||
|
|
mil = inch / 1000
|
||
|
|
pt = point = inch / 72 # typography
|
||
|
|
survey_foot = 1200.0 / 3937
|
||
|
|
survey_mile = 5280 * survey_foot
|
||
|
|
nautical_mile = 1852.0
|
||
|
|
fermi = 1e-15
|
||
|
|
angstrom = 1e-10
|
||
|
|
micron = 1e-6
|
||
|
|
au = astronomical_unit = 149597870700.0
|
||
|
|
light_year = Julian_year * c
|
||
|
|
parsec = au / arcsec
|
||
|
|
|
||
|
|
# pressure in pascal
|
||
|
|
atm = atmosphere = _cd('standard atmosphere')
|
||
|
|
bar = 1e5
|
||
|
|
torr = mmHg = atm / 760
|
||
|
|
psi = pound * g / (inch * inch)
|
||
|
|
|
||
|
|
# area in meter**2
|
||
|
|
hectare = 1e4
|
||
|
|
acre = 43560 * foot**2
|
||
|
|
|
||
|
|
# volume in meter**3
|
||
|
|
litre = liter = 1e-3
|
||
|
|
gallon = gallon_US = 231 * inch**3 # US
|
||
|
|
# pint = gallon_US / 8
|
||
|
|
fluid_ounce = fluid_ounce_US = gallon_US / 128
|
||
|
|
bbl = barrel = 42 * gallon_US # for oil
|
||
|
|
|
||
|
|
gallon_imp = 4.54609e-3 # UK
|
||
|
|
fluid_ounce_imp = gallon_imp / 160
|
||
|
|
|
||
|
|
# speed in meter per second
|
||
|
|
kmh = 1e3 / hour
|
||
|
|
mph = mile / hour
|
||
|
|
mach = speed_of_sound = 340.5 # approx value at 15 degrees in 1 atm. Is this a common value?
|
||
|
|
knot = nautical_mile / hour
|
||
|
|
|
||
|
|
# temperature in kelvin
|
||
|
|
zero_Celsius = 273.15
|
||
|
|
degree_Fahrenheit = 1/1.8 # only for differences
|
||
|
|
|
||
|
|
# energy in joule
|
||
|
|
eV = electron_volt = elementary_charge # * 1 Volt
|
||
|
|
calorie = calorie_th = 4.184
|
||
|
|
calorie_IT = 4.1868
|
||
|
|
erg = 1e-7
|
||
|
|
Btu_th = pound * degree_Fahrenheit * calorie_th / gram
|
||
|
|
Btu = Btu_IT = pound * degree_Fahrenheit * calorie_IT / gram
|
||
|
|
ton_TNT = 1e9 * calorie_th
|
||
|
|
# Wh = watt_hour
|
||
|
|
|
||
|
|
# power in watt
|
||
|
|
hp = horsepower = 550 * foot * pound * g
|
||
|
|
|
||
|
|
# force in newton
|
||
|
|
dyn = dyne = 1e-5
|
||
|
|
lbf = pound_force = pound * g
|
||
|
|
kgf = kilogram_force = g # * 1 kg
|
||
|
|
|
||
|
|
# functions for conversions that are not linear
|
||
|
|
|
||
|
|
|
||
|
|
def convert_temperature(
|
||
|
|
val: npt.ArrayLike,
|
||
|
|
old_scale: str,
|
||
|
|
new_scale: str,
|
||
|
|
) -> Any:
|
||
|
|
"""
|
||
|
|
Convert from a temperature scale to another one among Celsius, Kelvin,
|
||
|
|
Fahrenheit, and Rankine scales.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
val : array_like
|
||
|
|
Value(s) of the temperature(s) to be converted expressed in the
|
||
|
|
original scale.
|
||
|
|
old_scale : str
|
||
|
|
Specifies as a string the original scale from which the temperature
|
||
|
|
value(s) will be converted. Supported scales are Celsius ('Celsius',
|
||
|
|
'celsius', 'C' or 'c'), Kelvin ('Kelvin', 'kelvin', 'K', 'k'),
|
||
|
|
Fahrenheit ('Fahrenheit', 'fahrenheit', 'F' or 'f'), and Rankine
|
||
|
|
('Rankine', 'rankine', 'R', 'r').
|
||
|
|
new_scale : str
|
||
|
|
Specifies as a string the new scale to which the temperature
|
||
|
|
value(s) will be converted. Supported scales are Celsius ('Celsius',
|
||
|
|
'celsius', 'C' or 'c'), Kelvin ('Kelvin', 'kelvin', 'K', 'k'),
|
||
|
|
Fahrenheit ('Fahrenheit', 'fahrenheit', 'F' or 'f'), and Rankine
|
||
|
|
('Rankine', 'rankine', 'R', 'r').
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
res : float or array of floats
|
||
|
|
Value(s) of the converted temperature(s) expressed in the new scale.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
.. versionadded:: 0.18.0
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy.constants import convert_temperature
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> convert_temperature(np.array([-40, 40]), 'Celsius', 'Kelvin')
|
||
|
|
array([ 233.15, 313.15])
|
||
|
|
|
||
|
|
"""
|
||
|
|
# Convert from `old_scale` to Kelvin
|
||
|
|
if old_scale.lower() in ['celsius', 'c']:
|
||
|
|
tempo = _np.asanyarray(val) + zero_Celsius
|
||
|
|
elif old_scale.lower() in ['kelvin', 'k']:
|
||
|
|
tempo = _np.asanyarray(val)
|
||
|
|
elif old_scale.lower() in ['fahrenheit', 'f']:
|
||
|
|
tempo = (_np.asanyarray(val) - 32) * 5 / 9 + zero_Celsius
|
||
|
|
elif old_scale.lower() in ['rankine', 'r']:
|
||
|
|
tempo = _np.asanyarray(val) * 5 / 9
|
||
|
|
else:
|
||
|
|
raise NotImplementedError("%s scale is unsupported: supported scales "
|
||
|
|
"are Celsius, Kelvin, Fahrenheit, and "
|
||
|
|
"Rankine" % old_scale)
|
||
|
|
# and from Kelvin to `new_scale`.
|
||
|
|
if new_scale.lower() in ['celsius', 'c']:
|
||
|
|
res = tempo - zero_Celsius
|
||
|
|
elif new_scale.lower() in ['kelvin', 'k']:
|
||
|
|
res = tempo
|
||
|
|
elif new_scale.lower() in ['fahrenheit', 'f']:
|
||
|
|
res = (tempo - zero_Celsius) * 9 / 5 + 32
|
||
|
|
elif new_scale.lower() in ['rankine', 'r']:
|
||
|
|
res = tempo * 9 / 5
|
||
|
|
else:
|
||
|
|
raise NotImplementedError("'%s' scale is unsupported: supported "
|
||
|
|
"scales are 'Celsius', 'Kelvin', "
|
||
|
|
"'Fahrenheit', and 'Rankine'" % new_scale)
|
||
|
|
|
||
|
|
return res
|
||
|
|
|
||
|
|
|
||
|
|
# optics
|
||
|
|
|
||
|
|
|
||
|
|
def lambda2nu(lambda_: npt.ArrayLike) -> Any:
|
||
|
|
"""
|
||
|
|
Convert wavelength to optical frequency
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
lambda_ : array_like
|
||
|
|
Wavelength(s) to be converted.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
nu : float or array of floats
|
||
|
|
Equivalent optical frequency.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Computes ``nu = c / lambda`` where c = 299792458.0, i.e., the
|
||
|
|
(vacuum) speed of light in meters/second.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy.constants import lambda2nu, speed_of_light
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> lambda2nu(np.array((1, speed_of_light)))
|
||
|
|
array([ 2.99792458e+08, 1.00000000e+00])
|
||
|
|
|
||
|
|
"""
|
||
|
|
return c / _np.asanyarray(lambda_)
|
||
|
|
|
||
|
|
|
||
|
|
def nu2lambda(nu: npt.ArrayLike) -> Any:
|
||
|
|
"""
|
||
|
|
Convert optical frequency to wavelength.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
nu : array_like
|
||
|
|
Optical frequency to be converted.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
lambda : float or array of floats
|
||
|
|
Equivalent wavelength(s).
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Computes ``lambda = c / nu`` where c = 299792458.0, i.e., the
|
||
|
|
(vacuum) speed of light in meters/second.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy.constants import nu2lambda, speed_of_light
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> nu2lambda(np.array((1, speed_of_light)))
|
||
|
|
array([ 2.99792458e+08, 1.00000000e+00])
|
||
|
|
|
||
|
|
"""
|
||
|
|
return c / _np.asanyarray(nu)
|