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"""
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 a convenient list for everyday use.
"""
from __future__ import division, print_function, absolute_import
"""
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 one.
"""
import math as _math
from .codata import value as _cd
import numpy as _np
# 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
# 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 = 4e-7*pi
epsilon_0 = 1 / (mu_0*c*c)
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')
# weight in kg
gram = 1e-3
metric_ton = 1e3
grain = 64.79891e-6
lb = pound = 7000 * grain # avoirdupois
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 = 149597870691.0
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, old_scale, new_scale):
"""
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
>>> convert_temperature(np.array([-40, 40.0]), '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
@_np.deprecate(message="scipy.constants.C2K is deprecated in scipy 0.18.0. "
"Use scipy.constants.convert_temperature instead. "
"Note that the new function has a different signature.")
def C2K(C):
"""
Convert Celsius to Kelvin
Parameters
----------
C : array_like
Celsius temperature(s) to be converted.
Returns
-------
K : float or array of floats
Equivalent Kelvin temperature(s).
See also
--------
convert_temperature
Notes
-----
Computes ``K = C + zero_Celsius`` where `zero_Celsius` = 273.15, i.e.,
(the absolute value of) temperature "absolute zero" as measured in Celsius.
Examples
--------
>>> from scipy.constants import C2K
>>> C2K(np.array([-40, 40.0]))
array([ 233.15, 313.15])
"""
return _np.asanyarray(C) + zero_Celsius
@_np.deprecate(message="scipy.constants.K2C is deprecated in scipy 0.18.0. "
"Use scipy.constants.convert_temperature instead. "
"Note that the new function has a different signature.")
def K2C(K):
"""
Convert Kelvin to Celsius
Parameters
----------
K : array_like
Kelvin temperature(s) to be converted.
Returns
-------
C : float or array of floats
Equivalent Celsius temperature(s).
See also
--------
convert_temperature
Notes
-----
Computes ``C = K - zero_Celsius`` where `zero_Celsius` = 273.15, i.e.,
(the absolute value of) temperature "absolute zero" as measured in Celsius.
Examples
--------
>>> from scipy.constants import K2C
>>> K2C(np.array([233.15, 313.15]))
array([-40., 40.])
"""
return _np.asanyarray(K) - zero_Celsius
@_np.deprecate(message="scipy.constants.F2C is deprecated in scipy 0.18.0. "
"Use scipy.constants.convert_temperature instead. "
"Note that the new function has a different signature.")
def F2C(F):
"""
Convert Fahrenheit to Celsius
Parameters
----------
F : array_like
Fahrenheit temperature(s) to be converted.
Returns
-------
C : float or array of floats
Equivalent Celsius temperature(s).
See also
--------
convert_temperature
Notes
-----
Computes ``C = (F - 32) / 1.8``.
Examples
--------
>>> from scipy.constants import F2C
>>> F2C(np.array([-40, 40.0]))
array([-40. , 4.44444444])
"""
return (_np.asanyarray(F) - 32) / 1.8
@_np.deprecate(message="scipy.constants.C2F is deprecated in scipy 0.18.0. "
"Use scipy.constants.convert_temperature instead. "
"Note that the new function has a different signature.")
def C2F(C):
"""
Convert Celsius to Fahrenheit
Parameters
----------
C : array_like
Celsius temperature(s) to be converted.
Returns
-------
F : float or array of floats
Equivalent Fahrenheit temperature(s).
See also
--------
convert_temperature
Notes
-----
Computes ``F = 1.8 * C + 32``.
Examples
--------
>>> from scipy.constants import C2F
>>> C2F(np.array([-40, 40.0]))
array([ -40., 104.])
"""
return 1.8 * _np.asanyarray(C) + 32
@_np.deprecate(message="scipy.constants.F2K is deprecated in scipy 0.18.0. "
"Use scipy.constants.convert_temperature instead. "
"Note that the new function has a different signature.")
def F2K(F):
"""
Convert Fahrenheit to Kelvin
Parameters
----------
F : array_like
Fahrenheit temperature(s) to be converted.
Returns
-------
K : float or array of floats
Equivalent Kelvin temperature(s).
See also
--------
convert_temperature
Notes
-----
Computes ``K = (F - 32)/1.8 + zero_Celsius`` where `zero_Celsius` =
273.15, i.e., (the absolute value of) temperature "absolute zero" as
measured in Celsius.
Examples
--------
>>> from scipy.constants import F2K
>>> F2K(np.array([-40, 104]))
array([ 233.15, 313.15])
"""
return C2K(F2C(_np.asanyarray(F)))
@_np.deprecate(message="scipy.constants.K2F is deprecated in scipy 0.18.0. "
"Use scipy.constants.convert_temperature instead. "
"Note that the new function has a different signature.")
def K2F(K):
"""
Convert Kelvin to Fahrenheit
Parameters
----------
K : array_like
Kelvin temperature(s) to be converted.
Returns
-------
F : float or array of floats
Equivalent Fahrenheit temperature(s).
See also
--------
convert_temperature
Notes
-----
Computes ``F = 1.8 * (K - zero_Celsius) + 32`` where `zero_Celsius` =
273.15, i.e., (the absolute value of) temperature "absolute zero" as
measured in Celsius.
Examples
--------
>>> from scipy.constants import K2F
>>> K2F(np.array([233.15, 313.15]))
array([ -40., 104.])
"""
return C2F(K2C(_np.asanyarray(K)))
# optics
def lambda2nu(lambda_):
"""
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
>>> lambda2nu(np.array((1, speed_of_light)))
array([ 2.99792458e+08, 1.00000000e+00])
"""
return _np.asanyarray(c) / lambda_
def nu2lambda(nu):
"""
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
>>> nu2lambda(np.array((1, speed_of_light)))
array([ 2.99792458e+08, 1.00000000e+00])
"""
return c / _np.asanyarray(nu)