constants.py

"""
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.
"""
"""
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.
"""

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 = _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, 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]), '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_):
    """
    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 c / _np.asanyarray(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)