Lesson 43 - SciPy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Requirement already satisfied: scipy in c:\\programdata\\anaconda3\\lib\\site-packages (1.6.1)\nRequirement already satisfied: numpy>=1.16.5 in c:\\programdata\\anaconda3\\lib\\site-packages (from scipy) (1.19.2)\n"
     ]
    }
   ],
   "source": [
    "!pip install scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      " mom. ratio': (-0.68499694, '', 1.6e-07), 'Newtonian constant of gravitation': (6.6743e-11, 'm^3 kg^-1 s^-2', 1.5e-15), 'Newtonian constant of gravitation over h-bar c': (6.70883e-39, '(GeV/c^2)^-2', 1.5e-43), 'nuclear magneton': (5.0507837461e-27, 'J T^-1', 1.5e-36), 'nuclear magneton in eV/T': (3.15245125844e-08, 'eV T^-1', 9.6e-18), 'nuclear magneton in inverse meters per tesla': (0.02542623432, 'm^-1 T^-1', 1.6e-10), 'nuclear magneton in K/T': (0.00036582677756, 'K T^-1', 1.1e-13), 'nuclear magneton in MHz/T': (7.6225932291, 'MHz T^-1', 2.3e-09), 'Planck constant': (6.62607015e-34, 'J Hz^-1', 0.0), 'Planck constant in eV s': (4.135667662e-15, 'eV s', 2.5e-23), 'Planck constant over 2 pi': (1.0545718e-34, 'J s', 1.3e-42), 'Planck constant over 2 pi in eV s': (6.582119514e-16, 'eV s', 4e-24), 'Planck constant over 2 pi times c in MeV fm': (197.3269788, 'MeV fm', 1.2e-06), 'Planck length': (1.616255e-35, 'm', 1.8e-40), 'Planck mass': (2.176434e-08, 'kg', 2.4e-13), 'Planck mass energy equivalent in GeV': (1.22089e+19, 'GeV', 140000000000000.0), 'Planck temperature': (1.416784e+32, 'K', 1.6e+27), 'Planck time': (5.391247e-44, 's', 6e-49), 'proton charge to mass quotient': (95788331.56, 'C kg^-1', 0.029), 'proton Compton wavelength': (1.32140985539e-15, 'm', 4e-25), 'proton Compton wavelength over 2 pi': (2.10308910109e-16, 'm', 9.7e-26), 'proton-electron mass ratio': (1836.15267343, '', 1.1e-07), 'proton g factor': (5.5856946893, '', 1.6e-09), 'proton gyromag. ratio': (267522187.44, 's^-1 T^-1', 0.11), 'proton gyromag. ratio over 2 pi': (42.57747892, 'MHz T^-1', 2.9e-07), 'proton mag. mom.': (1.41060679736e-26, 'J T^-1', 6e-36), 'proton mag. mom. to Bohr magneton ratio': (0.0015210322023, '', 4.6e-13), 'proton mag. mom. to nuclear magneton ratio': (2.79284734463, '', 8.2e-10), 'proton mag. shielding correction': (2.5689e-05, '', 1.1e-08), 'proton mass': (1.67262192369e-27, 'kg', 5.1e-37), 'proton mass energy equivalent': (1.50327761598e-10, 'J', 4.6e-20), 'proton mass energy equivalent in MeV': (938.27208816, 'MeV', 2.9e-07), 'proton mass in u': (1.007276466621, 'u', 5.3e-11), 'proton molar mass': (0.00100727646627, 'kg mol^-1', 3.1e-13), 'proton-muon mass ratio': (8.88024337, '', 2e-07), 'proton-neutron mag. mom. ratio': (-1.45989805, '', 3.4e-07), 'proton-neutron mass ratio': (0.99862347812, '', 4.9e-10), 'proton rms charge radius': (8.414e-16, 'm', 1.9e-18), 'proton-tau mass ratio': (0.528051, '', 3.6e-05), 'quantum of circulation': (0.00036369475516, 'm^2 s^-1', 1.1e-13), 'quantum of circulation times 2': (0.00072738951032, 'm^2 s^-1', 2.2e-13), 'Rydberg constant': (10973731.56816, 'm^-1', 2.1e-05), 'Rydberg constant times c in Hz': (3289841960250800.0, 'Hz', 6400.0), 'Rydberg constant times hc in eV': (13.605693122994, 'eV', 2.6e-11), 'Rydberg constant times hc in J': (2.1798723611035e-18, 'J', 4.2e-30), 'Sackur-Tetrode constant (1 K, 100 kPa)': (-1.15170753706, '', 4.5e-10), 'Sackur-Tetrode constant (1 K, 101.325 kPa)': (-1.16487052358, '', 4.5e-10), 'second radiation constant': (0.01438776877, 'm K', 0.0), 'shielded helion gyromag. ratio': (203789456.9, 's^-1 T^-1', 2.4), 'shielded helion gyromag. ratio over 2 pi': (32.43409966, 'MHz T^-1', 4.3e-07), 'shielded helion mag. mom.': (-1.07455309e-26, 'J T^-1', 1.3e-34), 'shielded helion mag. mom. to Bohr magneton ratio': (-0.001158671471, '', 1.4e-11), 'shielded helion mag. mom. to nuclear magneton ratio': (-2.127497719, '', 2.5e-08), 'shielded helion to proton mag. mom. ratio': (-0.7617665618, '', 8.9e-09), 'shielded helion to shielded proton mag. mom. ratio': (-0.7617861313, '', 3.3e-09), 'shielded proton gyromag. ratio': (267515315.1, 's^-1 T^-1', 2.9), 'shielded proton gyromag. ratio over 2 pi': (42.57638507, 'MHz T^-1', 5.3e-07), 'shielded proton mag. mom.': (1.41057056e-26, 'J T^-1', 1.5e-34), 'shielded proton mag. mom. to Bohr magneton ratio': (0.001520993128, '', 1.7e-11), 'shielded proton mag. mom. to nuclear magneton ratio': (2.792775599, '', 3e-08), 'speed of light in vacuum': (299792458.0, 'm s^-1', 0.0), 'standard acceleration of gravity': (9.80665, 'm s^-2', 0.0), 'standard atmosphere': (101325.0, 'Pa', 0.0), 'Stefan-Boltzmann constant': (5.670374419e-08, 'W m^-2 K^-4', 0.0), 'tau Compton wavelength': (6.97771e-16, 'm', 4.7e-20), 'tau Compton wavelength over 2 pi': (1.11056e-16, 'm', 1e-20), 'tau-electron mass ratio': (3477.23, '', 0.23), 'tau mass': (3.16754e-27, 'kg', 2.1e-31), 'tau mass energy equivalent': (2.84684e-10, 'J', 1.9e-14), 'tau mass energy equivalent in MeV': (1776.82, 'MeV', 0.16), 'tau mass in u': (1.90754, 'u', 0.00013), 'tau molar mass': (0.00190754, 'kg mol^-1', 1.3e-07), 'tau-muon mass ratio': (16.817, '', 0.0011), 'tau-neutron mass ratio': (1.89115, '', 0.00013), 'tau-proton mass ratio': (1.89376, '', 0.00013), 'Thomson cross section': (6.6524587321e-29, 'm^2', 6e-38), 'triton-electron mag. mom. ratio': (-0.001620514423, '', 2.1e-11), 'triton-electron mass ratio': (5496.92153573, '', 2.7e-07), 'triton g factor': (5.957924931, '', 1.2e-08), 'triton mag. mom.': (1.5046095202e-26, 'J T^-1', 3e-35), 'triton mag. mom. to Bohr magneton ratio': (0.0016223936651, '', 3.2e-12), 'triton mag. mom. to nuclear magneton ratio': (2.9789624656, '', 5.9e-09), 'triton mass': (5.0073567446e-27, 'kg', 1.5e-36), 'triton mass energy equivalent': (4.500387806e-10, 'J', 1.4e-19), 'triton mass energy equivalent in MeV': (2808.92113298, 'MeV', 8.5e-07), 'triton mass in u': (3.01550071621, 'u', 1.2e-10), 'triton molar mass': (0.00301550071517, 'kg mol^-1', 9.2e-13), 'triton-neutron mag. mom. ratio': (-1.55718553, '', 3.7e-07), 'triton-proton mag. mom. ratio': (1.066639908, '', 1e-08), 'triton-proton mass ratio': (2.99371703414, '', 1.5e-10), 'unified atomic mass unit': (1.6605390666e-27, 'kg', 5e-37), 'von Klitzing constant': (25812.80745, 'ohm', 0.0), 'weak mixing angle': (0.2229, '', 0.0003), 'Wien frequency displacement law constant': (58789257570.0, 'Hz K^-1', 0.0), 'Wien wavelength displacement law constant': (0.002897771955, 'm K', 0.0), 'atomic unit of mom.um': (1.992851882e-24, 'kg m s^-1', 2.4e-32), 'electron-helion mass ratio': (0.0001819543074573, '', 7.9e-15), 'electron-triton mass ratio': (0.0001819200062251, '', 9e-15), 'helion g factor': (-4.255250615, '', 5e-08), 'helion mag. mom.': (-1.074617532e-26, 'J T^-1', 1.3e-34), 'helion mag. mom. to Bohr magneton ratio': (-0.001158740958, '', 1.4e-11), 'helion mag. mom. to nuclear magneton ratio': (-2.127625307, '', 2.5e-08), 'Loschmidt constant (273.15 K, 100 kPa)': (2.651645804e+25, 'm^-3', 0.0), 'natural unit of mom.um': (2.730924488e-22, 'kg m s^-1', 3.4e-30), 'natural unit of mom.um in MeV/c': (0.5109989461, 'MeV/c', 3.1e-09), 'neutron-proton mass difference': (2.30557435e-30, 'kg', 8.2e-37), 'neutron-proton mass difference energy equivalent': (2.07214689e-13, 'J', 7.4e-20), 'neutron-proton mass difference energy equivalent in MeV': (1.29333236, 'MeV', 4.6e-07), 'neutron-proton mass difference in u': (0.00138844933, 'u', 4.9e-10), 'standard-state pressure': (100000.0, 'Pa', 0.0), 'alpha particle relative atomic mass': (4.001506179127, '', 6.3e-11), 'Bohr magneton in inverse meter per tesla': (46.686447783, 'm^-1 T^-1', 1.4e-08), 'Boltzmann constant in inverse meter per kelvin': (69.50348004, 'm^-1 K^-1', 0.0), 'conventional value of ampere-90': (1.00000008887, 'A', 0.0), 'conventional value of coulomb-90': (1.00000008887, 'C', 0.0), 'conventional value of farad-90': (0.9999999822, 'F', 0.0), 'conventional value of henry-90': (1.00000001779, 'H', 0.0), 'conventional value of ohm-90': (1.00000001779, 'ohm', 0.0), 'conventional value of volt-90': (1.00000010666, 'V', 0.0), 'conventional value of watt-90': (1.00000019553, 'W', 0.0), 'deuteron relative atomic mass': (2.013553212745, '', 4e-11), 'electron gyromag. ratio in MHz/T': (28024.9514242, 'MHz T^-1', 8.5e-06), 'electron relative atomic mass': (0.000548579909065, '', 1.6e-14), 'elementary charge over h-bar': (1519267447000000.0, 'A J^-1', 0.0), 'helion relative atomic mass': (3.014932247175, '', 9.7e-11), 'helion shielding shift': (5.996743e-05, '', 1e-10), 'hyperfine transition frequency of Cs-133': (9192631770.0, 'Hz', 0.0), 'lattice spacing of ideal Si (220)': (1.920155716e-10, 'm', 3.2e-18), 'luminous efficacy': (683.0, 'lm W^-1', 0.0), 'neutron gyromag. ratio in MHz/T': (29.1646931, 'MHz T^-1', 6.9e-06), 'neutron relative atomic mass': (1.00866491595, '', 4.9e-10), 'nuclear magneton in inverse meter per tesla': (0.0254262341353, 'm^-1 T^-1', 7.8e-12), 'Planck constant in eV/Hz': (4.135667696e-15, 'eV Hz^-1', 0.0), 'proton gyromag. ratio in MHz/T': (42.577478518, 'MHz T^-1', 1.8e-08), 'proton relative atomic mass': (1.007276466621, '', 5.3e-11), 'reduced Compton wavelength': (3.8615926796e-13, 'm', 1.2e-22), 'reduced muon Compton wavelength': (1.867594306e-15, 'm', 4.2e-23), 'reduced neutron Compton wavelength': (2.1001941552e-16, 'm', 1.2e-25), 'reduced Planck constant': (1.054571817e-34, 'J s', 0.0), 'reduced Planck constant in eV s': (6.582119569e-16, 'eV s', 0.0), 'reduced Planck constant times c in MeV fm': (197.3269804, 'MeV fm', 0.0), 'reduced proton Compton wavelength': (2.10308910336e-16, 'm', 6.4e-26), 'reduced tau Compton wavelength': (1.110538e-16, 'm', 7.5e-21), 'shielded helion gyromag. ratio in MHz/T': (32.43409942, 'MHz T^-1', 3.8e-07), 'shielded proton gyromag. ratio in MHz/T': (42.57638474, 'MHz T^-1', 4.6e-07), 'shielding difference of d and p in HD': (2.02e-08, '', 2e-11), 'shielding difference of t and p in HT': (2.414e-08, '', 2e-11), 'tau energy equivalent': (1776.86, 'MeV', 0.12), 'triton relative atomic mass': (3.01550071621, '', 1.2e-10), 'triton to proton mag. mom. ratio': (1.0666399191, '', 2.1e-09), 'vacuum electric permittivity': (8.8541878128e-12, 'F m^-1', 1.3e-21), 'vacuum mag. permeability': (1.25663706212e-06, 'N A^-2', 1.9e-16), 'W to Z mass ratio': (0.88153, '', 0.00017)}, 'value': <function value at 0x000002A3044E2F70>, 'unit': <function unit at 0x000002A30454D040>, 'precision': <function precision at 0x000002A30454D0D0>, 'find': <function find at 0x000002A30454D160>, 'ConstantWarning': <class 'scipy.constants.codata.ConstantWarning'>, 'constants': <module 'scipy.constants.constants' from 'C:\\\\ProgramData\\\\Anaconda3\\\\lib\\\\site-packages\\\\scipy\\\\constants\\\\constants.py'>, 'pi': 3.141592653589793, 'golden': 1.618033988749895, 'golden_ratio': 1.618033988749895, 'yotta': 1e+24, 'zetta': 1e+21, 'exa': 1e+18, 'peta': 1000000000000000.0, 'tera': 1000000000000.0, 'giga': 1000000000.0, 'mega': 1000000.0, 'kilo': 1000.0, 'hecto': 100.0, 'deka': 10.0, 'deci': 0.1, 'centi': 0.01, 'milli': 0.001, 'micro': 1e-06, 'nano': 1e-09, 'pico': 1e-12, 'femto': 1e-15, 'atto': 1e-18, 'zepto': 1e-21, 'kibi': 1024, 'mebi': 1048576, 'gibi': 1073741824, 'tebi': 1099511627776, 'pebi': 1125899906842624, 'exbi': 1152921504606846976, 'zebi': 1180591620717411303424, 'yobi': 1208925819614629174706176, 'c': 299792458.0, 'speed_of_light': 299792458.0, 'mu_0': 1.25663706212e-06, 'epsilon_0': 8.8541878128e-12, 'h': 6.62607015e-34, 'Planck': 6.62607015e-34, 'hbar': 1.0545718176461565e-34, 'G': 6.6743e-11, 'gravitational_constant': 6.6743e-11, 'g': 9.80665, 'e': 1.602176634e-19, 'elementary_charge': 1.602176634e-19, 'R': 8.314462618, 'gas_constant': 8.314462618, 'alpha': 0.0072973525693, 'fine_structure': 0.0072973525693, 'N_A': 6.02214076e+23, 'Avogadro': 6.02214076e+23, 'k': 1.380649e-23, 'Boltzmann': 1.380649e-23, 'sigma': 5.670374419e-08, 'Stefan_Boltzmann': 5.670374419e-08, 'Wien': 0.002897771955, 'Rydberg': 10973731.56816, 'gram': 0.001, 'metric_ton': 1000.0, 'grain': 6.479891e-05, 'lb': 0.45359236999999997, 'pound': 0.45359236999999997, 'blob': 175.12683524647636, 'slinch': 175.12683524647636, 'slug': 14.593902937206364, 'oz': 0.028349523124999998, 'ounce': 0.028349523124999998, 'stone': 6.3502931799999995, 'long_ton': 1016.0469088, 'short_ton': 907.1847399999999, 'troy_ounce': 0.031103476799999998, 'troy_pound': 0.37324172159999996, 'carat': 0.0002, 'm_e': 9.1093837015e-31, 'electron_mass': 9.1093837015e-31, 'm_p': 1.67262192369e-27, 'proton_mass': 1.67262192369e-27, 'm_n': 1.67492749804e-27, 'neutron_mass': 1.67492749804e-27, 'm_u': 1.6605390666e-27, 'u': 1.6605390666e-27, 'atomic_mass': 1.6605390666e-27, 'degree': 0.017453292519943295, 'arcmin': 0.0002908882086657216, 'arcminute': 0.0002908882086657216, 'arcsec': 4.84813681109536e-06, 'arcsecond': 4.84813681109536e-06, 'minute': 60.0, 'hour': 3600.0, 'day': 86400.0, 'week': 604800.0, 'year': 31536000.0, 'Julian_year': 31557600.0, 'inch': 0.0254, 'foot': 0.30479999999999996, 'yard': 0.9143999999999999, 'mile': 1609.3439999999998, 'mil': 2.5399999999999997e-05, 'pt': 0.00035277777777777776, 'point': 0.00035277777777777776, 'survey_foot': 0.3048006096012192, 'survey_mile': 1609.3472186944373, 'nautical_mile': 1852.0, 'fermi': 1e-15, 'angstrom': 1e-10, 'micron': 1e-06, 'au': 149597870700.0, 'astronomical_unit': 149597870700.0, 'light_year': 9460730472580800.0, 'parsec': 3.085677581491367e+16, 'atm': 101325.0, 'atmosphere': 101325.0, 'bar': 100000.0, 'torr': 133.32236842105263, 'mmHg': 133.32236842105263, 'psi': 6894.757293168361, 'hectare': 10000.0, 'acre': 4046.8564223999992, 'litre': 0.001, 'liter': 0.001, 'gallon': 0.0037854117839999997, 'gallon_US': 0.0037854117839999997, 'fluid_ounce': 2.9573529562499998e-05, 'fluid_ounce_US': 2.9573529562499998e-05, 'bbl': 0.15898729492799998, 'barrel': 0.15898729492799998, 'gallon_imp': 0.00454609, 'fluid_ounce_imp': 2.84130625e-05, 'kmh': 0.2777777777777778, 'mph': 0.44703999999999994, 'mach': 340.5, 'speed_of_sound': 340.5, 'knot': 0.5144444444444445, 'zero_Celsius': 273.15, 'degree_Fahrenheit': 0.5555555555555556, 'eV': 1.602176634e-19, 'electron_volt': 1.602176634e-19, 'calorie': 4.184, 'calorie_th': 4.184, 'calorie_IT': 4.1868, 'erg': 1e-07, 'Btu_th': 1054.3502644888888, 'Btu': 1055.05585262, 'Btu_IT': 1055.05585262, 'ton_TNT': 4184000000.0, 'hp': 745.6998715822701, 'horsepower': 745.6998715822701, 'dyn': 1e-05, 'dyne': 1e-05, 'lbf': 4.4482216152605, 'pound_force': 4.4482216152605, 'kgf': 9.80665, 'kilogram_force': 9.80665, 'convert_temperature': <function convert_temperature at 0x000002A30454D310>, 'lambda2nu': <function lambda2nu at 0x000002A30454D430>, 'nu2lambda': <function nu2lambda at 0x000002A30454D4C0>, '_obsolete_constants': {'Wien displacement law constant': True, 'atomic unit of 1st hyperpolarizablity': True, 'atomic unit of 2nd hyperpolarizablity': True, 'atomic unit of electric dipole moment': True, 'atomic unit of electric polarizablity': True, 'atomic unit of electric quadrupole moment': True, 'atomic unit of magn. dipole moment': True, 'atomic unit of magn. flux density': True, 'deuteron magn. moment': True, 'deuteron magn. moment to Bohr magneton ratio': True, 'deuteron magn. moment to nuclear magneton ratio': True, 'deuteron-electron magn. moment ratio': True, 'deuteron-proton magn. moment ratio': True, 'deuteron-neutron magn. moment ratio': True, 'electron gyromagn. ratio': True, 'electron gyromagn. ratio over 2 pi': True, 'electron magn. moment': True, 'electron magn. moment to Bohr magneton ratio': True, 'electron magn. moment to nuclear magneton ratio': True, 'electron magn. moment anomaly': True, 'electron to shielded proton magn. moment ratio': True, 'electron to shielded helion magn. moment ratio': True, 'electron-deuteron magn. moment ratio': True, 'electron-muon magn. moment ratio': True, 'electron-neutron magn. moment ratio': True, 'electron-proton magn. moment ratio': True, 'magn. constant': True, 'magn. flux quantum': True, 'muon magn. moment': True, 'muon magn. moment to Bohr magneton ratio': True, 'muon magn. moment to nuclear magneton ratio': True, 'muon-proton magn. moment ratio': True, 'neutron gyromagn. ratio': True, 'neutron gyromagn. ratio over 2 pi': True, 'neutron magn. moment': True, 'neutron magn. moment to Bohr magneton ratio': True, 'neutron magn. moment to nuclear magneton ratio': True, 'neutron to shielded proton magn. moment ratio': True, 'neutron-electron magn. moment ratio': True, 'neutron-proton magn. moment ratio': True, 'proton gyromagn. ratio': True, 'proton gyromagn. ratio over 2 pi': True, 'proton magn. moment': True, 'proton magn. moment to Bohr magneton ratio': True, 'proton magn. moment to nuclear magneton ratio': True, 'proton magn. shielding correction': True, 'proton-neutron magn. moment ratio': True, 'shielded helion gyromagn. ratio': True, 'shielded helion gyromagn. ratio over 2 pi': True, 'shielded helion magn. moment': True, 'shielded helion magn. moment to Bohr magneton ratio': True, 'shielded helion magn. moment to nuclear magneton ratio': True, 'shielded helion to proton magn. moment ratio': True, 'shielded helion to shielded proton magn. moment ratio': True, 'shielded proton magn. moment': True, 'shielded proton magn. moment to Bohr magneton ratio': True, 'shielded proton magn. moment to nuclear magneton ratio': True, '{220} lattice spacing of silicon': True, 'lattice spacing of silicon': True, 'Bohr magneton in inverse meters per tesla': True, 'Boltzmann constant in inverse meters per kelvin': True, 'characteristic impedance of vacuum': True, 'Compton wavelength over 2 pi': True, 'electric constant': True, 'electron gyromag. ratio over 2 pi': True, 'elementary charge over h': True, 'Faraday constant for conventional electric current': True, 'mag. constant': True, 'molar Planck constant times c': True, 'muon Compton wavelength over 2 pi': True, 'neutron Compton wavelength over 2 pi': True, 'neutron gyromag. ratio over 2 pi': True, 'nuclear magneton in inverse meters per tesla': True, 'Planck constant in eV s': True, 'Planck constant over 2 pi': True, 'Planck constant over 2 pi in eV s': True, 'Planck constant over 2 pi times c in MeV fm': True, 'proton Compton wavelength over 2 pi': True, 'proton gyromag. ratio over 2 pi': True, 'shielded helion gyromag. ratio over 2 pi': True, 'shielded proton gyromag. ratio over 2 pi': True, 'tau Compton wavelength over 2 pi': True, 'tau mass energy equivalent in MeV': True, 'triton-electron mag. mom. ratio': True, 'triton-neutron mag. mom. ratio': True, 'triton-proton mag. mom. ratio': True, 'atomic unit of mom.um': True, 'natural unit of mom.um': True, 'natural unit of mom.um in MeV/c': True}, '__all__': ['Avogadro', 'Boltzmann', 'Btu', 'Btu_IT', 'Btu_th', 'ConstantWarning', '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', 'codata', 'constants', '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', 'find', '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', 'physical_constants', 'pi', 'pico', 'point', 'pound', 'pound_force', 'precision', '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', 'unit', 'value', 'week', 'yard', 'year', 'yobi', 'yotta', 'zebi', 'zepto', 'zero_Celsius', 'zetta'], 'test': <scipy._lib._testutils.PytestTester object at 0x000002A3044907C0>}\n"
     ]
    }
   ],
   "source": [
    "from scipy import constants\n",
    "print(constants.__dict__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.0254\n0.30479999999999996\n0.9143999999999999\n1609.3439999999998\n\n149597870700.0\n9460730472580800.0\n3.085677581491367e+16\n"
     ]
    }
   ],
   "source": [
    "# distance\n",
    "print(constants.inch)\n",
    "print(constants.foot)\n",
    "print(constants.yard)\n",
    "print(constants.mile)\n",
    "print()\n",
    "print(constants.astronomical_unit)\n",
    "print(constants.light_year)\n",
    "print(constants.parsec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "3.141592653589793\n1.618033988749895\n1.602176634e-19\n"
     ]
    }
   ],
   "source": [
    "# maths\n",
    "print(constants.pi)\n",
    "print(constants.golden)\n",
    "print(constants.e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "299792458.0\n299792458.0\n6.62607015e-34\n6.62607015e-34\n6.6743e-11\n6.6743e-11\n1.602176634e-19\n1.602176634e-19\n6.02214076e+23\n6.02214076e+23\n1.380649e-23\n1.380649e-23\n5.670374419e-08\n5.670374419e-08\n\n9.1093837015e-31\n9.1093837015e-31\n1.67262192369e-27\n1.67262192369e-27\n1.67492749804e-27\n1.67492749804e-27\n"
     ]
    }
   ],
   "source": [
    "# physical constants\n",
    "print(constants.c)\n",
    "print(constants.speed_of_light)\n",
    "print(constants.h)\n",
    "print(constants.Planck)\n",
    "print(constants.G)\n",
    "print(constants.gravitational_constant)\n",
    "print(constants.e)\n",
    "print(constants.elementary_charge)\n",
    "print(constants.N_A)\n",
    "print(constants.Avogadro)\n",
    "print(constants.k)\n",
    "print(constants.Boltzmann)\n",
    "print(constants.sigma)\n",
    "print(constants.Stefan_Boltzmann)\n",
    "print()\n",
    "print(constants.m_e)\n",
    "print(constants.electron_mass)\n",
    "print(constants.m_p)\n",
    "print(constants.proton_mass)\n",
    "print(constants.m_n)\n",
    "print(constants.neutron_mass)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "6.6743e-11\n(6.6743e-11, 'm^3 kg^-1 s^-2', 1.5e-15)\n"
     ]
    }
   ],
   "source": [
    "# physical constants\n",
    "print(constants.gravitational_constant)\n",
    "print(constants.physical_constants[\"Newtonian constant of gravitation\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1e+24\n1e+21\n1e+18\n1000000000000000.0\n1000000000000.0\n1000000000.0\n1000000.0\n1000.0\n100.0\n10.0\n0.1\n0.01\n0.001\n1e-06\n1e-09\n1e-12\n1e-15\n1e-18\n1e-21\n"
     ]
    }
   ],
   "source": [
    "# SI prefixes\n",
    "print(constants.yotta)\n",
    "print(constants.zetta)\n",
    "print(constants.exa)\n",
    "print(constants.peta)\n",
    "print(constants.tera)\n",
    "print(constants.giga)\n",
    "print(constants.mega)\n",
    "print(constants.kilo)\n",
    "print(constants.hecto)\n",
    "print(constants.deka)\n",
    "print(constants.deci)\n",
    "print(constants.centi)\n",
    "print(constants.milli)\n",
    "print(constants.micro)\n",
    "print(constants.nano)\n",
    "print(constants.pico)\n",
    "print(constants.femto)\n",
    "print(constants.atto)\n",
    "print(constants.zepto)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.001\n0.028349523124999998\n0.45359236999999997\n6.3502931799999995\n"
     ]
    }
   ],
   "source": [
    "# mass\n",
    "print(constants.gram)\n",
    "print(constants.oz)\n",
    "print(constants.lb)\n",
    "print(constants.stone)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.30116867893975674\n1.3817732906760363\n"
     ]
    }
   ],
   "source": [
    "# solving an equation\n",
    "\n",
    "import numpy as np\n",
    "def eqn(x):\n",
    "    return x * np.cos(x) + np.sin(x) / x\n",
    "\n",
    "print(eqn(-1))\n",
    "print(eqn(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# plot\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "x = np.linspace(-10,10)\n",
    "y = eqn(x)\n",
    "ax = plt.gca()\n",
    "ax.plot(x,y)\n",
    "ax.spines['left'].set_position('center')\n",
    "ax.spines['bottom'].set_position('center')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "    fjac: array([[-1.]])\n",
       "     fun: array([0.30116868])\n",
       " message: 'The iteration is not making good progress, as measured by the \\n  improvement from the last ten iterations.'\n",
       "    nfev: 13\n",
       "     qtf: array([-0.30116868])\n",
       "       r: array([-0.01031204])\n",
       "  status: 5\n",
       " success: False\n",
       "       x: array([-1.])"
      ]
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "# solve\n",
    "from scipy.optimize import root\n",
    "root(eqn,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "    fjac: array([[-1.]])\n",
       "     fun: array([1.11022302e-16])\n",
       " message: 'The solution converged.'\n",
       "    nfev: 10\n",
       "     qtf: array([-4.76934048e-11])\n",
       "       r: array([2.48952872])\n",
       "  status: 1\n",
       " success: True\n",
       "       x: array([1.85392746])"
      ]
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "root(eqn,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1\n1\n5\n"
     ]
    }
   ],
   "source": [
    "# minimise\n",
    "from scipy.optimize import minimize\n",
    "def eqn(x):\n",
    "    return x**4 + x**3 + x**2 + x + 1\n",
    "\n",
    "print(eqn(-1))\n",
    "print(eqn(0))\n",
    "print(eqn(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "x = np.linspace(-2,2)\n",
    "y = eqn(x)\n",
    "ax = plt.gca()\n",
    "ax.plot(x,y)\n",
    "ax.spines['left'].set_position('center')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "      fun: 0.6735532234810916\n",
       " hess_inv: array([[0.36367369]])\n",
       "      jac: array([-5.06639481e-06])\n",
       "  message: 'Optimization terminated successfully.'\n",
       "     nfev: 14\n",
       "      nit: 5\n",
       "     njev: 7\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([-0.60583142])"
      ]
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "minimize(eqn,0)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}