api_documentation_master.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Environmental Science for Symbolic Math <a class=\"tocSkip\">\n",
    "\n",
    "(Stan Schymanski and Jiri Kuncar)\n",
    "\n",
    "This notebook gives examples and common use cases for ESSM. The ESSM package documentation can be obtained from here:\n",
    "https://essm.readthedocs.io/en/latest/\n",
    "\n",
    "The code is openly available here:\n",
    "https://github.com/environmentalscience/essm\n",
    "\n",
    "# Installation \n",
    "\n",
    "See the documentation for different installation option, but the easiest is:\n",
    "```\n",
    "pip install essm\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_267803/2880507587.py:2: DeprecationWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html\n",
      "  import pkg_resources\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'1.1'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking for essm version installed\n",
    "import pkg_resources\n",
    "pkg_resources.get_distribution(\"essm\").version"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# General Jupyter setup\n",
    "We will first setup the IPython notebook to nicely render the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "before = [str(m) for m in sys.modules]  # This is to track what modules have been imported in this notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display, Markdown\n",
    "from sympy import init_printing\n",
    "init_printing() \n",
    "from sympy.printing import StrPrinter\n",
    "StrPrinter._print_Quantity = lambda self, expr: str(expr.abbrev)    # displays short units (m instead of meter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy as sc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing functions, variables and equations from sympy and essm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import various functions and units from sympy\n",
    "from sympy import Derivative, Eq, exp, log, solve, Symbol\n",
    "from sympy.physics.units import bar, convert_to, kelvin, kilo, mega, joule, kilogram, meter, second, inch, hour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import basic Variable class and utils from essm\n",
    "from essm.variables import Variable\n",
    "from essm.variables.utils import extract_variables, generate_metadata_table, markdown, replace_defaults, replace_variables, subs_eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import essm.variables.physics.thermodynamics as physics_vars\n",
    "import essm.equations.physics.thermodynamics as physics_eqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>Symbol</td><td>Name</td><td>Description</td><td>Definition</td><td>Default value</td><td>Units</td></tr><tr><td>$\\alpha_a$</td><td>alpha_a</td><td>Thermal diffusivity of dry air.</td><td></td><td>-</td><td>m$^{2}$ s$^{-1}$</td></tr><tr><td>$\\lambda_E$</td><td>lambda_E</td><td>Latent heat of evaporation.</td><td></td><td>2450000.0</td><td>J kg$^{-1}$</td></tr><tr><td>$\\nu_a$</td><td>nu_a</td><td>Kinematic viscosity of dry air.</td><td></td><td>-</td><td>m$^{2}$ s$^{-1}$</td></tr><tr><td>$\\rho_a$</td><td>rho_a</td><td>Density of dry air.</td><td></td><td>-</td><td>kg m$^{-3}$</td></tr><tr><td>$\\sigma$</td><td>sigm</td><td>Stefan-Boltzmann constant.</td><td></td><td>5.67e-08</td><td>J s$^{-1}$ m$^{-2}$ K$^{-4}$</td></tr><tr><td>$c_{pa,mol}$</td><td>c_pamol</td><td>Molar specific heat of dry air.\n",
       "\n",
       "    https://en.wikipedia.org/wiki/Heat_capacity#Specific_heat_capacity\n",
       "    </td><td></td><td>29.19</td><td>J K$^{-1}$ mol$^{-1}$</td></tr><tr><td>$c_{pa}$</td><td>c_pa</td><td>Specific heat of dry air.</td><td></td><td>1010.0</td><td>J K$^{-1}$ kg$^{-1}$</td></tr><tr><td>$c_{pv}$</td><td>c_pv</td><td>Specific heat of water vapour at 300 K.\n",
       "\n",
       "    http://www.engineeringtoolbox.com/water-vapor-d_979.html\n",
       "    </td><td></td><td>1864</td><td>J K$^{-1}$ kg$^{-1}$</td></tr><tr><td>$C_{wa}$</td><td>C_wa</td><td>Concentration of water in air.</td><td></td><td>-</td><td>mol m$^{-3}$</td></tr><tr><td>$D_{va}$</td><td>D_va</td><td>Binary diffusion coefficient of water vapour in air.</td><td></td><td>-</td><td>m$^{2}$ s$^{-1}$</td></tr><tr><td>$g$</td><td>g</td><td>Gravitational acceleration.</td><td></td><td>9.81</td><td>m s$^{-2}$</td></tr><tr><td>$h_c$</td><td>h_c</td><td>Average 1-sided convective heat transfer coefficient.</td><td></td><td>-</td><td>J K$^{-1}$ s$^{-1}$ m$^{-2}$</td></tr><tr><td>$k_a$</td><td>k_a</td><td>Thermal conductivity of dry air.</td><td></td><td>-</td><td>J K$^{-1}$ m$^{-1}$ s$^{-1}$</td></tr><tr><td>$M_w$</td><td>M_w</td><td>Molar mass of water.</td><td></td><td>0.018</td><td>kg mol$^{-1}$</td></tr><tr><td>$M_{air}$</td><td>M_air</td><td>Molar mass of air.\n",
       "\n",
       "    http://www.engineeringtoolbox.com/molecular-mass-air-d_679.html\n",
       "    </td><td></td><td>0.02897</td><td>kg mol$^{-1}$</td></tr><tr><td>$M_{N_2}$</td><td>M_N2</td><td>Molar mass of nitrogen.</td><td></td><td>0.028</td><td>kg mol$^{-1}$</td></tr><tr><td>$M_{O_2}$</td><td>M_O2</td><td>Molar mass of oxygen.</td><td></td><td>0.032</td><td>kg mol$^{-1}$</td></tr><tr><td>$N_{Gr_L}$</td><td>Gr</td><td>Grashof number.</td><td></td><td>-</td><td>1</td></tr><tr><td>$N_{Le}$</td><td>Le</td><td>Lewis number.</td><td></td><td>-</td><td>1</td></tr><tr><td>$N_{Nu_L}$</td><td>Nu</td><td>Average Nusselt number over given length.</td><td></td><td>-</td><td>1</td></tr><tr><td>$N_{Pr}$</td><td>Pr</td><td>Prandtl number (0.71 for air).</td><td></td><td>-</td><td>1</td></tr><tr><td>$N_{Re_c}$</td><td>Re_c</td><td>Critical Reynolds number for the onset of turbulence.</td><td></td><td>-</td><td>1</td></tr><tr><td>$N_{Re_L}$</td><td>Re</td><td>Average Reynolds number over given length.</td><td></td><td>-</td><td>1</td></tr><tr><td>$P_a$</td><td>P_a</td><td>Air pressure.</td><td></td><td>-</td><td>Pa</td></tr><tr><td>$P_{N2}$</td><td>P_N2</td><td>Partial pressure of nitrogen.</td><td></td><td>-</td><td>Pa</td></tr><tr><td>$P_{O2}$</td><td>P_O2</td><td>Partial pressure of oxygen.</td><td></td><td>-</td><td>Pa</td></tr><tr><td>$P_{was}$</td><td>P_was</td><td>Saturation water vapour pressure at air temperature.</td><td></td><td>-</td><td>Pa</td></tr><tr><td>$P_{wa}$</td><td>P_wa</td><td>Water vapour pressure in the atmosphere.</td><td></td><td>-</td><td>Pa</td></tr><tr><td>$R_d$</td><td>R_d</td><td>Downwelling global radiation.</td><td></td><td>-</td><td>W m$^{-2}$</td></tr><tr><td>$R_s$</td><td>R_s</td><td>Solar shortwave flux per area.</td><td></td><td>-</td><td>J s$^{-1}$ m$^{-2}$</td></tr><tr><td>$R_u$</td><td>R_u</td><td>Upwelling global radiation.</td><td></td><td>-</td><td>W m$^{-2}$</td></tr><tr><td>$R_{mol}$</td><td>R_mol</td><td>Molar gas constant.</td><td></td><td>8.314472</td><td>J K$^{-1}$ mol$^{-1}$</td></tr><tr><td>$T_0$</td><td>T0</td><td>Freezing point in Kelvin.</td><td></td><td>273.15</td><td>K</td></tr><tr><td>$T_a$</td><td>T_a</td><td>Air temperature.</td><td></td><td>-</td><td>K</td></tr><tr><td>$v_w$</td><td>v_w</td><td>Wind velocity.</td><td></td><td>-</td><td>m s$^{-1}$</td></tr><tr><td>$x_{N2}$</td><td>x_N2</td><td>Mole fraction of nitrogen in dry air.</td><td></td><td>0.79</td><td>1</td></tr><tr><td>$x_{O2}$</td><td>x_O2</td><td>Mole fraction of oxygen in dry air.</td><td></td><td>0.21</td><td>1</td></tr></table>"
      ],
      "text/plain": [
       "[('Symbol', 'Name', 'Description', 'Definition', 'Default value', 'Units'),\n",
       " ('$\\\\alpha_a$',\n",
       "  'alpha_a',\n",
       "  'Thermal diffusivity of dry air.',\n",
       "  '',\n",
       "  '-',\n",
       "  'm$^{2}$ s$^{-1}$'),\n",
       " ('$\\\\lambda_E$',\n",
       "  'lambda_E',\n",
       "  'Latent heat of evaporation.',\n",
       "  '',\n",
       "  '2450000.0',\n",
       "  'J kg$^{-1}$'),\n",
       " ('$\\\\nu_a$',\n",
       "  'nu_a',\n",
       "  'Kinematic viscosity of dry air.',\n",
       "  '',\n",
       "  '-',\n",
       "  'm$^{2}$ s$^{-1}$'),\n",
       " ('$\\\\rho_a$', 'rho_a', 'Density of dry air.', '', '-', 'kg m$^{-3}$'),\n",
       " ('$\\\\sigma$',\n",
       "  'sigm',\n",
       "  'Stefan-Boltzmann constant.',\n",
       "  '',\n",
       "  '5.67e-08',\n",
       "  'J s$^{-1}$ m$^{-2}$ K$^{-4}$'),\n",
       " ('$c_{pa,mol}$',\n",
       "  'c_pamol',\n",
       "  'Molar specific heat of dry air.\\n\\n    https://en.wikipedia.org/wiki/Heat_capacity#Specific_heat_capacity\\n    ',\n",
       "  '',\n",
       "  '29.19',\n",
       "  'J K$^{-1}$ mol$^{-1}$'),\n",
       " ('$c_{pa}$',\n",
       "  'c_pa',\n",
       "  'Specific heat of dry air.',\n",
       "  '',\n",
       "  '1010.0',\n",
       "  'J K$^{-1}$ kg$^{-1}$'),\n",
       " ('$c_{pv}$',\n",
       "  'c_pv',\n",
       "  'Specific heat of water vapour at 300 K.\\n\\n    http://www.engineeringtoolbox.com/water-vapor-d_979.html\\n    ',\n",
       "  '',\n",
       "  '1864',\n",
       "  'J K$^{-1}$ kg$^{-1}$'),\n",
       " ('$C_{wa}$',\n",
       "  'C_wa',\n",
       "  'Concentration of water in air.',\n",
       "  '',\n",
       "  '-',\n",
       "  'mol m$^{-3}$'),\n",
       " ('$D_{va}$',\n",
       "  'D_va',\n",
       "  'Binary diffusion coefficient of water vapour in air.',\n",
       "  '',\n",
       "  '-',\n",
       "  'm$^{2}$ s$^{-1}$'),\n",
       " ('$g$', 'g', 'Gravitational acceleration.', '', '9.81', 'm s$^{-2}$'),\n",
       " ('$h_c$',\n",
       "  'h_c',\n",
       "  'Average 1-sided convective heat transfer coefficient.',\n",
       "  '',\n",
       "  '-',\n",
       "  'J K$^{-1}$ s$^{-1}$ m$^{-2}$'),\n",
       " ('$k_a$',\n",
       "  'k_a',\n",
       "  'Thermal conductivity of dry air.',\n",
       "  '',\n",
       "  '-',\n",
       "  'J K$^{-1}$ m$^{-1}$ s$^{-1}$'),\n",
       " ('$M_w$', 'M_w', 'Molar mass of water.', '', '0.018', 'kg mol$^{-1}$'),\n",
       " ('$M_{air}$',\n",
       "  'M_air',\n",
       "  'Molar mass of air.\\n\\n    http://www.engineeringtoolbox.com/molecular-mass-air-d_679.html\\n    ',\n",
       "  '',\n",
       "  '0.02897',\n",
       "  'kg mol$^{-1}$'),\n",
       " ('$M_{N_2}$',\n",
       "  'M_N2',\n",
       "  'Molar mass of nitrogen.',\n",
       "  '',\n",
       "  '0.028',\n",
       "  'kg mol$^{-1}$'),\n",
       " ('$M_{O_2}$', 'M_O2', 'Molar mass of oxygen.', '', '0.032', 'kg mol$^{-1}$'),\n",
       " ('$N_{Gr_L}$', 'Gr', 'Grashof number.', '', '-', '1'),\n",
       " ('$N_{Le}$', 'Le', 'Lewis number.', '', '-', '1'),\n",
       " ('$N_{Nu_L}$',\n",
       "  'Nu',\n",
       "  'Average Nusselt number over given length.',\n",
       "  '',\n",
       "  '-',\n",
       "  '1'),\n",
       " ('$N_{Pr}$', 'Pr', 'Prandtl number (0.71 for air).', '', '-', '1'),\n",
       " ('$N_{Re_c}$',\n",
       "  'Re_c',\n",
       "  'Critical Reynolds number for the onset of turbulence.',\n",
       "  '',\n",
       "  '-',\n",
       "  '1'),\n",
       " ('$N_{Re_L}$',\n",
       "  'Re',\n",
       "  'Average Reynolds number over given length.',\n",
       "  '',\n",
       "  '-',\n",
       "  '1'),\n",
       " ('$P_a$', 'P_a', 'Air pressure.', '', '-', 'Pa'),\n",
       " ('$P_{N2}$', 'P_N2', 'Partial pressure of nitrogen.', '', '-', 'Pa'),\n",
       " ('$P_{O2}$', 'P_O2', 'Partial pressure of oxygen.', '', '-', 'Pa'),\n",
       " ('$P_{was}$',\n",
       "  'P_was',\n",
       "  'Saturation water vapour pressure at air temperature.',\n",
       "  '',\n",
       "  '-',\n",
       "  'Pa'),\n",
       " ('$P_{wa}$',\n",
       "  'P_wa',\n",
       "  'Water vapour pressure in the atmosphere.',\n",
       "  '',\n",
       "  '-',\n",
       "  'Pa'),\n",
       " ('$R_d$', 'R_d', 'Downwelling global radiation.', '', '-', 'W m$^{-2}$'),\n",
       " ('$R_s$',\n",
       "  'R_s',\n",
       "  'Solar shortwave flux per area.',\n",
       "  '',\n",
       "  '-',\n",
       "  'J s$^{-1}$ m$^{-2}$'),\n",
       " ('$R_u$', 'R_u', 'Upwelling global radiation.', '', '-', 'W m$^{-2}$'),\n",
       " ('$R_{mol}$',\n",
       "  'R_mol',\n",
       "  'Molar gas constant.',\n",
       "  '',\n",
       "  '8.314472',\n",
       "  'J K$^{-1}$ mol$^{-1}$'),\n",
       " ('$T_0$', 'T0', 'Freezing point in Kelvin.', '', '273.15', 'K'),\n",
       " ('$T_a$', 'T_a', 'Air temperature.', '', '-', 'K'),\n",
       " ('$v_w$', 'v_w', 'Wind velocity.', '', '-', 'm s$^{-1}$'),\n",
       " ('$x_{N2}$',\n",
       "  'x_N2',\n",
       "  'Mole fraction of nitrogen in dry air.',\n",
       "  '',\n",
       "  '0.79',\n",
       "  '1'),\n",
       " ('$x_{O2}$', 'x_O2', 'Mole fraction of oxygen in dry air.', '', '0.21', '1')]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vars = ['physics_vars.' + name for name in physics_vars.__all__]\n",
    "generate_metadata_table([eval(name) for name in vars])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('eq_Le',\n",
       " 'eq_Cwa',\n",
       " 'eq_Nu_forced_all',\n",
       " 'eq_Dva',\n",
       " 'eq_alphaa',\n",
       " 'eq_ka',\n",
       " 'eq_nua',\n",
       " 'eq_rhoa_Pwa_Ta',\n",
       " 'eq_Pa',\n",
       " 'eq_PN2_PO2',\n",
       " 'eq_PO2',\n",
       " 'eq_PN2',\n",
       " 'eq_rhoa')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "physics_eqs.__all__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_Le'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle N_{Le} = \\frac{\\alpha_a}{D_{va}}$"
      ],
      "text/plain": [
       "      αₐ\n",
       "Le = ───\n",
       "     Dᵥₐ"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_Cwa'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle C_{wa} = \\frac{P_{wa}}{R_{mol} T_a}$"
      ],
      "text/plain": [
       "         P_wa \n",
       "C_wa = ───────\n",
       "       Rₘₒₗ⋅Tₐ"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_Nu_forced_all'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle N_{Nu_L} = - \\frac{\\sqrt[3]{N_{Pr}} \\left(- 37 N_{Re_L}^{\\frac{4}{5}} + 37 \\left(N_{Re_L} + N_{Re_c} - \\frac{\\left|{N_{Re_L} - N_{Re_c}}\\right|}{2}\\right)^{\\frac{4}{5}} - 664 \\sqrt{N_{Re_L} + N_{Re_c} - \\frac{\\left|{N_{Re_L} - N_{Re_c}}\\right|}{2}}\\right)}{1000}$"
      ],
      "text/plain": [
       "            ⎛                                         4/5           __________\n",
       "     3 ____ ⎜       4/5      ⎛            │Re - Re_c│⎞             ╱          \n",
       "    -╲╱ Pr ⋅⎜- 37⋅Re    + 37⋅⎜Re + Re_c - ───────────⎟    - 664⋅  ╱  Re + Re_c\n",
       "            ⎝                ⎝                 2     ⎠          ╲╱            \n",
       "Ν = ──────────────────────────────────────────────────────────────────────────\n",
       "                                                1000                          \n",
       "\n",
       "_______________⎞ \n",
       "   │Re - Re_c│ ⎟ \n",
       " - ─────────── ⎟ \n",
       "        2      ⎠ \n",
       "─────────────────\n",
       "                 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_Dva'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle D_{va} = T_a p_1 - p_2$"
      ],
      "text/plain": [
       "Dᵥₐ = Tₐ⋅p_Dva1 - p_Dva2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_alphaa'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\alpha_a = T_a p_1 - p_2$"
      ],
      "text/plain": [
       "αₐ = Tₐ⋅pₐₗₚₕₐ₁ - pₐₗₚₕₐ₂"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_ka'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIUAAAASCAYAAAB1uR3HAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAERElEQVRoBe2a7U0cQQyGF0QBKOkAOoBQQUIHIakA6ACUf/xDSQfQQQIdhFTARwfQQQgdkOcZxqu5Y+9u9zjuQ8LS3Hg+97XH9ngXlh4fH6ujo6PVqqrOKB8o97TXqReGMv7rDPiO+iHzGw19a/Qp7wnrfuTxt6rQwIo8ylGJ29Qq9sq+BaM98N5QdrMsCT78PxiNfDt15B/aOkAYTjn0xqOBZBSFJvSs46K9KOwWB71TgqUdEeFX2Z/5n9RzaxRg/wS+NerTBuyv3rUcT8hAbF5E3yLU+fB/N2BVsVLTmAYzzxHR680yE6qNgqcbYh9Q8tx60AANDfKouDKajPxmAeUcIP7ku8vrQ8+qFYjSPtPeomixh/OqRHDVmMFZkvLcNeEesqZcXzHP69R91MMuxQhj+33me3IY+mZOk8C8ohRs5MGrgJPc1iAk2yaflhffbzzH/VRqF9Kre/KFUYuZ7+EpU1M+MWp5Of6VvXQIE9M/lGP49MZC/Z22/RGRYOeCXow5GQWixEFdIGziqc8pGoqveIO8sZMW2G+/04LxJ4c8TflEq12z7Jd5skZm1DkvFt/CHxTtmbOTwhxGkfIJpFKZV2yejIDa17zNmUvbHUB470uMWSNQfqnprcxIVDFnlWIuZvsLZR++lc6YNyhyvst7NznRsMjZGrP7Q9+eqnQtyqbrMIxCYzAiKMymYCmhELoWjpI8yPAwLvJYS+1eUr+BJUdyHkWjiXnJWNKKET+sazr0in6vbxPoTh/XmJ/kpQ4swzB7xvXz4SNVWF+hoRCGxx14rww3vKbWOCZqGOw3yDN45EAa5hnPFvGMSeUTsbeH35SwqqeUZ2U9iTNysVg7q3okZoDtgfeMEoZjjmTfxgqMIU+KwXh/V7kKekCpLRZeIzLseKfKm4lrdUaaocSc2jKHTnzZYHjJ0HyigxzuF7pJyFjrF1S98jB1zN9PG8yeRZx1jwTLtLQqD18hS4pD9tATZUX6JqIR6CUqa66SLfCE4fUcJP01tZUjz/Nq0EES0SevMXyE79fZ06QZ/rbFzLzTPvzqLeUkRgq9/TjkcCJFoU2YjAb1GLwhxjeUMBia6YNX2bZvqgQecXlYyuIhSoZGD+2Suo50aaS9HBF1fC0N49dJ/DvRTGXOcjRVnTEjizrz6jOnrMwpjBQ9RF+/EmPcq6b8ZvAsTMXEadbg7RrG28oRUdTcaqL51SvqpxNmdKcz6VTmkCnyGSlaEQv0QkvpIQLQI+2vYlP5eaWOcmj05beJaYnl4VjGodaY0UW6CqlTYMjtarntU1nQA5R2vIZpJHreQlBbOZinoau0+IA1Nfl4tld05y/IXTAzV9l8GzQ/3LDAG3Hvl/wnm7bEQq3Q68Nk857ixt6xt4x1FoJ1M6FRcjDu/eoblory2ojEGvY5MV89mKipH9d4/f6lf9A1zPBkaQzM/q+Jht9D7LP0H8KA8QtgCaTqAAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle k_a = T_a p_1 + p_2$"
      ],
      "text/plain": [
       "kₐ = Tₐ⋅pₖₐ₁ + pₖₐ₂"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_nua'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\nu_a = T_a p_1 - p_2$"
      ],
      "text/plain": [
       "νₐ = Tₐ⋅pₙᵤₐ₁ - pₙᵤₐ₂"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_rhoa_Pwa_Ta'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\rho_a = \\frac{M_{N_2} P_{N2} + M_{O_2} P_{O2} + M_w P_{wa}}{R_{mol} T_a}$"
      ],
      "text/plain": [
       "     M_N2⋅P_N2 + M_O2⋅P_O2 + M_w⋅P_wa\n",
       "ρₐ = ────────────────────────────────\n",
       "                 Rₘₒₗ⋅Tₐ             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_Pa'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAARCAYAAACo5fJYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAFG0lEQVRoBeWb7XEUORCG1y4H4IIIDjIALgPIALgIgAxw3T//u4IMIANjZwBEwEcGcBEAzsD3PIN6SrMzWq8W5mZnt6vakrpbmn4ltT5m1gdXV1eLnE5PT59TfgDfT/J3pJcpf0x6A/4In2Ab8qTermSXsNT27D5inxLzwXIgxYDhlBH2mfRuyCJF9pb8PfgP8lsdTPqMjzuDRTw1tI/Yp8B8ODQoOHInyc+G9Mhewe5OTwv6rRHPDQv+3od/S7/OBfsuYB4MJKIgP9YNBcWtJLw5pNwy2dywuEDJv4Pmgn32mEuB5B1pwUrxuTCajR5daccqVJtEvEtYajtwH7FPgrkUSK5kvmToUTouqPdlQynQevUmFOwSltpu3Efsk2A+Wh6ZFCiKfaHQEnKPc8/gh/AjyhetcoMM9b1nCbqGfPnxaN0K2MZdb1Qs6/rzf9rtI/YpMfcCicGOyf0njr3IBv8L+bfITjLZxlnaMSjHpios+KS9+EyfUX4dDiZd9McZ5ZfqSD3f/53s4u74BPllkk2VVGEPJ/Hbzx+3YcdbMv8C+demxB/yO4U5cP1KejRQOc6Ya6/8A21si6gKCxPkHewuZhAYNHkgqfNOeEHaTirtKLeLAnl32k+wE7BIyS4me27nd7pF3mamrNmRa7Hri5g9bbT4yLs4fCK9m8l3AnPWr7+cHQokO3QOd591wG+CxQB4Av9g4jyF22BCdjObTPF8bc7huFM6GZXdgYv9iK4NvmjIFLlH51ukzY6X6yrza2NPzzQ4esGP7Cv8hme7QDTBSTp7zJV9ea15J5DosLhTxKRY2QD2scV7DDDv6/BXdv7KiiixGfWORPtVWDJ/L6krG0Ae8/JAyszarAHhLz22hmqwY+uOcw5HkAzhcHzzb1tzx+wi4/zw+tKcvEidv81Om/L/Us534UWSe4zvzfdOIGHgA6TO5fynqPs3NeoR5gF5Vy0ds2yAXEvYD67I11Zc32BtLNFkwvAhlQ0id6WHsMc58YUuqiyQLweauOyP4m7UVh4vU4PdHVR/Vy2eLpAedxuaM2Z8N2A8LbyEryzDYnsMN3dcy7CbgeVmU9COfHG+H6LM6S8LVFrVqWHvAHhvyHefcCBspkxrsISfTsAGO7jsXINEnFKr+1ns/6WOwebRrPezqr71qJIa7NfiSpgG58QMMd8Az2v8dpxcQBxnyR0530DOKOdze+V8P7IFGnMXMfqcCJZt0Dd0q87pRnD+QmKdAbH5UWlDLOHTbepHxyqz87wPiM37Ua5T3xI6+097jwNFu7bCCBmeu8k46knRX9oUu9jysbbOAt3sMONz7DAuNvknHHF2TlNhK1Zo5Xw/0oIKVccs7I+pJucRa0R76VZum8XBUT8W8dwqLEt+dHymLVcsO7tZjZZs2yI2Tig/UDf3jFRekOb909qPleF5m2D3fqf/PaI9x9L7k58COkdVynPGLFY3jSZwEk6PePmu286F0GOfj2dnvh/aYi3RsA/JH6RTRrQPMnJnR2ASQ+8OhOwELukW1HNCOSC+ZPHsra11vsObUKdvN2mgso7B5z1Qv1tK5fcI/CbWuQdSnjtmcdrPMUb3FASBzxcrbVBR7owJZfuqM9+L/0YRjZZSGrMht3svYDpk53op/YKu0/HItprw9zkOOqFcCHo/fULvqjz4kRXdD3THcIeQH3QEW1zAV8fOXVf832Bfgzt5/kFn2qEdwez8dcxdPAOjuH0j13v5AuaV8/0/0mLMigAGKNEAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle P_a = P_{N2} + P_{O2} + P_{wa}$"
      ],
      "text/plain": [
       "Pₐ = P_N2 + P_O2 + P_wa"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_PN2_PO2'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{N2} = \\frac{P_{O2} x_{N2}}{x_{O2}}$"
      ],
      "text/plain": [
       "       P_O2⋅x_N2\n",
       "P_N2 = ─────────\n",
       "          x_O2  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_PO2'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{O2} = \\frac{P_a x_{O2} - P_{wa} x_{O2}}{x_{N2} + x_{O2}}$"
      ],
      "text/plain": [
       "       Pₐ⋅x_O2 - P_wa⋅x_O2\n",
       "P_O2 = ───────────────────\n",
       "           x_N2 + x_O2    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_PN2'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{N2} = \\frac{P_a x_{N2} - P_{wa} x_{N2}}{x_{N2} + x_{O2}}$"
      ],
      "text/plain": [
       "       Pₐ⋅x_N2 - P_wa⋅x_N2\n",
       "P_N2 = ───────────────────\n",
       "           x_N2 + x_O2    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'physics_eqs.eq_rhoa'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\rho_a = \\frac{x_{N2} \\left(M_{N_2} P_a - P_{wa} \\left(M_{N_2} - M_w\\right)\\right) + x_{O2} \\left(M_{O_2} P_a - P_{wa} \\left(M_{O_2} - M_w\\right)\\right)}{R_{mol} T_a x_{N2} + R_{mol} T_a x_{O2}}$"
      ],
      "text/plain": [
       "     x_N2⋅(M_N2⋅Pₐ - P_wa⋅(M_N2 - M_w)) + x_O2⋅(M_O2⋅Pₐ - P_wa⋅(M_O2 - M_w))\n",
       "ρₐ = ───────────────────────────────────────────────────────────────────────\n",
       "                           Rₘₒₗ⋅Tₐ⋅x_N2 + Rₘₒₗ⋅Tₐ⋅x_O2                      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eqs = ['physics_eqs.' + name for name in physics_eqs.__all__]\n",
    "for name in eqs:\n",
    "    display(name, eval(name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing all available variable definitions and equations from essm\n",
    "from essm.variables.leaf import *\n",
    "from essm.variables.physics.thermodynamics import *\n",
    "from essm.equations.leaf import * \n",
    "from essm.equations.physics.thermodynamics import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unit conversions\n",
    "Values for variables are often given in obscure units, but to convert to our standard units, we can use the dictionary `SI_EXTENDED_DIMENSIONS`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import units from sympy and tools from essm\n",
    "from sympy.physics.units import bar, convert_to, joule, kelvin, kilo, kilogram, mega, meter, mole, pascal, second, inch, hour\n",
    "from essm.variables.units import derive_base_dimension, derive_baseunit, derive_unit, Quantity, SI_EXTENDED_DIMENSIONS, SI_EXTENDED_UNITS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{\\text{mol}}{\\text{m}^{3}}$"
      ],
      "text/plain": [
       "mol\n",
       "───\n",
       "  3\n",
       " m "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derive_baseunit(eq_Cwa.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3*inch/hour\n",
      "2.11666666666667e-6*m/s\n"
     ]
    }
   ],
   "source": [
    "value1 = 0.3\n",
    "unit1 = inch/hour\n",
    "print(value1*unit1)\n",
    "unit2 = Variable.get_dimensional_expr(unit1).subs(SI_EXTENDED_DIMENSIONS)\n",
    "print(convert_to(value1*unit1, unit2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we work with custom units and want to convert calculated expression to different units, we need to make sure that each value substituted for a variable is a product of the value and compatible units:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_unit(expr):\n",
    "    \"\"\"Return unit of expression\"\"\"\n",
    "    return expr.subs({x: 1 for x in expr.args if not x.has(Quantity)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "inch/s**2\n",
      "m/s**2\n"
     ]
    }
   ],
   "source": [
    "val = 3*inch/second**2\n",
    "target_unit = meter / second ** 2\n",
    "print(get_unit(val))\n",
    "val_targetunit = convert_to(val, target_unit)\n",
    "print(get_unit(val_targetunit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R_mol*T_a has no defined units. Trying to deduce units from its base SI units or assuming it is dimensionless.\n",
      "Conversion error for C_wa: Target unit was: mol/m**3, but final unit was: mol**(1/10)/(kg**3*m**(3/10)) Please verify units in original vdict. Aborting.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{T_a: None,\n",
       " R_mol*T_a: 1800.0*kg*m**2/(mol*s**2),\n",
       " C_wa: 0.01*mol/kg**3,\n",
       " P_wa: 3000.0}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def fun_dict_standardunits(vdict):\n",
    "    \"\"\"\n",
    "    Convert vdict to dictionary consisting of \n",
    "    (key, value*standardunit) items, converting\n",
    "    units, if given, to standardunits, and adding\n",
    "    standardunits where units were not provided.\n",
    "    \n",
    "    vdict is a dictionary with symbolic expressions\n",
    "    as keys and floats or integers as values, or \n",
    "    products of floats or integers with units.\n",
    "    Returns dictionary with the same keys, but each\n",
    "    value multiplied by its units.\n",
    "    \"\"\"\n",
    "    for (key, val) in vdict.items():\n",
    "        if val:\n",
    "            if hasattr(key, 'definition'):\n",
    "                targetunit = (key.definition.unit)\n",
    "            else:\n",
    "                print(\"{0} has no defined units.\".format(key),\n",
    "                      \"Trying to deduce units from its base SI units\",\n",
    "                      \"or assuming it is dimensionless.\")\n",
    "                targetunit = derive_baseunit(key)\n",
    "            if type(val) == float or type(val) == int:\n",
    "                val1 = val*targetunit\n",
    "            else:\n",
    "                val1 = convert_to(val, targetunit)\n",
    "                convertedunit = get_unit(val1)\n",
    "                if convertedunit != targetunit:\n",
    "                    print(\"Conversion error for {0}:\".format(key),\n",
    "                          \"Target unit was: {0},\".format(targetunit),\n",
    "                          \"but final unit was: {0}\".format(convertedunit),\n",
    "                          \"Please verify units in original vdict. Aborting.\")\n",
    "                    return vdict\n",
    "            vdict[key] = val1\n",
    "    return vdict\n",
    "vdict = {}\n",
    "vdict[T_a] = None\n",
    "vdict[R_mol*T_a] = 1800.\n",
    "vdict[C_wa] = 0.01 * mole / kilogram ** 3\n",
    "vdict[P_wa] = 3000.\n",
    "fun_dict_standardunits(vdict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "vdict = Variable.__defaults__.copy()\n",
    "vdict1 = fun_dict_standardunits(vdict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{1010.0 \\text{J}}{\\text{K} \\text{kg}}$"
      ],
      "text/plain": [
       "1010.0⋅J\n",
       "────────\n",
       "  K⋅kg  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val = vdict1[c_pa]\n",
    "val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{\\text{J}}{\\text{K} \\text{kg}}$"
      ],
      "text/plain": [
       " J  \n",
       "────\n",
       "K⋅kg"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_unit(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mol/m**3\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle C_{wa} = \\frac{1.20272219330344 \\cdot 10^{-6} \\text{bar} \\text{mol}}{\\text{J}}$"
      ],
      "text/plain": [
       "       1.20272219330344e-6⋅bar⋅mol\n",
       "C_wa = ───────────────────────────\n",
       "                    J             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.120272219330344*mol/m**3\n",
      "1.97090855558838e-6*mol/inch**3\n"
     ]
    }
   ],
   "source": [
    "expr = eq_Cwa\n",
    "unit_expr = derive_baseunit(expr.rhs)\n",
    "print(unit_expr)\n",
    "vdict1[T_a] = 300*kelvin\n",
    "vdict1[P_wa] = 0.003*bar  # Using bar instead of pascal\n",
    "display(eq_Cwa.subs(vdict1))\n",
    "print(convert_to(eq_Cwa.rhs.subs(vdict), mole/meter**3))\n",
    "print(convert_to(eq_Cwa.rhs.subs(vdict), mole/inch**3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting\n",
    "A custom plotting function can be obtained from https://github.com/schymans/ESSM_plotting. To test that it behaves the same, we cloned it as a sub-repo in the folder ESSM_plotting, and will import it below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import pyplot and set standard figure size\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.dpi'] = 80 # modify size of displayed figures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function plot_expr2 in module plotting:\n",
      "\n",
      "plot_expr2(xvar_min_max, yldata, yllabel=None, yrdata=None, yrlabel='', clf=True, npoints=100, ylmin=None, ylmax=None, yrmin=None, yrmax=None, xlabel=None, xunit=None, ylunit=None, yrunit=None, colors=['black', 'red', 'blue', 'green'], loc_legend_left='best', loc_legend_right='right', linestylesl=['-', '--', '-.', ':'], linestylesr=['-', '--', '-.', ':'], fontsize=None, fontsize_ticks=None, fontsize_labels=None, fontsize_legend=None, xaxispos=None, yaxispos=None, fig1=None, legend=True, **args)\n",
      "    Plot expressions as function of xvar from xmin to xmax. \n",
      "    Expressions to be plotted are given as yldata (for left axis), or yrdata\n",
      "    (right axis), each of which can be an equation, list of equations or \n",
      "    (expr, name) tuples.\n",
      "    You can provide custom units for axes as xunit and yunit,\n",
      "    otherwise the default units of xvar and yvar will be assumed. \n",
      "    Note that if you provide custom units, you need to substitute values with\n",
      "    units into expressions before passing them to plot_expr2.\n",
      "    \n",
      "    \n",
      "    **Examples:**\n",
      "    \n",
      "    >>> from sympy import Eq\n",
      "    >>> from sympy.physics.units import bar, inch, kelvin, meter, mole\n",
      "    >>> from essm.variables import Variable\n",
      "    >>> from essm.variables.physics.thermodynamics import P_wa, T_a, nu_a\n",
      "    >>> from essm.equations.physics.thermodynamics import eq_Cwa, eq_nua, eq_ka\n",
      "    >>> vdict = Variable.__defaults__.copy()    \n",
      "    >>> expr = eq_nua.subs(vdict)\n",
      "    >>> exprr = eq_ka.subs(vdict)\n",
      "    >>> xvar = T_a\n",
      "    >>> yldata = [(expr.rhs, 'full'), (expr.rhs/2, 'half')]\n",
      "    >>> yrdata = exprr\n",
      "    >>> # Simplest plot of 1 function\n",
      "    >>> fig =  plot_expr2((T_a, 273, 373), expr)\n",
      "    >>> # When plotting 2 functions, need to define label\n",
      "    >>> fig = plot_expr2((T_a, 273, 373), yldata, yllabel = (nu_a))\n",
      "    >>> # Plot of two functions on left and one on right axis\n",
      "    >>> fig = plot_expr2((T_a, 273, 373), yldata, yllabel = (nu_a), yrdata=yrdata)\n",
      "    >>> # Same as above, but plotting the inverse on the right\n",
      "    >>> fig = plot_expr2((T_a, 273, 373), yldata, yllabel = (nu_a),\n",
      "    ...   yrdata=[Eq(1/exprr.lhs, 1/exprr.rhs)],\n",
      "    ...   loc_legend_right='lower right')\n",
      "    >>> # Using custom units\n",
      "    >>> vdict = Variable.__defaults__.copy()\n",
      "    >>> # Add units to vdict\n",
      "    >>> vdict = fun_dict_standardunits(vdict)\n",
      "    >>> vdict[T_a] = 300*kelvin\n",
      "    >>> expr = eq_Cwa.subs(vdict)\n",
      "    >>> fig = plot_expr2((P_wa, 0.01, 1), expr)\n",
      "    >>> fig = plot_expr2((P_wa, 0.01, 1), expr, ylunit= mole/inch**3)\n",
      "    >>> fig = plot_expr2((P_wa, 0.01, 1), yldata=expr, yrdata=expr,\n",
      "    ...     xunit=bar, ylunit= mole/meter**3, yrunit=mole/inch**3,\n",
      "    ...     linestylesr=['--'])\n",
      "    >>> # Modifying fig and ax attributes\n",
      "    >>> fig.set_dpi(100)\n",
      "    >>> ylim = fig.axes[0].set_ylim(ymin=0)\n",
      "    >>> fig.axes[0].grid()\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_267803/3023641493.py:1: DeprecationWarning: the imp module is deprecated in favour of importlib; see the module's documentation for alternative uses\n",
      "  import imp\n"
     ]
    }
   ],
   "source": [
    "import imp\n",
    "path_plotting = 'ESSM_plotting/plotting.py'\n",
    "\n",
    "# Importing plotting function\n",
    "mod = imp.load_source('plotting', path_plotting)\n",
    "plot_expr2 = getattr(mod, 'plot_expr2')\n",
    "help(plot_expr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    ">>> from sympy import Eq\n",
    ">>> from sympy.physics.units import bar, inch, kelvin, meter, mole\n",
    ">>> from essm.variables import Variable\n",
    ">>> from essm.variables.physics.thermodynamics import P_wa, T_a, nu_a\n",
    ">>> from essm.equations.physics.thermodynamics import eq_Cwa, eq_nua, eq_ka\n",
    ">>> vdict = Variable.__defaults__.copy()    \n",
    ">>> expr = eq_nua.subs(vdict)\n",
    ">>> exprr = eq_ka.subs(vdict)\n",
    ">>> xvar = T_a\n",
    ">>> yldata = [(expr.rhs, 'full'), (expr.rhs/2, 'half')]\n",
    ">>> yrdata = exprr\n",
    ">>> # Simplest plot of 1 function\n",
    ">>> fig =  plot_expr2((T_a, 273, 373), expr)\n",
    ">>> # When plotting 2 functions, need to define label\n",
    ">>> fig = plot_expr2((T_a, 273, 373), yldata, yllabel = (nu_a))\n",
    ">>> # Plot of two functions on left and one on right axis\n",
    ">>> fig = plot_expr2((T_a, 273, 373), yldata, yllabel = (nu_a), yrdata=yrdata)\n",
    ">>> # Same as above, but plotting the inverse on the right\n",
    ">>> fig = plot_expr2((T_a, 273, 373), yldata, yllabel = (nu_a),\n",
    "...   yrdata=[Eq(1/exprr.lhs, 1/exprr.rhs)],\n",
    "...   loc_legend_right='lower right')\n",
    ">>> # Using custom units\n",
    ">>> vdict = Variable.__defaults__.copy()\n",
    ">>> # Add units to vdict\n",
    ">>> vdict = fun_dict_standardunits(vdict)\n",
    ">>> vdict[T_a] = 300*kelvin\n",
    ">>> expr = eq_Cwa.subs(vdict)\n",
    ">>> fig = plot_expr2((P_wa, 0.01, 1), expr)\n",
    ">>> fig = plot_expr2((P_wa, 0.01, 1), expr, ylunit= mole/inch**3)\n",
    ">>> fig = plot_expr2((P_wa, 0.01, 1), yldata=expr, yrdata=expr,\n",
    "...     xunit=bar, ylunit= mole/meter**3, yrunit=mole/inch**3,\n",
    "...     linestylesr=['--'])\n",
    ">>> # Modifying fig and ax attributes\n",
    ">>> fig.set_dpi(100)\n",
    ">>> ylim = fig.axes[0].set_ylim(ymin=0)\n",
    ">>> fig.axes[0].grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Manipulate figure\n",
    "fig = plot_expr2((T_a, 273, 373), yldata, yllabel = (nu_a))\n",
    "%matplotlib inline\n",
    "fig.set_figwidth(8)\n",
    "fig.set_dpi(50)\n",
    "fig.axes[0].set_ylim(ymin=0)\n",
    "fig.axes[0].grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x240 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add scatter plot to line plot\n",
    "fig.axes[0].plot([285, 303, 321, 365], [0.6e-5, 0.9e-5, 0.8e-5, 1.1e-5], 'r.', label='data')\n",
    "fig.axes[0].legend()\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Creating new variables\n",
    "To create custom variables, first import `Variable`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from essm.variables import Variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To define units, you can either import these units from the library,\n",
    "e.g.\n",
    "\n",
    "`from essm.variables.units import joule, kelvin, meter`\n",
    "\n",
    "or import the appropriate units from sympy, e.g.\n",
    "\n",
    "`from sympy.physics.units import joule, kelvin, meter`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.physics.units import joule, kelvin, meter, mole, pascal, second"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then you can define a custom variable with its name, description, domain,\n",
    "latex_name, unit, and an optional default value, e.g.:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stan/miniforge3/envs/essm_py38/lib/python3.8/site-packages/essm/variables/_core.py:89: UserWarning: \"essm.variables.physics.thermodynamics:R_mol\" will be overridden by \"__main__:<class '__main__.R_mol'>\"\n",
      "  instance[expr] = instance\n"
     ]
    }
   ],
   "source": [
    "class R_mol(Variable):\n",
    "    \"\"\"Molar gas constant.\"\"\"\n",
    "    unit = joule/(kelvin*mole)\n",
    "    latex_name = 'R_{mol}'\n",
    "    default = 8.314472"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variables defined above hold information about their docstring, units, latex representations and default values if any. Each can be accessed by e.g.:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Molar gas constant.\n",
      "J/(K*mol)\n",
      "R_{mol}\n",
      "8.314472\n"
     ]
    }
   ],
   "source": [
    "print(R_mol.__doc__)\n",
    "print(R_mol.definition.unit)\n",
    "print(R_mol.definition.latex_name)\n",
    "print(R_mol.definition.default)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now define a few additional variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stan/miniforge3/envs/essm_py38/lib/python3.8/site-packages/essm/variables/_core.py:89: UserWarning: \"essm.variables.physics.thermodynamics:P_wa\" will be overridden by \"__main__:<class '__main__.P_wa'>\"\n",
      "  instance[expr] = instance\n"
     ]
    }
   ],
   "source": [
    "class P_g(Variable):\n",
    "    \"\"\"Pressure of gas.\"\"\"\n",
    "    unit = pascal\n",
    "\n",
    "class V_g(Variable):\n",
    "    \"\"\"Volume of gas.\"\"\"\n",
    "    unit = meter**3\n",
    "    \n",
    "class n_g(Variable):\n",
    "    \"\"\"Amount of gas.\"\"\"\n",
    "    unit = mole\n",
    "    \n",
    "class n_w(Variable):\n",
    "    \"\"\"Amount of water.\"\"\"\n",
    "    unit = mole\n",
    "\n",
    "class T_g(Variable):\n",
    "    \"\"\"Temperature of gas.\"\"\"\n",
    "    unit = kelvin\n",
    "    \n",
    "class P_wa(Variable):\n",
    "    \"\"\"Partial pressure of water vapour in air.\"\"\"\n",
    "    unit = pascal\n",
    "    latex_name = 'P_{wa}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variables with expressions as definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Delta_Pwa(Variable):\n",
    "    \"\"\"Slope of saturated vapour pressure, $\\partial P_{wa} / \\partial T_g$\"\"\"\n",
    "    expr = Derivative(P_wa,T_g)\n",
    "    latex_name = r'\\Delta'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{\\text{Pa}}{\\text{K}}$"
      ],
      "text/plain": [
       "Pa\n",
       "──\n",
       "K "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Delta_Pwa.definition.unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d T_g} P_{wa}$"
      ],
      "text/plain": [
       " d        \n",
       "────(P_wa)\n",
       "dT_g      "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Delta_Pwa.definition.expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>Symbol</td><td>Name</td><td>Description</td><td>Definition</td><td>Default value</td><td>Units</td></tr><tr><td>$\\Delta$</td><td>Delta_Pwa</td><td>Slope of saturated vapour pressure, $\\partial P_{wa} / \\partial T_g$</td><td>$\\frac{d}{d T_g} P_{wa}$</td><td>-</td><td>Pa K$^{-1}$</td></tr></table>"
      ],
      "text/plain": [
       "[('Symbol', 'Name', 'Description', 'Definition', 'Default value', 'Units'),\n",
       " ('$\\\\Delta$',\n",
       "  'Delta_Pwa',\n",
       "  'Slope of saturated vapour pressure, $\\\\partial P_{wa} / \\\\partial T_g$',\n",
       "  '$\\\\frac{d}{d T_g} P_{wa}$',\n",
       "  '-',\n",
       "  'Pa K$^{-1}$')]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "generate_metadata_table([Delta_Pwa])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linking assumptions to variables\n",
    "We can specify if a given variable is a complex, real, integer etc. by using the `assumptions` property during variable definition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1, 1]\n"
     ]
    }
   ],
   "source": [
    "class x(Variable):\n",
    "     \"\"\"Any variable.\"\"\"  \n",
    "\n",
    "print(solve(x**2 - 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]\n"
     ]
    }
   ],
   "source": [
    "class x(Variable):\n",
    "     \"\"\"Positive real variable.\"\"\"  \n",
    "     assumptions = {'positive': True, 'real': True}\n",
    "\n",
    "print(solve(x**2 - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating new equations\n",
    "Equations have a left hand side and a right hand side and if they contain variables with units, the units of each addend must be the same.\n",
    "\n",
    "## Custom equation\n",
    "To create custom equations, first import `Equation`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from essm.equations import Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now define an equation representing the ideal gas law, based on the variables defined above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "class eq_ideal_gas_law(Equation):\n",
    "    \"\"\"Ideal gas law.\"\"\"\n",
    "    \n",
    "    expr = Eq(P_g*V_g, n_g*R_mol*T_g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that whenever an equation is defined, its units are checked for consistency in the background and if they are not consistent, an error message will be printed. To illustrate this, we will try to define the above equation again, but omit temperature on the right hand side:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension of \"R_mol*n_g\" is Dimension(length**2*mass/(temperature*time**2)), but it should be the same as P_g*V_g, i.e. Dimension(length**2*mass/time**2)\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    class eq_ideal_gas_law(Equation):\n",
    "        \"\"\"Ideal gas law.\"\"\"\n",
    "\n",
    "        expr = Eq(P_g*V_g, n_g*R_mol)\n",
    "except Exception as exc1:\n",
    "    print(exc1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation can be displayed in typesetted form, and the documentation string can be accessed in a similar way as for Variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_g V_g = R_{mol} T_g n_g$"
      ],
      "text/plain": [
       "P_g⋅V_g = Rₘₒₗ⋅T_g⋅n_g"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ideal gas law.\n"
     ]
    }
   ],
   "source": [
    "display(eq_ideal_gas_law)\n",
    "print(eq_ideal_gas_law.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## New equation based on manipulation of previous equations\n",
    "We can use the above equation just as any Sympy expression, and e.g. solve it for pressure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{P_g: R_mol*T_g*n_g/V_g}]\n"
     ]
    }
   ],
   "source": [
    "soln = solve(eq_ideal_gas_law, P_g, dict=True); print(soln)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to define a new equation based on a manipulation of eq_ideal_gas_law we can specify that the parent of the new equation is `eq_ideal_gas_law.definition`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_g = \\frac{R_{mol} T_g n_g}{V_g}$"
      ],
      "text/plain": [
       "      Rₘₒₗ⋅T_g⋅n_g\n",
       "P_g = ────────────\n",
       "          V_g     "
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class eq_Pg(eq_ideal_gas_law.definition):\n",
    "    \"\"\"Calculate pressure of ideal gas.\"\"\"\n",
    "    \n",
    "    expr = Eq(P_g, soln[0][P_g])\n",
    "eq_Pg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also have nested inheritance, if we now define another equation based on eq_Pg:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{wa} = \\frac{R_{mol} T_g n_w}{V_g}$"
      ],
      "text/plain": [
       "       Rₘₒₗ⋅T_g⋅n_w\n",
       "P_wa = ────────────\n",
       "           V_g     "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class eq_Pwa_nw(eq_Pg.definition):\n",
    "    \"\"\"Calculate vapour pressure from amount of water in gas.\"\"\"\n",
    "    \n",
    "    expr = Eq(P_wa, eq_Pg.rhs.subs(n_g, n_w))\n",
    "eq_Pwa_nw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show inheritance of equations\n",
    "To see the inheritance of the newly created equation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(__main__.eq_Pg,)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_Pwa_nw.definition.__bases__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['eq_Pg']"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[parent.name for parent in eq_Pwa_nw.definition.__bases__]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ P_g = \\frac{R_{mol} T_g n_g}{V_g}\\right]$"
      ],
      "text/plain": [
       "⎡      Rₘₒₗ⋅T_g⋅n_g⎤\n",
       "⎢P_g = ────────────⎥\n",
       "⎣          V_g     ⎦"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[parent.expr for parent in eq_Pwa_nw.definition.__bases__]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also write a function to get all parents recursively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'eq_Pg', 'eq_ideal_gas_law'}"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_parents(equation, allparents=set()):\n",
    "    \"\"\"Return set of recursive parents of equation.\"\"\"\n",
    "    \n",
    "    parents = equation.definition.__bases__\n",
    "    for parent in parents:\n",
    "        if hasattr(parent, 'name'):\n",
    "            allparents.update([parent.name])\n",
    "            get_parents(eval(parent.name))\n",
    "    return allparents\n",
    "get_parents(eq_Pwa_nw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computational burden of deriving equations within class definition\n",
    "If we solve for a variable to derive a new equation, is the solve() command performed every time this equation is used?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{P_g: R_mol*T_g*n_g/V_g}]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stan/miniforge3/envs/essm_py38/lib/python3.8/site-packages/essm/equations/_core.py:107: UserWarning: \"__main__:eq_Pg\" will be overridden by \"__main__:<class '__main__.eq_Pg1'>\"\n",
      "  instance[expr] = instance\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_g = \\frac{R_{mol} T_g n_g}{V_g}$"
      ],
      "text/plain": [
       "      Rₘₒₗ⋅T_g⋅n_g\n",
       "P_g = ────────────\n",
       "          V_g     "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class eq_Pg1(eq_ideal_gas_law.definition):\n",
    "    \"\"\"Calculate pressure of ideal gas.\"\"\"\n",
    "    from sympy import solve\n",
    "    soln = solve(eq_ideal_gas_law, P_g, dict=True); print(soln)\n",
    "    expr = Eq(P_g, soln[0][P_g])\n",
    "eq_Pg1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1 µs, sys: 1 µs, total: 2 µs\n",
      "Wall time: 5.25 µs\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_g = 249.42$"
      ],
      "text/plain": [
       "P_g = 249.42"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time\n",
    "eq_Pg.subs({R_mol: 8.314, T_g: 300, n_g: 0.1, V_g: 1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1e+03 ns, sys: 0 ns, total: 1e+03 ns\n",
      "Wall time: 4.05 µs\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_g = 249.42$"
      ],
      "text/plain": [
       "P_g = 249.42"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time\n",
    "eq_Pg1.subs({R_mol: 8.314, T_g: 300, n_g: 0.1, V_g: 1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is actually no difference!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Empirical equations with internal variables\n",
    "Empirical equations not only contain variables but also numbers. As an example, we will try to define the Clausius-Clapeyron equation for saturation vapour pressure in the following example, after defining a few additional variables used in this equation.\n",
    "$$ P_{wa} = 611 e^\\frac{-M_w \\lambda_E (1/T_g - 1/273)}{R_{mol}}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stan/miniforge3/envs/essm_py38/lib/python3.8/site-packages/essm/variables/_core.py:89: UserWarning: \"essm.variables.physics.thermodynamics:lambda_E\" will be overridden by \"__main__:<class '__main__.lambda_E'>\"\n",
      "  instance[expr] = instance\n",
      "/home/stan/miniforge3/envs/essm_py38/lib/python3.8/site-packages/essm/variables/_core.py:89: UserWarning: \"essm.variables.physics.thermodynamics:M_w\" will be overridden by \"__main__:<class '__main__.M_w'>\"\n",
      "  instance[expr] = instance\n"
     ]
    }
   ],
   "source": [
    "from sympy.physics.units import joule, kilogram\n",
    "class lambda_E(Variable):\n",
    "    \"\"\"Latent heat of evaporation.\"\"\"\n",
    "    unit = joule/kilogram\n",
    "    latex_name = '\\\\lambda_E'\n",
    "    default = 2.45e6   \n",
    "\n",
    "class M_w(Variable):\n",
    "    \"\"\"Molar mass of water.\"\"\"\n",
    "    unit = kilogram/mole\n",
    "    default = 0.018"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension of \"1/T_g\" is Dimension(1/temperature), but it should be the same as -0.00366300366300366, i.e. Dimension(1)\n"
     ]
    }
   ],
   "source": [
    "from sympy import exp\n",
    "try:\n",
    "    class eq_Pwa_CC(Equation):\n",
    "        \"\"\"Clausius-Clapeyron P_wa as function of T_g. \n",
    "\n",
    "        \\cite[Eq. B3]{hartmann_global_1994}\n",
    "        \"\"\"\n",
    "\n",
    "        expr = Eq(P_wa, 611.*exp(-M_w*lambda_E*(1/T_g - 1/273.)/R_mol))\n",
    "except Exception as exc1:\n",
    "    print(exc1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The unit mismatch reported in the error message stems from the fact that the numbers in the empirical equation actually need units. Since the term in the exponent has to be non-dimensional, the units of `611` must be the same as those of `P_wa`, i.e. pascal. The units of the subtraction term in the exponent must match, meaning that `273` needs units of kelvin. To avoid the error message, we can define the empirical numbers as internal variables to the equation we want to define:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "class eq_Pwa_CC(Equation):\n",
    "    \"\"\"Clausius-Clapeyron P_wa as function of T_g. \n",
    "\n",
    "    Eq. B3 in :cite{hartmann_global_1994}\n",
    "    \"\"\"\n",
    "        \n",
    "    class p_CC1(Variable):\n",
    "        \"\"\"Internal parameter of eq_Pwl.\"\"\"\n",
    "        unit = pascal\n",
    "        latex_name = '611'\n",
    "        default = 611.   \n",
    "    \n",
    "    \n",
    "    \n",
    "    class p_CC2(Variable):\n",
    "        \"\"\"Internal parameter of eq_Pwl.\"\"\"\n",
    "        unit = kelvin\n",
    "        latex_name = '273'\n",
    "        default = 273.   \n",
    "    \n",
    "    expr = Eq(P_wa, p_CC1*exp(-M_w*lambda_E*(1/T_g - 1/p_CC2)/R_mol))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above, we defined the latex representation of the empirical constants as their actual values, so the equation displays in the familiar way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{wa} = 611 e^{- \\frac{M_w \\lambda_E \\left(- \\frac{1}{273} + \\frac{1}{T_g}\\right)}{R_{mol}}}$"
      ],
      "text/plain": [
       "                       ⎛    1      1 ⎞ \n",
       "              -M_w⋅λ_E⋅⎜- ───── + ───⎟ \n",
       "                       ⎝  p_CC2   T_g⎠ \n",
       "              ─────────────────────────\n",
       "                         Rₘₒₗ          \n",
       "P_wa = p_CC1⋅ℯ                         "
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_Pwa_CC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All default values of variables defined along with the variable definitions are stored in a dictionary that can be accessed as `Variable.__defaults__`. We can substitute the values from this dictionary into our empirical equation to plot saturation vapour pressure as a function of temperature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(P_wa, 167405731976.232*exp(-5304.00487246815/T_g))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr = eq_Pwa_CC.subs(Variable.__defaults__)\n",
    "print(expr)\n",
    "xvar = T_g\n",
    "p = plot_expr2((xvar, 273, 373), expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deduction of correct units for internal variables\n",
    "Sometimes, the correct units of internal variables in an empirical equation is not clear a priori. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Piecewise defined equations\n",
    "Saturation vapour pressure at 0 K should be 0, but `eq_Pwa_CC` would give `NaN` for $T_g=0$.\n",
    "To avoid this, we could define a piecewise function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{wa} = \\begin{cases} 0 & \\text{for}\\: T_g \\leq 0 \\\\611 e^{- \\frac{M_w \\lambda_E \\left(- \\frac{1}{273} + \\frac{1}{T_g}\\right)}{R_{mol}}} & \\text{otherwise} \\end{cases}$"
      ],
      "text/plain": [
       "       ⎧               0                  for T_g ≤ 0\n",
       "       ⎪                                             \n",
       "       ⎪                ⎛    1      1 ⎞              \n",
       "       ⎪       -M_w⋅λ_E⋅⎜- ───── + ───⎟              \n",
       "P_wa = ⎨                ⎝  p_CC2   T_g⎠              \n",
       "       ⎪       ─────────────────────────             \n",
       "       ⎪                  Rₘₒₗ                       \n",
       "       ⎪p_CC1⋅ℯ                            otherwise \n",
       "       ⎩                                             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Piecewise\n",
    "class eq1(Equation):\n",
    "     \"\"\"Test\"\"\"\n",
    "     expr = Eq(P_wa, Piecewise((0, T_g <= 0), (eq_Pwa_CC.rhs, T_g > 0)))\n",
    "display(eq1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{wa} = 0$"
      ],
      "text/plain": [
       "P_wa = 0"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1.subs(Variable.__defaults__).subs(T_g,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Substituting into integrals and derivatives and evaluating\n",
    "Above, we defined `Delta_Pwa` as a variable that represents the partial derivative of `P_wa` with respect to `T_g`:\n",
    "```\n",
    "class Delta_Pwa(Variable):\n",
    "    \"\"\"Slope of saturated vapour pressure, $\\partial P_{ws} / \\partial T_g\"\"\"\n",
    "    expr = P_wa(T_g).diff(T_g)\n",
    "    #unit = pascal/kelvin\n",
    "    latex_name = r'\\Delta'\n",
    "```\n",
    "This definition can be accessed by typing `Delta_Pwa.definition.expr`. Example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Derivative(P_wa, T_g)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\Delta = \\frac{d}{d T_g} P_{wa}$"
      ],
      "text/plain": [
       "         d        \n",
       "Δ_Pwa = ────(P_wa)\n",
       "        dT_g      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(Delta_Pwa.definition.expr)\n",
    "display(Eq(Delta_Pwa, Delta_Pwa.definition.expr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also defined the Clausius-Clapeyron approximation to $P_{wa}(T_g)$ as `eq_Pwa_CC`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{wa} = 611 e^{- \\frac{M_w \\lambda_E \\left(- \\frac{1}{273} + \\frac{1}{T_g}\\right)}{R_{mol}}}$"
      ],
      "text/plain": [
       "                       ⎛    1      1 ⎞ \n",
       "              -M_w⋅λ_E⋅⎜- ───── + ───⎟ \n",
       "                       ⎝  p_CC2   T_g⎠ \n",
       "              ─────────────────────────\n",
       "                         Rₘₒₗ          \n",
       "P_wa = p_CC1⋅ℯ                         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Clausius-Clapeyron P_wa as function of T_g. \n",
      "\n",
      "    Eq. B3 in :cite{hartmann_global_1994}\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "display(eq_Pwa_CC)\n",
    "print(eq_Pwa_CC.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to substitute this approximation into `Delta_Pwa.definition.expr`, we need to use `replace` instead of `subs` and evaluate the derivative using `doit()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\Delta = \\frac{M_w \\lambda_E 611 e^{- \\frac{M_w \\lambda_E \\left(- \\frac{1}{273} + \\frac{1}{T_g}\\right)}{R_{mol}}}}{R_{mol} T_g^{2}}$"
      ],
      "text/plain": [
       "                                ⎛    1      1 ⎞ \n",
       "                       -M_w⋅λ_E⋅⎜- ───── + ───⎟ \n",
       "                                ⎝  p_CC2   T_g⎠ \n",
       "                       ─────────────────────────\n",
       "                                  Rₘₒₗ          \n",
       "        M_w⋅λ_E⋅p_CC1⋅ℯ                         \n",
       "Δ_Pwa = ────────────────────────────────────────\n",
       "                               2                \n",
       "                       Rₘₒₗ⋅T_g                 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr = Eq(Delta_Pwa, Delta_Pwa.definition.expr.replace(P_wa, eq_Pwa_CC.rhs).doit())\n",
    "display(expr)\n",
    "p = plot_expr2((T_g, 273, 373), expr.subs(Variable.__defaults__))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we only had the slope of the curve, we could take the integral to get the absolute value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{wa} = P_{wa1} + \\int\\limits_{T_{a1}}^{T_{a2}} \\Delta\\, dT_g$"
      ],
      "text/plain": [
       "               Tₐ₂             \n",
       "                ⌠              \n",
       "P_wa = P_wa1 +  ⎮  Δ_Pwa d(T_g)\n",
       "                ⌡              \n",
       "               Tₐ₁             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Integral\n",
    "class T_a1(Variable):\n",
    "    \"\"\"Air temperature\"\"\"\n",
    "    unit = kelvin\n",
    "    latex_name = r'T_{a1}'\n",
    "    \n",
    "class T_a2(Variable):\n",
    "    \"\"\"Air temperature\"\"\"\n",
    "    unit = kelvin\n",
    "    latex_name = r'T_{a2}'\n",
    "    \n",
    "class P_wa1(Variable):\n",
    "    \"\"\"P_wa at T1\"\"\"\n",
    "    unit = pascal\n",
    "    latex_name = r'P_{wa1}'\n",
    "    \n",
    "class eq_Pwa_Delta(Equation):\n",
    "    \"\"\"P_wa deduced from the integral of Delta\"\"\"\n",
    "    expr = Eq(P_wa, P_wa1 + Integral(Delta_Pwa, (T_g, T_a1, T_a2)))\n",
    "display(eq_Pwa_Delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle P_{wa} = 167405731976.232 e^{- \\frac{5304.00487246815}{T_{a2}}}$"
      ],
      "text/plain": [
       "                         -5304.00487246815 \n",
       "                         ──────────────────\n",
       "                                Tₐ₂        \n",
       "P_wa = 167405731976.232⋅ℯ                  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr_Delta = eq_Pwa_CC.rhs.diff(T_g)\n",
    "expr = Eq(P_wa, eq_Pwa_Delta.rhs.replace(Delta_Pwa, expr_Delta).doit())\n",
    "vdict = Variable.__defaults__.copy()\n",
    "vdict[T_a1] = 273.\n",
    "vdict[P_wa1] = eq_Pwa_CC.rhs.subs(T_g, T_a1).subs(vdict)\n",
    "display(expr.subs(vdict))\n",
    "p = plot_expr2((T_a2, 273, 373), expr.subs(vdict))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exporting definitions\n",
    "The below example exports all relevant definitions from this jupyter notebook into a file called `test_definitions.py`, from which they can be re-imported into a different notebook just by executing `from test_definitions import *`, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import preorder_traversal\n",
    "def extract_units(expr):\n",
    "    \"\"\"Traverse through expression and return set of units.\"\"\"\n",
    "    return {\n",
    "        arg\n",
    "        for arg in preorder_traversal(expr) if isinstance(arg, Quantity)\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('test_definitions.py', 'wt') as file1:\n",
    "    file1.write('from essm.variables._core import BaseVariable, Variable\\n')\n",
    "    file1.write('from essm.equations import Equation\\n')\n",
    "    file1.write('from sympy import Abs, Derivative, Eq, exp, Integral, log, Piecewise, sqrt\\n')\n",
    "    # Create import strings for all units\n",
    "    StrPrinter._print_Quantity = lambda self, expr: str(expr.name)    # displays long units (meter instead of m)\n",
    "    s = set()\n",
    "    for unit in Variable.__units__.values():\n",
    "        for item in extract_units(unit):\n",
    "            s.add(item)\n",
    "    commandstr = 'from sympy.physics.units import ' + str(s)[1:-1]\n",
    "    file1.write(commandstr.replace(\"\\n\", \" \") + \"\\n\")\n",
    "    \n",
    "    for variable in Variable.__registry__.keys():\n",
    "        symbol = variable.definition.latex_name\n",
    "        name = variable.name\n",
    "        doc = variable.__doc__\n",
    "        unit = variable.definition.unit\n",
    "        assumptions = variable.definition.assumptions\n",
    "        latex_name = variable.definition.latex_name\n",
    "        expression = Variable.__expressions__.get(variable, None)\n",
    "        default = str(Variable.__defaults__.get(variable, None))\n",
    "        commandstr = '''{0} = type('{0}', (Variable,), {{'__doc__': \"\"\"{1}\"\"\", 'unit': {2}, 'assumptions': {3}, \\\n",
    "        'latex_name': r\"{4}\", 'default': {5}, 'expr': {6}}})'''.format(\n",
    "            name, doc.replace('\\n', ' ').replace('\\r', ''), unit, assumptions, latex_name,\\\n",
    "        default, expression)\n",
    "        file1.write(commandstr + \"\\n\")\n",
    "        \n",
    "    for eq in Equation.__registry__.keys():\n",
    "        name = eq.definition.name\n",
    "        doc = eq.__doc__\n",
    "        equ = eq\n",
    "        commandstr = '''{0} = type('{0}', (Equation,), {{'__doc__': \"\"\"{1}\"\"\", 'expr': {2}}})'''.format(\n",
    "            name, doc.replace('\\n', ' ').replace('\\r', ''), equ)\n",
    "        file1.write(commandstr + \"\\n\")\n",
    "        \n",
    "StrPrinter._print_Quantity = lambda self, expr: str(expr.abbrev)    # displays short units (m instead of meter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will now re-import all the definitions written to files, after de-activating warnings\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "from test_definitions import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical evaluations\n",
    "See here for detailed instructions on how to turn sympy expressions into code: https://docs.sympy.org/latest/modules/codegen.html\n",
    "\n",
    "We will first list all equations defined in this worksheet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eq_Le: Eq(Le, alpha_a/D_va)\n",
      "eq_Cwa: Eq(C_wa, P_wa/(R_mol*T_a))\n",
      "eq_Nu_forced_all: Eq(Nu, -Pr**(1/3)*(-37*Re**(4/5) + 37*(Re + Re_c - Abs(Re - Re_c)/2)**(4/5) - 664*sqrt(Re + Re_c - Abs(Re - Re_c)/2))/1000)\n",
      "eq_Dva: Eq(D_va, T_a*p_Dva1 - p_Dva2)\n",
      "eq_alphaa: Eq(alpha_a, T_a*p_alpha1 - p_alpha2)\n",
      "eq_ka: Eq(k_a, T_a*p_ka1 + p_ka2)\n",
      "eq_nua: Eq(nu_a, T_a*p_nua1 - p_nua2)\n",
      "eq_rhoa_Pwa_Ta: Eq(rho_a, (M_N2*P_N2 + M_O2*P_O2 + M_w*P_wa)/(R_mol*T_a))\n",
      "eq_Pa: Eq(P_a, P_N2 + P_O2 + P_wa)\n",
      "eq_PN2_PO2: Eq(P_N2, P_O2*x_N2/x_O2)\n",
      "eq_PO2: Eq(P_O2, (P_a*x_O2 - P_wa*x_O2)/(x_N2 + x_O2))\n",
      "eq_PN2: Eq(P_N2, (P_a*x_N2 - P_wa*x_N2)/(x_N2 + x_O2))\n",
      "eq_rhoa: Eq(rho_a, (x_N2*(M_N2*P_a - P_wa*(M_N2 - M_w)) + x_O2*(M_O2*P_a - P_wa*(M_O2 - M_w)))/(R_mol*T_a*x_N2 + R_mol*T_a*x_O2))\n",
      "eq_ideal_gas_law: Eq(P_g*V_g, R_mol*T_g*n_g)\n",
      "eq_Pg: Eq(P_g, R_mol*T_g*n_g/V_g)\n",
      "eq_Pwa_nw: Eq(P_wa, R_mol*T_g*n_w/V_g)\n",
      "eq_Pwa_CC: Eq(P_wa, p_CC1*exp(-M_w*lambda_E*(-1/p_CC2 + 1/T_g)/R_mol))\n",
      "eq1: Eq(P_wa, Piecewise((0, T_g <= 0), (p_CC1*exp(-M_w*lambda_E*(-1/p_CC2 + 1/T_g)/R_mol), True)))\n",
      "eq_Pwa_Delta: Eq(P_wa, P_wa1 + Integral(Delta_Pwa, (T_g, T_a1, T_a2)))\n",
      "eq_Nu_forced_all: Eq(Nu, -Pr**0.333333333333333*(-37*Re**0.8 - 664*sqrt(Re + Re_c - Abs(Re - Re_c)/2) + 37*(Re + Re_c - Abs(Re - Re_c)/2)**0.8)/1000)\n"
     ]
    }
   ],
   "source": [
    "for eq in Equation.__registry__.keys():\n",
    "        print(eq.definition.name + ': ' + str(eq))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Substitution of equations and values into equations\n",
    "The easiest way is to define a dictionary with all variables we want to substitute as keys. We start with the default variables and then add more. First, however, we will define a function to display the contents of a dictionary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_dict(vdict, list_vars=None):\n",
    "    \"\"\"Print values and units of variables in vdict.\"\"\"\n",
    "    if not list_vars:\n",
    "        list_vars = vdict.keys()\n",
    "    for var1 in list_vars:\n",
    "        unit1 = var1.definition.unit\n",
    "        if unit1 == 1:\n",
    "            unit1 = ''\n",
    "        if vdict[var1] is not None:\n",
    "            print('{0}: {1} {2}'.format(var1.name, str(vdict[var1]), str(unit1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c_pa: 1010.0 J/(K*kg)\n",
      "c_pamol: 29.19 J/(K*mol)\n",
      "c_pv: 1864 J/(K*kg)\n",
      "g: 9.81 m/s**2\n",
      "lambda_E: 2450000.0 J/kg\n",
      "M_air: 0.02897 kg/mol\n",
      "M_N2: 0.028 kg/mol\n",
      "M_O2: 0.032 kg/mol\n",
      "M_w: 0.018 kg/mol\n",
      "R_mol: 8.314472 J/(K*mol)\n",
      "sigm: 5.67e-08 J/(K**4*m**2*s)\n",
      "T0: 273.15 K\n",
      "x_N2: 0.79 \n",
      "x_O2: 0.21 \n",
      "p_Dva1: 1.49e-07 m**2/(K*s)\n",
      "p_Dva2: 1.96e-05 m**2/s\n",
      "p_alpha1: 1.32e-07 m**2/(K*s)\n",
      "p_alpha2: 1.73e-05 m**2/s\n",
      "p_ka1: 6.84e-05 J/(K**2*m*s)\n",
      "p_ka2: 0.00563 J/(K*m*s)\n",
      "p_nua1: 9e-08 m**2/(K*s)\n",
      "p_nua2: 1.13e-05 m**2/s\n",
      "p_CC1: 611.0 Pa\n",
      "p_CC2: 273.0 K\n"
     ]
    }
   ],
   "source": [
    "vdict = Variable.__defaults__.copy()\n",
    "print_dict(vdict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can substitute a range of equations into each other by using the custom function `subs_eq`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle N_{Le} = \\frac{T_a p_1 - p_2}{T_a p_1 - p_2}$"
      ],
      "text/plain": [
       "     Tₐ⋅pₐₗₚₕₐ₁ - pₐₗₚₕₐ₂\n",
       "Le = ────────────────────\n",
       "      Tₐ⋅p_Dva1 - p_Dva2 "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from essm.variables.utils import subs_eq\n",
    "subs_eq(eq_Le, [eq_alphaa, eq_Dva])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use subs_eq to substitute equations into each other and a dictionary with values. We will first add an entry for T_a into the dictionary and then substitute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOsAAAASCAYAAAC6lykEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAJIklEQVR4Ae2b2ZEUORBAe4gxYHbWAsADDg/AA1gsGPAAgi/4I8ADwAIOD2At4PAA1gJgPJh9T62skKpURzcNAbudESpJqVQqlZdU1TMHZ2dnqz3sNfAraeDhw4eXKB9Lmegf0T+m/lzi/0/tw/5mUcZdcNcp1/LY5YbiHHtMuUQ5pbyn3ITO9m8N7MF9CV8oFymPwS1yEOh0qPuUAPuvwL8NhPWu6Uremb92ucM6d/pjZZ/xWTpoQh8x9QW4LpBoX2DgXh68Qv3VfkmTx1IF3jVfUfSrMX/5mzF1F+vYFi6vq/q5hCc0yhn6kJ99bVvZRs7gnlpnOKY+ATcmayJjfFaXwXCMFvykLlvB+gSmT5j4htqg1PluUjpgzA2q7E+5ntxIN/EXb7CfD4j4iPq1olJr1A/U1ylLAlbjh0PIYkXfYD2iJJ4JuXaSXdJltl1lMISjd8hGY5QOeXUcxw285NDU9i0msVWmeUptck9A2+AOncU89ficYiAb0PKeAukEA0C9qzvt0vkZ7cU8M6376HRO+wY831B7yFT2Bu+ejIMVtTL8Q62/T/nAqC7l04MBLbzVyaQuz/WYpC4TDVKzi8q+kRmlsd7jNWOdAntjv1WXfdxG4Cqo8t40ZJlpm/vK8w32PpyAMOEl2DVd8I0a/t6MZmEBnQ7lKZoCLjM0QEqHNTC7AJAGek9ZfcL5CcCdUgwKaV9k9FT1Edo/KAeUixQDrfIz+5SlPLXtbegN0IDYV2cbBkwoXrVToEpI26T3njLqA9As0nnmN0Y7q8tmsMLUTOlmZCBUBhGBgAb0O9v/EfD20DqN3OM19qujToGnTXfCTBDumq5bChk9BXTqyrE7gtyYo2Ncp5bXs3IueG8Y5R71gU/g+rrRd0x8nha/AmjXSi/I1tKR+y6TUcju/KYPwGeRzmU0Qzury7FgVdFmLpWu8GamPkRA9/G/a19lfW0IH8ZzfAoMam8hXq1K5zXhlVl513SlTLdYuwqwcrBoz9GZnLV/y6ELNimhf56gK/VQzvupbeR7S/GkjtN0RTtO2WQb+iFrywf8fiFcWVfVc06XJfEUbYo15BjT+dFhyWmknZwNJl4jSkdIAT0y57dCF4aakvt4ahAevhJ4ZdYJvtH2OugpavCmdyLaK9u5vxM6eQrw9HpVJoWE7z8W0umUBqGnxi1KfGyrPpYxXn3LKNZy3opxT6StgLnptYTJf1I8oX1n3ZpfKQR8TLzp2kk7+TS1yUmylp2VQahuCtAv0rkT52gZn9XlIFiZ5Eb8uJSA/jOKTqDzlcE6lgHWE3/QM8uijJuA70BjypBPGGhqT5F5R9d1jSyfjqYzeCpbV/AD6HQinS1uAdV60WF8ER30sdcrzNHuCWibhPwy2iWfGIuaMQPVdbp5MbZB7fov4ZXsQS0/r9tew7vTcQN+iZS5yqbvXKUY+L6LluC+Wr7lPCH0soLXUl1uRLteZv3M8na6PCwHc9vr7aMe3iC9zeRrFK8UbqgL6JI2j3mN8uRw8+/AdS/sJe02bXgN3p+34bPFnMiuo1ORzT3rYJ6oJjj1pJN1Xxzpr3ZNB0t/plkSHLN08AmH9LfOMjkr+kvKc/D6QAokkT14Rd/bw9Y2Z275Xryi7ylvkKpTdbsVwMMATaczbW3lV+vSNifg/PKb/NxFaBuosdcyGc7q0vkZNqGNOdaVLs+VI7ndut7G6RAOoTL7WSlNZ3Mq1fcyM72K2NpoieHPeXydWOY4j8V7S5OUfXqamvnvUXQudRSnuQ6egoD6R9Atuf667ixdsbnSMQPt12734TV5AOxN/u499j2g+Q6E8lyAtyfNdwN8PEgMwvTTmgzB2T9P0W/vUvR719OfhaQT8It1uQnteon1k3kDXbaCVYErYKJCGoRmHIVvBXQ5R0fd+rpSMvoZbfYUez5qrBe4lvOW5Bo2klnCw1eH8CSQR1yvdkZX2GJStqV0Cg1t6CJq0X3QBypgng7szx7afmtgvu/4JoUxCHuMjQ/w8POWEFfZcjwOnLDNCjoPGU9C/9bAxKsN41ZlIgr/n9S5i2xCWwrFvKYuD3tECh1ZpByyrZM5rkNOGZLhRDd5XUUglX6f4h9W2FZJ/WsX6BqgMeN0yq1HR3tz76xONLkMnBBcnKyjySfvpZnAGNPAGlxHdp87o8vyXoWv16USdExPIfE6la8ss3TQR7IZ0wVsElSOyjyvlP4e2p2otJMuqSvaPH+q8tRu3XSSHeCXrrFTDBpjKfiZ6xfhOd9tTF+pz3T1Z77yLdWlOlhKm9aF/6guq2CF2qzYf18NJgqr4o360ewJjRsT5pxbBd6EPt4hdKwlwTqZBFx4S3B9E1IfLoMw2EeN7FguBkjLOQ3SMLa0u6JzrYGe4f8tr9cFzwZ0kKbrcj8BiFcXyt+tSVt765AR6NIJOt2sPRNl/fCDZp+XFCbobt16ymxP27Xesw08IfFlXWX2DyPO0072ptZ2ru3eV/SlHcgBfqDzTWgz70ldnpNIgLFC+TthEjIhh4/kzFmI4ega48Y0aMtpY44KMQAsOq58mx+sYsKPrpFBx/pKrcES0FYnf1FO1pi1nsCfUfpXNQOje/8p6E1uXu1CH7umi6XKWrktc9CkQ1ZvAjp3l7xot3ThyWFQHzHun8p1BZxXyVPqPsSV8rg/kPuJRzkGn/irnzL5lCRzPA3+yr/gqZ3dUymn++mf6u5PmrkTvalL5rZgQAv/WV0ePHjwwIkGj0FmW6EeMVmDDQC8jjd1sqoUg7VSLH15+1OATmAW8suiDq9yWlkP9M+FLKMOekr5QrlKUReVoeh7dVfm6pSnb2b0au+eAqrfJkXumi4Wgq+vCBpdWwracPA1fgM6daHdBIOr0gV81IPrtcBEnE4jB2nHSV36mQlMf6pOYPryjNPVddWn74/apYMNebpu6ZOuMfhDfnhGgop9D+zXCUAD+kU6d84ULWOzujzY9b/Isaj/c2cm6htAJWhsA1ka33HitKG7h70G9hqY0sC5qcFNxwg+TxahutOD98rhdTcyo+NBK/2Kschoqb9/7DWw10CtgcO6u32PYPO94lbm4Mlq06vEFYqBWV6dvY54BfEqYgBL1/ywBX4Pew3sNYAG/gXleRun3v3tJAAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle N_{Le} = 0.888446215139442$"
      ],
      "text/plain": [
       "Le = 0.888446215139442"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vdict[T_a] = 300.\n",
    "subs_eq(eq_Le, [eq_alphaa, eq_Dva], vdict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of equations for long lists of variable sets\n",
    "Substitution of variables into equations takes a lot of time if they need to be evaluated for a large number of variables. We can use theano to speed this up:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import theano\n",
    "import numpy as np\n",
    "np.bool = bool\n",
    "from sympy.printing.theanocode import theano_function\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now create two long lists of values representing T_g and n_g respectively and show how long it takes to compute ideal gas law values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "npoints = 10000\n",
    "xmin = 290.\n",
    "xmax = 310.\n",
    "Tvals = np.arange(xmin, xmax, (xmax - xmin)/npoints)\n",
    "xmin = 0.1\n",
    "xmax = 0.5\n",
    "nvals = np.arange(xmin, xmax, (xmax-xmin)/npoints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.65 s, sys: 35.6 ms, total: 5.68 s\n",
      "Wall time: 5.71 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# looping\n",
    "expr = eq_ideal_gas_law.rhs.subs(Variable.__defaults__)\n",
    "resvals0 = []\n",
    "for i in range(len(Tvals)):\n",
    "    resvals0.append(expr.subs({T_g: Tvals[i], n_g: nvals[i]}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 23.2 ms, sys: 13.4 ms, total: 36.6 ms\n",
      "Wall time: 642 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Using theano\n",
    "f1 = theano_function([T_g, n_g], [eq_ideal_gas_law.rhs.subs(Variable.__defaults__)], dims={T_g:1, n_g:1})\n",
    "resvals1 = f1(Tvals,nvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(resvals0) == list(resvals1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Both approaches give identical results, but `theano_function` makes it a lot faster.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical solution\n",
    "Some equations cannot be solved analytically for a given variable, e.g. eq_Nu_forced_all cannot be solved analytically for Re if Nu is given, so we can use numerical solvers instead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import nsolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 690263.034644599$"
      ],
      "text/plain": [
       "690263.034644599"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vdict = Variable.__defaults__.copy()\n",
    "vdict[Pr] = 0.71\n",
    "vdict[Re_c] = 3000.\n",
    "vdict[Nu] = 1000.\n",
    "expr = eq_Nu_forced_all.subs(vdict)\n",
    "nsolve(expr, 1000.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now applying to a long list of Nu-values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "npoints = 100\n",
    "xmin = 1000.\n",
    "xmax = 1200.\n",
    "Nuvals = np.arange(xmin, xmax, (xmax - xmin)/npoints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.17 s, sys: 8.58 ms, total: 1.18 s\n",
      "Wall time: 1.18 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Solving for a range of Nu values\n",
    "vdict = Variable.__defaults__.copy()\n",
    "vdict[Pr] = 0.71\n",
    "vdict[Re_c] = 3000.\n",
    "resvals = []\n",
    "for Nu1 in Nuvals:\n",
    "    vdict[Nu] = Nu1\n",
    "    resvals.append(nsolve(eq_Nu_forced_all.subs(vdict), 1000.))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now again use a theano function to make it faster. First we import optimize from scipy and preapre the theano_function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as sciopt\n",
    "vdict = Variable.__defaults__.copy()\n",
    "vdict[Pr] = 0.71\n",
    "vdict[Re_c] = 3000.\n",
    "expr = eq_Nu_forced_all.subs(vdict)\n",
    "expr1 = expr.rhs - expr.lhs\n",
    "fun_tf = theano_function([Re, Nu], [expr1], dims={Nu:1, Re:1})\n",
    "x0vals = np.full(Nuvals.shape, fill_value=2000.) # array of same shape as Nuvals, with initial guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.25 ms, sys: 0 ns, total: 3.25 ms\n",
      "Wall time: 3.25 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Solving for a range of Nu values\n",
    "resvals1 = sciopt.fsolve(fun_tf, args=Nuvals, x0=x0vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 5.35658271661622 \\cdot 10^{-11}$"
      ],
      "text/plain": [
       "5.35658271661622e-11"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(abs((resvals - resvals1)/resvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Using theano and scipy makes it 2 orders of magnitude faster and the results are different only by 10$^{-10}$%!**\n",
    "**Note, however, that scipy gets slowed down for large arrays, so it is more efficient to re-run it repreatedly with subsections of the arra:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "npoints = 1000\n",
    "xmin = 1000.\n",
    "xmax = 1200.\n",
    "Nuvals = np.arange(xmin, xmax, (xmax - xmin)/npoints)\n",
    "x0vals = np.full(Nuvals.shape, fill_value=2000.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.06 s, sys: 2.33 ms, total: 1.06 s\n",
      "Wall time: 1.06 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Solving for a range of Nu values\n",
    "resvals1 = sciopt.fsolve(fun_tf, args=Nuvals, x0=x0vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now test that we can process Nuvals bit by bit and re-create it consistently:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "# Solving for a range of Nu values\n",
    "imax = len(Nuvals)\n",
    "i0 = 0\n",
    "idiff = 100\n",
    "i1 = i0\n",
    "resvals2 = []\n",
    "while i1 < imax - 1:\n",
    "    i0 = i1    # note that resvals[0:2] + resvals[2:4] = resvals[0:4]\n",
    "    i1 = min(i0+idiff, imax)\n",
    "    resvals0 = Nuvals[i0:i1]\n",
    "    resvals2 = np.append(resvals2,resvals0)\n",
    "print(list(resvals2) == list(Nuvals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will run fsolve for portions of Nuvals bit by bit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 29.4 ms, sys: 559 µs, total: 30 ms\n",
      "Wall time: 31.2 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Solving for a range of Nu values\n",
    "imax = len(Nuvals)\n",
    "i0 = 0\n",
    "idiff = 100\n",
    "i1 = i0\n",
    "resvals2 = []\n",
    "while i1 < imax - 1:\n",
    "    i0 = i1    # note that resvals[0:2] + resvals[2:4] = resvals[0:4]\n",
    "    i1 = min(i0+idiff, imax)\n",
    "    resvals0 = sciopt.fsolve(fun_tf, args=Nuvals[i0:i1], x0=x0vals[i0:i1])\n",
    "    resvals2 = np.append(resvals2,resvals0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 7.123089704764712e-10$"
      ],
      "text/plain": [
       "7.123089704764712e-10"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(abs((resvals1 - resvals2)/resvals1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**It is strange that resvals1 and resvals2 are different at all, but anyway, it is clear that slicing the data in relatively small portions is important to keep `scipy.optimize.fsolve` time-efficient.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate code from sympy expressions and execute\n",
    "Need to install gfortran system-wide first!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.utilities.autowrap import autowrap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import symbols\n",
    "x, y, z = symbols('x y z')\n",
    "expr = ((x - y + z)**(13)).expand()\n",
    "binary_func = autowrap(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5 µs, sys: 2 µs, total: 7 µs\n",
      "Wall time: 10 µs\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -1.0$"
      ],
      "text/plain": [
       "-1.0"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "binary_func(1, 4, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 34.4 ms, sys: 3.35 ms, total: 37.7 ms\n",
      "Wall time: 37.3 ms\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABgAAAAOCAYAAAA1+Nx+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAj0lEQVQ4EWP8//8/A7VAQ0ODEdCs1UBsDGR/AJnLAiIoAUCDBID6ZwPxOyA2AWIlIIYDalgAcmkoyESgZWVACuQLOGCCs2jEGLWAYMDSPIhYoMlsL9ApoORGLAgF6jtHjGKQBaBkZkyMYnLU0DyIhpwFwtBgFIIFJyM1CjtgPIIKOBBwAWJQYgElgHtAvBsAO3sgJ/LwrLIAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "expr.subs({x:1, y:4, z:2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0mbinary_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msymfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Returns a sympy function with expr as binary implementation\n",
       "\n",
       "This is a convenience function that automates the steps needed to\n",
       "autowrap the SymPy expression and attaching it to a Function object\n",
       "with implemented_function().\n",
       "\n",
       "Parameters\n",
       "==========\n",
       "\n",
       "symfunc : sympy Function\n",
       "    The function to bind the callable to.\n",
       "expr : sympy Expression\n",
       "    The expression used to generate the function.\n",
       "kwargs : dict\n",
       "    Any kwargs accepted by autowrap.\n",
       "\n",
       "Examples\n",
       "========\n",
       "\n",
       ">>> from sympy.abc import x, y\n",
       ">>> from sympy.utilities.autowrap import binary_function\n",
       ">>> expr = ((x - y)**(25)).expand()\n",
       ">>> f = binary_function('f', expr)\n",
       ">>> type(f)\n",
       "<class 'sympy.core.function.UndefinedFunction'>\n",
       ">>> 2*f(x, y)\n",
       "2*f(x, y)\n",
       ">>> f(x, y).evalf(2, subs={x: 1, y: 2})\n",
       "-1.0\n",
       "\u001b[0;31mFile:\u001b[0m      ~/miniforge3/envs/essm_py38/lib/python3.8/site-packages/sympy/utilities/autowrap.py\n",
       "\u001b[0;31mType:\u001b[0m      function"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy.utilities.autowrap import binary_function\n",
    "binary_function?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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