plot_test_interp.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot interpolation test results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from scipy import interpolate as interp\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mpl.rcParams['figure.dpi'] = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt(\"scvh_hhe_y0.275_dt_cgs_lowrhot.csv\", delimiter=\",\", skiprows=0) \n",
    "\n",
    "logT_table   = data[:, 0] \n",
    "logrho_table = data[:, 1]\n",
    "logP_table   = data[:, 2]\n",
    "logu_table   = data[:, 3]\n",
    "logs_table   = data[:, 4]\n",
    "\n",
    "# All SCVH EOS tables obtained from Ravit have the same size\n",
    "#nRho = 201\n",
    "#nT   = 100\n",
    "nRho = 80\n",
    "nT   = 48\n",
    "\n",
    "logrho_table = logrho_table[0:nRho]\n",
    "logT_table = logT_table[0:np.size(logT_table):nRho]\n",
    "\n",
    "logrho_min = np.min(logrho_table)\n",
    "logrho_max = np.max(logrho_table)\n",
    "logT_min   = np.min(logT_table)\n",
    "logT_max   = np.max(logT_table)\n",
    "    \n",
    "dlogrho = logrho_table[1:]-logrho_table[:-1]\n",
    "dlogT = logT_table[1:]-logT_table[:-1]\n",
    "\n",
    "print(\"logrho_min = {:}\".format(logrho_min))\n",
    "print(\"logrho_max = {:}\".format(logrho_max))\n",
    "print(\"logT_min   = {:}\".format(logT_min))\n",
    "print(\"logT_max   = {:}\".format(logT_max))\n",
    "print()\n",
    "#print(\"logrho_table = {:}\".format(logrho_table))\n",
    "#print(\"logT_table   = {:}\".format(logT_table))\n",
    "#print()\n",
    "\n",
    "# Mark where the original SCvH EOS table was extended below T=100K\n",
    "index = np.min(np.where(logT_table>=2.0))\n",
    "print(\"The EOS table was extended until index={:} logT={:}\".format(index, logT_table[index]))\n",
    "\n",
    "# Split into arrays of constant T\n",
    "logP_array = np.split(logP_table, nT)\n",
    "logu_array = np.split(logu_table, nT)\n",
    "logs_array = np.split(logs_table, nT)\n",
    "\n",
    "# Generate 2d arrays\n",
    "logP = np.vstack(logP_array)\n",
    "logu = np.vstack(logu_array)\n",
    "logs = np.vstack(logs_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load interpolated values\n",
    "logrho_int = np.loadtxt(\"testscvheosinterp_rhoaxis.txt\")\n",
    "logT_int = np.loadtxt(\"testscvheosinterp_taxis.txt\")\n",
    "\n",
    "# Interpolation in logarithmic variables\n",
    "logP_int = np.loadtxt(\"testscvheosinterp_logpress.txt\")\n",
    "logu_int = np.loadtxt(\"testscvheosinterp_logintenergy.txt\")\n",
    "logs_int = np.loadtxt(\"testscvheosinterp_logentropy.txt\")\n",
    "\n",
    "rho_int = 10**logrho_int\n",
    "T_int = 10**logT_int\n",
    "\n",
    "# Interpolation in normal variables (but still on a logarithmic grid)\n",
    "P_int = np.loadtxt(\"testscvheosinterp_press.txt\")\n",
    "u_int = np.loadtxt(\"testscvheosinterp_intenergy.txt\")\n",
    "s_int = np.loadtxt(\"testscvheosinterp_entropy.txt\")\n",
    "\n",
    "\n",
    "nRho_int = np.size(logrho_int)\n",
    "nT_int = np.size(logT_int)\n",
    "\n",
    "print(\"nRho_int= {:} nT_int= {:}\".format(nRho_int, nT_int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Skip some curves otherwise the plots are very hard to read\n",
    "nSkipT = 4\n",
    "nSkipRho = 8\n",
    "\n",
    "nSkipT = 1\n",
    "nSkipRho = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we first plot $\\log\\left( P \\right)$, $\\log\\left( u \\right)$ and $\\log\\left( s \\right)$ form the EOS table and interpolated curves (in logarithmic variables, bilinear)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot log(P), log(u) and log(s) of the eos table and the interpolated curves\n",
    "fig, ax = plt.subplots(3, 2)\n",
    "\n",
    "x, y = fig.get_size_inches()\n",
    "\n",
    "fig.set_size_inches(2*x, 3*y)\n",
    "\n",
    "# P(rho, T=const)\n",
    "ax[0][0].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nT, nSkipT):\n",
    "    ax[0][0].plot(logrho_table, logP[i,:], '-')\n",
    "\n",
    "for i in range(0, nT_int, nSkipT):\n",
    "    ax[0][0].plot(logrho_int, logP_int[i,:], '--')\n",
    "    \n",
    "ax[0][0].set(xlabel=\"log(rho) [g cm^${-3}$]\", ylabel=\"log(P) [erg cm$^{-3}$]\")\n",
    "ax[0][0].set(title=\"SCvH EOS H-He, T=const.)\")\n",
    "\n",
    "# P(rho=const, T)\n",
    "ax[0][1].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nRho, nSkipRho):\n",
    "    ax[0][1].plot(logT_table, logP[:,i], '-')\n",
    "\n",
    "for i in range(0, nRho_int, nSkipRho):\n",
    "    ax[0][1].plot(logT_int, logP_int[:,i], '--')\n",
    "\n",
    "\n",
    "ax[0][1].set(xlabel=\"log(T) [K]\", ylabel=\"log(P) [erg cm$^{-3}$]\")\n",
    "ax[0][1].set(title=\"SCvH EOS H-He (rho=const.)\")\n",
    "\n",
    "# u(rho, T=const)\n",
    "ax[1][0].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nT, nSkipT):\n",
    "    ax[1][0].plot(logrho_table, logu[i,:], '-')\n",
    "\n",
    "for i in range(0, nT_int, nSkipT):\n",
    "    ax[1][0].plot(logrho_int, logu_int[i,:], '--')\n",
    "\n",
    "ax[1][0].set(xlabel=\"log(rho) [g cm^${-3}$]\", ylabel=\"log(u) [erg g$^{-1}$]\")\n",
    "\n",
    "# u(rho=const, T)\n",
    "ax[1][1].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nRho, nSkipRho):\n",
    "    ax[1][1].plot(logT_table, logu[:,i], '-')\n",
    "\n",
    "for i in range(0, nRho_int, nSkipRho):\n",
    "    ax[1][1].plot(logT_int, logu_int[:,i], '--')\n",
    "\n",
    "ax[1][1].set(xlabel=\"log(T) [K]\", ylabel=\"log(u) [erg g$^{-1}$]\")\n",
    "\n",
    "# s(rho, T=const)\n",
    "ax[2][0].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nT, nSkipT):\n",
    "    ax[2][0].plot(logrho_table, logs[i,:], '-')\n",
    "\n",
    "for i in range(0, nT_int, nSkipT):\n",
    "    ax[2][0].plot(logrho_int, logs_int[i,:], '--')\n",
    "    \n",
    "ax[2][0].set(xlabel=\"log(rho) [g cm^${-3}$]\", ylabel=\"log(s) [erg g$^{-1}$ K$^{-1}$]\")\n",
    "\n",
    "# s(rho=const, T)\n",
    "ax[2][1].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nRho, nSkipRho):\n",
    "    ax[2][1].plot(logT_table, logs[:,i], '-')\n",
    "\n",
    "for i in range(0, nRho_int, nSkipRho):\n",
    "    ax[2][1].plot(logT_int, logs_int[:,i], '--')\n",
    "\n",
    "ax[2][1].set(xlabel=\"log(T) [K]\", ylabel=\"log(s) [erg g$^{-1}$ K$^{-1}$]\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we plot $P \\left( \\rho, T \\right)$, $u \\left( \\rho, T \\right)$ and $s \\left( \\rho, T \\right)$ from the EOS table and interpolated curves (again in logarithmic variables, bilinear) to test if the functions ```scvheosPofRhoT()```, ```scvheosPofRhoT()``` and ```scvheosPofRhoT()``` work."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot P, u and s of the eos table and the interpolated curves\n",
    "fig, ax = plt.subplots(3, 2)\n",
    "\n",
    "x, y = fig.get_size_inches()\n",
    "\n",
    "fig.set_size_inches(2*x, 3*y)\n",
    "\n",
    "# P(rho, T=const)\n",
    "ax[0][0].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nT, nSkipT):\n",
    "    ax[0][0].loglog(10**logrho_table, 10**logP[i,:], '-')\n",
    "\n",
    "for i in range(0, nT_int, nSkipT):\n",
    "    ax[0][0].loglog(rho_int, P_int[i,:], '--')\n",
    "    \n",
    "ax[0][0].set(xlabel=\"rho [g cm^${-3}$]\", ylabel=\"P [erg cm$^{-3}$]\")\n",
    "ax[0][0].set(title=\"SCvH EOS H-He, T=const.)\")\n",
    "\n",
    "# P(rho=const, T)\n",
    "ax[0][1].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nRho, nSkipRho):\n",
    "    ax[0][1].loglog(10**logT_table, 10**logP[:,i], '-')\n",
    "\n",
    "for i in range(0, nRho_int, nSkipRho):\n",
    "    ax[0][1].loglog(T_int, P_int[:,i], '--')\n",
    "\n",
    "\n",
    "ax[0][1].set(xlabel=\"T [K]\", ylabel=\"P [erg cm$^{-3}$]\")\n",
    "ax[0][1].set(title=\"SCvH EOS H-He (rho=const.)\")\n",
    "\n",
    "# u(rho, T=const)\n",
    "ax[1][0].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nT, nSkipT):\n",
    "    ax[1][0].loglog(10**logrho_table, 10**logu[i,:], '-')\n",
    "\n",
    "for i in range(0, nT_int, nSkipT):\n",
    "    ax[1][0].loglog(rho_int, u_int[i,:], '--')\n",
    "\n",
    "ax[1][0].set(xlabel=\"rho [g cm^${-3}$]\", ylabel=\"u [erg g$^{-1}$]\")\n",
    "\n",
    "# u(rho=const, T)\n",
    "ax[1][1].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nRho, nSkipRho):\n",
    "    ax[1][1].loglog(10**logT_table, 10**logu[:,i], '-')\n",
    "\n",
    "for i in range(0, nRho_int, nSkipRho):\n",
    "    ax[1][1].loglog(T_int, u_int[:,i], '--')\n",
    "\n",
    "ax[1][1].set(xlabel=\"T [K]\", ylabel=\"u [erg g$^{-1}$]\")\n",
    "\n",
    "# s(rho, T=const)\n",
    "ax[2][0].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nT, nSkipT):\n",
    "    ax[2][0].loglog(10**logrho_table, 10**logs[i,:], '-')\n",
    "\n",
    "for i in range(0, nT_int, nSkipT):\n",
    "    ax[2][0].plot(rho_int, s_int[i,:], '--')\n",
    "    \n",
    "ax[2][0].set(xlabel=\"rho [g cm^${-3}$]\", ylabel=\"s [erg g$^{-1}$ K$^{-1}$]\")\n",
    "\n",
    "# s(rho=const, T)\n",
    "ax[2][1].set_prop_cycle(None)\n",
    "\n",
    "for i in range(0, nRho, nSkipRho):\n",
    "    ax[2][1].loglog(10**logT_table, 10**logs[:,i], '-')\n",
    "\n",
    "for i in range(0, nRho_int, nSkipRho):\n",
    "    ax[2][1].loglog(T_int, s_int[:,i], '--')\n",
    "\n",
    "ax[2][1].set(xlabel=\"T [K]\", ylabel=\"s [erg g$^{-1}$ K$^{-1}$]\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now generate interpolation functions with ```scipy.interp.interp2d``` to see if the two independent implementations agree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate interpolation functions\n",
    "logP_interp = interp.interp2d(logrho_table, logT_table, logP, kind='linear')\n",
    "logu_interp = interp.interp2d(logrho_table, logT_table, logu, kind='linear')\n",
    "logs_interp = interp.interp2d(logrho_table, logT_table, logs, kind='linear')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the difference\n",
    "rel_err = np.abs(logP_interp(logrho_int, logT_int)-logP_int)/logP_interp(logrho_int, logT_int)\n",
    "\n",
    "# Plot the difference\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "mark = np.zeros(rel_err.shape)\n",
    "\n",
    "mark[np.where(rel_err >=0)] = 4\n",
    "mark[np.where(rel_err < 1e-1)] = 3\n",
    "mark[np.where(rel_err < 1e-3)] = 2\n",
    "mark[np.where(rel_err < 1e-6)] = 1\n",
    "mark[np.where(rel_err < 1e-10)] = 0\n",
    "\n",
    "plt.imshow(mark, cmap=plt.cm.get_cmap('viridis', 5), origin='lower', interpolation='none', extent=[logrho_min, logrho_max, logT_min, logT_max], aspect='auto')\n",
    "cbar = plt.colorbar()\n",
    "\n",
    "plt.clim(-0.5, 4.5);\n",
    "\n",
    "cbar.set_ticks(range(0, 5))\n",
    "cbar.set_ticklabels([\"$<10^{-10}$\", \"$<10^{-6}$\", \"$<10^{-3}$\", \"$<10^{-1}$\", \"$\\geq 10^{-1}$\"])\n",
    "\n",
    "plt.xlabel(\"log(rho) [g cm^${-3}$]\")\n",
    "plt.ylabel(\"log(T) [K]\")\n",
    "plt.title(\"Pressure (relative error)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the difference\n",
    "rel_err = np.abs(logu_interp(logrho_int, logT_int)-logu_int)/logu_interp(logrho_int, logT_int)\n",
    "\n",
    "# Plot the difference\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "mark = np.zeros(rel_err.shape)\n",
    "\n",
    "mark[np.where(rel_err >=0)] = 4\n",
    "mark[np.where(rel_err < 1e-1)] = 3\n",
    "mark[np.where(rel_err < 1e-3)] = 2\n",
    "mark[np.where(rel_err < 1e-6)] = 1\n",
    "mark[np.where(rel_err < 1e-10)] = 0\n",
    "\n",
    "plt.imshow(mark, cmap=plt.cm.get_cmap('viridis', 5), origin='lower', interpolation='none', extent=[logrho_min, logrho_max, logT_min, logT_max], aspect='auto')\n",
    "cbar = plt.colorbar()\n",
    "\n",
    "plt.clim(-0.5, 4.5);\n",
    "\n",
    "cbar.set_ticks(range(0, 5))\n",
    "cbar.set_ticklabels([\"$<10^{-10}$\", \"$<10^{-6}$\", \"$<10^{-3}$\", \"$<10^{-1}$\", \"$\\geq 10^{-1}$\"])\n",
    "\n",
    "plt.xlabel(\"log(rho) [g cm^${-3}$]\")\n",
    "plt.ylabel(\"log(T) [K]\")\n",
    "plt.title(\"Int. energy (relative error)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the difference\n",
    "rel_err = np.abs(logs_interp(logrho_int, logT_int)-logs_int)/logs_interp(logrho_int, logT_int)\n",
    "\n",
    "# Plot the difference\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "mark = np.zeros(rel_err.shape)\n",
    "\n",
    "mark[np.where(rel_err >=0)] = 4\n",
    "mark[np.where(rel_err < 1e-1)] = 3\n",
    "mark[np.where(rel_err < 1e-3)] = 2\n",
    "mark[np.where(rel_err < 1e-6)] = 1\n",
    "mark[np.where(rel_err < 1e-10)] = 0\n",
    "\n",
    "plt.imshow(mark, cmap=plt.cm.get_cmap('viridis', 5), origin='lower', interpolation='none', extent=[logrho_min, logrho_max, logT_min, logT_max], aspect='auto')\n",
    "cbar = plt.colorbar()\n",
    "\n",
    "plt.clim(-0.5, 4.5);\n",
    "\n",
    "cbar.set_ticks(range(0, 5))\n",
    "cbar.set_ticklabels([\"$<10^{-10}$\", \"$<10^{-6}$\", \"$<10^{-3}$\", \"$<10^{-1}$\", \"$\\geq 10^{-1}$\"])\n",
    "\n",
    "plt.xlabel(\"log(rho) [g cm^${-3}$]\")\n",
    "plt.ylabel(\"log(T) [K]\")\n",
    "plt.title(\"Entropy (relative error)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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