notebooks/09c-rank-deficient-least-squares-reaction-rate.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ChEn-3170: Computational Methods in Chemical Engineering Spring 2020 UMass Lowell; Prof. V. F. de Almeida **23Mar20**\n",
    "\n",
    "# 09c. Rank-Deficient Least-Squares Reaction Rates\n",
    "$  \n",
    "  \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n",
    "  \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n",
    "  \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n",
    "  \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n",
    "  \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n",
    "  \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
    "  \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
    "  \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
    "  \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n",
    "  \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n",
    "  \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
    "  \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
    "  \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
    "  \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
    "  \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
    "  \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
    "  \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
    "  \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
    "  \\DeclareMathOperator{\\rank}{rank}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Table of Contents\n",
    "* [Rank-Deficient Reaction mechanism](#rxnmech)\n",
    "* [Full-Rank Reaction Sub-Mechanisms](#submech)\n",
    "* [Full-Rank Least-Squares Reaction Rates](#lsr)\n",
    "* [Residuals of All Sub-Mechanisms](#residuals)\n",
    "* [Rank-Deficient Basic Least-Squares Reaction Rate Solution](#rankdef1)\n",
    "* [Rank-Deficient Mininum Norm Least-Squares Reaction Rate Solution](#rankdef2)\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rank-deficient reaction mechanism<a id=\"rxnmech\"></a>\n",
    "Refer to course Notebook 09."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['H2', 'H', 'CO2', 'OH', 'H2O', 'CO']\n",
      "r0 :  H2O + CO <=> CO2 + H2\n",
      "r1 :  H2O + H  <=> H2  + OH\n",
      "r2 :  OH  + CO <=> CO2 + H\n",
      "n_reactions = 3\n"
     ]
    }
   ],
   "source": [
    "'''Read a reaction mechanism and create data structures'''\n",
    "\n",
    "from chen_3170.toolkit import reaction_mechanism # replace with your code\n",
    "\n",
    "# build the stoichiometric matrix\n",
    "(species, reactions, stoic_mtrx, dummy, dummy) = reaction_mechanism('data/water-gas-shift-rxn.txt', shuffle=False)\n",
    "\n",
    "print(species)\n",
    "from chen_3170.help import print_reactions\n",
    "print_reactions(reactions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matrix shape = (3, 6)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stoic_mtrx=\n",
      " [[ 1.  0.  1.  0. -1. -1.]\n",
      " [ 1. -1.  0.  1. -1.  0.]\n",
      " [ 0.  1.  1. -1.  0. -1.]]\n"
     ]
    }
   ],
   "source": [
    "'''Check the stoichiometric matrix'''\n",
    "\n",
    "from chen_3170.help import plot_matrix\n",
    "\n",
    "plot_matrix(stoic_mtrx, title='Stoichiometric Matrix')\n",
    "import numpy as np\n",
    "np.set_printoptions(precision=3,threshold=100,edgeitems=5)\n",
    "print('stoic_mtrx=\\n',stoic_mtrx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full-rank, reaction sub-mechanisms<a id=\"submech\"></a>\n",
    "Refer to course Notebook 07."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# reactions =  3\n",
      "# species   =  6\n",
      "rank of S =  2\n",
      "# of all possible sub_mechanisms = 3\n",
      "# of full-rank sub_mechanisms = 3\n"
     ]
    }
   ],
   "source": [
    "'''Build the full-rank sub-mechanism reactions list'''\n",
    "\n",
    "from chen_3170.toolkit import sub_mechanisms # replace with your code\n",
    "\n",
    "sub_mechanisms = sub_mechanisms( species, reactions, stoic_mtrx )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 1), ['H2O + CO <=> CO2 + H2', 'H2O + H  <=> H2  + OH'], array([[ 1.,  0.,  1.,  0., -1., -1.],\n",
      "       [ 1., -1.,  0.,  1., -1.,  0.]]), 10.0]\n"
     ]
    }
   ],
   "source": [
    "'''Top reaction sub-mechanism'''\n",
    "\n",
    "sub_mechanism_1 = sub_mechanisms[0]\n",
    "print(sub_mechanism_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S_1=\n",
      " [[ 1.  0.  1.  0. -1. -1.]\n",
      " [ 1. -1.  0.  1. -1.  0.]]\n"
     ]
    }
   ],
   "source": [
    "'''Top reaction sub-mechanism stoichiometric matrix'''\n",
    "\n",
    "stoic_mtrx_1 = sub_mechanism_1[2]\n",
    "\n",
    "#( dummy, dummy, stoic_mtrx_1 ) = reaction_mechanism( reactions = reactions_1 ) # taking advantage of this function\n",
    "\n",
    "#plot_matrix(stoic_mtrx_1, title='Sub-Mech 1')\n",
    "print('S_1=\\n',stoic_mtrx_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 2), ['H2O + CO <=> CO2 + H2', 'OH  + CO <=> CO2 + H'], array([[ 1.,  0.,  1.,  0., -1., -1.],\n",
      "       [ 0.,  1.,  1., -1.,  0., -1.]]), 10.0]\n"
     ]
    }
   ],
   "source": [
    "'''Another top reaction sub-mechanism'''\n",
    "\n",
    "sub_mechanism_2 = sub_mechanisms[1]\n",
    "print(sub_mechanism_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S_2=\n",
      " [[ 1.  0.  1.  0. -1. -1.]\n",
      " [ 0.  1.  1. -1.  0. -1.]]\n"
     ]
    }
   ],
   "source": [
    "'''Another top reaction sub-mechanism stoichiometric matrix'''\n",
    "\n",
    "stoic_mtrx_2 = sub_mechanism_2[2]\n",
    "\n",
    "#( dummy, dummy, stoic_mtrx_2 ) = reaction_mechanism( reactions = reactions_2 ) # taking advantage of this function\n",
    "\n",
    "#plot_matrix(stoic_mtrx_1, title='Sub-Mech 2')\n",
    "print('S_2=\\n',stoic_mtrx_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full-rank least-squares reaction rates<a id=\"lsr\"></a>\n",
    "Refer to course Notebook 07."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''Use given production rate'''\n",
    "\n",
    "import numpy as np\n",
    "#                ['OH', 'CO', 'CO2', 'H2', 'H', 'H2O']\n",
    "g_exp = dict()\n",
    "\n",
    "g_exp['H']   = -1\n",
    "g_exp['H2']  =  3\n",
    "g_exp['OH']  =  1\n",
    "g_exp['H2O'] = -3\n",
    "g_exp['CO']  = -2\n",
    "g_exp['CO2'] =  2\n",
    "\n",
    "g_vec = np.array( [g_exp[spc] for spc in species] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, let's compute $\\rvec_1$ for \n",
    "$\n",
    "\\Smtrx_1\\,\\Smtrx_1^\\top\\,\\rvec_1  = \\Smtrx_1\\,\\gvec .\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "species production rates g_vec = [ 3 -1  2  1 -3 -2]\n",
      "reaction rates r_vec_1= [2. 1.]\n",
      "residual norm g - ST_1 r_1 = 0.00000e+00\n"
     ]
    }
   ],
   "source": [
    "'''Compute the LS reaction rates for random species production rates'''\n",
    "\n",
    "# build A x = b LS problem\n",
    "a_mtrx = stoic_mtrx_1 @ stoic_mtrx_1.transpose() # A = S ST, A is the normal matrix\n",
    "b_vec  = stoic_mtrx_1 @ g_vec                    # b = S g\n",
    "\n",
    "from chen_3170.toolkit import lu_factorization # replace with your code\n",
    "\n",
    "# matrix LU factorization of A, the normal matrix\n",
    "(P,L,U,s_rank) = lu_factorization( a_mtrx, 'partial' ) # matrix is full rank; partial pivoting works\n",
    "assert s_rank == np.linalg.matrix_rank(stoic_mtrx_1)\n",
    "\n",
    "from chen_3170.help import forward_solve\n",
    "from chen_3170.toolkit import backward_solve # replace with your code\n",
    "\n",
    "# solve the LS problem: A x = b\n",
    "y_vec = forward_solve( L, P @ b_vec)   # L y = P b\n",
    "x_vec = backward_solve( U, y_vec)      # U x = y\n",
    "assert np.linalg.norm(x_vec - np.linalg.solve(a_mtrx,b_vec)) < 1e-12\n",
    "\n",
    "print('species production rates g_vec =',g_vec)\n",
    "\n",
    "r_vec_1 = x_vec # r_1 = x\n",
    "print('reaction rates r_vec_1=',r_vec_1)\n",
    "residual_vec_1 = g_vec - stoic_mtrx_1.transpose() @ r_vec_1\n",
    "print('residual norm g - ST_1 r_1 = %8.5e'%np.linalg.norm(residual_vec_1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r0 :  H2O + CO <=> CO2 + H2\n",
      "r1 :  H2O + H  <=> H2  + OH\n",
      "n_reactions = 2\n",
      "(0, 1)\n",
      "\n",
      "r0 :  H2O + CO <=> CO2 + H2\n",
      "r1 :  H2O + H  <=> H2  + OH\n",
      "r2 :  OH  + CO <=> CO2 + H\n",
      "n_reactions = 3\n"
     ]
    }
   ],
   "source": [
    "'''Which reaction rates are these?'''\n",
    "\n",
    "from chen_3170.help import print_reactions\n",
    "\n",
    "print_reactions(sub_mechanism_1[1])\n",
    "print(sub_mechanism_1[0])\n",
    "print('')\n",
    "print_reactions(reactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, let's compute $\\rvec_2$ for \n",
    "$\n",
    "\\Smtrx_2\\,\\Smtrx_2^\\top\\,\\rvec_2  = \\Smtrx_2\\,\\gvec .\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "species production rates g_vec = [ 3 -1  2  1 -3 -2]\n",
      "reaction rates r_vec_2= [ 3. -1.]\n",
      "residual norm g - ST_2 r_2 = 0.00000e+00\n"
     ]
    }
   ],
   "source": [
    "'''Compute the LS reaction rates for random species production rates'''\n",
    "\n",
    "# build A x = b LS problem\n",
    "a_mtrx = stoic_mtrx_2 @ stoic_mtrx_2.transpose() # A = S ST, A is the normal matrix\n",
    "b_vec  = stoic_mtrx_2 @ g_vec                    # b = S g\n",
    "\n",
    "from chen_3170.toolkit import lu_factorization # replace with your code\n",
    "\n",
    "# matrix LU factorization of A\n",
    "(P,L,U,s_rank) = lu_factorization( a_mtrx, 'partial' ) # matrix is full rank; partial pivoting works\n",
    "assert s_rank == np.linalg.matrix_rank(stoic_mtrx_2)\n",
    "\n",
    "from chen_3170.help import forward_solve\n",
    "from chen_3170.toolkit import backward_solve # replace with your code\n",
    "\n",
    "# solve the LS problem: A x = b\n",
    "y_vec = forward_solve( L, P @ b_vec )\n",
    "x_vec = backward_solve( U, y_vec )\n",
    "assert np.linalg.norm(x_vec - np.linalg.solve(a_mtrx,b_vec)) < 1e-12\n",
    "\n",
    "print('species production rates g_vec =',g_vec)\n",
    "\n",
    "r_vec_2 = x_vec # r_2 = x\n",
    "print('reaction rates r_vec_2=',r_vec_2)\n",
    "residual_vec_2 = g_vec - stoic_mtrx_2.transpose() @ r_vec_2\n",
    "print('residual norm g - ST_2 r_2 = %8.5e'%np.linalg.norm(residual_vec_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r0 :  H2O + CO <=> CO2 + H2\n",
      "r1 :  OH  + CO <=> CO2 + H\n",
      "n_reactions = 2\n",
      "(0, 2)\n",
      "\n",
      "r0 :  H2O + CO <=> CO2 + H2\n",
      "r1 :  H2O + H  <=> H2  + OH\n",
      "r2 :  OH  + CO <=> CO2 + H\n",
      "n_reactions = 3\n"
     ]
    }
   ],
   "source": [
    "'''Which reaction rates are these?'''\n",
    "\n",
    "from chen_3170.help import print_reactions\n",
    "\n",
    "print_reactions(sub_mechanism_2[1])\n",
    "print(sub_mechanism_2[0])\n",
    "print('')\n",
    "print_reactions(reactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the sub-mechanisms rates $\\rvec_1$ and $\\rvec_2$ are different, but the corresponding residuals $\\gvec - \\Smtrx_1^\\top\\,\\rvec_1$, and $\\gvec - \\Smtrx_2^\\top\\,\\rvec_2$, are equal!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r_vec_1 - r_vec_2             = [-1.  2.]\n",
      "g - ST_1 r_1 - (g - ST_2 r_2) = [0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "print('r_vec_1 - r_vec_2             =',r_vec_1 - r_vec_2)\n",
    "np.set_printoptions(precision=3)\n",
    "print('g - ST_1 r_1 - (g - ST_2 r_2) =',(g_vec-stoic_mtrx_1.transpose()@r_vec_1)-(g_vec-stoic_mtrx_2.transpose()@r_vec_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residuals of all sub-mechanisms<a id=\"residuals\"></a>\n",
    "Let us verify the previous residual result for all sub-mechanims. Here we will compute $\\Smtrx_k$ for $k=1,\\ldots,$# of full-rank sub-mechanisms and the corresponding LS reaction rates $\\rvec_k$ and residuals\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "\\gvec - \\Smtrx_k^\\top\\,\\rvec_k .\n",
    "\\end{equation*}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rxns ids = (0, 1)\n",
      "       r = [2. 1.]\n",
      "   ||r|| = 2.236e+00\n",
      "g - ST r     = [0. 0. 0. 0. 0. 0.]\n",
      "||g - ST r|| = 0.000e+00\n",
      "\n",
      "rxns ids = (0, 2)\n",
      "       r = [ 3. -1.]\n",
      "   ||r|| = 3.162e+00\n",
      "g - ST r     = [0. 0. 0. 0. 0. 0.]\n",
      "||g - ST r|| = 0.000e+00\n",
      "\n",
      "rxns ids = (1, 2)\n",
      "       r = [3. 2.]\n",
      "   ||r|| = 3.606e+00\n",
      "g - ST r     = [0. 0. 0. 0. 0. 0.]\n",
      "||g - ST r|| = 0.000e+00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "'''Compute the LS residual for all full-rank reaction sub-mechanisms'''\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "sub_mech_rxn_rates_mtrx = np.zeros( (s_rank,len(sub_mechanisms)) )       # column-wise storage of all r_k's\n",
    "sub_mech_residuals_mtrx = np.zeros( (len(species),len(sub_mechanisms)) ) # column-wise storage of all g - ST_k r_k\n",
    "\n",
    "np.set_printoptions(precision=2)\n",
    "\n",
    "for sub_mech in sub_mechanisms:\n",
    "    \n",
    "    stoic_mtrx_k = sub_mech[2] # view of stoichiometric matrix for sub-mechanism\n",
    "  \n",
    "    # assemble LS problem matrix and right side\n",
    "    a_mtrx = stoic_mtrx_k @ stoic_mtrx_k.transpose()  # A = S ST, A is the normal matrix\n",
    "    b_vec  = stoic_mtrx_k @ g_vec                     # b = S g\n",
    "\n",
    "    # matrix LU factorization of A\n",
    "    (P,L,U,s_rank) = lu_factorization( a_mtrx, 'partial' ) # matrix is full rank; partial pivoting works\n",
    "    assert s_rank == np.linalg.matrix_rank(stoic_mtrx_k)\n",
    "\n",
    "    # solve the LS problem: A x = b\n",
    "    y_vec = forward_solve( L, P @ b_vec)  # L y = P b\n",
    "    x_vec = backward_solve( U, y_vec)     # U x = y\n",
    "    assert np.linalg.norm(x_vec - np.linalg.solve(a_mtrx,b_vec)) < 1e-12\n",
    "    \n",
    "    r_vec = x_vec  # r = x\n",
    "    sub_mech_rxn_rates_mtrx[:,sub_mechanisms.index(sub_mech)] = r_vec\n",
    "    \n",
    "    print('rxns ids =',sub_mech[0])\n",
    "    print('       r =', r_vec)\n",
    "    \n",
    "    rate_norm = np.linalg.norm(r_vec)\n",
    "    print('   ||r|| = %8.3e'%rate_norm)\n",
    "    \n",
    "    residual = g_vec - stoic_mtrx_k.transpose() @ r_vec\n",
    "    sub_mech_residuals_mtrx[:,sub_mechanisms.index(sub_mech)] = residual\n",
    "    print('g - ST r     =',residual)\n",
    "    print('||g - ST r|| = %8.3e'%np.linalg.norm(residual))\n",
    "    print('')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot the LS reaction rates for all full-rank sub-mechanisms'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "\n",
    "ax.plot(range(sub_mech_rxn_rates_mtrx.shape[1]), np.linalg.norm(sub_mech_rxn_rates_mtrx,axis=0), \n",
    "        '-.',color='black', marker='*',markersize=12)\n",
    "\n",
    "plt.xticks(range(sub_mech_rxn_rates_mtrx.shape[1]),[sm[0] for sm in sub_mechanisms],rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Reaction Rate Norm',fontsize=16)\n",
    "ax.set_xlabel('Reaction Sub-Mechanism',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Full-Rank (%i) LS Reaction Rates Magnitude of All Sub-Mechanisms'%(s_rank),fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sub-mechanism id.              = 0\n",
      "minimum norm sub-mech rxn rate = 2.2361e+00\n",
      "sub-mechanism rxn id           = (0, 1)\n",
      "r0 :  H2O + CO <=> CO2 + H2\n",
      "r1 :  H2O + H  <=> H2  + OH\n",
      "n_reactions = 2\n",
      "sub-mechanism rxn score        = 10.00\n"
     ]
    }
   ],
   "source": [
    "'''Print the LS reaction rate with minimum norm (unique)'''\n",
    "\n",
    "rate_min = np.linalg.norm(sub_mech_rxn_rates_mtrx,axis=0).min()\n",
    "idx_min = np.argmin( np.linalg.norm(sub_mech_rxn_rates_mtrx,axis=0) )\n",
    "print('sub-mechanism id.              = %i'%idx_min)\n",
    "print('minimum norm sub-mech rxn rate = %8.4e'%rate_min)\n",
    "print('sub-mechanism rxn id           =', sub_mechanisms[idx_min][0])\n",
    "print_reactions(sub_mechanisms[idx_min][1])\n",
    "print('sub-mechanism rxn score        = %4.2f'%sub_mechanisms[idx_min][3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot the LS residual norms of all full-rank sub-mechanisms'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "\n",
    "ax.plot(range(sub_mech_residuals_mtrx.shape[1]), np.linalg.norm(sub_mech_residuals_mtrx,axis=0),\n",
    "        '-.',color='red',marker='*',markersize=12)\n",
    "\n",
    "plt.xticks(range(sub_mech_residuals_mtrx.shape[1]),[smr[0] for smr in sub_mechanisms],rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Residual Norm',fontsize=16)\n",
    "ax.set_xlabel('Reaction Sub-Mechanisms',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Full-Rank LS Residuals of All Sub-Mechanisms w/ Rank = '+str(s_rank),fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rank-deficient basic least-squares reaction rate solution<a id=\"rankdef1\"></a>\n",
    "Despite all the foregoing development, we have not solved the original problem yet, namely\n",
    "\n",
    "\\begin{equation*}\n",
    "\\Smtrx^\\top\\,\\rvec = \\gvec .\n",
    "\\end{equation*}\n",
    "\n",
    "However this problem is related to the series of sub-mechanisms we just analyzed. To see this, assemble the matrix of sub-mechanism reaction rates mapped into the original reaction dimension $m$ by completing the additional entries with zeros. We denote this vector mapping $\\rvec_k\\longrightarrow\\hat{\\rvec}_k$ and the vectors \n",
    "$\\hat{\\rvec}_k$ as **basic** vectors. \n",
    "\n",
    "Then we show that all **basic** vectors produce the same residual vectors, that is:\n",
    "\n",
    "\\begin{equation*}\n",
    "\\gvec - \\Smtrx^\\top\\,\\hat{\\rvec}_k\n",
    "\\end{equation*}\n",
    "\n",
    "is invariant for any $\\hat{\\rvec}_k$ and has the same norm as the residuals $\\gvec - \\Smtrx_k^\\top\\,\\rvec_k$. All residuals being equal, we choose the rank-deficient least-squares **basic** solution as the $\\hat{\\rvec}_k$ of minimum norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''Map r_k --> \\hat{r} rates'''\n",
    "\n",
    "mech_rxn_rates_mtrx = np.zeros((len(reactions),len(sub_mechanisms)))\n",
    "\n",
    "for sm in sub_mechanisms:\n",
    "    sm_idx = sub_mechanisms.index(sm)\n",
    "    rxn_idxs = sm[0]\n",
    "    mech_rxn_rates_mtrx[rxn_idxs,sm_idx] = sub_mech_rxn_rates_mtrx[:,sm_idx] # map "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matrix shape = (3, 3)\n"
     ]
    },
    {
     "data": {
      "image/png": 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ws8+w2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2.  3.  0.]\n",
      " [ 1.  0.  3.]\n",
      " [ 0. -1.  2.]]\n"
     ]
    }
   ],
   "source": [
    "'''Show the mapping in the form of a matrix'''\n",
    "\n",
    "from chen_3170.help import plot_matrix\n",
    "\n",
    "plot_matrix(mech_rxn_rates_mtrx)\n",
    "np.set_printoptions(precision=2,threshold=100,edgeitems=5)\n",
    "print(mech_rxn_rates_mtrx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute $\\gvec - \\Smtrx^\\top\\,\\hat{\\rvec}_k$ for all $k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "residual k = 0 [0. 0. 0. 0. 0. 0.]\n",
      "residual k = 1 [0. 0. 0. 0. 0. 0.]\n",
      "residual k = 2 [0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "'''Subtract above from g column by column'''\n",
    "\n",
    "np.set_printoptions(precision=3)\n",
    "\n",
    "for j in range(mech_rxn_rates_mtrx.shape[1]):\n",
    "    tmp = g_vec - (stoic_mtrx.transpose() @ mech_rxn_rates_mtrx)[:,j]\n",
    "    print('residual k = %i'%j,tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R5A5Ttn9lhquGPaaq7jzZOA6jXO30TA9Jpxonu35/hquzPW5i37fJEOickeSts+5zwf58vH3qRPC1PUPg8vPzrYYxeIcn+ZU19rXesdmpz01V3XqNz/LOnsPHZ/gb/CKTnY+Tk78xw3DFwybquWeGedrOzBC+TVr5vH1wxjoAYCEMhQPg4uKYJG+tqrdmuHz4zZLcN8OEtv9zYtu/zzCvyhOr6mZJvpBhgt77ZPgy/aAp+/+nDJNuH1tVH87Q2+iz3X3MOjXtleRpSQ6vqk9m6ElwRoYrbt0hyU0yzBHz6CmP/VaG+WI+X1XvGPf14AzDlF7c3R9e2bC7v1RVv5fk6AyT/B6bIRDZK8MVou6U5NRc0KMhGSZnPj7JX1TVg8afK8n1Mlwx7IaZ3iti5Tn/qaqekOFS8/9eVe9O8rUMQdl1MvQgOyHDcLck+ZMk96qq45N8NckPk/xqhmN+Ri64sthu091dVb+bIWR5Y1W9PUOvpBtk6H1yVpLfmZjg/ElJ7p7kcWOYdEKG9+Q3k7w7yX+d8lR/kyFUeskYXn49w/l5+yTvTHKhQLS7T6uqh2aYT+iDVfWeDJee/4UME75fO8NVBlf8U5KHjFdVOylDj5cPrz5Hpnh0hmDtyKq6V4ZJua+d5Dcy9PJ5ZHeftc7jN0x3nzi+Fw/MMJ/QS8em5yb52yT/r6r+IUModIcModIxGeYrm7TmsZnjc/PQJH9QVR/K8DvmjAzB9QMy/D543owv8R8yfB4OyTCJ/aT/leQ2SZ48BoufzPCZ+rUMPScvciXGsdfW3ZN8ubs/P2MdALAY3W2xWCwWy25fMsx70xPrDhzXv2KNxxw/5TGPGB/ziAxf0P85Q1jz/Qxf4K6/xr5+NUMQcFaGkOP4DGHIz/c3sf0+SV6S5JQMX07XrHPVYy6VIVj56ySfSPLNDF+Gz8oQFDwvyYFTHrd9XK6Y5EUZJnE+O8kXMwwdqzWe7yZJXpHh6ndnZwjVPp/hi/ndpmy/b5JnZei189PxmH0myTOSXG69476q7Y5J3jS+tnMyfBH/zPiat63a7l4ZAr0vZOhx8aPxeV+Q5Dq7ct6ss+2659Oq7W6Q5NUZwryfjbevSXKDNba/eoYw4tQMEyV/ZjxvDh6f74g1jtOHM/Rq+UGGeYRumqHnUyc5eI1z9FXj+39OhknDP5Tk0IntrprkdWP7eatrWO8YZJjD6SXj+XJOktOSvC3JraZs+4hM+VxMvC/H7+T7sn2dbW6WIeA6JcllJur4zHj+nJYhCL7JWsdxvWOzs5+bDGHPS5J8dtzmJxkCpr9PcuNZz+FxX5/O8JnZY432q2T4DH1tfG9OT/L2JLddY/t7ja/tcTtTh8VisVgsi1iqe9arowLA8hmHE/19hh4Wr9jcahajqrYnSY9XzAIuXqrqtzIEXr/e3bs85HDswXWXJL/U3btt0nUASMyxBAAAu9sbMvRiPGKcJ2puVXXzDMPkjhAqAbAZBEsAALAb9TBk4NAMQ/kuMvn9TrpGhgnP/3ZX6wKAeZi8GwAAdrPu/pcMc63t6n7ek+Q9u14RAMzHHEsAAAAAzMVQOAAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmIlgCAAAAYC6CJQAAAADmsudmF7Cr9ttvvz7wwAM3uww20DnnnJO99957s8uAnebcZSty3rJVOXfZqpy7bFXO3Yu/k0466bTu3n9H2235YOnAAw/MiSeeuNllsIG2b98e4SFbkXOXrch5y1bl3GWrcu6yVTl3L/6q6uRZtjMUDgAAAIC5CJYAAAAAmItgCQAAAIC5CJYAAAAAmItgCQAAAIC5CJYAAAAAmItgCQAAAIC5CJYAAAAAmItgCQAAAIC5LFWwVFWXqapPVtVnq+pfq+qpm10TAAAAANPtudkFTDg7yd26+4dVtVeSE6rqPd398c0uDAAAAIALW6pgqbs7yQ/Hu3uNS29eRQAAAACsZamGwiVJVe1RVZ9J8t0k7+/uT2x2TQAAAABc1NIFS919XnffPMm1kty6qm48uU1VHVpVJ1bViaeeeuruL3KDVFmmLcceu/k1LOMCAAAAm23pgqUV3f39JMcnufeUtqO6e1t3b9t///13e20AAAAALFmwVFX7V9WVxp8vm+QeSb60uVUBAAAAMM1STd6d5BpJXllVe2QIvd7U3e/c5JoAAAAAmGKpgqXu/pckt9jsOgAAAADYsaUaCgcAAADA1iFYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5iJYAgAAAGAugiUAAAAA5rJUwVJVXbuqPlhVX6yqf62qx252TQAAAABMt+dmFzDh3CR/0t2frqorJDmpqt7f3V/Y7MIAAAAAuLCl6rHU3d/q7k+PP5+V5ItJrrm5VQEAAAAwzVIFS6tV1YFJbpHkE5tbCQAAAADTLGWwVFWXT/IPSR7X3T+Y0n5oVZ1YVSeeeuqpu79AAC4WqiyTy7HHbn4Ny7gAADDd0gVLVbVXhlDptd39j9O26e6juntbd2/bf//9d2+BAAAAACTZyWCpqi5VVTeuqrtU1T6LLqaqKsnLk3yxu/960fsHAAAAYHFmDpaq6g+SfDvJZ5N8IMkNxvVvq6o/XlA9d0jy8CR3q6rPjMt9F7RvAAAAABZoz1k2qqrfT/L8JEcneV+SN61q/kiSByV5wa4W090nJDGTAQAAAMAWMGuPpf+V5K+6+9Akb51o+1LG3ksAAAAAXHLMGiwdlOS9a7T9KMmVFlMOAAAAAFvFrMHSaUkOXKPtBkm+sZBqAAAAANgyZg2WjklyWFVdd9W6rqr9kjw+ydsWXhkAAAAAS23WYOkpSc5O8vkkxyXpDJN1fzHJeUmetiHVAQAAALC0ZgqWuvv0JNuSPDPJXkn+I8MV5V6Y5HbdfeaGVQgAAADAUtpz1g27+6wkTx8XAAAAAC7hZuqxVFVfraqbrdF246r66mLLAgAAAGDZzTrH0oFJLr1G22WSXGch1QAAAACwZcwaLCXDhN3TbEvy/QXUAgAAAMAWsuYcS1X1+CSPH+92kmOq6pyJzS6b5CpJ3rAx5QEAAACwrNabvPurSf5p/Pl3k5yY5NSJbc5O8oUkL1t8aQAAAAAsszWDpe5+e5K3J0lVJcnTuvtru6kuAAAAAJbcej2Wfq67H7nRhQAAAACwtcwULCVJVe2d5D5JbpDhSnCrdXc/fZGFAQAAALDcZgqWquoXk5yQ5MAME3nX2LT6SnGCJQAAAIBLkEvNuN2RGSbuPiBDqHSbJNdN8owkXxl/BgAAAOASZNahcHdK8r+TfHO8f353b09yWFXtkeQFSR64+PIAAAAAWFaz9ljaN8k3u/v8JD9KcuVVbR9IcvCC6wIAAABgyc0aLJ2SZL/x5/9Icq9VbbdO8tNFFgUAAADA8pt1KNwHk9wlyduSvDTJi6rq5kl+luSQcR0AAAAAlyCzBktPSXKVJOnul1TVnkl+M8nlkjw7ydM2pjwAAAAAltVMwVJ3n5bktFX3/ybJ32xUUQAAAAAsv1nnWFpTVV26qh67iGIAAAAA2DpmCpaqar+qqol1l62qP0myPclfb0BtAAAAACyxNYOlsSfS86vqh0m+k+T0qnrM2PawJF9NcmSS/0xy791RLAAAAADLY705lg5L8kdJjkvy6SQHJXl+Vf1Kkj9I8m9JDu3uYza8SgAAAACWznrB0m8meXF3/+HKiqr6vSQvS/L+JA/o7nM2uD4AAAAAltR6cyxdO8lbJ9b943j710IlAAAAgEu29YKlvZKcNbFu5f6pG1MOAAAAAFvFekPhkuSaVXXdVff3WLX++6s37O6vLrQyAAAAAJbajoKlt6yx/m1T1u0xZR0AAAAAF1PrBUuP3G1VAAAAALDlrBksdfcrd2chAAAAAGwt603eDQAAAABrEiwBAAAAMBfBEgAAAABzESwBAAAAMBfBEgAAAABzESwBAAAAMJc9Z92wqn4hyX2THJDkMhPN3d1PX0RBVXV0kvsn+W5333gR+wQAAABg8WYKlqrqDkmOSXKlNTbpJAsJlpK8IskLk7xqQfsDAAAAYAPMOhTueUm2J7lVkst096Umlj0WVVB3fzjJ9xa1PwAAAAA2xqxD4W6U5L9390kbWQwAAAAAW8esPZb+M8mlN7KQnVFVh1bViVV14qmnnrrZ5QAA7DZVlmnLscdufg3LuADARps1WHpqkieME3hvuu4+qru3dfe2/ffff7PLAQAAALhEmnUo3P2TXC3J16rqn3PROZC6u393oZUBAAAAsNRmDZbumOHKbz9I8qtT2ntRBVXV65McnGS/qjolyeHd/fJF7R8AAACAxZgpWOrugza6kFXP9Vu767kAAAAAmN+scywBAAAAwIXMOhQuVXW5JL+X5C5JrpLk9CTHJ3lFd/94Q6oDAAAAYGnN1GOpqq6e5NNJXpBkW5LLJblVkhcmOamqrrZhFQIAAACwlGYdCvfsJFdOcqfuPqi7bzfOu3THJFdK8qyNKhAAAACA5TRrsHSfJE/s7o+uXtndH0vylCT3W3RhAAAAACy3WYOlyyf55hptp4ztAAAAAFyCzBosfTnJw9doe1iSLy2mHAAAAAC2ilmvCvecJK8aJ+l+XZJvJbl6kockuUfWDp0AAAAAuJiaKVjq7tdU1eWSPC3Jy1Y1fSfJo7v7dRtRHAAAAADLa9YeS+nuo6rqZUlukOQqSb6X5Mvdff5GFQcAAADA8po5WEqSMUT64gbVAgAAAMAWsmawVFW/k+Rd3X36+PO6uvtVC60MAAAAgKW2Xo+lVyS5bZLTx5/X00kESwAAAACXIOsFSwdluPrbys8AAAAA8HNrBkvdffK0nwEAAAAgSS41y0ZVdV5V3XqNtltW1XmLLQsAAACAZTdTsJSk1mnbI8McSwAAAABcgqw3x1Kq6lK5IFS61Hh/tcsmuU+S0zagNgAAAACW2JrBUlUdnuSw8W4n+eg6+3nxIosCAAAAYPmt12Pp+PG2MgRML09yysQ2Zyf5QpJ3LrwyAAAAAJbaeleF+1CSDyVJVXWSv+vub+6uwgAAAABYbrNO3v3iJJef1lBV16+q/RZXEgAAAABbwc4ES3+yRtvjY44lAAAAgEucWYOlOyZ57xpt70tyh8WUAwAAAMBWMWuwdOUkZ67R9oMk+y6mHAAAAAC2ilmDpVOS3GaNttsk+dZiygEAAABgq5g1WHpLkidV1f1WrxzvPyHJmxZdGAAAAADLbc8Zt3takjsneUdVfTvJN5JcM8nVk3w8yVM3pjwAAAAAltVMwVJ3/7iq7pLk4UnumWFOpa9kmLj7Nd197saVCAAAAMAymrXHUrr7Z0mOHhcAAAAALuFmnWMJAAAAAC5kph5LVfW1JL3OJt3dv7SYkgAAAADYCmYdCvehXDRY2jfJ7ZP8MMkHFlkUAAAAAMtv1sm7HzFtfVVdKcmxSY5bYE0AAAAAbAG7NMdSd38/yZFJDltMOQAAAABsFYuYvPunSa61gP0AAAAAsIXMOsfSRVTVnklunOSIJP+6qIIAAAAA2BpmvSrc+Vn7qnA/SHK/hVUEAAAAwJYwa4+lp+WiwdJPk5yc5D3dfeZCqwIAAABg6c16VbgjNrgOAAAAALa6cPrrAAAgAElEQVSYRUzevVBVde+q+nJVfaWqnrDZ9QAAAAAw3Zo9lqrq6J3YT3f3/9jVYqpqjyQvSnLPJKck+VRVvaO7v7Cr+wYAAABgsdYbCne3XHhepSsluWKSc5OcnmTf8fFnJjljQfXcOslXuvurSVJVb0jywCSCJQAAAIAls+ZQuO4+sLsP6u6Dkjw8yQ+TPCTJZbv7Gkkum+S3xvUPW1A910zy9VX3TxnXAQAAALBkZr0q3F8neWZ3v2llRXefl+SNVbVfkudl6G20q2rKusmr0aWqDk1yaJIccMABC3ja5dAXeaUkyfbtjs2yq2mfXPKSlySPecxmV7F8lunzvEy1LAu/c5ef92c65+7y8/fCdP5emG6ZPs/O3emcu9Mt07m7u8w6efdNknxljbZ/T3LjxZSTU5Jce9X9ayX55uRG3X1Ud2/r7m3777//gp4aAAAAgJ0xa7D07ST/fY22hyT5zmLKyaeSXK+qDqqqvcd9v2NB+wYAAABggWYdCve8JM+tqmskeXOGIOlqGcKmQ5I8bhHFdPe5VfWHSd6bZI8kR3f3vy5i3wAAAAAs1kzBUnc/v6p+mOTwJPdZ1fT1JL/f3UcvqqDufneSdy9qfwAAAABsjFl7LKW7X15VR2eY9+gaSb6V5JTuS+LUVAAAAADMHCwlyRgifX1cAAAAALgEm3Xy7lTVTarqLVV1alWdW1Xfrao3VdVNNrJAAAAAAJbTTD2WqupWST6U5CcZrtL27SRXT/KAJPerqjt390kbViUAAAAAS2fWoXDPTPL5JHfv7rNWVlbVFZIcN7bfa/HlAQAAALCsZh0Kd9skz1wdKiXJeP9ZSW636MIAAAAAWG6zBks7uvKbK8MBAAAAXMLMGix9IsmTxqFvP1dV+yT5syQfX3RhAAAAACy3WedYelKS45OcXFXvTPKtDJN33y/JZZMcvBHFAQAAALC8ZgqWuvuTVXXbJIclOSTJVZJ8L8kHkjy9uz+3cSUCAAAAsIxmCpaq6opJvtzdD97gegAAAADYInY4x1JV7Znk9CT32vhyAAAAANgqdhgsdfe5Sb6T5LyNLwcAAACArWLWq8K9JsmjNrIQAAAAALaWWa8Ktz3JQ6vqU0nenuGqcL16g+4+erGlAQAAALDMZg2WXjTeXjPJLae0dxLBEgAAAMAlyKzB0kEbWgUAAAAAW85MwVJ3n7zRhQAAAACwtaw7eXdV3bWq3lZVn6+qE6rqj3ZXYQAAAAAstzWDpao6JMlxSe6S5EdJrpvkeVX1pN1UGwAAAABLbL0eS09KckKSA7r7NkmuneRlSf6sqmp3FAcAAADA8lovWLpRkr/q7rOSpLvPS/L0JFfIEDIBAAAAcAm2XrC0X5JvT6z71ni778aUAwAAAMBWse7k3Ul6t1QBAAAAwJaz5w7aj6mqc6asf3dV/WzV/e7u6yywLgAAAACW3HrB0it3WxUAAAAAbDlrBkvd/cjdWQgAAAAAW8uO5lgCAAAAgKkESwAAAADMRbAEAAAAwFwESwAAAADMRbAEAAAAwFwESwAAAADMZaZgqapuX1X3X3V/36p6fVV9rqqeU1V7bFyJAAAAACyjWXss/WWSW666f2SS+yb5tySPSfKkBdcFAAAAwJKbNVi6UZITk6Sq9kry4CSP7+4HJXlykoduTHkAAAAALKtZg6XLJ/nB+POtk+yT5J3j/U8nOWDBdQEAAACw5GYNlr6R5Gbjz/dJ8vnu/u54/8pJfrzowgAAAABYbnvOuN3rk/xFVR2cYW6lw1e1/Zck/77gugAAAABYcrMGS0ck+WmS22aYyPu5q9puluTNiy0LAAAAgGU3U7DU3eclecYabf9toRUBAAAAsCXMOsdSkqSqblpVf1hVh1fV1cd1v1xVV9jVQqrqN6rqX6vq/Kratqv7AwAAAGBjzdRjqaouneQ1SX49SSXpJMck+XaSZyf5tyRP2MVaPj/u/6W7uB8AAAAAdoNZeyw9I8k9kjw8ydUyhEsr3pPkkF0tpLu/2N1f3tX9AAAAALB7zDp5928leUp3v66q9pho+1qSAxdaFQAAAABLb9Zgad8kX1yj7VJJLj3LTqrquCRXn9L05O5++4y1pKoOTXJokhxwwAGzPgzYIN2bXcFy2r7dsQEAAC7eZg2Wvpbkdkk+MKXt1klmGsLW3feY8fl2tJ+jkhyVJNu2bfO1DQAAAGATzDrH0quSPKGqfjvJ3uO6rqq7Jnl8kqM3ojgAAAAAlteswdKzk7wryauTfG9cd0KS45Ic291/s6uFVNWvVdUpGXpGvauq3rur+wQAAABg48w0FK67z0vykKp6UYYrwF01yekZQqUPLaKQ7n5rkrcuYl8AAAAAbLxZ51hKknT3R5J8ZINqAQAAAGALmXUoHAAAAABcyJrBUlWdV1W3Hn8+f7y/1nLu7isZAAAAgGWw3lC4pyU5ZdXPvfHlAAAAALBVrBksdfdTV/18xG6pBgAAAIAtY6Y5lqpqr6raZ422fapqr8WWBQAAAMCym/WqcC8ft33olLaXJjknye8tqigAAAAAlt+sV4U7OMnb12h7R5K7L6QaAAAAALaMWYOlqyb57hptpya52mLKAQAAAGCrmDVY+m6Sm6zRdpMkpy+mHAAAAAC2ilmDpXcm+fOquunqlVV1kyRPTnLMogsDAAAAYLnNOnn3YUnumeSkqvpUklOSXDPJrZN8LclTNqY8AAAAAJbVTD2Wuvu0JLdK8swkleTm4+0zktxqbAcAAADgEmTWHkvp7u9n6Ll02MaVAwAAAMBWMXOwlCRVtV+S2ybZN8kx3f29qrpMknO6+/yNKBAAAACA5TTTULgaHJlhbqV3JDk6yYFj89szTOANAAAAwCXIrFeFe2KSP0zytCS3yTC/0opjktx/wXUBAAAAsORmHQr3qCRP6+5nVtUeE21fSfJLiy0LAAAAgGU3a4+layb5+Bpt5yTZZzHlAAAAALBVzBosfSPJjddou1mSry2mHAAAAAC2ilmDpTcnOayq7rBqXVfV9ZP8SZI3LLwyAAAAAJbarMHSEUm+lOTDSf59XPfmJJ8b7//lwisDAAAAYKnNNHl3d/+kqg5O8tAkh2SYsPv0JE9P8truPnfDKgQAAABgKc16Vbh093lJXj0uAAAAAFzCzRwsJUlV/XKSW2e4StwpST7V3V/ZiMIAAAAAWG4zBUtVdZkkL07y8CR7rGo6r6pemeQPuvvsDagPAAAAgCU16+Tdz0ny20kOT/LLSa4w3h6RIWw6ciOKAwAAAGB5zToU7iFJntrdf7Fq3VeTPKOqkuTxSf54wbUBAAAAsMRm7bF06SSfXKPtE0n2Xkw5AAAAAGwVswZLxyW51xpt90rygcWUAwAAAMBWMetQuL9O8uqq2ifJm5N8J8nVkvz3JPdN8rCquu7Kxt391UUXCgAAAMBymTVY+tB4+5gkj161vibaV+wRAAAAAC7WZg2WHrmhVQAAAACw5cwULHX3Kze6EAAAAAC2llkn776QqrpiVW2rqmstuiAAAAAAtoY1g6WqOqSq/nLK+icl+W6STyQ5uapeV1WzDqkDAAAA4GJivUDo0Ul69YqqumeS/5vkc0leluRGSf6/JCcl+asNqhEAAACAJbResHSLJE+fWPfIJD9Nckh3fztJqipJHhrBEgAAAMAlynpzLF01yX9MrLtnkhNWQqXRu5Jcf9GFAQAAALDc1guWzkqyz8qdqrpekn2TfHxiux8k2WPxpQEAAACwzNYLlr6U5IGr7j8ww5xL75vY7qAk39nVQqrqyKr6UlX9S1W9taqutKv7BAAAAGDjrBcsPTfJo6rqLVX1oiRPzTBp90cntvu1JJ9dQC3vT3Lj7r5pkn9L8sQF7BMAAACADbJmsNTdb0vyuCS3SvI7GYbA/UZ3//xKcVV1rSR3TfLuXS2ku9/X3eeOdz+e5Fq7uk8AAAAANs56V4VLd78gyQvWaT8lyUYMWfu9JG/cgP0CAAAAsCDrBkuLVlXHJbn6lKYnd/fbx22enOTcJK9dZz+HJjk0SQ444IANqBQAAACSC8bssNr27Y4Ng90aLHX3PdZrr6rfTXL/JHdfPeRuyn6OSnJUkmzbts2pDAAAALAJdmuwtJ6quneSP0tyl+7+8WbXAwAAAMD61rsq3O72wiRXSPL+qvpMVf3tZhcEAAAAwNqWpsdSd//yZtcAAAAAwOyWqccSAAAAAFuIYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJiLYAkAAACAuQiWAAAAAJjL0gRLVfX0qvqXqvpMVb2vqn5xs2sCAAAAYG1LEywlObK7b9rdN0/yziSHbXZBAAAAAKxtaYKl7v7Bqrv7JOnNqgUAAACAHdtzswtYraqekeR3kpyZ5K6bXA4AAAAA69itwVJVHZfk6lOantzdb+/uJyd5clU9MckfJjl8jf0cmuTQJDnggAM2qlwAAGBB2niEqbZvd2yArW23BkvdfY8ZN31dkndljWCpu49KclSSbNu2za9hAAAAgE2wNHMsVdX1Vt39r0m+tFm1AAAAALBjyzTH0l9W1Q2SnJ/k5CSP3uR6AAAAAFjH0gRL3f2gza4BAAAAgNktzVA4AAAAALYWwRIAAAAAcxEsAQAAADAXwRIAAAAAcxEsAQAAADAXwRIAAAAAcxEsAQAAADAXwRIAAAAAcxEsAQAAADCX6u7NrmGXVNWpSU7e7DrYUPslOW2zi4A5OHfZipy3bFXOXbYq5y5blXP34u863b3/jjba8sESF39VdWJ3b9vsOmBnOXfZipy3bFXOXbYq5y5blXOXFYbCAQAAADAXwRIAAAAAcxEssRUctdkFwJycu2xFzlu2KucuW5Vzl63KuUsScywBAAAAMCc9lgAAAACYi2AJAAAAgLkIlgAAAACYi2AJAAAAgLkIlgAWpKruWVX7bnYdsKuqqlbfArDxJn/3+h3MVlJVe2x2DWwewRJLafIfUv+wsuyq6jJJXp7k36vqUc5Ztri9q2rvHi8dW1X+XmBpVdW9q+oLVXX7za4FdkV3d1XVyu/eVb+D/U3B0qmqW1bV7arqbknS3eeN6/3NcAnkTWdpVdUvjL+srrvyDyssq+7+aZI7JDkqyfOTfLKq7ri5VcHOq6r/meTtGULSZyRJd5+/uVXBuk5JcmqSD1bVa6rq2ptdEOysqrpuVR2W5K1V9eqqelxV/ZfkgoAJlkFV3b2qXp/khCQfTfL6qvq3qnpI4m+GS6rye4plVFV/lORhSX4xyY+SvCjJCxP/uLLcxm7A+yf5UpJfSPKWJH/W3V/b1MJgBlX12CSPSvKxJF9J8qdJXtfdj1v9v+iwbKrqskkOSfLUJFdL8pwkL+run2xqYTCDqnp4kt9Pcv0kJya57vjzZ5O8JMmrk5zjdzCbraqunOTTSY7L8J9Qpye5c5L7ZvgP1qOT/J/u/v6mFcmmECyxdKrq1knek+QJGX5Z3TLDH4sP6u6TJ7b1RYelsDKuvLvPq6pbJTk2yeFJHpnkRkmOTPKc7j5r86qEtY3DOb+Z5FHd/Y/juj9K8sdJbpvke37fsmxW/g6oqj3G379PTvLEJD9L8r0kT+juN29ulbC2MRT9RpIjkry2u08f198/ybOTXDPJQ7r7PZtWJIyq6s1J9k7ya6t7JlXVryT5gyS/neHviLdsUolsEsESS6eqPpjkpO7+3+P9q2VIxV/T3c9a+eNxU4uEUVVdYSUsWvXF5sQkH+r/v717j7Z7PvM4/v6chLjUpeISg9FQg7p1pkrrTimTmSlqUXWrabvQIV1MlLjP0rBQLdVFZ1AsZLnF/TLEuFZroS6DtooQMW6JWxAkwmf++H63bDuJJEea307O57VW1j779/vts5+VddY5+/v8nu/z2MMkLQ3sAxxTX/JF2xObijdiZuoWuG8D37L9btvxJ4FDbV9Xn28ILGn79mYijfik2g9sSl2g/x+wP3AfcCyl+vkRYH/bjzYYZsQMSfoVsJbt7erzj2+a1l41twArAlvZfrW5SKOvkzQYuI2S6Ly/Hvt4XSapP3A1MAjY1PaUxoKNeS49lqKrSFoPWAK4qT7vsf0KcBWlxLJVEbKypOvqh8iIRtQPfBdJOkzSwPqzuTflD+pJALbftH0GpeLjoCSVohvVxrDvA5OBAfXYwvX0A8DObdeNBv6hgTAjPiZpVUnfBmhbvJwFPGR7lO3nKQmmbYFFgfWbiTRi5iQtDgwGrmwda0sqLVQrQn5GqXxevZEgI6bpASbSlkNoTyrZnkpZwy0G9G8kwmhMEkvRbSZSenu0tgu1SupGAoMlrVSfnwYMSu+EaNhA4EPKovscSbtQEkrDbU+od24AsD3G9mUNxRnxqepCZhRwtO036h3z1mL9bmDD+vWRwNu2T20izog2PwJOkfRrSatLWpVScXd06wLbH9n+HbCx7YubCjRiRurv2UmUbUUb12Ptnxs+qF8+RqnAW2qeBxnxSVMoCc5tYFobiKq1m+Rp4D1g6XkbWjQtiaXoGpK2pdwxP832A/Dx2NV+wHOUZNO6kr5MWcjv2FiwEYDtCcCulIVMP+BkYBFgbD0/VVJPxx/eiK5k+y3bD9en7XcabwWWqlvgfkLpuRTRtJHAxcB6lGax9wI32L4PyoKnNaLd9uTGooyYtWeBzSWtXCs+PpFgoiSeVgXSDDkaVStBrwcOlLRee2uSth6M+wFjbb/YRIzRnPRYiq5Qm8Y+RdmCMdz2eW3nWo05bwCepEweuNf20GaijZhe3Za5B6WfUn/gDuBs2+MaDSxiNtSk0cLAorZvazs+wPZkSbcDWwG32t6+oTAjptPWMHYrYDxletZFrWqPDPmIbidpLcr2ofHACNs3tJ0bAJwDrGJ764ZCjD5O0vqUptz3UrbH3wisAYwA/hOYCnyO8jn4aGCdJJb6niSWomtIWgU4qP77E3CI7Xvazu8DXACMtz2okSAjZqE2mz8Y2BKYRPmweHoWNtGNJH0D+CGwEyWxP4GyJflY25e2XXcmZevR4M7pnBHzUh11/U1ga2AFSs+vu4ANKD/Hfwf8mZJcyhSt6Dqdyc7az+4HlGmGkykL99GUCujtKFV529t+toFwo4+TNAi4lvJ79QrbN0raBBhK2UEyCXgFWI3SzmSk7d80FW80J4ml6Cp1y9BywBPAkpSeH8NtP1P7J9wMHGH7mgbDjJil2oj+BGCM7UOajieiU12gP0SZunkt8BqlInQIsClle9Fhtt+UtDzwJdt3NhRuBPXn8AJgXeAtyiJ8bcrP7nGUBsi7URY7awP72b61kWAjZqJu0VwCWIdys3RMPf5Vynbj9YC/Bd4FrgMutH1XQ+FGHyfpeuAN4ICOibErUoYibAgsT9lVcoXt8Y0EGo1LYim6QqsHTZ2q9VVKAulY4PuUD4enUhp2r2r7kcYCjZgD9ed6QPsf4ohuIekKyva3nevkodbx1taiPYEf2h7VUIgRnyDpRkpT2BNtP1QrRL9Amf62L3CG7YMlfQXYzvZJjQUbMROShgJ7ASsB71C2Ev2qbbrWmpQmybL9TGOBRp8naSPgv4FNbP+lHutp/8xQj2XLcSSxFM2StITtt+vX/Wpi6Q/AXbaHSVqa0rPmWMof2TVb10dERO9IGgzcBuxu+/56rF/72GDgamAQsFmaH0fTJH2dsrV4g87edZKWA4ZRGstvZPvxBkKMmKW2hfpwSqXdV4DtgV1mts04i/ZoiqRhwD8Cu9l+veNcj+2PJJ1IKQLYrW2SYfRBmQoXjZHUA1wk6TBJA2tSaW/KQuYkANtv2j6DMoZ1WJJKERFzRQ+ll9LHnwPak0p1MtFNwGKUiYcRTduW0kvp5c5Jm3VC55GUqVnfaSC2iNl1MnC+7XNsXwWcQelvtztMNw0O+MS0rYh5bSKwdiup1Jq0CdBWtfQgpZJ0up/d6FuSWIomDQQ+pPRCOEfSLpSE0nDbE9r/uNoeY/uShuKMiFjQTAFWB7aBaduRq9b44KcpHxaXnrehRczQBErV8pR6I+rjBU6t6PgIuIcsbqJL1d6LS1CS9q2Kj1eAqyi97bA9VdLKkq6r02YjmvQ8sKKkfSQt1Epytv/+pWybn2D7vUYijK6RxFI0pt5h3JUylrIf5S7OIsDYen6qpJ7OO5MREfHZ2H4euB44UNJ6rWqleq51d3w/YGxGBkeXGAesOYsFzhJMS4xGdJuJlKlZrer71u/akcBgSSvV56cBg7JQjy5wD3AfcAwwRNLSra2ZkhaTtCdlK+dxjUYZXSE9lqIr1Lsye1D6KfUH7gDO7uyjEBERvSdpfcrdxXspI61vBNYARlAayE4FPkf5fXw0sE4SS9ENJC1OmWC4LHAocCfwVl3g9KNUfFwOrGj7zcYCjZgBSdsCjwKL23627Xg/yufeh4B/p4xt/wOwiu2Xmog1op2kLwKXUvooXQn8FniJ8lliXeA826c1F2F0iySWoqvUCS8HA1sCkyjlwqdnf3lExGcjaRBwLfBnykjgGyVtAgylbEmeRFnUrEa5qz7S9m+aijeiU8cCZxTwO+AFSnPZLYCLbZ/SXIQR05O0CPAUpZfScNvntZ1rVX/cQBnXvgVwr+2hzUQbMT1JywAHUCbGLkuptnsMONX2ZU3GFt0jiaXoSnUf+gnAGNuHNB1PRMT8TtL1wBvAAbbfbTu+IrA+sCGwPGVxc4Xt8Y0EGvEpJA0E9mfaAgdKJciZti9oKq6ITyNpFeCg+u9PwCG272k7vw9wATDe9qBGgoyYDXVC51hKxeikhsOJLpLEUnStWh48oH0BFBERc65txPUmtv9Sj/W0TXVpXZex1jHfqAuccZQFTqbGRlern2uXA54AlqRU3Q23/YykVYGbgSNsX9NgmBGzJZ8XolOad0fXsv1hkkoREXPF5sDDlMlawLRRwZJ66uOJwFWSFmokwog5ZPte2y8kqRTdTFI/Sf3qkIRVKA3mh1Imcz4u6XjgLeC7SSrF/CJJpeiUxFJERMSCbyKwtu3X4ZOTtNqqlh4E3iPj2iMiPjNJS0C5Udp2+NfABbbPBL4BDAf+DfgjMGaeBxkRMZcksRQREbHgex5YcRaj2vcEJmTEdUTEZ1MrQS+SdJikgbY/lLQ3MAg4CcD2m7bPADYGhqXyLiLmZ7krGRERseC7B7gPOAaYKOkuYGKdRrQYZSrc9sBKDcYYEbGgGEjZ8rYz8DVJIykJpcNtT5DU3/ZUANtjSLVSRMzn0rw7IiKiD+gY1X4l8FvgJUql0rrAebZPay7CiIgFR61a2hr4MbAO8Hlgx9Y0uHpeHVvlIiLmS0ksRURE9BGSlgEOYNqodgOPAafavqzJ2CIiFkSSFgX2APah7Ba5Azjb9rhGA4uImIuSWIqIiOiD6qj2sZRR7ZMaDiciYoEmaQXgYGBLYBJwE3B6pmtFxIIgiaWIiIg+TJKysImImDckrQecAIyxfUjT8UREzA1JLEVERERERMwjkvoBA2y/23QsERFzQxJLERERERERERHRKz1NBxAREREREREREfOnJJYiIiIiIiIiIqJXkliKiIiIiIiIiIheSWIpIiIiIiIiIiJ6JYmliIiI6JMk7STpbknjJb0n6TlJ10jaoeG4/kNSpqtERETEfCGJpYiIiOhzJP0YuBp4CvgB8E/AiHp6m6biqs4Fvt5wDBERERGzRXZuiEVERETfImkc8KDtnWdwrsf2Rw2EFRERETHfScVSRERE9EXLAC/P6ER7UknSvpIsaYu6Te4dSa9JOlPSou2vk7SYpJMlPStpSn08SlJPx3XLSTpL0vOSJtfHiyQNqOen2wonqb+kIyQ9UV/zoqSfS1qk45qfShoj6X1Jr0q6R9Jmc+H/KyIiImKG+jcdQEREREQD7ge+J+kZ4FrbT87i+ouBy4GzgI2AY4HFgX2hJHWAW4AvAT8FHgO+BhxDSWINq9d9Hvh9PTYCeBRYHtgRWBiY/Cnv/y/AyfX1a9f3+QKwS73mcOAQ4CjgEWBJYMP6XhERERF/FUksRURERF90ADAKOAU4RdJrwK3A+bZHz+D6m2wfWr8eXSuKjpd0Yk1KfRfYDNjS9t31utskARwn6WTb4ymJn9WADW0/3Pb9L5lZoJI2B74DfM/2hfXw/0h6HbhY0pdtP0LpyzTa9i/bXn79bP5/RERERPRKtsJFREREn1OTQX8PbAmcQKnw2Rm4RdLRM3jJ5R3PL6V8jtqoPt8BeA74fd2S1r9WMY0GFqJULwF8E3igI6k0KzsAU4ArZ/C9Abaojw8AQySdIGkzSQvPwXtERERE9EoqliIiIqJPsv0hcHf9h6S/AW6mVBidafuNtstf6Xh56/lK9XF5YFXgg5m83cC2x/+dw1CXp2yTe2cW3/tE4H1gL+BI4B1Jo4Cf2H51Dt8zIiIiYrYksRQREREB2H5R0rnAL4E1KH2YWlYA/tjxHOCF+vga8Cyw20y+/dj6+CrTklGz6zVKwmjzmZx/EcD2B5QeTCdLGgT8M/ALYDHKVrqIiIiIuS6JpYiIiOhzJK1i+/kZnFqrPnZOjNsNuL3t+e7AR0xLPt1MaaL9ju0nPuWtRwNHS9rA9uxWLt1Macy9lO3bZucFtl8GzpU0BFh3Nt8nIiIiYo4lsT9vHlMAAAGCSURBVBQRERF90eOS7gCuplQaLQkMoTT1vtz2uI7rh0j6GSUxtBFwHHBh2zS5kcC/Uhp2/5yy3W1hYHXgW8BOtt8FTgP2oDTfHkGZHrcsZSrcAbbf7gzU9p2SLgFGSfoFJZn1EWUi3BDgcNtPSrq2vu9DwBuUHlI7AP/1mf6nIiIiIj5FEksRERHRFx1OScocT9nW9iHwJDAcOH0G1+8FDAN+RGmkfQ7QmhKH7Q8kbV9fvx8wGJgEjAFurK/B9puSNgVG1GsHUvo13d66Zib2AoYC3weOAiZTttfdwrR+T3cDuwIHUra/jaNMvTthdv5DIiIiInpDtpuOISIiIqIrSdoXOB9Yw/bTDYcTERER0XV6mg4gIiIiIiIiIiLmT0ksRUREREREREREr2QrXERERERERERE9EoqliIiIiIiIiIioleSWIqIiIiIiIiIiF5JYikiIiIiIiIiInoliaWIiIiIiIiIiOiVJJYiIiIiIiIiIqJXkliKiIiIiIiIiIhe+X/bL7FefGSxjAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot of the input species production rate'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "\n",
    "ax.bar(range(len(species)), g_vec, color='blue')\n",
    "plt.xticks(range(len(species)),species,rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Species Production Rate',fontsize=16)\n",
    "ax.set_xlabel('Species',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Input Species Production Rates ('+str(len(species))+')',fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Select as **basic** solution of the rank-deficient LS problem: \n",
    "\n",
    "\\begin{equation*}\n",
    "\\min\\limits_k \\norm{\\hat{\\rvec}_k} \\quad\\ \\forall \\quad\\ k=1,\\ldots,\\text{# of full-rank sub-mechanisms} .\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Basic least-squares reaction rates'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "ax.bar(range(len(reactions)), mech_rxn_rates_mtrx[:,idx_min], color='orange')\n",
    "plt.xticks(range(len(reactions)),reactions,rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Reaction rate',fontsize=16)\n",
    "ax.set_xlabel('Reaction',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Basic LS Reaction Rates (%s)'%str(s_rank),fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rank-deficient minimum norm least-squares reaction rate solution<a id=\"rankdef2\"></a>\n",
    "\n",
    "To compute the reaction rates vector $\\rvec$ for a given species production vector $\\gvec$ we need to solve:\n",
    "\n",
    "\\begin{equation*}\n",
    "\\Smtrx^\\top\\,\\rvec = \\gvec .\n",
    "\\end{equation*}\n",
    "\n",
    "Since $\\Smtrx$ is rank deficient, a **unique** mininum-norm least squares solution, $\\rvec_\\text{MNLS}$, exists as follows,\n",
    "\n",
    "\\begin{equation*}\n",
    " \\lim\\limits_{\\delta\\rightarrow 0}\\,\\min\\limits_\\rvec \\bigl( \\norm{\\gvec - \\Smtrx^\\top\\,\\rvec_\\text{MNLS}}^2 + \\delta\\norm{\\rvec_\\text{MNLS}}^2 \\bigr) \\quad\\  \\forall \\quad\\ \\rvec.\n",
    "\\end{equation*}\n",
    "\n",
    "This solution is obtained by solving:\n",
    "\n",
    "\\begin{equation*}\n",
    "\\lim\\limits_{\\delta\\rightarrow 0}\\,\\bigl(\\Smtrx\\,\\Smtrx^\\top + \\delta\\Imtrx\\bigr) \\rvec_\\text{MNLS}  = \\Smtrx\\,\\gvec ,\n",
    "\\end{equation*}\n",
    "\n",
    "where $\\Smtrx\\,\\Smtrx^\\top$ is square, symmetric and singular. The least-squares problem is just $\\Amtrx\\,\\xvec=\\bvec$ with\n",
    "$\\Amtrx = \\Smtrx\\,\\Smtrx^\\top + \\delta\\Imtrx$ and $\\bvec = \\Smtrx\\,\\gvec$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "species production rates g_vec = [ 3 -1  2  1 -3 -2]\n",
      "reaction rates r_vec= [1.666 1.333 0.333]\n",
      "   ||r|| = 2.160e+00\n",
      "||g - ST r|| + ||r|| = 2.16077e+00\n"
     ]
    }
   ],
   "source": [
    "'''Compute the LS reaction rates for random species production rates'''\n",
    "\n",
    "# Overdetermined\n",
    "assert stoic_mtrx.transpose().shape[0] > stoic_mtrx.transpose().shape[1]\n",
    "# build A x = b LS problem\n",
    "delta = 1e-3\n",
    "a_mtrx = stoic_mtrx @ stoic_mtrx.transpose() + delta * np.eye(3) # A = S ST + delta I, A is the normal matrix\n",
    "b_vec  = stoic_mtrx @ g_vec                    # b = S g\n",
    "\n",
    "from chen_3170.toolkit import lu_factorization # replace with your code\n",
    "\n",
    "# matrix LU factorization of A, the normal matrix\n",
    "(P,L,U,a_rank) = lu_factorization( a_mtrx, 'partial' ) # matrix is full rank; partial pivoting works\n",
    "assert a_rank == np.linalg.matrix_rank(stoic_mtrx@stoic_mtrx.transpose()+np.eye(3))\n",
    "\n",
    "from chen_3170.help import forward_solve\n",
    "from chen_3170.toolkit import backward_solve # replace with your code\n",
    "\n",
    "# solve the LS problem: A x = b\n",
    "y_vec = forward_solve( L, P @ b_vec)   # L y = P b\n",
    "x_vec = backward_solve( U, y_vec)      # U x = y\n",
    "assert np.linalg.norm(x_vec - np.linalg.solve(a_mtrx,b_vec)) < 1e-12\n",
    "\n",
    "print('species production rates g_vec =',g_vec)\n",
    "\n",
    "r_vec = x_vec # r = x\n",
    "print('reaction rates r_vec=',r_vec)\n",
    "rate_norm = np.linalg.norm(r_vec)\n",
    "print('   ||r|| = %8.3e'%rate_norm)\n",
    "residual_vec = g_vec - stoic_mtrx.transpose() @ r_vec\n",
    "print('||g - ST r|| + ||r|| = %8.5e'%(np.linalg.norm(residual_vec)+rate_norm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Minimum norm least-squares reaction rates'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "ax.bar(range(len(reactions)), r_vec, color='orange')\n",
    "plt.xticks(range(len(reactions)),reactions,rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Reaction rate',fontsize=16)\n",
    "ax.set_xlabel('Reaction',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Minimum Norm LS Reaction Rates (%s)'%str(s_rank),fontsize=20)\n",
    "plt.show()"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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    "version": 3
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