{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# The Non Random Two Liquids (NRTL) model for *excess Gibbs energy* ($g^E$) in a case study of Liquid-Liquid equilibria of Ethyl acetate (1) + water (2) + ethanol (3) --  the  scipy verified numerical methods approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Having discussed Excess properties, the NRTL model specifically, and VLE,\n",
    "Having successfully discussed LLE\n",
    "A parentheses to discuss the verified scipy numerical methods approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Requirements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The NumPy package\n",
    "for array structures and operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.3144598\n"
     ]
    }
   ],
   "source": [
    "from scipy.constants import R\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# scipy optmization package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import optimize as opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The NRTL model\n",
    "as presented in previous lecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "reproduced below in minimalist numpy/numba format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numba import jit\n",
    "@jit\n",
    "def Gamma(T,c_x,q_alpha, q_A):\n",
    "    q_tau     = q_A/T\n",
    "    q_G       = np.exp(-(q_alpha*q_tau))\n",
    "    l_D       = ((1/((q_G.T) @ c_x)).T)\n",
    "    q_E       = (q_tau*q_G) * l_D \n",
    "    gamma     = np.exp(((q_E+(q_E.T))-(((q_G * l_D) * (c_x.T)) @ (q_E.T))) @ c_x)\n",
    "    return gamma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# fited parameters\n",
    " \n",
    " Renon and Prausnitz, 1969"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Ethyl acetate (1) + water (2) + ethanol (3)\n",
    "\n",
    "alpha12 = 0.4\n",
    "\n",
    "alpha23 = 0.3\n",
    "\n",
    "alpha13 = 0.3\n",
    "\n",
    "# 6 binary Aij parameters\n",
    "Dg12 = 1335 * 4.184 #J/K\n",
    "Dg21 = 2510 * 4.184 #J/K\n",
    "\n",
    "Dg23 = 976 * 4.184 #J/K\n",
    "Dg32 = 88 * 4.184 #J/K\n",
    "\n",
    "Dg13 = 301 * 4.184 #J/K\n",
    "Dg31 = 322 * 4.184 #J/K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feeding the fitted parameters to the model in matrix structure:\n",
    "we will assemble the parameters in a matrix structure compatible with the current imlementation of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#assemble matrix with regressed parameters Dg_i,j, according to the model all diagonal terms are zero\n",
    "Dg = np.array([[0, Dg12, Dg13],\n",
    "             [Dg21, 0, Dg23],\n",
    "             [Dg31, Dg32, 0]])\n",
    "\n",
    "\n",
    "#assemble symmetric matrix alpha\n",
    "alpha = np.array([[0, alpha12, alpha13],\n",
    "                [alpha12, 0, alpha23],\n",
    "                [alpha13, alpha23, 0]])\n",
    "\n",
    "A= Dg/R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "T = 273+70 #K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Liq-Liq Equilibria Flash\n",
    "already discussed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# initial guess\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Estimativas Iniciais\n",
    "\n",
    "def iguess(Z,MODEL):\n",
    "    #print(Z)\n",
    "\n",
    "    gama0 = MODEL(Z/np.sum(Z))\n",
    "    \n",
    "    Xlin = 1/(gama0.T @ Z) * (gama0*Z)\n",
    "\n",
    "    gamalin = MODEL(Xlin/np.sum(Xlin))\n",
    "\n",
    "    Klin = (1./gamalin) * gama0\n",
    "\n",
    "    KlinMin = np.min(Klin)\n",
    "    KlinMax = np.max(Klin)\n",
    "\n",
    "    NT = (KlinMax - KlinMin)\n",
    "    \n",
    "    nI0 = (KlinMax - Klin) * Z\n",
    "\n",
    "    nII0 = (Klin-KlinMin) * Z\n",
    "    \n",
    "    beta0 = np.array([[ 1/(KlinMax-KlinMin) * np.sum(nII0) ]])\n",
    "    \n",
    "    ###\n",
    "    \n",
    "    XI0 = 1/(np.sum(nI0)) * nI0\n",
    "\n",
    "    gamaI0=MODEL(XI0/np.sum(XI0))\n",
    "\n",
    "    XII0 = 1/(np.sum(nII0)) * nII0\n",
    "\n",
    "    gamaII0=MODEL(XII0/np.sum(XII0))\n",
    "    \n",
    "    K0 = (gamaI0)/(gamaII0)\n",
    "    \n",
    "    #print(XI0, XII0, gamaI0, gamaII0, K0)\n",
    "    \n",
    "    return beta0, K0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# algorithm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as before:\n",
    "* explict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def ELLflash_explicit(Z,beta0,K0,MODEL,qolog):\n",
    "    \n",
    "    #copy intial guesses to local variables\n",
    "    beta=beta0.copy()\n",
    "    K=K0.copy()\n",
    "\n",
    "    converged = 0 # flag indicating not converged yet\n",
    "    \n",
    "    if qolog:\n",
    "        itlogi=0\n",
    "        itlogv=np.ndarray(2,dtype=object)\n",
    "        itlogv[0]=np.zeros(100*100)\n",
    "        itlogv[1]=np.zeros([100*100,3])\n",
    "    \n",
    "    #initialize local arrays\n",
    "    a = np.zeros(3)\n",
    "    XI = np.zeros(3)\n",
    "    XII = np.zeros(3)\n",
    "    \n",
    "    looped2=0\n",
    "    looped3=0\n",
    "    \n",
    "    #managing loop for fixed point point algorithm\n",
    "    looping2 = 0\n",
    "    while ( (looping2 == 0) # means do at least once\n",
    "           or ((ResK)>0.0001 # convergence criteria\n",
    "               and looping2 < 100) ): # max number of iterations\n",
    "\n",
    "        prevK = K.copy()\n",
    "        \n",
    "        #print(np.may_share_memory(K,prevK))\n",
    "        \n",
    "        #Solve RachfordRice equation with a newton raphson loop\n",
    "        looping3 = 0\n",
    "        while ( (looping3 == 0) # means do at least once\n",
    "               or ((ResBeta)>0.0001 # convergence criteria\n",
    "                   and looping3 < 100) ): #max number of iterations\n",
    "            \n",
    "            prevbeta = beta.copy()\n",
    "\n",
    "            for i in range(3):\n",
    "                a[i] = ( (K[i]-1) / (1+beta*(K[i]-1)) )            \n",
    "                \n",
    "            R=0 #residue funtion (F)\n",
    "            for j in range(3):\n",
    "                R+=Z[j]*a[j]\n",
    "\n",
    "            J=0 #jacobian (Fprime)\n",
    "            for j in range(3):\n",
    "                J-=Z[j]*a[j]*a[j]\n",
    "                            \n",
    "            beta -= R/J #NR step            \n",
    "            \n",
    "            if beta[0,0]<0:\n",
    "                beta[0,0]=0\n",
    "                \n",
    "            if 1<beta[0,0]:\n",
    "                beta[0,0]=1\n",
    "            \n",
    "            ResBeta = abs(beta[0,0]-prevbeta[0,0])\n",
    "            \n",
    "            looping3 += 1        \n",
    "            \n",
    "            if qolog:\n",
    "                #print(looping3,beta0,prevbeta[0,0],beta[0,0],ResBeta)\n",
    "                itlogv[0][itlogi] = beta[0,0]\n",
    "                itlogv[1][itlogi,0:3] = K[0:3,0]\n",
    "                itlogi += 1\n",
    "            \n",
    "        looped3+= looping3\n",
    "\n",
    "        for i in range(3):\n",
    "            XI[i] = Z[i] * (1./(1+beta * (K[i]-1))) #Rachford-Rice composition updating scheme\n",
    "                \n",
    "        gamaI = MODEL(XI/np.sum(XI)) #enforce normalization in the MODEL call\n",
    "        \n",
    "        for i in range(3):\n",
    "            XII[i] = K[i]*XI[i]\n",
    "\n",
    "        gamaII = MODEL(XII/np.sum(XII)) #enforce normalization in the MODEL call\n",
    "        \n",
    "        for i in range(3):\n",
    "            K[i] = (gamaI[i])/(gamaII[i]) #definition of K\n",
    "        \n",
    "        ResK=0\n",
    "        for i in range(3):\n",
    "            ResK += np.sqrt((prevK[i]-K[i])**2)\n",
    "        looping2 += 1\n",
    "    \n",
    "    looped2 += looping2\n",
    "        \n",
    "    #print('Calculation has ended')\n",
    "    if (looping2 < 100 and looping3 < 100 and (0.<=beta[0,0]<=1.) ):\n",
    "        converged = 1\n",
    "    \n",
    "    if qolog:\n",
    "        return XI, XII, beta, converged, looped2, looped3, itlogv\n",
    "    else:\n",
    "        return XI, XII, beta, converged, looping2, looped3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "* linalg version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def ELLflash_linalg(Z,beta0,K0,MODEL): #ELLflash_linalg\n",
    "    \n",
    "    beta=beta0.copy()\n",
    "    K=K0.copy()\n",
    "    \n",
    "    converged = 0\n",
    "    \n",
    "    looped2 = 0\n",
    "    looped3 = 0\n",
    "    \n",
    "    looping2 = 0\n",
    "    while ( (looping2 == 0) # means do at least once\n",
    "           or ((ResK)>0.0001 # convergence criteria\n",
    "               and looping2 < 100) ): # max number of iterations\n",
    "\n",
    "        prevK = K.copy()        \n",
    "        \n",
    "        looping3 = 0\n",
    "        while ( (looping3 == 0)\n",
    "               or (ResBeta>0.0001 # convergence criteria\n",
    "                   and looping3 < 100) ): #max number of iterations\n",
    "            \n",
    "            prevbeta = beta.copy()\n",
    "            \n",
    "            a = (1/(1+beta*(K-1))) * (K-1)\n",
    "            beta = beta+(1/((Z.T*a.T) @ a)) @ (Z.T @ a)\n",
    "\n",
    "            if beta[0,0]<0:\n",
    "                beta[0,0]=0\n",
    "                \n",
    "            if 1<beta[0,0]:\n",
    "                beta[0,0]=1\n",
    "            \n",
    "            ResBeta = beta[0,0]-prevbeta[0,0]\n",
    "\n",
    "            looping3 += 1\n",
    "            \n",
    "        looped3 += looping3\n",
    "\n",
    "        XI = (1./(1+beta * (K-1))) * Z\n",
    "\n",
    "        gamaI = MODEL(XI/np.sum(XI))\n",
    "        \n",
    "        XII = K*XI\n",
    "\n",
    "        gamaII = MODEL(XII/np.sum(XII))\n",
    "        \n",
    "        K = (gamaI)/(gamaII)\n",
    "        \n",
    "        ResK = np.linalg.norm(K-prevK)\n",
    "        \n",
    "        looping2 += 1 \n",
    "        \n",
    "    looped2 += looping2\n",
    "\n",
    "    #print('Calculation has ended')\n",
    "    if (looping2 < 100 and looping3 < 100  and ( 0. <= beta[0,0] <= 1.)  ):\n",
    "        converged = 1\n",
    "    \n",
    "    return XI, XII, beta, converged, looped2, looped3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* new here: a jit version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@jit(nopython=True)\n",
    "def ELLflash_fast(Z,beta0,K0,T,alpha,A):\n",
    "    beta=beta0.copy()\n",
    "    prevbeta=beta.copy()\n",
    "    K=K0.copy()\n",
    "    prevK=K.copy()\n",
    "    XI=Z.copy()\n",
    "    XII=Z.copy()\n",
    "    looping2=0\n",
    "    looping3=0\n",
    "    converged = 0\n",
    "    looped2 = 0\n",
    "    looped3 = 0\n",
    "    ResK=1\n",
    "    ResBeta=1\n",
    "    \n",
    "    looping2 = 0\n",
    "    while ( (looping2 == 0) # means do at least once\n",
    "           or ((ResK)>0.0001 # convergence criteria\n",
    "               and looping2 < 100) ): # max number of iterations\n",
    "\n",
    "        prevK = K.copy()        \n",
    "        \n",
    "        looping3 = 0\n",
    "        while ( (looping3 == 0)\n",
    "               or (ResBeta>0.0001 # convergence criteria\n",
    "                   and looping3 < 100) ): #max number of iterations\n",
    "            \n",
    "            prevbeta = beta.copy()\n",
    "            \n",
    "            a = (1/(1+beta*(K-1))) * (K-1)\n",
    "            beta = beta+(1/((Z.T*a.T) @ a)) @ (Z.T @ a)\n",
    "\n",
    "            if beta[0,0]<0:\n",
    "                beta[0,0]=0\n",
    "                \n",
    "            if 1<beta[0,0]:\n",
    "                beta[0,0]=1\n",
    "            \n",
    "            ResBeta = np.abs(beta[0,0]-prevbeta[0,0])\n",
    "\n",
    "            looping3 += 1\n",
    "            \n",
    "        looped3 += looping3\n",
    "\n",
    "\n",
    "        XI = (1./(1+beta * (K-1))) * Z\n",
    "\n",
    "        gamaI = Gamma(T,XI/np.sum(XI),alpha,A)\n",
    "        \n",
    "        XII = K*XI\n",
    "\n",
    "        gamaII = Gamma(T,XII/np.sum(XII),alpha,A)\n",
    "        \n",
    "        K = (gamaI)/(gamaII)\n",
    "        \n",
    "        ResK = np.linalg.norm(K-prevK)\n",
    "        \n",
    "        looping2 += 1    \n",
    "    \n",
    "    looped2 += looping2\n",
    "    #print('Calculation has ended')\n",
    "    if (looping2 < 100 and looping3 < 100  and ( 0. <= beta[0,0] <= 1.)  ):\n",
    "        converged = 1\n",
    "    \n",
    "    return XI, XII, beta, converged, looped2, looped3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* new here: a scipy based version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def ELLflash_sci(Z,beta0,K0,MODEL):\n",
    "    #prepare FP input\n",
    "    def fix(kxixiibeta): \n",
    "        #local varaibles translation\n",
    "        K=np.array([kxixiibeta[0:3]]).T\n",
    "        beta0 = np.array([[kxixiibeta[9]]])\n",
    "        #prepare NR input\n",
    "        F = lambda beta, K=K, Z=Z: (Z.T @ ((1/(1+beta*(K-1))) * (K-1)))\n",
    "        J = lambda beta, K=K, Z=Z: -(((Z.T*((1/(1+beta*(K-1))) * (K-1)).T) @ ((1/(1+beta*(K-1))) * (K-1))))\n",
    "        #run NR\n",
    "        beta = opt.newton(func=F,x0=beta0,fprime=J,tol=1e-4, maxiter=100)\n",
    "        #run XI, gammaI, XII, gammaII\n",
    "        XI = (1./(1+beta * (K-1))) * Z\n",
    "        gamaI = MODEL(XI/np.sum(XI))\n",
    "        XII = K*XI\n",
    "        gamaII = MODEL(XII/np.sum(XII))\n",
    "        #prepare return-format solution\n",
    "        return np.concatenate( ( ((gamaI)/(gamaII))[0:,0], XI[0:,0], XII[0:,0], beta[0:,0] ), axis=0 )\n",
    "    #prepare FP input\n",
    "    point0 = np.concatenate( ( K0[0:,0], np.zeros(3), np.zeros(3), beta0[0:,0] ), axis=0 )\n",
    "    #sanity check\n",
    "    if np.isnan(point0).any() or np.isinf(point0).any():\n",
    "        print('nans or infs here')\n",
    "        raise ValueError\n",
    "    #run FP    \n",
    "    point = opt.fixed_point(func = fix, x0 = point0, xtol=1e-04, maxiter=100,method='iteration')\n",
    "    #prepare return-format solution\n",
    "    K = np.array([point[0:3]]).T\n",
    "    XI = np.array([point[3:6]]).T\n",
    "    XII = np.array([point[6:9]]).T\n",
    "    beta = np.array([point[9:10]]).T\n",
    "    converged=1\n",
    "    return XI, XII, beta, converged"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#test\n",
    "\n",
    "#exact ad-hoc NRTL solution\n",
    "#Ztest = np.array([[ 0.10526316,  0.84210526,  0.05263158]]).T\n",
    "#XItest = np.array([[ 0.02616646,  0.93009914,  0.0437344 ]]).T\n",
    "#XIItest = np.array([[ 0.51520944,  0.38604626,  0.0987443 ]]).T\n",
    "#BETAtest = np.array([[ 0.16173772]])\n",
    "\n",
    "#appproximate\n",
    "Ztest = np.array([[ 0.1,  0.85,  0.05]]).T\n",
    "XItest = np.array([[ 0.025,  0.93,  0.045 ]]).T\n",
    "XIItest = np.array([[ 0.5,  0.39,  0.11 ]]).T\n",
    "BETAtest = np.array([[ 0.16]])\n",
    "\n",
    "\n",
    "Ktest=1/(XItest/XIItest)\n",
    "\n",
    "#beta0=BETAtest\n",
    "#k0=Ktest\n",
    "Z=Ztest\n",
    "\n",
    "MODEL = lambda x: Gamma(T,x,alpha,A)\n",
    "\n",
    "beta0, k0 = iguess(Z,MODEL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at T 343 Z [[ 0.1   0.85  0.05]]\n",
      "with ig of k0 [[ 53.51704507   0.08210211   1.89504205]] beta0 [[ 0.10903288]]\n",
      "solution is\n",
      "xi [ 0.02558676  0.93241488  0.04199836]\n",
      "xii [ 0.52333357  0.38114549  0.09552094]\n",
      "beta [[ 0.14950019]]\n",
      "converged? 1 -- 1 means yes\n",
      "at T 343 Z [[ 0.1   0.85  0.05]]\n",
      "with ig of k0 [[ 53.51704507   0.08210211   1.89504205]] beta0 [[ 0.10903288]]\n",
      "solution is\n",
      "xi [[ 0.02558676  0.93241488  0.04199837]]\n",
      "xii [[ 0.52333358  0.38114547  0.09552094]]\n",
      "beta [[ 0.14950018]]\n",
      "converged? 1 -- 1 means yes\n",
      "at T 343 Z [[ 0.1   0.85  0.05]]\n",
      "with ig of k0 [[ 53.51704507   0.08210211   1.89504205]] beta0 [[ 0.10903288]]\n",
      "solution is\n",
      "xi [[ 0.02558676  0.93241488  0.04199836]]\n",
      "xii [[ 0.52333357  0.38114549  0.09552094]]\n",
      "beta [[ 0.14950019]]\n",
      "converged? 1 -- 1 means yes\n",
      "at T 343 Z [[ 0.1   0.85  0.05]]\n",
      "with ig of k0 [[ 53.51704507   0.08210211   1.89504205]] beta0 [[ 0.10903288]]\n",
      "solution is\n",
      "xi [[ 0.02558847  0.93240983  0.0420017 ]]\n",
      "xii [[ 0.52354738  0.38092664  0.09552599]]\n",
      "beta [[ 0.14943308]]\n",
      "converged? 1 -- 1 means yes\n"
     ]
    }
   ],
   "source": [
    "ans=ELLflash_explicit(Z,beta0,k0,MODEL,False)\n",
    "\n",
    "print('at T', T, 'Z', Z.T)\n",
    "print('with ig of k0', k0.T,'beta0', beta0)\n",
    "print('solution is')\n",
    "print('xi',ans[0].T)\n",
    "print('xii',ans[1].T)\n",
    "print('beta',ans[2])\n",
    "print('converged?',ans[3], '-- 1 means yes')\n",
    "\n",
    "ans=ELLflash_linalg(Z,beta0,k0,MODEL)\n",
    "\n",
    "print('at T', T, 'Z', Z.T)\n",
    "print('with ig of k0', k0.T,'beta0', beta0)\n",
    "print('solution is')\n",
    "print('xi',ans[0].T)\n",
    "print('xii',ans[1].T)\n",
    "print('beta',ans[2])\n",
    "print('converged?',ans[3], '-- 1 means yes')\n",
    "\n",
    "ans=ELLflash_fast(Z,beta0,k0,T,alpha,A)\n",
    "\n",
    "print('at T', T, 'Z', Z.T)\n",
    "print('with ig of k0', k0.T,'beta0', beta0)\n",
    "print('solution is')\n",
    "print('xi',ans[0].T)\n",
    "print('xii',ans[1].T)\n",
    "print('beta',ans[2])\n",
    "print('converged?',ans[3], '-- 1 means yes')\n",
    "\n",
    "ans=ELLflash_sci(Z,beta0,k0,MODEL)\n",
    "\n",
    "print('at T', T, 'Z', Z.T)\n",
    "print('with ig of k0', k0.T,'beta0', beta0)\n",
    "print('solution is')\n",
    "print('xi',ans[0].T)\n",
    "print('xii',ans[1].T)\n",
    "print('beta',ans[2])\n",
    "print('converged?',ans[3], '-- 1 means yes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 20.6 ms per loop\n",
      "1 [[ 0.14950019]]\n",
      "100 loops, best of 3: 12.1 ms per loop\n",
      "1 [[ 0.14950018]]\n",
      "1000 loops, best of 3: 751 µs per loop\n",
      "1 [[ 0.14950019]]\n",
      "100 loops, best of 3: 19.4 ms per loop\n",
      "1 [[ 0.14943308]]\n",
      " \n"
     ]
    }
   ],
   "source": [
    "#all , with objective initial guess\n",
    "\n",
    "# explicit\n",
    "%timeit ELLflash_explicit(Z,beta0,k0,MODEL,False)\n",
    "ans=ELLflash_explicit(Z,beta0,k0,MODEL,False)\n",
    "print(ans[3],ans[2])\n",
    "\n",
    "# linalg\n",
    "%timeit ELLflash_linalg(Z,beta0,k0,MODEL)\n",
    "ans=ELLflash_linalg(Z,beta0,k0,MODEL)\n",
    "print(ans[3],ans[2])\n",
    "\n",
    "# fast\n",
    "%timeit ELLflash_fast(Z,beta0,k0,T,alpha,A)\n",
    "ans=ELLflash_fast(Z,beta0,k0,T,alpha,A)\n",
    "print(ans[3],ans[2])\n",
    "\n",
    "\n",
    "# sci\n",
    "%timeit ELLflash_sci(Z,beta0,k0,MODEL)\n",
    "ans=ELLflash_sci(Z,beta0,k0,MODEL)\n",
    "print(ans[3],ans[2])\n",
    "\n",
    "#my results:\n",
    "'''\n",
    "The slowest run took 12.71 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
    "100 loops, best of 3: 1.37 ms per loop\n",
    "6 [[ 0.22367347]]\n",
    "1000 loops, best of 3: 769 µs per loop\n",
    "6 [[ 0.22367347]]\n",
    "10000 loops, best of 3: 61 µs per loop\n",
    "6 [[ 0.22367347]]\n",
    "100 loops, best of 3: 2.36 ms per loop\n",
    "1 [[ 0.22367347]]\n",
    "'''\n",
    "\n",
    "'''\n",
    "The slowest run took 4.01 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
    "100 loops, best of 3: 1.4 ms per loop\n",
    "6 [[ 0.22367347]]\n",
    "1000 loops, best of 3: 770 µs per loop\n",
    "6 [[ 0.22367347]]\n",
    "10000 loops, best of 3: 60.7 µs per loop\n",
    "6 [[ 0.22367347]]\n",
    "100 loops, best of 3: 2.36 ms per loop\n",
    "1 [[ 0.22367347]]\n",
    "'''\n",
    "# a 2x speedup using linalg, another 10x speedup using numba/jit, a 30% slowdown using scipy\n",
    "\n",
    "'''10 loops, best of 3: 18.9 ms per loop\n",
    "1 [[ 0.19194152]]\n",
    "100 loops, best of 3: 9.65 ms per loop\n",
    "1 [[ 0.19194152]]\n",
    "1000 loops, best of 3: 649 µs per loop\n",
    "1 [[ 0.19194152]]\n",
    "100 loops, best of 3: 8.24 ms per loop\n",
    "1 [[ 0.19194782]]\n",
    " \n",
    "'''\n",
    "\n",
    "'''10 loops, best of 3: 20.6 ms per loop\n",
    "1 [[ 0.14950019]]\n",
    "100 loops, best of 3: 12.1 ms per loop\n",
    "1 [[ 0.14950018]]\n",
    "1000 loops, best of 3: 751 µs per loop\n",
    "1 [[ 0.14950019]]\n",
    "100 loops, best of 3: 19.4 ms per loop\n",
    "1 [[ 0.14943308]]\n",
    " '''\n",
    "\n",
    "print(' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# grid calc plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "210\n",
      "done 34\n"
     ]
    }
   ],
   "source": [
    "nspace = 20\n",
    "\n",
    "Z2 = np.linspace(0,1,nspace)\n",
    "Z3 = np.linspace(0,1,nspace)\n",
    "\n",
    "Z2[0]=1e-9\n",
    "Z3[0]=1e-9\n",
    "\n",
    "\n",
    "Z2[-1]=1-1e-9\n",
    "Z3[-1]=1-1e-9\n",
    "\n",
    "\n",
    "rawZs = np.ndarray((nspace,nspace), dtype=object)\n",
    "\n",
    "flags = np.zeros((nspace,nspace))\n",
    "\n",
    "for i in range(nspace):\n",
    "    for j in range(nspace):\n",
    "        rawZs[i,j]=np.array([1-Z2[i]-Z3[j],Z2[i],Z3[j]])\n",
    "        if ( Z2[i] + Z3[j] <= 1 ):\n",
    "            flags[i,j] = 1\n",
    "        \n",
    "\n",
    "            \n",
    "Zs = rawZs[np.where(flags==1)]\n",
    "\n",
    "npts = Zs.shape[0]\n",
    "print(npts)\n",
    "\n",
    "Resultados_beta = np.zeros([npts])\n",
    "Resultados_conv = np.zeros([npts])\n",
    "Resultados_Z = np.zeros([npts,3])\n",
    "Resultados_XI = np.zeros([npts,3])\n",
    "Resultados_XII = np.zeros([npts,3])\n",
    "\n",
    "MODEL = lambda x: Gamma(T,x,alpha,A)\n",
    "\n",
    "l=0\n",
    "for k in range(npts):\n",
    "    beta0, K0 = iguess(np.array([Zs[k]]).T,MODEL)\n",
    "    #print(beta0,K0)\n",
    "    #print(Zs[k],beta0,K0)\n",
    "    try:\n",
    "        ans = ELLflash_sci(np.array([Zs[k]]).T,beta0,K0,MODEL)\n",
    "\n",
    "        #succeeds:\n",
    "\n",
    "        if (0<ans[2] and 1>ans[2] and ans[3]!=0):\n",
    "            #print(ans[0][0][0],ans[0][1][0],ans[0][2][0])\n",
    "            #print(ans[0][0:3,0])\n",
    "            Resultados_XI[l,:] = ans[0][0:3,0]#np.array([ans[0][0][0],ans[0][1][0],ans[0][2][0]])\n",
    "            Resultados_XII[l,:] = ans[1][0:3,0] #np.array([ans[1][0][0],ans[1][1][0],ans[1][2][0]])\n",
    "            Resultados_beta[l] = ans[2]\n",
    "            Resultados_conv[l] = ans[3]\n",
    "\n",
    "            Resultados_Z[l,:] = Zs[k]\n",
    "            \n",
    "            #print('l++')\n",
    "            l+=1\n",
    "\n",
    "    except RuntimeError:\n",
    "        #print('no converge here')\n",
    "        pass\n",
    "    except ValueError:\n",
    "        #print('no converge here')\n",
    "        pass\n",
    "    finally:\n",
    "        #print('k++')\n",
    "        pass\n",
    "    \n",
    "        \n",
    "print('done',l)\n",
    "ndone=l\n",
    "    \n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* of a grid with 210 points we foundo solutions for 28 points\n",
    "* lets soon see wether we tried calculations at conditions that do not have solution, or at conds that had solutions but our algorithms missed\n",
    "\n",
    "# note we have 34 convergences here with scipy, before we had 33 convergences,\n",
    "\n",
    "# we can tweak scipy options and use better methods provided by scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fResultados_XI = Resultados_XI[:][np.where(Resultados_conv!=0)]\n",
    "fResultados_XII = Resultados_XII[:][np.where(Resultados_conv!=0)]\n",
    "fResultados_beta = Resultados_beta[np.where(Resultados_conv!=0)]\n",
    "fResultados_Z = Resultados_Z[:][np.where(Resultados_conv!=0)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# barycentric coords: (a,b,c)\n",
    "a=fResultados_XI[:,0]\n",
    "b=fResultados_XI[:,1]\n",
    "c=fResultados_XI[:,2]\n",
    "\n",
    "d=fResultados_XII[:,0]\n",
    "e=fResultados_XII[:,1]\n",
    "f=fResultados_XII[:,2]\n",
    "\n",
    "g=fResultados_Z[:,0]\n",
    "h=fResultados_Z[:,1]\n",
    "ii=fResultados_Z[:,2]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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URRGRnFiiunJlhO7fz9Pxc+fyPIE/7NgBdOzIMw+33kr56Dx5uLw/dy6zJUaN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\n2wdvb/ngojT7oGJfHCcDZlD7SpsPui4f5Km+q+Icpe05E5U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B6NFy7d98E6W8VfZoP/8c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toUz1kQ+5tFKyLaw+rV8nuoYn/z0Ufl7es69rFl91DF/qYK//vHH+GDDJ1Q7G9OnSpv32xGwqLs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\nRG/bAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f3502c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([0,1,0,1])\n",
    "    \n",
    "plt.scatter(a,c)    \n",
    "plt.scatter(d,f)    \n",
    "\n",
    "ZS=np.zeros([npts,3])\n",
    "for i in range(npts):\n",
    "    ZS[i,:]=Zs[i]\n",
    "\n",
    "plt.scatter(ZS[:,0],ZS[:,2],marker='o',s=80, facecolors='none', edgecolors='r')    \n",
    "    \n",
    "plt.scatter(g,ii,marker='*')\n",
    "\n",
    "#UNCOMMENT THIS LINE TO PLOT THE FAILED POINT\n",
    "#failedpoint= [0.42105263 , 0.52631579 , 0.05263158]\n",
    "#plt.scatter(bug[0],bug[2],marker='d')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# scipy missed the same points with solution than before\n",
    "# note however in the plots below tha scipy' algorithm was able to converge 1 calculation closer to the critical point than before!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# x crit = 0.2 aprox\n",
    "\n",
    "\n",
    "#refiltrar a e b LEFT and RIGHT of the crit point\n",
    "\n",
    "crit=.2\n",
    "\n",
    "al=a[np.where(a<=crit)]\n",
    "ar=a[np.where(a>crit)]\n",
    "dl=d[np.where(d<=crit)]\n",
    "dr=d[np.where(d>crit)]\n",
    "\n",
    "bl=b[np.where(a<=crit)]\n",
    "br=b[np.where(a>crit)]\n",
    "el=e[np.where(d<=crit)]\n",
    "er=e[np.where(d>crit)]\n",
    "\n",
    "cl=c[np.where(a<=crit)]\n",
    "cr=c[np.where(a>crit)]\n",
    "fl=f[np.where(d<=crit)]\n",
    "fr=f[np.where(d>crit)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(34,) (34,) (34,) (34,)\n",
      "(23,) (23,) (11,) (11,)\n",
      "(11,) (11,) (23,) (23,)\n",
      "(34,) (34,) (34,) (34,)\n"
     ]
    }
   ],
   "source": [
    "Ly = np.concatenate((al,dl),axis=0)\n",
    "Lx = np.concatenate((cl,fl),axis=0)\n",
    "\n",
    "Ry = np.concatenate((ar,dr),axis=0)\n",
    "Rx = np.concatenate((cr,fr),axis=0)\n",
    "\n",
    "sLy=np.sort(Ly)\n",
    "sLx=np.sort(Lx)\n",
    "sRy=np.sort(Ry)\n",
    "sRx=-np.sort(-Rx)\n",
    "\n",
    "print(a.shape,b.shape,d.shape,e.shape)\n",
    "print(al.shape,bl.shape,dl.shape,el.shape)\n",
    "print(ar.shape,br.shape,dr.shape,er.shape)\n",
    "print(Ly.shape,Ry.shape,Lx.shape,Rx.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iIiKTUSQ9IDjnqlCxqYiIiEQoogBiZlnAOUA+w3pRnHMPRaFdIiIiMokdcwAxs7cDPwXS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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1f34dcf390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis([0,1,0,1])\n",
    "    \n",
    "plt.scatter(Ly,Lx)    \n",
    "plt.scatter(Ry,Rx)    \n",
    "\n",
    "plt.plot(sLy,sLx)\n",
    "plt.plot(sRy,sRx)\n",
    "\n",
    "\n",
    "for i in range(0,ndone):\n",
    "    plt.plot([a[i],d[i]],[c[i],f[i]])\n",
    "\n",
    "\n",
    "plt.scatter(g,ii, marker='*')\n",
    "\n",
    "plt.xlabel('mol. frac. water')\n",
    "plt.ylabel('mol. frac. ethanol')\n",
    "plt.title('LLE at '+str(T-273)+'degC')    \n",
    "    \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}