{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the HyShot II Scramjet\n",
    "\n",
    "__Paul Constantine__, Colorado School of Mines, <pconstan@mines.edu>\n",
    "\n",
    "__Michael Emory__, Stanford University, <memory@stanford.edu>\n",
    "\n",
    "__Johan Larsson__, University of Maryland, <jola@umd.edu>\n",
    "\n",
    "__Gianluca Iaccarino__, Stanford University, <jops@stanford.edu>\n",
    "\n",
    "__Ryan Howard__, Colorado School of Mines, <ryhoward@mines.edu>\n",
    "\n",
    "\n",
    "<br>\n",
    "\n",
    "In this notebook, we'll be summarizing the active subspaces-based uncertainty quantification presented in [[1]][R1].\n",
    "\n",
    "A scramjet is an engine designed to intake air and combust fuel at supersonic speeds. Because physically prototyping and experimenting is expensive, we must use numerical simulations to explore the behavior of these machines. The simulation we use is based on the HyShot II vehicle and has 7 input parameters:\n",
    "\n",
    "Parameter | Lower bound | Upper bound\n",
    "--- | --- | --- \n",
    "Angle of attack | 2.6 | 4.6 \n",
    "Turbulence intensity | 0.1 | 1.9 \n",
    "Turbulence length scale | 122.5 | 367.5 \n",
    "Stagnation pressure | 1.6448e7 | 1.9012e7 \n",
    "Stagnation enthalpy | 3.0551e6 | 3.4280e6 \n",
    "Cowl transition location | 0.03 | 0.07 \n",
    "Ramp transition location | 0.087 | 0.203 \n",
    "\n",
    "These parameters are used in our complex multiphysics simulation modelling the fluid flow in the scramjet. From our simulation, we compute our quantity of interest, a normalized integral of pressure over the end of the engine:\n",
    "\n",
    "$$\n",
    "\\frac{1}{vol(V)}\\iiint\\limits_VP\\ dx\\ dy\\ dz\n",
    "$$\n",
    "\n",
    "where V is a 3D region at the end of the scramjet and vol(V) is the volume of this region. This quantity can be used as a metric for judging performance and determining whether _unstart_ has occured (unstart is a catastrophic failure resulting in loss of thrust). For each combination of parameters used in our simulation, we compute this quantity for fuel-air equivalence ratios of .30 and .35.\n",
    "\n",
    "We'll use the notation $f(\\mathbf{x})$ to denote the quantity of interest as a function of normalized input parameters ($\\mathbf x$). For the purposes of uncertainty quantification, we'd like to estimate bounds of $f$, identify sets of inputs that result in $f$ remaining below a certain threshold, and estimate a cumulative distribution function of $f$ given a density on $\\mathbf x$.\n",
    "\n",
    "The most straightforward way to achieve our objective would be to exhaustively sample the space of input parameters and use the resulting data to calculate what we want. However, because our input space is high-dimensional and the simulation is very expensive, this is infeasible. To compute what we want, we reduce the dimensionality of the problem by identifying the 'most important' direction in the input space and examining our quantity of interest along this direction. We use an _active subspace_ approach (see [[2]][R2]) based on the matrix\n",
    "\n",
    "$$\n",
    "\\mathbf C = \\int\\nabla f(\\mathbf x)\\nabla f(\\mathbf x)^T \\rho(\\mathbf x)\\ d\\mathbf x = \\mathbf W \\Lambda\\mathbf W^T\n",
    "$$\n",
    "\n",
    "where $\\rho$ is a probability density on $\\mathbf x$ and $\\mathbf W \\Lambda\\mathbf W^T$ is the eigendecomposition of $\\mathbf C$. The active subspace is the space spanned by the first several eigenvectors, and we can use it to construct an approximation of $f$:\n",
    "\n",
    "$$\n",
    "f(\\mathbf x)\\approx g(\\mathbf W_1^T\\mathbf x)\n",
    "$$\n",
    "\n",
    "where $\\mathbf W_1$ contains the first $n$ columns of $\\mathbf W$ and $g$ is a function from $R^n$ to $R$. Since we don't have access to the gradient of $f$, we use the following least squares-based algorithm to identify the single most important direction in the parameter space:\n",
    "1. Using $M$ data points, determine the parameters $\\hat u_0, \\hat u_1,\\dots,\\hat u_m$ of the linear approximation $f(\\mathbf x)\\approx \\hat u_0 + \\hat u_1x_1 + \\cdots + \\hat u_mx_m$ such that $\\hat{\\mathbf u} = argmin_{\\mathbf u}||\\mathbf{Au}-\\mathbf f||_2^2$ where\n",
    "$$\n",
    "\\mathbf A = \\left[\\begin{matrix}1 & \\mathbf x_1^T\\\\\\vdots & \\vdots\\\\ 1 & \\mathbf x_M^T\\end{matrix}\\right],\\ \\mathbf f = \\left[\\begin{matrix}f_1\\\\\\vdots\\\\f_M\\end{matrix}\\right],\\ \\hat{\\mathbf u} = \\left[\\begin{matrix}\\hat u_0\\\\\\vdots\\\\\\hat u_m\\end{matrix}\\right]\n",
    "$$<br>\n",
    "2. Compute $\\mathbf w = \\hat{\\mathbf u}'/||\\hat{\\mathbf u}'||$ where $\\hat{\\mathbf u}' = [\\hat u_1, \\cdots, \\hat u_m]^T$. $\\mathbf w$ is the vector pointing in the most important direction in the parameter space.\n",
    "\n",
    "To examine the effects of variability in $\\mathbf w$, we use a bootstrap algorithm:\n",
    "1. Choose the number $N$ of bootstrap replicates\n",
    "2. For $k$ from 1 to $N$:\n",
    "    1. Let $\\boldsymbol{\\pi}^k = [\\pi_1^k,\\cdots,\\pi_M^k]$ be integers from 1 to $M$ sampled uniformly with replacement.\n",
    "    2. Let $\\mathbf f^k$ be the vector whose $i^{th}$ element is $f_{\\pi^k}$ and $\\mathbf A^k$ be the matrix whose $i^{th}$ row is $[1,\\ \\mathbf x_{\\pi^k}^T]$.\n",
    "    3. Compute $\\mathbf w^k$ using $\\mathbf A = \\mathbf A^k$ and $\\mathbf f = \\mathbf f^k$ as above.\n",
    "    \n",
    "### References:\n",
    "\n",
    "[[1]][R1] P.G. Constantine, M. Emory, J. Larsson, and G. Iaccarino. _Exploiting active subspaces to quantify uncertainty in the numerical simulation of the HyShot II scramjet_. J. Comput. Phys., 302, 1-20, 2015\n",
    "\n",
    "[[2]][R2] P.G. Constantine, E. Dow, and Q. Wang. _Active subspaces in theory and practice: applications to kriging surfaces_. SIAM J. Sci. Comput., 36(4), A1500–A1524, 2014\n",
    "\n",
    "[R1]: http://dx.doi.org/10.1016/j.jcp.2015.09.001\n",
    "[R2]: http://dx.doi.org/10.1137/130916138\n",
    "\n",
    "### Acknowledgments\n",
    "\n",
    "This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0011077.\n",
    "\n",
    "<br>\n",
    "\n",
    "We'll now code up the analysis using the [Python Active-subspaces Utility Library](https://github.com/paulcon/active_subspaces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pn\n",
    "import active_subspaces as ac\n",
    "import matplotlib.pyplot as plt\n",
    "np.set_printoptions(formatter={'all' : '{:<15}'.format})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we import the data and separate inputs (X) from outputs (F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = pn.DataFrame.from_csv('HyShotII35.txt')\n",
    "data = df.as_matrix()\n",
    "#The last 2 rows (for the extreme values) are already normalized\n",
    "X = data[:-2,0:7]\n",
    "F = data[:,7:9]\n",
    "labels = df.keys()\n",
    "in_labels = labels[:7]\n",
    "out_labels = labels[7:9]\n",
    "\n",
    "#The data for equivalence ratio .30 is already normalized\n",
    "df30 = pn.DataFrame.from_csv('HyShotII30.txt', header=None, index_col=None)\n",
    "data30 = df30.as_matrix()\n",
    "XX30 = data30[:,0:7]\n",
    "F30 = data30[:,7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we normalize each of the input parameters to the interval [-1, 1] and separate our outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#normalize the ratio = .35 data\n",
    "xl = np.array([2.6, 0.1, 122.5, 1.6448e7, 3.0551e6, 0.6*0.05, 0.6*0.145])\n",
    "xu = np.array([4.6, 1.9, 367.5, 1.9012e7, 3.4280e6, 1.4*0.05, 1.4*0.145])\n",
    "XX = ac.utils.misc.BoundedNormalizer(xl, xu).normalize(X)\n",
    "XX = np.vstack((XX, data[-2:,:7]))\n",
    "\n",
    "f30 = F30[:]\n",
    "out_label30 = out_labels[0]\n",
    "f35 = F[:,1]\n",
    "out_label35 = out_labels[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up our subspaces. The last two rows of each data set were from simulations done after initial subspace analysis was conducted, for the purpose of verifying predicted extrema; we exclude those data points initially to mirror the process of discovering the subspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ss30 = ac.subspaces.Subspaces()\n",
    "ss35 = ac.subspaces.Subspaces()\n",
    "\n",
    "#Compute OLS subspaces\n",
    "ss30.compute(X=XX30[:-2,:], f=f30[:-2,np.newaxis], sstype='OLS', nboot=500)\n",
    "ss35.compute(X=XX[:-2,:], f=f35[:-2,np.newaxis], sstype='OLS', nboot=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the quantity of interest against $\\mathbf w^T\\mathbf x$ for each equivalence ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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HqMdfKKWeJ9kLzHX351KOT03T9ljgOXd/uPhhiUjYDJ/eseTF4zff/HkmTeoHZgJLkt7R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\newCbLO0sjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3766aa0690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fdPf6Xn1ZREQkS8GepJmdC3zB3TPxzwW5+zXlCG4u1JMUEZFsZX2epJndCxzv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\nioiIFPD/Ab5dfNAg/BrcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f376424ccd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#active variable values associated with XX, XX30\n",
    "y30 = np.dot(XX30, ss30.W1)\n",
    "y35 = np.dot(XX, ss35.W1)\n",
    "\n",
    "#plots of response (pressure) vs. active variable\n",
    "ac.utils.plotters.sufficient_summary(y30[:-2], f30[:-2], out_label30)\n",
    "ac.utils.plotters.sufficient_summary(y35[:-2], f35[:-2], out_label35)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see a very tight univariate trend in each case (see also Figure 7 of [[1]][R1]); we can use this low-dimensional structure to perform our uncertainty quantification.\n",
    "[R1]: http://dx.doi.org/10.1016/j.jcp.2015.09.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For ratio .30, the components of w are:\n",
      "[[0.6506          AoA            ]\n",
      " [0.5565          Turb int       ]\n",
      " [-0.0002         Turb len       ]\n",
      " [0.3685          Stag pres      ]\n",
      " [-0.3566         Stag enth      ]\n",
      " [-0.0196         Cowl trans     ]\n",
      " [0.0607          Ramp trans     ]]\n",
      "\n",
      "For ratio .35, the components of w are:\n",
      "[[0.6996          AoA            ]\n",
      " [0.4823          Turb int       ]\n",
      " [-0.027          Turb len       ]\n",
      " [0.1997          Stag pres      ]\n",
      " [-0.4738         Stag enth      ]\n",
      " [-0.0602         Cowl trans     ]\n",
      " [0.0957          Ramp trans     ]]\n"
     ]
    }
   ],
   "source": [
    "#Display the components of w\n",
    "print \"For ratio .30, the components of w are:\"\n",
    "print np.hstack((np.round(ss30.W1, 4), in_labels[:,np.newaxis]))\n",
    "print \"\\nFor ratio .35, the components of w are:\"\n",
    "print np.hstack((np.round(ss35.W1, 4), in_labels[:,np.newaxis]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The components of $\\mathbf w$ tell us how sensitive the quantity of interest is to each parameter. From the above output, we can see that Angle of Attack, Turbulence Intensity, and Stagnation conditions (pressure and enthalpy) dominate the active subspace, and (perhaps by coincidence) the components are roughly the same between the fuel-air equivalence ratios, except for an exchange of weight between stagnation pressure and stagnation enthalpy.\n",
    "\n",
    "We'll now demonstrate the bootstrap for equivalence ratio .30."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = int(1e5) #Number of bootstrap replicates\n",
    "M,m = XX30.shape\n",
    "w_boot = np.empty(shape=(m, N)) #matrix containing replicates\n",
    "for k in range(N):\n",
    "    mask = np.random.randint(0, M, size=(M,))\n",
    "    f = np.matrix(f30[mask].reshape(M,1))\n",
    "    A = np.matrix(np.hstack((np.ones((M,1)), XX30[mask])))\n",
    "    u = (A.T.dot(A)).I.dot(A.T).dot(f)\n",
    "    w_boot[:,k] = np.squeeze(u[1:])/np.linalg.norm(np.squeeze(u[1:]))\n",
    "w_br = np.empty(shape=(m, 2)) #min-to-max range of bootstrap values\n",
    "w_br[:,0] = np.squeeze(np.apply_over_axes(np.amin, w_boot, axes=(1)))\n",
    "w_br[:,1] = np.squeeze(np.apply_over_axes(np.amax, w_boot, axes=(1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jlCpVyt7h2IXUdWQMQMYAZAxAapxWy507N+3atXvh8Y6cOXNSvXp1qlevDsCtW7cIDQ3l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\nAWCMMV6qUaMGBQsWZN26dcnOFStWjKJFi7JixYoUX9+kSRPGjx/vdhm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THa4KHHTXaIrI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\nIDgBYIDgBIABghMABtwAdj3axfZa+IIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3766aa0d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qORcF6zcATMwlKxzzQM5egHe371vx2OXjuAh8+MMf3vYQWIP69W1I/e6///58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\nADCC/x/UaNEM03qEowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f376417fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot eigenvector components with bootstrap ranges\n",
    "ac.utils.plotters.eigenvectors(ss30.W1, w_br, in_labels, out_label30)\n",
    "plt.figure(figsize=(14, 5*4))\n",
    "for k in range(m): #plot histograms\n",
    "    plt.subplot(4, 2, k+1)\n",
    "    plt.grid(True)\n",
    "    plt.xlabel(in_labels[k])\n",
    "    plt.xlim([-1, 1])\n",
    "    plt.vlines(ss30.W1[k], 0, .5, 'r', lw=2)\n",
    "    plt.hist(w_boot[k,:], bins=10,\\\n",
    "             weights=1.0*np.ones_like(w_boot[k,:])/float(len(w_boot[k,:])))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the histograms are tightly concentrated around our estimated values (the red vertical lines), indicating that our estimates are close to their true values. Because we have only a few data points for the equivalence ratio of .35, the bootstrap ranges would be much wider in that case, but our confirmation of the results in the .30 case and the similarities between the two cases lead us to be confident for both ratios (see also Figures 8 and 9 of [[1]][R1]).\n",
    "[R1]: http://dx.doi.org/10.1016/j.jcp.2015.09.001\n",
    "\n",
    "Now that we are confident in our subspace, we can begin the uncertainty quantification (estimating ranges on $f$, identifying safe operating conditions, and estimating a cdf on $f$). Range estimation is sraightforward given the monotonic nature of the subspace: we can maximize $f$ by maximizing the value of our active variable, $\\mathbf w^T\\mathbf x$, over our input space, and running our simulation at these values of $\\mathbf x$ (four runs: 1 max and 1 min for each equivalence ratio). We plot the initial data (blue dots) and the acquired extreme values (red squares) below (see also Figure 7 of [[1]][R1]).\n",
    "[R1]: http://dx.doi.org/10.1016/j.jcp.2015.09.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f3763740f90>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0mubmFaxZs5UdO6Cm5jZ27DiDYAOfTcBbs1rnjlMW9tBDUxk69H4tLyeDRqlj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\nbepxgb14a3nVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3766aa0e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zcOHsusc0Wnk+D4OUQ/PlPf6sDDVPcg3wIqICeTSwBXik4n2Pt79Vt+hEGmTw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\nSRERkQQqkiIiIgn+P5p1e/dNme8QAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f376379f390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot initial data (blue dots) and extrema (red squares)\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.plot(y30[:-2], f30[:-2], 'bo', y30[-2:], f30[-2:], 'rs', ms=12); plt.grid(True)\n",
    "plt.xlabel('Active Variable'); plt.ylabel(out_label30)\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.plot(y35[:-2], f35[:-2], 'bo', y35[-2:], f35[-2:], 'rs', ms=12); plt.grid(True)\n",
    "plt.xlabel('Active Variable'); plt.ylabel(out_label35)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose now that the engine remained safe so long as exit pressure is below 2.8 and becomes unsafe when pressure rises above this. We might reasonably be interested in what regions of our parameter space result in safe operating conditions and which don't. To constrain the exit pressure, we can construct response surfaces from the data points $\\{(y_i,f_i)\\}$, where $y_i$ are the active variable values and $f_i$ are the values of the quantity of interest, and use them to place a bound on how high the active variable can become before the engine becomes unsafe, and map the safe active-variable region to the original parameter space.\n",
    "\n",
    "Below, we plot our response surfaces (obtained from OLS on a quadratic model) and an upper prediction limit that is 2.33 standard errors above our mean response (see also Figure 10 of [[1]][R1]). We also find the active variable value that marks the boundary between safe and unsafe operation. The shaded regions denote safe operation.\n",
    "[R1]: http://dx.doi.org/10.1016/j.jcp.2015.09.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f376350c450>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Tn3e6fw07TaKriCzKJG4ncF2Gc9elnHfpk08OXHl2SinlBWr+MoOy21axsM94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\nPRVDERFJeyqGIiKS9v4P7b2EAKJWEcUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3763109f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zl/v3u+XWa9ZA+/a2wvyqVXaG9e23YcsWuzUxvwRCV+XYalJjzD6gLPANcMeV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\nEUm8/wdyO1VTHV+edAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f376358da10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Quadratic response surfaces\n",
    "surface30 = ac.utils.response_surfaces.PolynomialApproximation(2)\n",
    "surface35 = ac.utils.response_surfaces.PolynomialApproximation(2)\n",
    "\n",
    "#Training the surfaces with our data\n",
    "surface30.train(y30, f30[:,None])\n",
    "surface35.train(y35, f35[:,None])\n",
    "\n",
    "M30 = len(y30); M35 = len(y35)#Number of data points for each ratio\n",
    "\n",
    "#sums of squares required for computing standard error\n",
    "sf30 = np.sqrt(sum((ac.utils.misc.atleast_2d_col(f30) -\\\n",
    "                    surface30.predict(y30)[0])**2)/(M30 - 3))\n",
    "sy30 = sum((y30 - y30.mean())**2)\n",
    "#predicted response using mean response + 2.33 std errors\n",
    "predlim30 = lambda x: surface30.predict(x)[0] + 2.33*sf30*np.sqrt(1 +\\\n",
    "                      1/M30 + (x - y30.mean())**2/sy30)\n",
    "\n",
    "sf35 = np.sqrt(sum((ac.utils.misc.atleast_2d_col(f35) -\\\n",
    "                    surface35.predict(y35)[0])**2)/(M35 - 3))\n",
    "sy35 = sum((y35 - y35.mean())**2)\n",
    "predlim35 = lambda x: surface35.predict(x)[0] + 2.33*sf35*np.sqrt(1 +\\\n",
    "                      1/M35 + (x - y35.mean())**2/sy35)\n",
    "\n",
    "x = ac.utils.misc.atleast_2d_col(np.linspace(-2, 3, 800))\n",
    "#maximum Active variable value s.t. f(x) <= 2.8 according to prediction interval\n",
    "avmaxval30 = x[np.argmin(abs(predlim30(x) - 2.8))]\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.plot(x, surface30.predict(x)[0], 'b-', x, predlim30(x), 'r:', lw=2)\n",
    "plt.plot(x, 2.8*np.ones_like(x), 'k-')\n",
    "plt.vlines(avmaxval30, 2, 3, 'k')\n",
    "plt.fill_between(x[x <= avmaxval30], 2, 2.8, alpha=.3)\n",
    "plt.ylim([2, 3])\n",
    "plt.xlabel('Active Variable'); plt.ylabel(out_label30)\n",
    "plt.legend(['mean response', 'prediction limit'], loc=2)\n",
    "\n",
    "avmaxval35 = x[np.argmin(abs(predlim35(x) - 2.8))]\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.plot(x, surface35.predict(x)[0], 'b-', x, predlim35(x), 'r:', lw=2)\n",
    "plt.plot(x, 2.8*np.ones_like(x), 'k-')\n",
    "plt.vlines(avmaxval35, 2, 3.6, 'k')\n",
    "plt.fill_between(x[x <= avmaxval35], 2, 2.8, alpha=.3)\n",
    "plt.ylim([2, 3.6]); plt.xlim([-2, 3])\n",
    "plt.xlabel('Active Variable'); plt.ylabel(out_label35)\n",
    "plt.legend(['mean response', 'prediction limit'], loc=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The set of normalized parameters resulting in safe operation is $S = \\{\\mathbf x : \\mathbf w^T\\mathbf x \\leq y_{max},\\ -\\mathbf 1 \\leq \\mathbf x\\leq \\mathbf 1\\}$, where $y_{max}$ is the maximum safe active variable value. We will find ranges of input parameters that guarantee safety by finding the largest 'box' that can fit within the set $S$ by solving the optimization problem: maximize$_{\\mathbf x}\\prod_{i=1}^m|x_i-x_{i,min}|,\\ s.t.\\ \\mathbf x\\in S$, where the $x_{i,min}$ are the components of xmin above (the minimizer of the active variable, $\\mathbf w^T\\mathbf x$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as op\n",
    "\n",
    "#Functions to minimize (-log(prod(x_i-x_{i,min})))\n",
    "minfun30 = lambda x: -1.0*np.sum(np.log(abs(x - XX30[-2,:].reshape(x.shape))))\n",
    "minfun35 = lambda x: -1.0*np.sum(np.log(abs(x - XX[-2,:].reshape(x.shape))))\n",
    "#constraint functions of the form c(x) >= 0\n",
    "cfun30 = lambda x: avmaxval30 - x.dot(ss30.W1)\n",
    "cfun35 = lambda x: avmaxval35 - x.dot(ss35.W1)\n",
    "#constraint dictionaries passed to minimizer\n",
    "cdict30 = {'type': 'ineq', 'fun': cfun30}\n",
    "cdict35 = {'type': 'ineq', 'fun': cfun35}\n",
    "\n",
    "#Normalized parameter values defining the edge of the largest box assuring safe operation\n",
    "xop30 = op.minimize(minfun30, XX30[-1,:],\\\n",
    "                    bounds=zip(-1.0*np.ones_like(xl), 1.0*np.ones_like(xl)),\\\n",
    "                    constraints=cdict30)\n",
    "xop35 = op.minimize(minfun35, XX[-1,:],\\\n",
    "                    bounds=zip(-1.0*np.ones_like(xl), 1.0*np.ones_like(xl)),\\\n",
    "                    constraints=cdict35)\n",
    "\n",
    "#un-normalizing inputs to original parameter space\n",
    "xop30 = ac.utils.misc.BoundedNormalizer(xl, xu).unnormalize(xop30.x[None,:]).reshape(m, 1)\n",
    "xop35 = ac.utils.misc.BoundedNormalizer(xl, xu).unnormalize(xop35.x[None,:]).reshape(m, 1)\n",
    "min30 = ac.utils.misc.BoundedNormalizer(xl, xu).unnormalize(XX30[-2,:][None,:]).reshape(m, 1)\n",
    "min35 = ac.utils.misc.BoundedNormalizer(xl, xu).unnormalize(XX[-2,:][None,:]).reshape(m, 1)\n",
    "\n",
    "#sorting bounds for display convenience\n",
    "A30 = np.round(np.sort(np.hstack((min30, xop30)), axis=1), 4)\n",
    "A35 = np.round(np.sort(np.hstack((min35, xop35)), axis=1), 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For ratio .30, the ranges providing safe operation are:\n",
      "2.60e+00 \t 4.60e+00\t AoA\n",
      "1.00e-01 \t 1.90e+00\t Turb int\n",
      "1.22e+02 \t 3.67e+02\t Turb len\n",
      "1.64e+07 \t 1.90e+07\t Stag pres\n",
      "3.06e+06 \t 3.43e+06\t Stag enth\n",
      "3.00e-02 \t 7.00e-02\t Cowl trans\n",
      "8.70e-02 \t 2.03e-01\t Ramp trans\n",
      "\n",
      "For ratio .35, the ranges providing safe operation are:\n",
      "2.60e+00 \t 3.25e+00\t AoA\n",
      "1.00e-01 \t 9.53e-01\t Turb int\n",
      "1.22e+02 \t 3.67e+02\t Turb len\n",
      "1.64e+07 \t 1.90e+07\t Stag pres\n",
      "3.25e+06 \t 3.43e+06\t Stag enth\n",
      "3.00e-02 \t 7.00e-02\t Cowl trans\n",
      "8.70e-02 \t 2.03e-01\t Ramp trans\n"
     ]
    }
   ],
   "source": [
    "#Display the safe operating ranges\n",
    "print \"For ratio .30, the ranges providing safe operation are:\"\n",
    "for i in range(7):\n",
    "    print \"{:0.2e} \\t {:0.2e}\\t {}\".format(A30[i,0],A30[i,1],in_labels[i])\n",
    "print \"\\nFor ratio .35, the ranges providing safe operation are:\"\n",
    "for i in range(7):\n",
    "    print \"{:0.2e} \\t {:0.2e}\\t {}\".format(A35[i,0],A35[i,1],in_labels[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly, we can construct a cumulative distribution of $f$ by randomly sampling the (normalized) parameter space, computing the active variable, and computing the response surface value at each point (see also Figure 11 of [[1]][R1]).\n",
    "[R1]: http://dx.doi.org/10.1016/j.jcp.2015.09.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7f37637852d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NV9/+1PnZOCcB3wP6EOzXZDo/09fQvmzyuZmVxdbNrAYYntjKSnq9rbtvSng+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3763049390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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nxLatBfoDuPs24FyCVv58gmGcfd29PJtBi4hI+lJK/O6+w90HunsLd/+2u/82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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f376355e290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = int(1e5) #Number of random samples\n",
    "x = np.random.uniform(-1, 1, (N, m))\n",
    "a30 = x.dot(ss30.W1); a35 = x.dot(ss35.W1) #active variable values\n",
    "s30 = surface30.predict(a30)[0]; s35 = surface35.predict(a35)[0] #response surface values\n",
    "x = np.linspace(1.5, 3.5, 300)\n",
    "c30 = np.vectorize(lambda x: sum(s30 <= x)/(1.0*N)) #CDF functions\n",
    "c35 = np.vectorize(lambda x: sum(s35 <= x)/(1.0*N))\n",
    "\n",
    "plt.plot(x, c30(x), 'k-')\n",
    "plt.ylim([0, 1.1])\n",
    "plt.xlabel(out_label30)\n",
    "plt.vlines(f30[-2:], 0, 1.1, 'k', 'dashed')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x, c35(x), 'k-')\n",
    "plt.ylim([0, 1.1])\n",
    "plt.xlabel(out_label35)\n",
    "plt.vlines(f35[-2:], 0, 1.1, 'k', 'dashed')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}