05_optimization.ipynb

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    "# ASTR 21100 \n",
    "\n",
    "# \"Computational Techniques in Astrophysics\"\n",
    "\n",
    "## Instructor: Andrey Kravtsov\n",
    "\n",
    "### office: ERC 415; email: kravtsov@uchicago.edu\n",
    "### office hours: Tue, 10:30am-noon (unless noted otherwise)\n",
    "\n",
    "#### Teaching Assistants: \n",
    "#### Dimitrios Tanoglidis (dtanoglidis@uchicaago.edu)\n",
    "#### Georgios Zakharegkas (gzakharegkas@uchicago.edu)"
   ]
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    "## Optimization methods \n",
    "\n",
    "Optimization is numerical computations of the function parameter values, for which the function has minimum or maximum. \n",
    "\n",
    "Given that any maximum of $f(\\mathbf{x})$ is a minimum of $-f(\\mathbf{x})$, the actual methods focus on minimizing the function. The same methods can be used for finding the maximum if we apply it to the negative of the function. "
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    "import numpy as np \n",
    "\n",
    "# use jupyter \"magic\" command to tell it to embed plot into the notebook \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "# reusing my codes from the repository\n",
    "from codes.plot_utils import plot_pretty\n",
    "plot_pretty(dpi=150, fontsize=12)"
   ]
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   "source": [
    "plot_pretty(dpi=150, fontsize=12)"
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    "### Taylor expansion of a multi-dimensional function\n",
    "\n",
    "Taylor expansion of the function of $D$ variables combined in a vector $\\mathbf{x}=(x_0, x_1,\\ldots, x_{D-1})$ of size $D$ around some point $\\mathbf{x}_0$ is\n",
    "\n",
    "$$f(\\mathbf{x})\\approx f(\\mathbf{x}_0)+ \\nabla f(\\mathbf{x}_0)\\,(\\mathbf{x}-\\mathbf{x}_0) + \\frac{1}{2}\\,(\\mathbf{x}-\\mathbf{x}_0)^\\intercal\\,\\nabla^2f(\\mathbf{x}_0)\\, (\\mathbf{x}-\\mathbf{x}_0).$$ \n",
    "\n",
    "Here $^\\intercal$ indicates <a href=\"https://en.wikipedia.org/wiki/Transpose\">transpose</a> of the vector, while $\\nabla$ and $\\nabla^2$ are called the ***gradient*** vector and the ***Hessian*** matrix, respectively, and are the first and second derivatives in $D$-dimensions:\n",
    "\n",
    "$$\\mathbf{g}(\\mathbf{x})=\\nabla f = \\left(\\frac{\\partial f}{\\partial x_0}, \\frac{\\partial f}{\\partial x_1},\\ldots,\\frac{\\partial f}{\\partial x_{D-1}}\\right)$$\n",
    "\n",
    "$$\\mathbf{H}(\\mathbf{x})=\\nabla^2 f = \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial^2f}{\\partial x_0^2} & \\frac{\\partial^2f}{\\partial x_0\\partial x_1} &\\ldots &\\ldots & \\frac{\\partial^2f}{\\partial x_0\\partial x_{D-1}}\\\\\n",
    "\\frac{\\partial^2f}{\\partial x_1\\partial x_0} & \\frac{\\partial^2f}{\\partial x_1^2} & \\frac{\\partial^2f}{\\partial x_1\\partial x_2} & \\ldots & \\frac{\\partial^2f}{\\partial x_1\\partial x_{D-1}}\\\\\n",
    "\\vdots & & \\ddots & & \\vdots\\\\\n",
    "\\frac{\\partial^2f}{\\partial x_{D-1}\\partial x_0} & \\frac{\\partial^2f}{\\partial x_{D-1}\\partial x_1} & \\ldots& \\dots& \\frac{\\partial^2f}{\\partial x_{D-1}^2} \n",
    "\\end{bmatrix}\n",
    "$$"
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    "### Properties of the gradient and Hessian around function extrema\n",
    "\n",
    "We will use $g(\\mathbf{x})=\\nabla f(\\mathbf{x})$ and $H(\\mathbf{x})=\\nabla^2 f(\\mathbf{x})$ to denote the gradient and Hessian for convenience. \n",
    "\n",
    "Minima and maxima of a function are called its *extrema* and from calculus it is known that at an extremum point $\\mathbf{x}_{\\rm ex}$, gradient is zero:\n",
    "\n",
    "$$g(\\mathbf{x}_{\\rm ex})=0.$$\n",
    "\n",
    "The sign of $H(\\mathbf{x}_{\\rm ex})$ determines whether $\\mathbf{x}_{\\rm ex}$ is minimum or maximum:\n",
    "\n",
    "$$\\mathbf{x}_{\\rm ex}\\ \\ \\mathrm{is}\\ \\ \\ \n",
    "\\begin{cases}\n",
    "\\mathrm{minimum},\\ H(\\mathbf{x}_{\\rm ex})\\ {\\rm is\\ positive\\ semi-definite},\\\\\n",
    "\\mathrm{maximum},\\ H(\\mathbf{x}_{\\rm ex})\\ {\\rm is\\ negative\\ semi-definite},\n",
    "\\end{cases}$$"
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    "The first couple of terms of the Taylor expansion for the gradient $g(\\mathbf{x})=\\nabla f(\\mathbf{x})$ are: \n",
    "\n",
    "$$\\mathbf{g}(\\mathbf{x})=\\nabla f(\\mathbf{x})= \\nabla f(\\mathbf{x}_0) +\\nabla^2 f(\\mathbf{x}_0)(\\mathbf{x}- \\mathbf{x}_0) + \\ldots = \\mathbf{g}(\\mathbf{x}_0) + \\mathbf{H}(\\mathbf{x}_0)\\,(\\mathbf{x}- \\mathbf{x}_0)+\\ldots.$$\n",
    "\n",
    "If $\\mathbf{x}=\\mathbf{x}_{\\rm ex}$ is an extremum, $\\nabla f(\\mathbf{x}_{\\rm ex})=0$ and thus\n",
    "\n",
    "$$\\mathbf{g}(\\mathbf{x}_0) + \\mathbf{H}(\\mathbf{x}_0)\\,(\\mathbf{x}_{\\rm ex}- \\mathbf{x}_0)\\approx 0$$\n",
    "\n",
    "or solving for $\\mathbf{x}_{\\rm ex}$ we have\n",
    "\n",
    "$$\\mathbf{x}_{\\rm ex} \\approx \\mathbf{x}_0 - \\mathbf{H}^{-1}(\\mathbf{x}_0)\\cdot \\mathbf{g}(\\mathbf{x}_0),$$\n",
    "\n",
    "where $\\mathbf{H}^{-1}$ is the inverse of the Hessian matrix. "
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    "\n",
    "Many optimization methods are based on this because it gives an approximation for where extremum is relative to the point $\\mathbf{x}_0$. \n",
    "\n",
    "$$\\mathbf{x}_{\\rm ex} \\approx \\mathbf{x}_0 - \\mathbf{H}^{-1}(\\mathbf{x}_0)\\cdot \\mathbf{g}(\\mathbf{x}_0),$$\n",
    "\n",
    " \n",
    "Different methods make different assumptions about $\\mathbf{H}^{-1}$ or choices for its calculation. "
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    "### Steepest descent method\n",
    "\n",
    "assumes that the inverse of the Hessian matrix is equal to the identity matrix (matrix with 1's on the diagonal and zeros elsewhere), $\\mathbf{H}^{-1}=I$, which turns the equation into \n",
    "\n",
    "$$\\mathbf{x}_{\\rm ex} = \\mathbf{x}_0 -  \\mathbf{g}(\\mathbf{x}_0),$$\n",
    "\n",
    "The method proceeds from the starting point $\\mathbf{x}_0$ by making a number of steps, with each $(n+1)$-th step moving from point $ \\mathbf{x}_n$ to  $\\mathbf{x}_{n+1}$ as follows:\n",
    "\n",
    "$$ \\mathbf{x}_{n+1} =  \\mathbf{x}_n - \\gamma\\, \\mathbf{g}( \\mathbf{x}_n),$$\n",
    "\n",
    "where $\\gamma$ is a parameter that controls the size of the steps relative to the gradient. "
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    "In these methods $\\gamma$ needs to be chosen somehow and tuned, if optimal performance is needed. However, optimal value of $\\gamma$ will differ for different functions $f$. \n",
    "\n",
    "Thus, in the gradient methods like there is a problem of optimal choice of step size parameter."
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    "### Conjugate Gradient method\n",
    "\n",
    "Conjugate gradient methods dispense with the Hessian matrix\n",
    "altogether, opting instead to use line optimizations in conjugate directions\n",
    "to avoid computing second-order derivatives."
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    "### Quasi-Newton methods \n",
    "\n",
    "Use user-provided (in cases when second derivatives can be computed analytically) or approximate the inverse of the Hessian matrix in different ways and inolve substantial linear algebra calculations. \n",
    "\n",
    "These methods  include the <a href=\"https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm\">Broyden–Fletcher–\n",
    "Goldfarb–Shanno</a> (BFGS) method "
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    "### Examples: finding minimum of the Rosenbrock function\n",
    "\n",
    "Rosenbrock function is described by the following equation in 2D (i.e. for two parameters $x$ and $y$): \n",
    "\n",
    "$$r(x,y) = (a-x)^2 + b(y-x^2)^2,$$\n",
    "\n",
    "which is often used for testing optimization and sampling algorithms, particularly with $a=1$, $b=100$ most often used. It has a global minimum at $(x,y)=(a,a^2)$ at which $f(x,y)=0$, as is clear from the equation above. "
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    "This is because this function is quite \"difficult\" despite its benign-looking functional form. The function spans a wide range of values over small change of parameters has a strongly \"curved\" valley in the $x-y$ plane which extends  values to large values of $x$ and $y$. \n",
    "\n",
    "The function is named after Howard H. Rosenbrock, who introduced it as a test case for a minimization algorithm he developed in a <a href=\"https://academic.oup.com/comjnl/article/3/3/175/345501\">paper</a> in 1960. "
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    "The multi-dimensional extension of the Rosenbrock function for $D$-dimensional space of parameters $\\mathbf{x}=\\{x_0,x_1.\\ldots,x_{D-1}\\}$ is\n",
    "\n",
    "$$r(\\mathbf{x})=\\sum\\limits_{i=0}^{D-1}\\left[b(x_{i+1}-x_i^2)^2 + (a-x_i)^2\\right].$$"
   ]
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    "Note that $-r(\\mathbf{x})$ will be a function with a long curved \"ridge\" instead of \"valley\". Such function is often used in testing sampling algorithm and we will see it again when we talk about MCMC sampling. \n",
    "\n",
    "The routine below that was taken from the SciPy optimize package tutorials uses Python's vector slicing to calculate the function for $a=1$, $b=100$. Note that this implementation does not explicitly deal with dimensionality of the input vector $\\mathbf{x}$, this is done automatically using vector operations. Thus, the same code works for $\\mathbf{x}$ of different dimensions. Below we will use this function as a test case to find its minimum for 2D and 5D cases.    "
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    "def rosenbrock(x):\n",
    "    \"\"\"The Rosenbrock \"banana\" function\n",
    "    x is a vector of points in 2 or more dimensional space\n",
    "    \"\"\"\n",
    "    return sum(100.0*(x[1:]-x[:-1]**2.0)**2.0 + (1-x[:-1])**2.0)\n"
   ]
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   "cell_type": "code",
   "execution_count": 5,
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   "source": [
    "# define a grid of x and y for calculations and plotting\n",
    "xmin, xmax, ng = -10, 10, 100\n",
    "ymin, ymax = -50, 100\n",
    "x = np.linspace(xmin, xmax, ng)\n",
    "y = np.linspace(ymin, ymax, ng)\n",
    "\n",
    "# generate a 2d grid of x and y points\n",
    "xg, yg = np.meshgrid(x, y)\n",
    "\n",
    "# form a single array of 2D vectors \n",
    "x = np.vstack([xg.ravel(), yg.ravel()])\n",
    "\n",
    "# compute the Rosenbrock function and reshape the output into ng x ng grid for plotting\n",
    "rg = rosenbrock(x).reshape((ng,ng))\n"
   ]
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   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "from codes.plot_utils import plot_color_map\n"
   ]
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   "cell_type": "code",
   "execution_count": 7,
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\n",
      "text/plain": [
       "<Figure size 450x450 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#xg, yg are 2D \"grids\" of x and y generated by meshgrid\n",
    "# rg is 2D array with values of the Rosenbrock function for xg-yg grid\n",
    "\n",
    "# contour levels; fairly arbitrary choice here, just to show the range of function values.\n",
    "levs = np.log10(rg.min()+0.1*np.arange(1,10)**7)\n",
    "\n",
    "plot_color_map(xg, yg, np.log10(rg), xlim=[xmin,xmax], ylim=[ymin,ymax], \n",
    "                   xlabel = r'$x$', ylabel = '$y$', cmap='plasma', colorbar=True, \n",
    "                   plot_title=r'$\\rm \\log_{10} Rosenbrock\\ function\\ in\\ 2D$', contours=True, contcmap='plasma', levels = levs, \n",
    "                   figsize=3.0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Derivatives of the Rosenbrock function in 2D with respect to $x$ and $y$ are relatively straightforward:\n",
    "\n",
    "$$\\frac{\\partial r}{\\partial x} = -400(y-x^2) - 2(1-x);\\ \\ \\ \\ \\ \\ \\frac{\\partial r}{\\partial y}=200(y-x^2).$$\n",
    "\n",
    "Derivatives in more dimensions have, of course, more terms, but overall have similar structure with respect to $x_i$ and $x_{i+1}$. These are implemented for an arbitrary number of dimensions in the routine below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def rosen_der(x):\n",
    "    xm = x[1:-1]\n",
    "    xm_m1 = x[:-2]\n",
    "    xm_p1 = x[2:]\n",
    "    der = np.zeros_like(x)\n",
    "    der[1:-1] = 200.*(xm-xm_m1**2) - 400.*(xm_p1 - xm**2)*xm - 2.*(1-xm)\n",
    "    der[0] = -400.*x[0]*(x[1]-x[0]**2) - 2.*(1-x[0])\n",
    "    der[-1] = 200.*(x[-1]-x[-2]**2)\n",
    "    return der\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We can use the knowledge of analytic derivative expression to employ methods that rely on gradient of the functions, such as Conjugate Gradient method and BFGS. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 32\n",
      "         Function evaluations: 78\n",
      "         Gradient evaluations: 78\n",
      "minimum at : [1. 1.]\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "x0 = [-10, 10]\n",
    "\n",
    "res = minimize(rosenbrock, x0, method='CG', jac=rosen_der,\n",
    "               options={ 'disp': True})\n",
    "\n",
    "print(\"minimum at :\",res.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from timeit import default_timer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 3.930839\n",
      "         Iterations: 120\n",
      "         Function evaluations: 221\n",
      "         Gradient evaluations: 221\n",
      "completed in 0.0122 sec\n",
      "minimum at: [-0.96205103  0.9357394   0.88071361  0.77787768  0.60509367]\n"
     ]
    }
   ],
   "source": [
    "# try in 5D\n",
    "x0 = [-10, 10, -5, 10, 5]\n",
    "\n",
    "tstart = default_timer()\n",
    "res = minimize(rosenbrock, x0, method='CG', jac=rosen_der, options={ 'disp': True})\n",
    "\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(\"minimum at:\", res.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "This does not look too good, although result depends on the starting point. For example, changing the first value in $\\mathbf{x}_0$ from $-10$ to $10$ results in the correct minimum. \n",
    "\n",
    "The same applies to the BFGS algorithm used below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 3.930839\n",
      "         Iterations: 107\n",
      "         Function evaluations: 124\n",
      "         Gradient evaluations: 123\n",
      "completed in 0.0119 sec\n",
      "minimum at : [-0.96205102  0.9357394   0.8807136   0.77787768  0.60509368]\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "x0 = [-10, 10, -5, 10, 5]\n",
    "\n",
    "tstart = default_timer()\n",
    "res = minimize(rosenbrock, x0, method='BFGS', jac=rosen_der,\n",
    "               options={'gtol': 1e-10,  'disp': True})\n",
    "\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(\"minimum at :\",res.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "These issues in many dimensions is what motivates methods based on the knowledge or approximations of the Hessian matrix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def rosen_hess(x):\n",
    "    \"\"\"\n",
    "    Hessian matrix of the multivariate Rosenbrock function\n",
    "    \"\"\"\n",
    "    x = np.asarray(x)\n",
    "    H = np.diag(-400.*x[:-1],1) - np.diag(400.*x[:-1],-1)\n",
    "    diagonal = np.zeros_like(x)\n",
    "    diagonal[0] = 1200.*x[0]**2  -400.*x[1]+2\n",
    "    diagonal[-1] = 200.\n",
    "    diagonal[1:-1] = 202. + 1200.*x[1:-1]**2 - 400.*x[2:]\n",
    "    H = H + np.diag(diagonal)\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "A quasi-Newton method Newton-Conjugate Gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 67\n",
      "         Function evaluations: 82\n",
      "         Gradient evaluations: 148\n",
      "         Hessian evaluations: 67\n",
      "completed in 0.0139 sec\n",
      "[1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "tstart = default_timer()\n",
    "res = minimize(rosenbrock, x0, method='Newton-CG',\n",
    "               jac=rosen_der, hess=rosen_hess,\n",
    "               options={'xtol': 1e-10, 'disp': True})\n",
    "\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(res.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "A different implementation of Newton-CG method that allows definition of boundaries. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 69\n",
      "         Function evaluations: 70\n",
      "         Gradient evaluations: 60\n",
      "         Hessian evaluations: 59\n",
      "completed in 0.0148 sec\n",
      "[1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "tstart = default_timer()\n",
    "res = minimize(rosenbrock, x0, method='trust-ncg',\n",
    "               jac=rosen_der, hess=rosen_hess,\n",
    "               options={'gtol': 1e-8, 'disp': True})\n",
    "\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(res.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 41\n",
      "         Function evaluations: 42\n",
      "         Gradient evaluations: 35\n",
      "         Hessian evaluations: 42\n",
      "completed in 0.0265 sec\n",
      "[1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "tstart = default_timer()\n",
    "res = minimize(rosenbrock, x0, method='trust-exact',\n",
    "               jac=rosen_der, hess=rosen_hess,\n",
    "               options={'gtol': 1e-10, 'disp': True})\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(res.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "What about the cases when analytical expressions for derivative do not exist? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Numerical evaluation of derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Taylor expansion of $f(x)$ arond $x_0$:\n",
    "$$f(x) =f(x_0)+f^\\prime(x_0)\\,(x-x_0)+\\frac{1}{2}f^{\\prime\\prime}(x_0)\\,(x-x_0)^2 + \\frac{1}{6}f^{(3)}(x_0)\\,(x-x_0)^3+ \\mathcal{O}[(x-x_0)^4].$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The term $\\mathcal{O}[(x-x_0)^4]$ is the standard shorthand for ``and terms of order 4 and higher''."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use this expression to evaluate it at $x=x_0-h$ and $x=x_0+h$, where $h$ is some small value:\n",
    "\n",
    "$$f(x-h) = f(x_0) - f^\\prime(x_0)\\,h+\\frac{1}{2}f^{\\prime\\prime}(x_0)\\,h^2 - \\frac{1}{6}f^{(3)}(x_0)\\,h^3+ \\mathcal{O}(h^4).$$\n",
    "\n",
    "$$f(x+h) = f(x_0) + f^\\prime(x_0)\\,h+\\frac{1}{2}f^{\\prime\\prime}(x_0)\\,h^2 + \\frac{1}{6}f^{(3)}(x_0)\\,h^3+ \\mathcal{O}(h^4).$$\n",
    "\n",
    "Thus, $$f(x+h)-f(x-h) = 2\\,f^\\prime(x_0)\\,h+ \\frac{1}{3}f^{(3)}(x_0)\\,h^3 + \\mathcal{O}(h^5),$$\n",
    "\n",
    "which gives \n",
    "\n",
    "$$f^\\prime(x_0)=\\frac{f(x+h)-f(x-h)}{2h} - \\frac{1}{6}f^{(3)}(x_0)\\,h^2 + \\mathcal{O}(h^4)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def der(func, x, h):\n",
    "    return 0.5*(func(x+h) - func(x-h))/h\n",
    "\n",
    "def der1(func, x, h):\n",
    "    return (4.*der(func, x, h/2)-der(func,x,h)) / 3.\n",
    "\n",
    "def der2(func, x, h):\n",
    "    return (16.*der1(func, x, h/2)-der1(func,x,h)) / 15.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsteps = np.arange(25)\n",
    "ders = np.zeros(np.shape(nsteps)[0])\n",
    "\n",
    "hsteps = 1.0 / np.power(2., nsteps)\n",
    "x0 = 1.0\n",
    "\n",
    "for i, ns in enumerate(nsteps):\n",
    "    ders[i] = der2(np.exp, x0, hsteps[i])\n",
    "     \n",
    "fexact = np.e\n",
    "ferr = np.abs(1. - ders/fexact)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from codes.plot_utils import plot_line_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ferr_model = ferr[0] * (hsteps/hsteps[0])**6\n",
    "\n",
    "plot_line_points(np.log10(hsteps), np.log10(ferr_model), \n",
    "                 xp=np.log10(hsteps), yp=np.log10(np.maximum(2.e-16,ferr)), points=True,\n",
    "                 xlabel=r'$h$', ylabel=r'$\\log_{10}\\vert\\rm fractional\\ error\\vert$', \n",
    "                 plot_title='error scaling of the first numerical derivative',\n",
    "                 legendloc='lower right', grid=True, figsize=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "I will leave you derivation of this equation as an exercise, because it is completely similar to how we derive corresponding equation for the Romberg integration.\n",
    "\n",
    "$$f^\\prime(x) = \\frac{4^m R_m(h/2) - R_m(h)}{4^m-1} + \\mathcal{O}(h^{2(m+1)})$$\n",
    "\n",
    "where\n",
    "\n",
    "$$R_{m+1} = \\frac{4^m R_m(h/2) - R_m(h)}{4^m-1}.$$\n",
    "\n",
    "is an estimate of the derivative which has truncation error of order $\\mathcal{O}(h^{2(m+1)})$. Computing derivative by increasing $m$ in this estimateor is called the ***Richardson approach to the limit.***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The general method of improving accuracy and order of the scheme by eliminating leading truncation error terms was proposed by English mathematician, physicist, meteorologist, psychologist and pacifist Lewis Fry Richardson in 1922, when he attempted pioneering computations of air flows using a system of differential equations for weather prediction. This general approach is known as *Richardson's extrapolation.*\n",
    "<p>\n",
    "<center>\n",
    "<img width=300 src=\"img/Lewis_Fry_Richardson.png\"></img>\n",
    "Lewis Fry Richardson (1881-1953)\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Royal Albert Hall in London\n",
    "\n",
    "which Richardson envisioned filled with people doing parallel computations.\n",
    "\n",
    "<img width=600 src=\"https://d15v4l58k2n80w.cloudfront.net/file/1396975600/48487571697/width=1280/height=720/format=-1/fit=crop/crop=0x0+7951x4476/rev=4/t=436739/e=never/k=d6183c30/032.jpg\"></img>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### This was actually realized, although never on such huge scale\n",
    "\n",
    "<img width=600 src=\"http://ece.umich.edu/bicentennial/images/timeline/human-computers.jpg\"></img>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Thus, derivatives of smooth functions can be estimated numerically quite accurately using such approach to compute gradients and Hessian matrix. However, this can be quite expensive, especially for the Hessian where second derivatives are needed. \n",
    "\n",
    "Plus, there are many functions that are encountered that are discontinuous and for which derivatives can be ill-behaved. Thus, many *derivative-free* methods have been developed. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Finding minimum/maximum of a function\n",
    "\n",
    "Last week I reviewed several methods that rely on the 1st and 2nd derivatives of the function in its $D$ parameters (forming the gradient and Hessian matrix, respectively). \n",
    "\n",
    "We did tests of several methods using multi-D Rosenbrock function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 450x450 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#xg, yg are 2D \"grids\" of x and y generated by meshgrid\n",
    "# rg is 2D array with values of the Rosenbrock function for xg-yg grid\n",
    "\n",
    "# contour levels; fairly arbitrary choice here, just to show the range of function values.\n",
    "levs = np.log10(rg.min()+0.1*np.arange(1,10)**7)\n",
    "\n",
    "plot_color_map(xg, yg, np.log10(rg), xlim=[xmin,xmax], ylim=[ymin,ymax], \n",
    "                   xlabel = r'$x$', ylabel = '$y$', cmap='plasma', colorbar=True, \n",
    "                   plot_title=r'$\\rm \\log_{10} Rosenbrock\\ function\\ in\\ 2D$', contours=True, contcmap='plasma', levels = levs, \n",
    "                   figsize=3.0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Derivatives of the Rosenbrock function in 2D with respect to $x$ and $y$ are relatively straightforward:\n",
    "\n",
    "$$\\frac{\\partial r}{\\partial x} = -400(y-x^2) - 2(1-x);\\ \\ \\ \\ \\ \\ \\frac{\\partial r}{\\partial y}=200(y-x^2).$$\n",
    "\n",
    "Derivatives in more dimensions have, of course, more terms, but overall have similar structure with respect to $x_i$ and $x_{i+1}$. These are implemented for an arbitrary number of dimensions in the routine below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Lessons learned\n",
    "\n",
    "* Gradient methods work in some cases when function is smooth, but their results can depend on the starting position.\n",
    "\n",
    "\n",
    "* Quasi-Newton methods that use Hessian matrix are much more reliable and have the same speed.\n",
    "\n",
    "\n",
    "* Even when analytic expressions for derivatives are not available, for smooth functions accurate derivatives can be obtained using Richardson's method, which uses knowledge of the truncation error terms to construct higher order estimates of the derivative similarly to the Romberg integration. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Dependence of the results on the initial position arises because initial position determines the path through along the \"landscape\" of the function that algorithm takes. Just like starting at different places in the mountains may make a hike to a particular destination more or less difficult. \n",
    "\n",
    "Hessian adds a significant information about the local curvature of the function, i.e. how fast gradient changes. This allows methods that use the Hessian matrix to getting off the cliff in the steep and rapidly changing parts of the function. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "but what if accurate derivatives are not available (for example, function is not smooth) or are too expensive to compute?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Derivative-free methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### A naive method: random walk\n",
    "\n",
    "Follows a random walk of a *\"walker*:\n",
    "\n",
    "1. start at some initial point $\\mathbf{x}=\\mathbf{x}_0$. \n",
    "\n",
    "2. propose a step in a random direction $\\mathbf{x}^\\prime = \\mathbf{x} + \\Delta\\mathbf{x}$\n",
    "\n",
    "3. if $f(\\mathbf{x}^\\prime)< f(\\mathbf{x})$, accept the step $\\mathbf{x}=\\mathbf{x}^\\prime$, else go back to step 2.\n",
    "\n",
    "Steps are terminated when some convergence is reached, for example no new step is accepted after some maximum number of proposed steps (it means that the walker is likely very close to the minimum). \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Components of the step vector $\\Delta\\mathbf{x}$ are usually chosen to follow Gaussian distribution, i.e. for a component $i$: \n",
    "\n",
    "$$p(\\Delta x_i) = \\frac{1}{\\sqrt{2\\pi}\\,\\sigma}\\,\\exp\\left(-\\frac{1}{2}\\frac{\\Delta x_i^2}{\\sigma_i^2}\\right) $$\n",
    "\n",
    "\n",
    "The method requires choice of an optimal step sizes scale, $\\sigma_i$. Performance and accuracy of the result will depend on this choice. However, this method is simple to implement, it does not require derivatives, and will do much better than the brute force search for a minimum. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def minimize_by_random_walk(func, x0, stepsize, atol=1.e-6, verbose=True):\n",
    "    assert(atol > 0.)\n",
    "    nd = np.shape(x0)[0]\n",
    "    xold = x0 + 100.*atol # just to get things started\n",
    "    xnew = x0 # initial position\n",
    "    step = stepsize # initial step size\n",
    "    while np.abs(xnew - xold).max() > atol:\n",
    "        xold = xnew\n",
    "        fold = func(xold)\n",
    "        xtry = xold + np.random.normal(scale=step, size=nd) # generate a random Gaussian-distributed step\n",
    "        while func(xtry) >= fold:\n",
    "            xtry = xold + np.random.normal(scale=step, size=nd)\n",
    "        xnew = xtry\n",
    "        if verbose:\n",
    "            print(xnew, np.abs(xnew - xold))\n",
    "\n",
    "    return xnew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed in 7.62 sec\n",
      "[1.0000232  1.00005669]\n"
     ]
    }
   ],
   "source": [
    "x0 = np.array([0.5, 0.5])\n",
    "#x0 = np.array([-10, 10, -5, 10, 5])\n",
    "\n",
    "tstart = default_timer()\n",
    "res = minimize_by_random_walk(rosenbrock, x0, .025, atol=5.e-4, verbose=False)\n",
    "\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# if you want to get info on the np.random.normal execute this cell\n",
    "?np.random.normal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The method works robustly, even for the \"difficult\" starting position, and it would be very simple to introduce boundary control in this algorithm by simply discarding any trial steps outside specified boundary. \n",
    "\n",
    "However, as this test illustrates the algorithm can be very slow, especially if high accuracy is required."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  Derivative-free methods: Nelder-Mead (aka simplex) method\n",
    "\n",
    "The algorithm begins by forming an inital $(D + 1)$-dimensional polyhedron, or *simplex*,\n",
    "of $D + 1$ points, $\\mathbf{x}_i$, $i = 0, 1,\\ldots, D$, that are randomly distributed throughout\n",
    "the problem space domain. Indices of the points are sorted in ascending order of $f(\\mathbf{x})$ so that $f(\\mathbf{x}_0)$ is smallest and\n",
    "$f(\\mathbf{x}_D)$ is largest. It then proceeds as follows: \n",
    "\n",
    "1. To obtain a new trial point, $\\mathbf{x}_r$, the worst point, $\\mathbf{x}_D$, is reflected through the opposite face of the polyhedron using a scaling factor, $s_1$:\n",
    "\n",
    "$$\\mathbf{x}_r=\\mathbf{x}_D + s_1\\,(\\mathbf{x}_m - \\mathbf{x}_D),$$\n",
    "\n",
    "where $\\mathbf{x}_m$ is mean (the centroid) of all $\\mathbf{x}$, excluding $\\mathbf{x}_D$:\n",
    "\n",
    "$$\\mathbf{x}_m = \\frac{1}{D}\\,\\sum\\limits_{i=0}^{D-1}\\mathbf{x}_i.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "For example, when $D = 2$, the simplex is a triangle."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "2. If $f(\\mathbf{x}_r)<f(\\mathbf{x}_0)$, then take another step in the same direction with scaling factor of $s_2$:\n",
    "\n",
    "$$\\mathbf{x}_e=\\mathbf{x}_r + s_2\\,(\\mathbf{x}_m - \\mathbf{x}_D),$$\n",
    "\n",
    "If $f(\\mathbf{x}_e)<f(\\mathbf{x}_0)$, then $\\mathbf{x}_D=\\mathbf{x}_e$ and we go to step 1 above, else\n",
    "    $\\mathbf{x}_D=\\mathbf{x}_r$.\n",
    "    \n",
    "3. Else if $f(\\mathbf{x}_r)>f(\\mathbf{x}_0)$, compare $f(\\mathbf{x}_r)$ to $f(\\mathbf{x}_{D-1})$ and if $f(\\mathbf{x}_r)$ is smaller $\\mathbf{x}_{D-1}=\\mathbf{x}_r$, if not than *shrink the entire simplex* by the scaling factor of $s_3$.\n",
    "\n",
    "This description is not fully complete, as there are a number of checks and choices made in the last step. It is meant to give an idea of how the algorithm works. It'd be easier to examine the pseudo-code for the algorithm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img width=500 src=\"img/simplex_pseudo_code.PNG\"></img>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Using Nelder-Mead (simplex) minimization method that does not rely on function derivatives to find the minimum of the Rosenbrock function.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed in 0.0289 sec\n",
      "minimum at : [0.99513568 0.98998451 0.98069012 0.96593587 0.93354015]\n"
     ]
    }
   ],
   "source": [
    "x0 = [-10, 10]\n",
    "x0 = [-10, 10, -5, 10, 5]\n",
    "\n",
    "tstart = default_timer()\n",
    "res = minimize(rosenbrock, x0, method='nelder-mead', tol=1.e-12)\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "\n",
    "print(\"minimum at :\",res.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Maximum number of function evaluations has been exceeded.\n",
      "completed in 0.0659 sec\n",
      "minimum at : [0.99513568 0.98998451 0.98069012 0.96593587 0.93354015]\n"
     ]
    }
   ],
   "source": [
    "tstart = default_timer()\n",
    "res = minimize(rosenbrock, x0, method='Nelder-Mead', options={'xtol': 1e-10, 'disp': True})\n",
    "\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(\"minimum at :\",res.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  Derivative-free methods: differential evolution\n",
    "\n",
    "Developed by R. Storn and K. Price in 1997 (<a href=\"https://link.springer.com/article/10.1023%2FA%3A1008202821328\">Storn & Price 1997</a>), the <a href=\"https://en.wikipedia.org/wiki/Differential_evolution\">differential evolution algorithm</a> is remarkably simple to implement, works in arbitrary number of dimensions, does not require function derivatives, allows imposing bounds on the domain, and is quite efficient. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The reason the method is called \"differential evolution\" is because the initial population of points in $D$ dimensions can be thought of as evolving towards a minimum during algorithm iterations. The evolution is differential because it is driven by scaled differences between point locations. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Interestingly, one of the initial drivers for development of this algorithm was a problem of solving the least squares mimimization problem to find coefficients of the 5D polynomial approximation using Chebyshev polynomial expansion, which was intractable with other methods. Since then, DE algorithm was successfully applied for this problem for up to 33-dimensional polynomials. \n",
    "\n",
    "In depth description of the differential algorithm, its variations, tests, and applications can be found in a book by R. Storn, K. Price and J. Lampinen \"*Differential evolution : a practical approach to global optimization*\" <a href=\"https://catalog.lib.uchicago.edu/vufind/Record/8875926\">available online</a> through U.Chicago library. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Start with $N_p$ members of the population randomly distributed in the problem domain. Vector of coordinates for each member is indexed from $0$ to $N_p-1$ and collection of all vectors $\\mathbf{X}_{\\rm now}=(\\mathbf{x}_{\\rm now,0},\\mathbf{x}_{\\rm now,1},\\ldots,\\mathbf{x}_{{\\rm now},N_p-1})$ forms the current population, where each $\\mathbf{x}_{\\rm now,i}$ is a $D$-dimensional vector, where $D$ is the number of parameters of the minimized function.   \n",
    "\n",
    "The algorithm then proceeds through iterations (called evolutionary or generational cycles) that lead to evolution of the population towards function minimum. Each cycle consists of the *\"mutation\"* and *\"selection* stages for each point vector $\\mathbf{x}_i$ in $\\mathbf{X}_{\\rm now}$ (each member of the population) that leads to formation of the new population $\\mathbf{X}_{\\rm next}$:\n",
    "\n",
    "* *Mutation stage:*  select three random indices from $0$ to $N_p-1$, $r_1$, $r_2$, $r_3$. \n",
    "Perturb vector with index $r_3$ by the scaled difference of vectors with indices $r_2$ and $r_3$: \n",
    "$\\mathbf{x}^\\prime_i=\\mathbf{x}_{{\\rm now}, r_3} + s\\,(\\mathbf{x}_{{\\rm now}, r_2}-\\mathbf{x}_{{\\rm now}, r_1})$, where $s$ is a parameter. \n",
    "\n",
    "\n",
    "* *Selection stage:* if $f(\\mathbf{x}^\\prime_i)\\leq f(\\mathbf{x}_{{\\rm now},i})$, then $\\mathbf{x}_{{\\rm next},i}=\\mathbf{x}^\\prime_i$, else $\\mathbf{x}_{{\\rm next},i}=\\mathbf{x}_{{\\rm now},i}$ (no mutation). \n",
    "\n",
    "Once all members of the population went through mutation and selection stages go back to the next iteration and $\\mathbf{X}_{\\rm next}$ becomes $\\mathbf{X}_{\\rm now}$ and the cycle repeats. \n",
    "\n",
    "Evolutionary cycles continue until some convergence criterion is met. For example, maximum difference between vectors in $\\mathbf{X}_{\\rm next}$ and $X_{\\rm now}$ is smaller than the specified threshold. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Differential evolution method is implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html#scipy.optimize.differential_evolution\"><tt>scipy.optimize.differential_evolution</tt></a> routine. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here is pseudo-code for the simplest version of the differential evolution algorithm, which already should work quite well, but can be further improved by various modifications. \n",
    "\n",
    "    npop = np.size(x0)[0] # the number of population members\n",
    "    fnow = func(xnow)\n",
    "    xnow = np.copy(x0)\n",
    "    xnext = np.zeros_like(xnow)\n",
    "    ....\n",
    "    while some convergence criterion is not met: \n",
    "        # xnow is a vector of coordinate vectors of the current population\n",
    "        # xnext is a vector of coordinate vector of the next gen population\n",
    "        for i in range(npop):\n",
    "            # generate random indices  ir1, ir2, ir3 \n",
    "            # where all indices are not equal to each other and not equal to i\n",
    "            # s can be a constant for large npop, but it's more safe to make it a Gaussian random number\n",
    "            xtry = xnow[ir3] + s * (xnow[ir1] - xnor[ir2])\n",
    "            if func(xtry) <= fnow[i]:\n",
    "                xnext[i] = xtry\n",
    "            else:\n",
    "                xnext[i] = xnow[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Initialization of the population for the DE algorithm \n",
    "\n",
    "Mutation stage of the algorithm requires that population members are in different locations, otherwise the difference $\\mathbf{x}_{{\\rm now}, r_2}-\\mathbf{x}_{{\\rm now}, r_1}$ will be zero and location of $\\mathbf{x}_{{\\rm now}, r_3}$ will simply be duplicated to location of $\\mathbf{x}^\\prime_i$ in the mutation stage.\n",
    "\n",
    "Thus, initial population members positions must be different. There are different ways to place population members. Assuming that we are searching for a minimum within some rectangular domain defined by the minimum and maximum values along each coordinate axis: $\\mathbf{x}_{\\rm min}$ and $\\mathbf{x}_{\\rm max}$, we can initialize the members as \n",
    "\n",
    "$$\\mathbf{x}_0 = \\mathbf{x}_{\\rm min} + (\\mathbf{x}_{\\rm max}-\\mathbf{x}_{\\rm min}) \\times \\mathrm{rand}(0,1),$$\n",
    "\n",
    "where $\\mathrm{rand}(0,1)$ is a random number uniformly distributed from 0 to 1. This choice makes sense if we do not know location of the minimum and we are spreading the population members as widely as possible. To make the distribution of members more uniform, certain placement strategies can be used instead of random distribution above, such as <a href=\"https://www.johndcook.com/blog/2009/03/16/quasi-random-sequences-in-art-and-integration/\">quasi-random sequences</a>.\n",
    "\n",
    "Another possibility is to initialize locations of population members around a given point $\\mathbf{x}_{0c}$ by using random numbers drawn from a Gaussian distribution centered at $\\mathbf{x}_{0c}$:\n",
    "\n",
    "$$\\mathbf{x}_0 = \\mathrm{gaussian}(\\mathbf{x}_{0c}, \\Sigma),$$\n",
    "\n",
    "where $\\Sigma$ is a vector of the rms dispersions along each of the coordinates (can be the same for all coordinates) or a <a href=\"https://datascienceplus.com/understanding-the-covariance-matrix/\">covariance matrix</a>. This choice makes sense if we have a good idea where the minimum is roughly, so that we can choose $\\mathbf{x}_{0c}$ to be near the suspected location. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Modification of the DE algorithm using randomized $s$ scaling factor\n",
    "\n",
    "Although this is unlikely when the size of the evolved population is large (say $>10-20D$), for small population sizes it is possible that the same combinations of <tt>ir1, ir2, ir3</tt> will be drawn for multiple members. If the trial step is successful, this will result in multiple members having the same location. Several of such events can lead to all population members having the same location. Given that the algorithm relies on existence of multiple population members at different locations (population diversity), if population degenerates to a single point, the DE algorithm can longer work. \n",
    "\n",
    "To avoid this, one can replace constant scaling factor $s$ for each population member with a number randomly drawn from, say, Gaussian distribution centered at $s$ and with the rms dispersion of say $0.1s>0$ (this can be a parameter). In this case, the mutation stage will result in different locations, even if the <tt>ir1, ir2, ir3</tt> are the same for different population members. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Modification of the DE algorithm with the crossover stage\n",
    "\n",
    "One of the modifications to this basic algorithm is introduction of the ***crossover stage*** so that the mutation and crossover stages together are as follows: \n",
    "\n",
    "* compute mutation vector $\\mathbf{x}^\\prime_i=\\mathbf{x}_{{\\rm now}, r_3} + s\\,(\\mathbf{x}_{{\\rm now}, r_2}-\\mathbf{x}_{{\\rm now}, r_1})$, as before, where vector $\\mathbf{x}^\\prime_i$ has components $\\mathbf{x}^\\prime_i=[x^{\\prime}_{0i}, x^{\\prime}_{1i}, \\ldots, x^{\\prime}_{(D-1)i}]$, and $D$ is the number of parameters of the minimized function (i.e., dimensionality of the problem). \n",
    "\n",
    "* \"***crossover stage***\": form the trial vector $\\mathbf{x}^{\\prime\\prime}_i=[x^{\\prime\\prime}_{0i}, x^{\\prime\\prime}_{1i}, \\ldots, x^{\\prime\\prime}_{(D-1)i}]$, where \n",
    "\n",
    "\\begin{equation}\n",
    "x^{\\prime\\prime}_{ji} = \n",
    "\\begin{cases}\n",
    "x^{\\prime}_{ji}, \\ {\\rm if\\ }r_j\\leq \\mathrm{cr\\ or\\ } j= \\mathrm{ir}_i,\\\\\n",
    "x_{{\\rm now},ji}, \\ {\\rm if\\ }r_j> \\mathrm{cr\\ or\\ } j\\ne \\mathrm{ir}_i,\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "and $r_j$ is the random floating point number uniformly distributed in the interval $[0,1]$ that is generated for the index $j$, and $\\mathrm{ir}_i$ is the random integer uniformly distributed in the range $[0, D-1]$ generated for index $i$, which ensures that $\\mathbf{x}^{\\prime\\prime}_i$ gets at least one element from $\\mathbf{x}^\\prime_i$. The crossover parameter $\\mathrm{cr}\\in [0,1]$ is a constant set by user. \n",
    "\n",
    "* *Selection stage:* if $f(\\mathbf{x}^{\\prime\\prime}_i)\\leq f(\\mathbf{x}_{{\\rm now},i})$, then $\\mathbf{x}_{{\\rm next},i}=\\mathbf{x}^{\\prime\\prime}_i$, else $\\mathbf{x}_{{\\rm next},i}=\\mathbf{x}_{{\\rm now},i}$ (no mutation). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "completed in 1.66 sec\n",
      "minimum at : [1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import differential_evolution\n",
    "\n",
    "xmin, xmax, ymin, ymax = -10., 10., -10., 10.\n",
    "x0 = [-10, 10]\n",
    "#bounds = [(xmin, xmax), (ymin, ymax)]\n",
    "x0 = [-10, 10, -5, 10, 5]\n",
    "bounds = [(xmin, xmax), (ymin, ymax), (xmin, xmax), (ymin, ymax), (xmin, xmax)]\n",
    "\n",
    "tstart = default_timer()\n",
    "res = differential_evolution(rosenbrock, bounds)\n",
    "\n",
    "print(\"completed in %.3g sec\"%(default_timer() - tstart))\n",
    "print(\"minimum at :\",res.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### DE algorithm: parallelization\n",
    "\n",
    "Each iteration of the DE algorithm can be fairly easily parallelized because mutation and selection of each population member is independent. This allows using large population sizes and is particularly useful when function evaluation is expensive. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Optimization methods\n",
    "\n",
    "We reviewed just a subset of the commonly used methods. A larger number of variants of these methods and other, more sophisticated methods exist. \n",
    "\n",
    "| method class   |    single-point                  |  multi-point  |\n",
    "|----------------|----------------------------------|---------------|\n",
    "| derivative-based | Steepest descent              | multi-start   |\n",
    "|                |     Conjugate gradient          |               |\n",
    "|                | Quasi-Newton methods (BFGS)       |               |\n",
    "|                |                                |               |\n",
    "| derivative-free |  Random walk                  | Simplex (aka Nelder-Mead method) |\n",
    "|                |   Hooke and Jeeves             | Differential evolution |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "SciPy's <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize\"><tt>scipy.optimize.minimize</tt></a> routine finds minima of functions and has options to use different methods. \n",
    "\n",
    "For example, \n",
    "\n",
    "| <tt>minimize method</tt> option   |    method name                  |  method class  |\n",
    "|----------------|----------------------------------|---------------|\n",
    "| <tt>Nelder-Mead</tt> | Nelder-Mead  (aka simplex) | derivative-free |\n",
    "|     <tt>Powell</tt>  |     <a href=\"https://en.wikipedia.org/wiki/Powell%27s_method\">Powell's conjugate gradient</a>    |    derivative-based           |\n",
    "|     <tt>CG</tt>      |     Conjugate gradient          |    derivative-based           |\n",
    " | <tt>BFGS</tt>   |    <a href=\"https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm\">Broyden–Fletcher–Goldfarb–Shanno</a>          | derivative-based, Quasi-Newton   |\n",
    " | <tt>L-BFGS-M</tt>   |  <a href=\"https://en.wikipedia.org/wiki/Limited-memory_BFGS\"> limited-memory Broyden–Fletcher–Goldfarb–Shanno</a>          | derivative-based, Quasi-Newton   |\n",
    "|     <tt>Newton-CG</tt>       |   Newton conjugate gradient            | derivative based            |\n",
    "|     <tt>TNC</tt>       |   Truncated Newton            | derivative based            |\n",
    "|          <tt>COBYLA</tt>      | <a href=\"https://en.wikipedia.org/wiki/COBYLA\">Constrained Optimization BY Linear Approximation</a>     |  derivative-free             |\n",
    "\n",
    "plus several more. Only some of these methods (e.g., L-BFGS-B, TNC, SLSQP and\n",
    "        trust-constr and COBYLA methods) allow any constraint on the boundaries of parameter space that the algorithm will explore. This is critical if we use approximation for the function that was constructed on a limited sub-space, like we did for $d_L$ approximating it for $\\Omega_{\\rm m0}\\in[0,1]$ and $\\Omega_\\Lambda\\in [0,1]$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Description of these different methods and examples of their use with the <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize\"><tt>scipy.optimize.minimize</tt></a> routine is described <a href=\"https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html\">here</a> and <a href=\"https://scipy-lectures.org/advanced/mathematical_optimization/index.html\">here</a>. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Conclusions\n",
    "\n",
    "* Correct results are not always guaranteed. Results need to be checked by re-running from different starting points and using different methods. \n",
    "\n",
    "\n",
    "* Methods differ significantly in the number of function evaluations they need to determine the minimum to the required accuracy. \n",
    "\n",
    "\n",
    "* Availability of the analytic expressions for the gradient and Hessian can help greatly, but these are not always available. \n",
    "\n",
    "\n",
    "* The number of methods that allow bounds or other type of constraints on $\\mathbf{x}$ is limited. "
   ]
  }
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