{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Min-Norm and Dual Approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dual approximation\n",
    "\n",
    "### Dual Approximation theorem\n",
    "Let $\\{y_1, y_2, ..., y_m\\}$ be linearly independent vectors in a Hilbert space S. Let $M = span(y_1, y_2, ...,y_m)$. The element $x \\in S$ that satisfies the constraints:\n",
    "\n",
    "$$\n",
    "\\langle x, y_1 \\rangle = b_1\\\\\n",
    "\\vdots\\\\\n",
    "\\langle x, y_m \\rangle = b_m\n",
    "$$\n",
    "\n",
    "and which has minimum norm is also in $M$. $x$ is given by: \n",
    "\\begin{equation*}\n",
    "x = \\sum_{i=1}^{m}c_i y_i\n",
    "\\end{equation*}\n",
    "where the coefficients $c_i$ satisfy\n",
    "\\begin{equation*}\n",
    "\\begin{bmatrix} \\langle y_j, y_i \\rangle \\end{bmatrix}\n",
    "\\mathbf{c}\n",
    "= \n",
    "\\mathbf{b}\n",
    "\\end{equation*}\n",
    "\n",
    "For a proof of this theorem, see pp. 179-181 in Moon's book.\n",
    "\n",
    "The matrix $\\begin{bmatrix} \\langle y_j, y_i \\rangle \\end{bmatrix}$ is also known as the Gramian. If A is of the form: \n",
    "$$\n",
    "A = \\begin{bmatrix} y_1^H \\\\ \\vdots \\\\ y_m^H \\end{bmatrix}\n",
    "$$\n",
    "then the Gramian is $R = A A^H$.\n",
    "Using this notation, if we have the constraints in the form of a matrix $A$, then the min-norm solution that satisfies the constraints can be found as:\n",
    "$$\n",
    "\\mathbf{\\hat{x}} = A^H (A A^H)^{-1} \\mathbf{b}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minimum-norm solution to underdetermined system of equations\n",
    "An underdetermined system of equations is one with fewer equations than variables. Recall that for this type of system, there are two possibilities: an infinite number of solutions or no solution (if the equations are inconsistent). Here, we will address the case of an infinite number of solutions.\n",
    "\n",
    "In array form, the problem is formulated as $A\\mathbf{x} = \\mathbf{b}$, where $A$ is an $m \\times n$ matrix, with $m < n$.\n",
    "\n",
    "\n",
    "### Simple example\n",
    "\n",
    "Let's take the system:\n",
    "\\begin{equation*}\n",
    "\\begin{bmatrix} 1 & 2 & 3 \\\\ 5 & 3 & 1 \\end{bmatrix}\n",
    "\\begin{bmatrix} x \\\\ y \\\\ z \\end{bmatrix}\n",
    "= \\begin{bmatrix} 0 \\\\ 2 \\end{bmatrix}\n",
    "\\end{equation*}\n",
    "\n",
    "This can be thought of as two planes in $\\mathbb{R}^3$, given by:\n",
    "\\begin{equation*}\n",
    "x + 2y + 3z = 0\n",
    "\\end{equation*}\n",
    "\\begin{equation*}\n",
    "5x + 3y + z = 2\n",
    "\\end{equation*}\n",
    "\n",
    "It can be shown algebraically that the intersection of these planes is a line given by:\n",
    "$$\n",
    "\\begin{cases}\n",
    "x = t \\\\\n",
    "y = \\frac{6}{7} - 2t \\\\\n",
    "z = -\\frac{4}{7} + t\n",
    "\\end{cases}\\\\ \\forall t \\in \\mathbb{R}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the intersection of 2 planes\n",
    "\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "A = np.array([(1,2,3),(5,3,1)])\n",
    "b = np.array([(0),(2)])\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "# data for planes\n",
    "x1 = np.arange(-10,10,0.25)\n",
    "y1 = np.arange(-20,20,0.25)\n",
    "x1, y1 = np.meshgrid(x1, y1)\n",
    "z1 = (b[0] - A[0,0]*x1 - A[0,1]*y1) / A[0,2]\n",
    "x2 = np.arange(-10,10,0.25)\n",
    "y2 = np.arange(-20,20,0.25)\n",
    "x2,y2 = np.meshgrid(x2,y2)\n",
    "z2 = (b[1] - A[1,0]*x2 - A[1,1]*y2) / A[1,2]\n",
    "\n",
    "# line\n",
    "tL = np.arange(-10,10,0.25)\n",
    "xL = tL\n",
    "yL = 6/7 - 2*tL\n",
    "zL = -4/7 + tL\n",
    "\n",
    "ax.plot_surface(x1, y1, z1)\n",
    "ax.plot_surface(x2, y2, z2)\n",
    "ax.plot(xL, yL, zL)\n",
    "\n",
    "ax.view_init(elev=35., azim=-65)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rather than finding all possible solutions for $\\mathbf{x}$, we will choose the solution that has the minimum norm.\n",
    "\n",
    "$$\n",
    "\\mathbf{\\hat{x}} = A^H (A A^H)^{-1} \\mathbf{b} \\\\\n",
    "\\mathbf{\\hat{x}} = \\begin{bmatrix} 0.3810 \\\\ 0.0952 \\\\ -0.1905 \\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2 = plt.figure()\n",
    "ax2 = fig2.gca(projection='3d')\n",
    "\n",
    "ax2.plot(xL, yL, zL, c='g')\n",
    "ax2.scatter(0.3810, 0.0952, -0.1905, c='r')\n",
    "\n",
    "ax2.view_init(elev=30, azim=30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This was a simple finite-dimensional example, but the concept extends to infinite dimensional spaces. If there are a finite number of constraints that can be written as inner products, then it can be framed in terms of the dual approximation theorem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applied example\n",
    "Some problems involving sets of continuous functions can be solved with finite matrices although the solutions are in an infinite dimensional space, as long as the constraints can be written as inner products and the solution space is a Hilbert space, such as $L_2$.\n",
    "\n",
    "Suppose you know the dynamics of a system to be:\n",
    "$$\n",
    "\\ddot{y} + 5\\dot{y} + 6y = 7\\dot{u} + u\n",
    "$$\n",
    "\n",
    "We'd like to find the input $u(t)$ from $t = 0$ to $t=5$ that will move the system to position $y=10$ with the least amount of energy, and also with the condition that $\\int_0^5 u(t) dt = 0$.\n",
    "\n",
    "The energy of a signal $u(t)$ is\n",
    "$$\\int_0^T \\lvert\\lvert u(t) \\rvert\\rvert^2 dt$$\n",
    "which is the square of the $L_2$ norm. Since minimizing the energy also means minimizing the norm, this suggests the use of the dual approximation theorem. \n",
    "\n",
    "Since we're solving for $u$, we want to write inner product constraints in the form:\n",
    "$$ \n",
    "\\langle u, y_1 \\rangle = b_1 \\\\\n",
    "\\langle u, y_2 \\rangle = b_2$$\n",
    "\n",
    "The final position constraint can be written as $y(5) = 10 = \\langle u(t) , h(5-t) \\rangle$, since this $L_2$ norm is the convolution integral.\n",
    "\n",
    "The last condition can be written as $\\langle u(t) , 1 \\rangle = 0$.\n",
    "\n",
    "We have $b = \\begin{bmatrix} 10 \\\\ 0 \\end{bmatrix}$ from these constraint equations.\n",
    "\n",
    "$h(t)$ can be found by finding $Y(s)/U(s)$ in the Laplace domain on the dynamics equation, and then going back to time domain. Letting $y_1 = h(5-t)$ and $y_2 = 1$, we can calculate the needed inner products for the Gramian, then solve algebraically for $c1$ and $c2$.\n",
    "\n",
    "Then $u(t)$ is simply a linear combination of $y_1$ and $y_2$:\n",
    "$$u(t) = c_1 y_1 + c_2 y_2$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Homework Problem 1\n",
    "by Kavindu Kusal\n",
    "Assume that you are the project manger of a software development project, which has been estimated \n",
    "for \\\\$40,000 salary plus operational cost and you are going to come up with a team of 12 which \n",
    "consisists of interns, engineers, senior engineers and team leaders. Project has been budgeted for \n",
    "1000 engineering hours and you can assume that as a thumb rule, an intern would take 1h 15min for a work completed by and engineer and senior engineer, team leader would take 45 and 30 mins respectively. So, the operational cost of the project is propotional to the norm of the group. It is expected to pay \\\\$25, \\\\$35, \\\\$45, \\\\$55 per hour for intern, engineer, senior engineer and team leader respectively. using dual approximation come up with a suitable team structure to minimize the operational cost of the project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem1 - solution\n",
    "According to the description, company could pay $$ \\frac{$40,000}{1000} = $40 $$ per engineering hour.\n",
    "Lets, assume that the number of interns, engineers, senior engineers and team leaders are x1, x2, x3, x4 respectively.\n",
    "As per the description, completed project hours per hour would be 1/1.25 = 0.8, 1/1 = 1, 1/0.75 = 4/3 and 1/0.5 = 2 for intern, engineer, senior engineer and team leader respectively.\n",
    "So, the number of project hours completed by the team per hour would be, $$ x1\\times 0.8 + x2\\times1 + x3\\times\\frac{4}{3} + x4\\times2$$\n",
    "So, the company can allocate following amount to pay for the team per an hour$$ $30\\times(1\\times 0.8 + x2\\times1 + x3\\times\\frac{4}{3} + x4\\times2) = x1\\times 24 + x2\\times30 + x3\\times40 + x4\\times60 $$\n",
    "According to salary rates, company would have to pay, $$ x1\\times25 + x2\\times35 + x3\\times45 + x4\\times55 $$\n",
    "These two values, should be Equal, then the first constraint should be,\n",
    "$$ \\begin{align}\n",
    "    x1\\times 24 + x2\\times30 + x3\\times 40 + x4\\times60 &= x1\\times25 + x2\\times35 + x3\\times45 + x4\\times55  \\nonumber \\\\\n",
    "    x1\\times 1 + x2\\times5 + x3\\times5 + x4\\times-5 &= 0\n",
    "\\end{align}\n",
    "$$\n",
    "The second constraint of the problem should be, $$ x1 + x2 + x3 + x4 = 12 $$\n",
    "from the constrains, we can come up with below equations,\n",
    "$$\n",
    "\\langle x, y_1 \\rangle = 0\\\\\n",
    "\\langle x, y_2 \\rangle = 12\n",
    "$$\n",
    "According to the dual approximation theorm, $$\n",
    "\\begin{equation*}\n",
    "\\begin{bmatrix} \\langle y1,y1\\rangle & \\langle y1,y2\\rangle \\\\ \\langle y2,y1\\rangle & \\langle y2,y2\\rangle  \\end{bmatrix}\n",
    "\\begin{bmatrix} c1 \\\\ c2 \\end{bmatrix}\n",
    "= \\begin{bmatrix} \\langle x, y_1 \\rangle \\\\ \\langle x, y_2 \\rangle \\end{bmatrix}\n",
    "\\end{equation*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.13432836 2.05970149 2.05970149 4.74626866]\n"
     ]
    }
   ],
   "source": [
    "#python implementation of this problem would be like this\n",
    "import numpy as np\n",
    "\n",
    "c1 = np.array([1, 1, 1, 1])\n",
    "\n",
    "projHrscompletedbyteamPerHr = np.array([ 1./1.25, 1./1., 1/0.75, 1/0.5 ])\n",
    "affordableHourlyCost = 30 * projHrscompletedbyteamPerHr\n",
    "actualTeamHourLyCost = np.array([25, 35, 45, 55])\n",
    "c2 = affordableHourlyCost - actualTeamHourLyCost\n",
    "\n",
    "grammian = np.array([[c1 @ c1, c1 @ c2], \n",
    "                      [c2 @ c1, c2 @ c2]])\n",
    "\n",
    "b = np.array([[12], [0]])\n",
    "\n",
    "c = np.linalg.inv(grammian) @ b\n",
    "\n",
    "x = c[0,0]*c1 + c[1,0]*c2\n",
    "\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, in order to not to exceed the limit, I would go with a team of 4 interns, 2 Engineers, 2 Senior Engineers and 4 Project Managers to minimize the overall operation cost of the project."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}