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   "source": [
    "# HW6 Q5\n",
    "### EECS 16A: Designing Information Devices and Systems I, Fall 2016"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Circuit solver\n",
    "In this question we will write a program that solves circuits methodically, able to include both voltage and current souces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import linalg\n",
    "from __future__ import print_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(i) Write the incidence matrix F for the graph, considering $v_1$ and $v_4$ as a combined \"supernode\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "F = \n",
    "print('\\nF:\\n',F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(ii) Specify the resistance matrix R and the vector of voltage sources $\\vec{b}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "R = \n",
    "\n",
    "b = \n",
    "\n",
    "# For convenience, we will define the conductance matrix G as the inverse of R.\n",
    "G = np.linalg.inv(R)\n",
    "\n",
    "print('\\nR:\\n',R)\n",
    "print('\\nb:\\n',b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(iii) Write down the vector f so that KCL is satisfied as: $F^T i + f = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f = \n",
    "print('\\nf:\\n', f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(iii) What is the rank of F? Does it have a null space? If so, what is it?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Edit your answer to (iii) here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# any code you write to help you answer above\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(iv) Setting a potential in v to 0 corresponds to deleting a column of F. Let $v_4 = 0$, and write down our new \"grounded\" matrix F: F_grounded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "F_grounded = \n",
    "print('\\nF_grounded:\\n', F_grounded)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(v) Implement your algebraic solution to compute v in terms of F, G, $\\vec{f}$, and $\\vec{b}$. You may also have to slice $\\vec{f}$ and $\\vec{b}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "A = \n",
    "print('\\nA:\\n', A)\n",
    "\n",
    "B = \n",
    "print('\\nB:\\n', B)\n",
    "\n",
    "v = \n",
    "print('\\nv:\\n', v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(vi) Compute $\\vec{i}$ with your solution of $\\vec{v}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "i = \n",
    "\n",
    "print('\\ni:\\n', i)"
   ]
  }
 ],
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