20190806_inverse_matrix.ipynb

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     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\kappa & 0 & 0 & 0 & 0\\\\\\kappa & - \\gamma - \\tau & 0 & 0 & 0\\\\0 & \\tau & - \\gamma & 0 & 0\\\\0 & \\gamma m & 0 & - \\omega_{I} & 0\\\\0 & 0 & \\epsilon \\gamma m & 0 & - \\omega_{H}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-κ    0       0     0     0  ⎤\n",
       "⎢                             ⎥\n",
       "⎢κ   -γ - τ    0     0     0  ⎥\n",
       "⎢                             ⎥\n",
       "⎢0     τ      -γ     0     0  ⎥\n",
       "⎢                             ⎥\n",
       "⎢0    γ⋅m      0    -ω_I   0  ⎥\n",
       "⎢                             ⎥\n",
       "⎣0     0     ε⋅γ⋅m   0    -ω_H⎦"
      ]
     },
     "execution_count": 9,
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   "source": [
    "import sympy as sym\n",
    "\n",
    "# Not necessary but gives nice-looking latex output\n",
    "# More info at: http://docs.sympy.org/latest/tutorial/printing.html\n",
    "sym.init_printing()\n",
    "\n",
    "kappa, gamma, tau, gamma, m, omega_I, omega_H, epsilon = sym.symbols('kappa gamma tau gamma, m omega_I omega_H epsilon')\n",
    "matrix = sym.Matrix([[-kappa,0,0,0,0], \n",
    "                     [kappa,-gamma-tau,0,0,0],\n",
    "                     [0,tau,-gamma,0,0],\n",
    "                     [0,gamma*m,0,-omega_I,0],\n",
    "                     [0,0,epsilon*gamma*m,0,-omega_H]])\n",
    "\n",
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{1}{\\kappa} & 0 & 0 & 0 & 0\\\\\\frac{1}{- \\gamma - \\tau} & \\frac{1}{- \\gamma - \\tau} & 0 & 0 & 0\\\\\\frac{\\tau}{\\gamma \\left(- \\gamma - \\tau\\right)} & \\frac{\\tau}{\\gamma \\left(- \\gamma - \\tau\\right)} & - \\frac{1}{\\gamma} & 0 & 0\\\\\\frac{\\gamma m}{\\omega_{I} \\left(- \\gamma - \\tau\\right)} & \\frac{\\gamma m}{\\omega_{I} \\left(- \\gamma - \\tau\\right)} & 0 & - \\frac{1}{\\omega_{I}} & 0\\\\\\frac{\\epsilon m \\tau}{\\omega_{H} \\left(- \\gamma - \\tau\\right)} & \\frac{\\epsilon m \\tau}{\\omega_{H} \\left(- \\gamma - \\tau\\right)} & - \\frac{\\epsilon m}{\\omega_{H}} & 0 & - \\frac{1}{\\omega_{H}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡    -1                                     ⎤\n",
       "⎢    ───            0          0     0    0 ⎥\n",
       "⎢     κ                                     ⎥\n",
       "⎢                                           ⎥\n",
       "⎢     1             1                       ⎥\n",
       "⎢   ──────        ──────       0     0    0 ⎥\n",
       "⎢   -γ - τ        -γ - τ                    ⎥\n",
       "⎢                                           ⎥\n",
       "⎢     τ             τ         -1            ⎥\n",
       "⎢ ──────────    ──────────    ───    0    0 ⎥\n",
       "⎢ γ⋅(-γ - τ)    γ⋅(-γ - τ)     γ            ⎥\n",
       "⎢                                           ⎥\n",
       "⎢    γ⋅m           γ⋅m              -1      ⎥\n",
       "⎢────────────  ────────────    0    ───   0 ⎥\n",
       "⎢ω_I⋅(-γ - τ)  ω_I⋅(-γ - τ)         ω_I     ⎥\n",
       "⎢                                           ⎥\n",
       "⎢   ε⋅m⋅τ         ε⋅m⋅τ      -ε⋅m        -1 ⎥\n",
       "⎢────────────  ────────────  ─────   0   ───⎥\n",
       "⎣ω_H⋅(-γ - τ)  ω_H⋅(-γ - τ)   ω_H        ω_H⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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