schrodinger_1d_all.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical handling of schrodinger equation\n",
    "\n",
    "Consider the following one dimensional schrodinger equation -\n",
    "\n",
    "$$\n",
    "\\frac{-\\hbar^2}{2m} \\frac{d^2\\Psi(x)}{dx^2} + V(x)\\Psi(x) = E\\Psi(x)\n",
    "$$\n",
    "\n",
    "in range $x \\in [a, b]$ with boundary condition $\\Psi(x=a)=\\Psi_a$, and $\\Psi(x=b)=\\Psi_b$\n",
    "\n",
    "- We first descretize the `position' space and define $x_n = a + t n$ where $t = \\frac{b - a}{N}$, $N$ being the number of samples. $x_0 = a$, and $x_N = b$\n",
    "\n",
    "- We approximate the double derivatives using central difference formula\n",
    "\n",
    "$$\n",
    "\\frac{d^2\\Psi}{d x^2}\\biggr|_{x=x_n} \\approx {\\Psi_{n+1} -2 \\Psi_{n} + \\Psi_{n-1} \\over t^2}\n",
    "$$\n",
    "\n",
    "We approximate the double derivatives using central difference formula\n",
    "\n",
    "$$\n",
    "-\\frac{\\hbar^2}{2mt^2}\\left({\\Psi_{n+1} -2 \\Psi_{n} + \\Psi_{n-1}}\\right) + V_n\\Psi_n = E\\Psi_n\n",
    "$$\n",
    "\n",
    "or, rearranging the terms we get\n",
    "\n",
    "$$\n",
    "\\left(-{\\Psi_{n+1} +2 \\Psi_{n} - \\Psi_{n-1}}\\right) + \\frac{2mt^2}{\\hbar^2}V_n\\Psi_n = E\\Psi_n\n",
    "$$\n",
    "\n",
    "equivalently\n",
    "\n",
    "$$\n",
    "-\\Psi_{n+1} +(2 + \\frac{2mt^2}{\\hbar^2}V_n)\\Psi_n - \\Psi_{n-1} = E\\Psi_n\n",
    "$$\n",
    "\n",
    "Using $v_n = 2(1 + \\frac{mt^2}{\\hbar^2})V_n$, we can simplify the recurrance relation as following \n",
    "$$\n",
    "-\\Psi_{n+1} + v_n\\Psi_{n} -\\Psi_{n-1} = E\\Psi_n\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We approximate the double derivatives using central difference formula\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ast import Del\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# constants\n",
    "\n",
    "Box_Width = 3.0\n",
    "Delta = 0.1 * Box_Width\n",
    "V0 = 30.0\n",
    "\n",
    "alpha = 1.0\n",
    "Npoints = 1000\n",
    "\n",
    "def potential_box(x):\n",
    "    f = 0.0\n",
    "    if abs(x) <= Box_Width:\n",
    "        f = 0.0\n",
    "    else:\n",
    "        if abs(x) > Box_Width and abs(x) <= Box_Width + Delta:\n",
    "            f = V0\n",
    "        else:\n",
    "            f = 100 * V0\n",
    "    #\n",
    "    return f\n",
    "\n",
    "def potential_harmonic(x):\n",
    "    return x**2\n",
    "#\n",
    "potential = potential_box\n",
    "Fvec = np.vectorize(potential)\n",
    "\n",
    "xi, dx = np.linspace(-Box_Width - Delta, Box_Width + Delta, Npoints, retstep=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vi = Fvec(xi)\n",
    "vi = 2 * (1 + alpha * dx**2 * Vi)\n",
    "Psi = np.zeros(xi.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_matrix(vi):\n",
    "    n = vi.shape[0]\n",
    "    mat = np.zeros((n, n))\n",
    "    for i in range(1, n):\n",
    "        mat[i, i - 1] = -1\n",
    "        mat[i-1, i] = -1\n",
    "    #\n",
    "    np.fill_diagonal(mat, vi)\n",
    "    return mat\n",
    "#\n",
    "\n",
    "M = get_matrix(vi)\n",
    "eig, vecs = np.linalg.eigh(M)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xi, vi)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(xi, Vi)\n",
    "plt.show()\n",
    "for i in range(6):\n",
    "    plt.plot(xi, vecs[:, i])\n",
    "#plt.plot(vecs[0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x147efc406880>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def boundary(E):\n",
    "    Psi[1] = 0.0001\n",
    "    for i in range(2, Npoints):\n",
    "        Psi[i] = 2 * Psi[i-1] - (1.0 - alpha * Vi[i-2]) * Psi[i-2] - alpha * E * Psi[i-2]\n",
    "    return Psi[-1]\n",
    "#\n",
    "\n",
    "\n",
    "Psi[0] = 0\n",
    "Psi[1] = 0.1\n",
    "E = 0.001\n",
    "for i in range(2, Npoints):\n",
    "    Psi[i] =   (2 * (1+dx**2 * Vi[i-1]) - E) * Psi[i-1] - Psi[i-2]\n",
    "#\n",
    "plt.plot(xi, Psi, '-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_97823/2944095705.py:4: RuntimeWarning: overflow encountered in double_scalars\n",
      "  Psi[i] = 2 * Psi[i-1] - (1.0 - alpha * Vi[i-2]) * Psi[i-2] - alpha * E * Psi[i-2]\n",
      "/tmp/ipykernel_97823/2944095705.py:4: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  Psi[i] = 2 * Psi[i-1] - (1.0 - alpha * Vi[i-2]) * Psi[i-2] - alpha * E * Psi[i-2]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x147efc258250>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Es = np.linspace(10, 30, 300)\n",
    "B = [boundary(e) for e in Es]\n",
    "plt.plot(Es, np.abs(B))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30.,\n",
       "       30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30.,\n",
       "       30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30., 30.,\n",
       "       30., 30., 30., 30., 30., 30., 30.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
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      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fvec(xi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(eig);plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.00018639, -0.00037319, -0.00056083, -0.00074971, -0.00094025,\n",
       "       -0.00113289, -0.00132804, -0.00152615, -0.00172765, -0.00193299,\n",
       "       -0.00214263, -0.00235703, -0.00257667, -0.00280203, -0.00303363,\n",
       "       -0.00327197, -0.00351758, -0.00377101, -0.00403282, -0.0043036 ,\n",
       "       -0.00458394, -0.00487448, -0.00517585, -0.00548872, -0.00581379,\n",
       "       -0.00615179, -0.00650347, -0.00686959, -0.00725099, -0.00764851,\n",
       "       -0.00806303, -0.00849547, -0.0089468 , -0.00941802, -0.00991017,\n",
       "       -0.01042434, -0.0109617 , -0.01152341, -0.01211074, -0.012725  ,\n",
       "       -0.01336754, -0.01403979, -0.01474325, -0.01547949, -0.01625013,\n",
       "       -0.0170569 , -0.01790158, -0.01873917, -0.01956935, -0.02039177,\n",
       "       -0.02120612, -0.02201207, -0.02280931, -0.02359752, -0.02437638,\n",
       "       -0.02514559, -0.02590484, -0.02665384, -0.02739228, -0.02811988,\n",
       "       -0.02883634, -0.02954139, -0.03023474, -0.03091611, -0.03158525,\n",
       "       -0.03224187, -0.03288573, -0.03351657, -0.03413414, -0.0347382 ,\n",
       "       -0.0353285 , -0.03590481, -0.0364669 , -0.03701455, -0.03754755,\n",
       "       -0.03806568, -0.03856874, -0.03905652, -0.03952885, -0.03998552,\n",
       "       -0.04042635, -0.04085118, -0.04125984, -0.04165216, -0.04202798,\n",
       "       -0.04238717, -0.04272957, -0.04305505, -0.04336348, -0.04365474,\n",
       "       -0.04392872, -0.04418531, -0.04442439, -0.04464589, -0.04484971,\n",
       "       -0.04503577, -0.045204  , -0.04535433, -0.04548671, -0.04560107,\n",
       "       -0.04569737, -0.04577559, -0.04583567, -0.04587761, -0.04590138,\n",
       "       -0.04590698, -0.0458944 , -0.04586364, -0.04581473, -0.04574768,\n",
       "       -0.04566251, -0.04555926, -0.04543797, -0.04529869, -0.04514148,\n",
       "       -0.04496639, -0.04477349, -0.04456287, -0.0443346 , -0.04408878,\n",
       "       -0.0438255 , -0.04354487, -0.04324699, -0.04293199, -0.0426    ,\n",
       "       -0.04225113, -0.04188554, -0.04150336, -0.04110474, -0.04068985,\n",
       "       -0.04025885, -0.03981191, -0.0393492 , -0.03887092, -0.03837724,\n",
       "       -0.03786837, -0.0373445 , -0.03680584, -0.03625262, -0.03568503,\n",
       "       -0.03510332, -0.03450771, -0.03389844, -0.03327574, -0.03263987,\n",
       "       -0.03199107, -0.0313296 , -0.03065573, -0.02996973, -0.02927185,\n",
       "       -0.02856239, -0.02784161, -0.02710981, -0.02636728, -0.02561431,\n",
       "       -0.02485119, -0.02407824, -0.02329575, -0.02250403, -0.02170341,\n",
       "       -0.02089419, -0.0200767 , -0.01925126, -0.0184182 , -0.01757784,\n",
       "       -0.01673052, -0.01587658, -0.01501636, -0.01415018, -0.01327841,\n",
       "       -0.01240137, -0.01151943, -0.01063293, -0.00974221, -0.00884764,\n",
       "       -0.00794956, -0.00704834, -0.00614432, -0.00523787, -0.00432935,\n",
       "       -0.00341912, -0.00250753, -0.00159495, -0.00068173,  0.00023175,\n",
       "        0.00114514,  0.00205808,  0.00297021,  0.00388115,  0.00479057,\n",
       "        0.00569808,  0.00660334,  0.00750598,  0.00840565,  0.009302  ,\n",
       "        0.01019465,  0.01108328,  0.01196751,  0.01284701,  0.01372142,\n",
       "        0.01459039,  0.01545359,  0.01631067,  0.01716129,  0.01800512,\n",
       "        0.01884182,  0.01967105,  0.0204925 ,  0.02130584,  0.02211073,\n",
       "        0.02290687,  0.02369395,  0.02447164,  0.02523964,  0.02599765,\n",
       "        0.02674536,  0.02748248,  0.02820872,  0.02892379,  0.02962741,\n",
       "        0.0303193 ,  0.03099918,  0.03166679,  0.03232186,  0.03296413,\n",
       "        0.03359335,  0.03420927,  0.03481164,  0.03540023,  0.0359748 ,\n",
       "        0.03653513,  0.03708099,  0.03761217,  0.03812845,  0.03862964,\n",
       "        0.03911553,  0.03958593,  0.04004066,  0.04047954,  0.04090239,\n",
       "        0.04130904,  0.04169933,  0.04207312,  0.04243024,  0.04277057,\n",
       "        0.04309395,  0.04340028,  0.04368942,  0.04396126,  0.0442157 ,\n",
       "        0.04445262,  0.04467195,  0.04487359,  0.04505746,  0.04522349,\n",
       "        0.04537161,  0.04550176,  0.0456139 ,  0.04570798,  0.04578396,\n",
       "        0.04584182,  0.04588152,  0.04590305,  0.04590641,  0.04589159,\n",
       "        0.0458586 ,  0.04580745,  0.04573817,  0.04565077,  0.0455453 ,\n",
       "        0.04542179,  0.0452803 ,  0.04512088,  0.04494359,  0.04474851,\n",
       "        0.04453571,  0.04430528,  0.0440573 ,  0.04379187,  0.04350911,\n",
       "        0.04320912,  0.04289202,  0.04255794,  0.04220701,  0.04183936,\n",
       "        0.04145515,  0.04105452,  0.04063764,  0.04020467,  0.03975577,\n",
       "        0.03929114,  0.03881095,  0.03831539,  0.03780466,  0.03727896,\n",
       "        0.0367385 ,  0.03618349,  0.03561415,  0.03503072,  0.03443341,\n",
       "        0.03382247,  0.03319814,  0.03256066,  0.03191029,  0.03124728,\n",
       "        0.0305719 ,  0.02988442,  0.0291851 ,  0.02847423,  0.02775208,\n",
       "        0.02701894,  0.02627511,  0.02552087,  0.02475653,  0.02398238,\n",
       "        0.02319874,  0.02240591,  0.02160421,  0.02079396,  0.01997547,\n",
       "        0.01914907,  0.01831509,  0.01747386,  0.01662571,  0.01577098,\n",
       "        0.01491   ,  0.01404312,  0.01317068,  0.01229302,  0.01141049,\n",
       "        0.01052345,  0.00963224,  0.00873722,  0.00783874,  0.00693715,\n",
       "        0.00603282,  0.00512609,  0.00421734,  0.00330692,  0.00239519,\n",
       "        0.00148251,  0.00056924, -0.00034425, -0.00125761, -0.00217046,\n",
       "       -0.00308246, -0.00399324, -0.00490244, -0.00580969, -0.00671465,\n",
       "       -0.00761695, -0.00851623, -0.00941213, -0.01030432, -0.01119242,\n",
       "       -0.01207609, -0.01295498, -0.01382873, -0.01469702, -0.01555948,\n",
       "       -0.01641578, -0.01726559, -0.01810855, -0.01894435, -0.01977264,\n",
       "       -0.02059311, -0.02140542, -0.02220926, -0.0230043 , -0.02379023,\n",
       "       -0.02456675, -0.02533353, -0.02609029, -0.02683671, -0.02757251,\n",
       "       -0.02829739, -0.02901107, -0.02971326, -0.03040368, -0.03108207,\n",
       "       -0.03174815, -0.03240165, -0.03304233, -0.03366993, -0.03428419,\n",
       "       -0.03488488, -0.03547175, -0.03604458, -0.03660314, -0.0371472 ,\n",
       "       -0.03767656, -0.03819099, -0.03869031, -0.0391743 , -0.03964279,\n",
       "       -0.04009557, -0.04053248, -0.04095334, -0.04135799, -0.04174626,\n",
       "       -0.042118  , -0.04247306, -0.04281131, -0.0431326 , -0.04343682,\n",
       "       -0.04372383, -0.04399354, -0.04424582, -0.04448059, -0.04469774,\n",
       "       -0.04489719, -0.04507887, -0.0452427 , -0.04538861, -0.04551655,\n",
       "       -0.04562647, -0.04571832, -0.04579207, -0.04584769, -0.04588515,\n",
       "       -0.04590445, -0.04590557, -0.04588851, -0.04585328, -0.0457999 ,\n",
       "       -0.04572838, -0.04563875, -0.04553106, -0.04540534, -0.04526163,\n",
       "       -0.04510001, -0.04492053, -0.04472326, -0.04450828, -0.04427568,\n",
       "       -0.04402555, -0.04375799, -0.0434731 , -0.04317099, -0.04285179,\n",
       "       -0.04251563, -0.04216263, -0.04179294, -0.04140669, -0.04100406,\n",
       "       -0.04058518, -0.04015024, -0.0396994 , -0.03923284, -0.03875074,\n",
       "       -0.0382533 , -0.03774072, -0.03721319, -0.03667093, -0.03611414,\n",
       "       -0.03554306, -0.0349579 , -0.0343589 , -0.0337463 , -0.03312033,\n",
       "       -0.03248125, -0.03182931, -0.03116477, -0.03048788, -0.02979893,\n",
       "       -0.02909817, -0.0283859 , -0.02766238, -0.02692791, -0.02618278,\n",
       "       -0.02542728, -0.02466171, -0.02388638, -0.02310159, -0.02230765,\n",
       "       -0.02150488, -0.0206936 , -0.01987412, -0.01904677, -0.01821188,\n",
       "       -0.01736978, -0.0165208 , -0.01566528, -0.01480355, -0.01393597,\n",
       "       -0.01306287, -0.01218459, -0.01130149, -0.01041392, -0.00952222,\n",
       "       -0.00862675, -0.00772786, -0.00682592, -0.00592127, -0.00501428,\n",
       "       -0.0041053 , -0.0031947 , -0.00228283, -0.00137006, -0.00045675,\n",
       "        0.00045675,  0.00137006,  0.00228283,  0.0031947 ,  0.0041053 ,\n",
       "        0.00501428,  0.00592127,  0.00682592,  0.00772786,  0.00862675,\n",
       "        0.00952222,  0.01041392,  0.01130149,  0.01218459,  0.01306287,\n",
       "        0.01393597,  0.01480355,  0.01566528,  0.0165208 ,  0.01736978,\n",
       "        0.01821188,  0.01904677,  0.01987412,  0.0206936 ,  0.02150488,\n",
       "        0.02230765,  0.02310159,  0.02388638,  0.02466171,  0.02542728,\n",
       "        0.02618278,  0.02692791,  0.02766238,  0.0283859 ,  0.02909817,\n",
       "        0.02979893,  0.03048788,  0.03116477,  0.03182931,  0.03248125,\n",
       "        0.03312033,  0.0337463 ,  0.0343589 ,  0.0349579 ,  0.03554306,\n",
       "        0.03611414,  0.03667093,  0.03721319,  0.03774072,  0.0382533 ,\n",
       "        0.03875074,  0.03923284,  0.0396994 ,  0.04015024,  0.04058518,\n",
       "        0.04100406,  0.04140669,  0.04179294,  0.04216263,  0.04251563,\n",
       "        0.04285179,  0.04317099,  0.0434731 ,  0.04375799,  0.04402555,\n",
       "        0.04427568,  0.04450828,  0.04472326,  0.04492053,  0.04510001,\n",
       "        0.04526163,  0.04540534,  0.04553106,  0.04563875,  0.04572838,\n",
       "        0.0457999 ,  0.04585328,  0.04588851,  0.04590557,  0.04590445,\n",
       "        0.04588515,  0.04584769,  0.04579207,  0.04571832,  0.04562647,\n",
       "        0.04551655,  0.04538861,  0.0452427 ,  0.04507887,  0.04489719,\n",
       "        0.04469774,  0.04448059,  0.04424582,  0.04399354,  0.04372383,\n",
       "        0.04343682,  0.0431326 ,  0.04281131,  0.04247306,  0.042118  ,\n",
       "        0.04174626,  0.04135799,  0.04095334,  0.04053248,  0.04009557,\n",
       "        0.03964279,  0.0391743 ,  0.03869031,  0.03819099,  0.03767656,\n",
       "        0.0371472 ,  0.03660314,  0.03604458,  0.03547175,  0.03488488,\n",
       "        0.03428419,  0.03366993,  0.03304233,  0.03240165,  0.03174815,\n",
       "        0.03108207,  0.03040368,  0.02971326,  0.02901107,  0.02829739,\n",
       "        0.02757251,  0.02683671,  0.02609029,  0.02533353,  0.02456675,\n",
       "        0.02379023,  0.0230043 ,  0.02220926,  0.02140542,  0.02059311,\n",
       "        0.01977264,  0.01894435,  0.01810855,  0.01726559,  0.01641578,\n",
       "        0.01555948,  0.01469702,  0.01382873,  0.01295498,  0.01207609,\n",
       "        0.01119242,  0.01030432,  0.00941213,  0.00851623,  0.00761695,\n",
       "        0.00671465,  0.00580969,  0.00490244,  0.00399324,  0.00308246,\n",
       "        0.00217046,  0.00125761,  0.00034425, -0.00056924, -0.00148251,\n",
       "       -0.00239519, -0.00330692, -0.00421734, -0.00512609, -0.00603282,\n",
       "       -0.00693715, -0.00783874, -0.00873722, -0.00963224, -0.01052345,\n",
       "       -0.01141049, -0.01229302, -0.01317068, -0.01404312, -0.01491   ,\n",
       "       -0.01577098, -0.01662571, -0.01747386, -0.01831509, -0.01914907,\n",
       "       -0.01997547, -0.02079396, -0.02160421, -0.02240591, -0.02319874,\n",
       "       -0.02398238, -0.02475653, -0.02552087, -0.02627511, -0.02701894,\n",
       "       -0.02775208, -0.02847423, -0.0291851 , -0.02988442, -0.0305719 ,\n",
       "       -0.03124728, -0.03191029, -0.03256066, -0.03319814, -0.03382247,\n",
       "       -0.03443341, -0.03503072, -0.03561415, -0.03618349, -0.0367385 ,\n",
       "       -0.03727896, -0.03780466, -0.03831539, -0.03881095, -0.03929114,\n",
       "       -0.03975577, -0.04020467, -0.04063764, -0.04105452, -0.04145515,\n",
       "       -0.04183936, -0.04220701, -0.04255794, -0.04289202, -0.04320912,\n",
       "       -0.04350911, -0.04379187, -0.0440573 , -0.04430528, -0.04453571,\n",
       "       -0.04474851, -0.04494359, -0.04512088, -0.0452803 , -0.04542179,\n",
       "       -0.0455453 , -0.04565077, -0.04573817, -0.04580745, -0.0458586 ,\n",
       "       -0.04589159, -0.04590641, -0.04590305, -0.04588152, -0.04584182,\n",
       "       -0.04578396, -0.04570798, -0.0456139 , -0.04550176, -0.04537161,\n",
       "       -0.04522349, -0.04505746, -0.04487359, -0.04467195, -0.04445262,\n",
       "       -0.0442157 , -0.04396126, -0.04368942, -0.04340028, -0.04309395,\n",
       "       -0.04277057, -0.04243024, -0.04207312, -0.04169933, -0.04130904,\n",
       "       -0.04090239, -0.04047954, -0.04004066, -0.03958593, -0.03911553,\n",
       "       -0.03862964, -0.03812845, -0.03761217, -0.03708099, -0.03653513,\n",
       "       -0.0359748 , -0.03540023, -0.03481164, -0.03420927, -0.03359335,\n",
       "       -0.03296413, -0.03232186, -0.03166679, -0.03099918, -0.0303193 ,\n",
       "       -0.02962741, -0.02892379, -0.02820872, -0.02748248, -0.02674536,\n",
       "       -0.02599765, -0.02523964, -0.02447164, -0.02369395, -0.02290687,\n",
       "       -0.02211073, -0.02130584, -0.0204925 , -0.01967105, -0.01884182,\n",
       "       -0.01800512, -0.01716129, -0.01631067, -0.01545359, -0.01459039,\n",
       "       -0.01372142, -0.01284701, -0.01196751, -0.01108328, -0.01019465,\n",
       "       -0.009302  , -0.00840565, -0.00750598, -0.00660334, -0.00569808,\n",
       "       -0.00479057, -0.00388115, -0.00297021, -0.00205808, -0.00114514,\n",
       "       -0.00023175,  0.00068173,  0.00159495,  0.00250753,  0.00341912,\n",
       "        0.00432935,  0.00523787,  0.00614432,  0.00704834,  0.00794956,\n",
       "        0.00884764,  0.00974221,  0.01063293,  0.01151943,  0.01240137,\n",
       "        0.01327841,  0.01415018,  0.01501636,  0.01587658,  0.01673052,\n",
       "        0.01757784,  0.0184182 ,  0.01925126,  0.0200767 ,  0.02089419,\n",
       "        0.02170341,  0.02250403,  0.02329575,  0.02407824,  0.02485119,\n",
       "        0.02561431,  0.02636728,  0.02710981,  0.02784161,  0.02856239,\n",
       "        0.02927185,  0.02996973,  0.03065573,  0.0313296 ,  0.03199107,\n",
       "        0.03263987,  0.03327574,  0.03389844,  0.03450771,  0.03510332,\n",
       "        0.03568503,  0.03625262,  0.03680584,  0.0373445 ,  0.03786837,\n",
       "        0.03837724,  0.03887092,  0.0393492 ,  0.03981191,  0.04025885,\n",
       "        0.04068985,  0.04110474,  0.04150336,  0.04188554,  0.04225113,\n",
       "        0.0426    ,  0.04293199,  0.04324699,  0.04354487,  0.0438255 ,\n",
       "        0.04408878,  0.0443346 ,  0.04456287,  0.04477349,  0.04496639,\n",
       "        0.04514148,  0.04529869,  0.04543797,  0.04555926,  0.04566251,\n",
       "        0.04574768,  0.04581473,  0.04586364,  0.0458944 ,  0.04590698,\n",
       "        0.04590138,  0.04587761,  0.04583567,  0.04577559,  0.04569737,\n",
       "        0.04560107,  0.04548671,  0.04535433,  0.045204  ,  0.04503577,\n",
       "        0.04484971,  0.04464589,  0.04442439,  0.04418531,  0.04392872,\n",
       "        0.04365474,  0.04336348,  0.04305505,  0.04272957,  0.04238717,\n",
       "        0.04202798,  0.04165216,  0.04125984,  0.04085118,  0.04042635,\n",
       "        0.03998552,  0.03952885,  0.03905652,  0.03856874,  0.03806568,\n",
       "        0.03754755,  0.03701455,  0.0364669 ,  0.03590481,  0.0353285 ,\n",
       "        0.0347382 ,  0.03413414,  0.03351657,  0.03288573,  0.03224187,\n",
       "        0.03158525,  0.03091611,  0.03023474,  0.02954139,  0.02883634,\n",
       "        0.02811988,  0.02739228,  0.02665384,  0.02590484,  0.02514559,\n",
       "        0.02437638,  0.02359752,  0.02280931,  0.02201207,  0.02120612,\n",
       "        0.02039177,  0.01956935,  0.01873917,  0.01790158,  0.0170569 ,\n",
       "        0.01625013,  0.01547949,  0.01474325,  0.01403979,  0.01336754,\n",
       "        0.012725  ,  0.01211074,  0.01152341,  0.0109617 ,  0.01042434,\n",
       "        0.00991017,  0.00941802,  0.0089468 ,  0.00849547,  0.00806303,\n",
       "        0.00764851,  0.00725099,  0.00686959,  0.00650347,  0.00615179,\n",
       "        0.00581379,  0.00548872,  0.00517585,  0.00487448,  0.00458394,\n",
       "        0.0043036 ,  0.00403282,  0.00377101,  0.00351758,  0.00327197,\n",
       "        0.00303363,  0.00280203,  0.00257667,  0.00235703,  0.00214263,\n",
       "        0.00193299,  0.00172765,  0.00152615,  0.00132804,  0.00113289,\n",
       "        0.00094025,  0.00074971,  0.00056083,  0.00037319,  0.00018639])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vecs[:, i] # is the i'th eigenvector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = np.zeros(M.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "92.7 µs ± 870 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit for i in range(mat.shape[0]): mat[i, i] = vi[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 µs ± 96.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit np.fill_diagonal(mat, vi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.00261884, 0.        , 0.        , ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 2.00261884, 0.        , ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 2.00261884, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       ...,\n",
       "       [0.        , 0.        , 0.        , ..., 2.00261884, 0.        ,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.        , 2.00261884,\n",
       "        0.        ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.        , 0.        ,\n",
       "        2.00261884]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[0;31mSignature:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiag_indices\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mndim\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mDocstring:\u001b[0m\n",
      "Return the indices to access the main diagonal of an array.\n",
      "\n",
      "This returns a tuple of indices that can be used to access the main\n",
      "diagonal of an array `a` with ``a.ndim >= 2`` dimensions and shape\n",
      "(n, n, ..., n). For ``a.ndim = 2`` this is the usual diagonal, for\n",
      "``a.ndim > 2`` this is the set of indices to access ``a[i, i, ..., i]``\n",
      "for ``i = [0..n-1]``.\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "n : int\n",
      "  The size, along each dimension, of the arrays for which the returned\n",
      "  indices can be used.\n",
      "\n",
      "ndim : int, optional\n",
      "  The number of dimensions.\n",
      "\n",
      "See Also\n",
      "--------\n",
      "diag_indices_from\n",
      "\n",
      "Notes\n",
      "-----\n",
      ".. versionadded:: 1.4.0\n",
      "\n",
      "Examples\n",
      "--------\n",
      "Create a set of indices to access the diagonal of a (4, 4) array:\n",
      "\n",
      ">>> di = np.diag_indices(4)\n",
      ">>> di\n",
      "(array([0, 1, 2, 3]), array([0, 1, 2, 3]))\n",
      ">>> a = np.arange(16).reshape(4, 4)\n",
      ">>> a\n",
      "array([[ 0,  1,  2,  3],\n",
      "       [ 4,  5,  6,  7],\n",
      "       [ 8,  9, 10, 11],\n",
      "       [12, 13, 14, 15]])\n",
      ">>> a[di] = 100\n",
      ">>> a\n",
      "array([[100,   1,   2,   3],\n",
      "       [  4, 100,   6,   7],\n",
      "       [  8,   9, 100,  11],\n",
      "       [ 12,  13,  14, 100]])\n",
      "\n",
      "Now, we create indices to manipulate a 3-D array:\n",
      "\n",
      ">>> d3 = np.diag_indices(2, 3)\n",
      ">>> d3\n",
      "(array([0, 1]), array([0, 1]), array([0, 1]))\n",
      "\n",
      "And use it to set the diagonal of an array of zeros to 1:\n",
      "\n",
      ">>> a = np.zeros((2, 2, 2), dtype=int)\n",
      ">>> a[d3] = 1\n",
      ">>> a\n",
      "array([[[1, 0],\n",
      "        [0, 0]],\n",
      "       [[0, 0],\n",
      "        [0, 1]]])\n",
      "\u001b[0;31mFile:\u001b[0m      ~/miniconda3/lib/python3.9/site-packages/numpy/lib/index_tricks.py\n",
      "\u001b[0;31mType:\u001b[0m      function\n"
     ]
    }
   ],
   "source": [
    "np.diag_indices?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "126 ms ± 7.21 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit eig, vecs = np.linalg.eigh(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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