A11_Abhishek_1911007.ipynb

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      "authorship_tag": "ABX9TyOfk/7j4jjSlzf1HUNs8puW",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/physicsme1729/Numerical-methods-in-physics/blob/main/12_swarup_kumar_giri_phy_p745.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Problem-1:***"
      ],
      "metadata": {
        "id": "md8dEefk_p5W"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Linear regression can be extended to data that depend on two or more variables\n",
        "(called multiple linear regression). If the dependent variable is z and independent variables are x and y, the data to be fitted have the form\n",
        "\n",
        "|      |              |           |\n",
        "|------|--------------|-----------|\n",
        "| x1   | y1           | z1        |\n",
        "| x2   | y2           | z2        |\n",
        "| x3   | y3           | z3        |\n",
        "| x4   | y4           | z4        |\n",
        "| ---- | ----         | ----      |\n",
        "| ---- | ----         |-----      |\n",
        "| xn   | yn           | zn        |\n",
        "\n",
        "Instead of a straight line, the fitting function now represents a plane:\n",
        "\n",
        "f(x, y) = a + bx + cy\n",
        "\n",
        "Show that the normal equations for the coefficients are\n",
        "\n",
        "$\\begin{bmatrix}\n",
        "n & \\sum{x_i} & \\sum {y_i}& \\\\\n",
        "\\sum{x_i} &\\sum{x_i^2} & \\sum{x_iy_i} \\\\\n",
        "\\sum {y_i} & \\sum{x_iy_i} &\\sum{y_i^2} \\\\\n",
        "\\end{bmatrix}\n",
        "\\begin{bmatrix}\n",
        "a \\\\\n",
        "b\\\\\n",
        "c\\\\\n",
        "\\end{bmatrix}$\n",
        "=\n",
        "$\\begin{bmatrix}\n",
        "\\sum {z_i}\\\\\n",
        "\\sum{x_iz_i} \\\\\n",
        "\\sum{y_iz_i}\n",
        "\\end{bmatrix}$\n"
      ],
      "metadata": {
        "id": "jsLHOoHJ_tuu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Ans:-***"
      ],
      "metadata": {
        "id": "AscApXNeFI3t"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "To derive the normal equations for the coefficients of a multiple linear regression model, we start with the equation for the plane:\n",
        "\n",
        "$\n",
        "f(x, y) = a + bx + cy\n",
        "$\n",
        "\n",
        "We have data points in the form of (x, y, z). The goal is to find the values of the coefficients a, b, and c that minimize the sum of squared differences between the observed z values and the values predicted by the plane.\n",
        "\n",
        "The sum of squared differences (the cost or error function) is given by:\n",
        "\n",
        "\n",
        "$E = \\sum_{i=1}^{n}(z_i - f(x_i, y_i))^2$\n",
        "\n",
        "Now, let's differentiate \\(E\\) with respect to each of the coefficients a, b, and c and set the derivatives equal to zero. This will give us the normal equations. Here's how you can do it:\n",
        "\n",
        "1. Differentiate E with respect to a:\n",
        "\n",
        "\n",
        "$\\frac{dE}{da} = -2\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i))$\n",
        "\n",
        "Setting this derivative to zero:\n",
        "\n",
        "$-2\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i)) = 0$\n",
        "\n",
        "Dividing by -2:\n",
        "\n",
        "\n",
        "$\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i)) = 0$\n",
        "\n",
        "Now, let's rearrange this equation:\n",
        "\n",
        "\n",
        "$\\sum_{i=1}^{n}z_i - \\sum_{i=1}^{n}(a + bx_i + cy_i) = 0$\n",
        "\n",
        "\n",
        "$\\sum_{i=1}^{n}z_i - a\\sum_{i=1}^{n} - b\\sum_{i=1}^{n}x_i - c\\sum_{i=1}^{n}y_i = 0$\n",
        "\n",
        "2. Differentiate E with respect to b:\n",
        "\n",
        "\n",
        "$\\frac{dE}{db} = -2\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i))x_i$\n",
        "\n",
        "Setting this derivative to zero:\n",
        "\n",
        "\n",
        "$-2\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i))x_i = 0$\n",
        "\n",
        "Dividing by -2:\n",
        "\n",
        "\n",
        "$\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i))x_i = 0$\n",
        "\n",
        "Now, let's rearrange this equation:\n",
        "\n",
        "\n",
        "$\\sum_{i=1}^{n}z_ix_i - a\\sum_{i=1}^{n}x_i - b\\sum_{i=1}^{n}x_i^2 - c\\sum_{i=1}^{n}x_iy_i = 0$\n",
        "\n",
        "3. Differentiate E with respect to c:\n",
        "\n",
        "\n",
        "$\\frac{dE}{dc} = -2\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i))y_i$\n",
        "\n",
        "Setting this derivative to zero:\n",
        "\n",
        "\n",
        "$-2\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i))y_i = 0$\n",
        "Dividing by -2:\n",
        "\n",
        "\n",
        "$\\sum_{i=1}^{n}(z_i - (a + bx_i + cy_i))y_i = 0$\n",
        "\n",
        "Now, let's rearrange this equation:\n",
        "\n",
        "\n",
        "$\\sum_{i=1}^{n}z_iy_i - a\\sum_{i=1}^{n}y_i - b\\sum_{i=1}^{n}x_iy_i - c\\sum_{i=1}^{n}y_i^2 = 0$\n",
        "\n",
        "Now, we have three equations for a, b, and c. Rearrange them as a matrix equation:\n",
        "\n",
        "$\\begin{bmatrix}\n",
        "n & \\sum{x_i} & \\sum {y_i}& \\\\\n",
        "\\sum{x_i} &\\sum{x_i^2} & \\sum{x_iy_i} \\\\\n",
        "\\sum {y_i} & \\sum{x_iy_i} &\\sum{y_i^2} \\\\\n",
        "\\end{bmatrix}\n",
        "\\begin{bmatrix}\n",
        "a \\\\\n",
        "b\\\\\n",
        "c\\\\\n",
        "\\end{bmatrix}$\n",
        "=\n",
        "$\\begin{bmatrix}\n",
        "\\sum {z_i}\\\\\n",
        "\\sum{x_iz_i} \\\\\n",
        "\\sum{y_iz_i}\n",
        "\\end{bmatrix}$\n",
        "\n",
        "\n",
        "These are the normal equations for the coefficients a, b, and c in the multiple linear regression model. The solution to this system of equations will give us the values of a, b, and c that minimize the sum of squared differences between the observed and predicted z values.\n"
      ],
      "metadata": {
        "id": "7Xk8H4lqMPw1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Problem-2:***"
      ],
      "metadata": {
        "id": "qcvlFRj1O1ti"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use multiple linear regression explained in Prob. 1 to determine the function\n",
        "\n",
        "f(x, y) = a + bx + cy\n",
        "\n",
        "\n",
        "that fits the following data:\n",
        "\n",
        "\n",
        "| x    | y              | z                |\n",
        "|------|----------------|------------------|\n",
        "| 0    | 0              | 1.42             |\n",
        "| 0    | 1              | 1.85             |\n",
        "| 1    | 0              | 0.78             |\n",
        "| 2    | 0              | 0.18             |\n",
        "| 2    | 1              | 0.60             |\n",
        "| 2    | 2              | 1.05             |\n"
      ],
      "metadata": {
        "id": "EXD6lXyhPX2u"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Ans:-***"
      ],
      "metadata": {
        "id": "oaWi1_wISLIe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "To determine the function f(x, y) = a + bx + cy that fits the provided data using multiple linear regression, we'll first set up the normal equations based on the data points. The normal equations are:\n",
        "\n",
        "\n",
        "$\\begin{bmatrix}\n",
        "n & \\sum{x_i} & \\sum{y_i} \\\\\n",
        "\\sum{x_i} & \\sum{x_i^2} & \\sum{x_iy_i} \\\\\n",
        "\\sum{y_i} & \\sum{x_iy_i} & \\sum{y_i^2} \\\\\n",
        "\\end{bmatrix}\n",
        "\\begin{bmatrix}\n",
        "a \\\\\n",
        "b \\\\\n",
        "c \\\\\n",
        "\\end{bmatrix}\n",
        "=\n",
        "\\begin{bmatrix}\n",
        "\\sum{z_i} \\\\\n",
        "\\sum{x_iz_i} \\\\\n",
        "\\sum{y_iz_i} \\\\\n",
        "\\end{bmatrix}$\n",
        "\n",
        "Let's calculate the values needed for this matrix equation using the provided data:\n",
        "\n",
        "\n",
        "n = 6\n",
        "\n",
        "$\\sum{x_i} = 0 + 0 + 1 + 2 + 2 + 2 = 7$\n",
        "\n",
        "$\\sum{y_i} = 0 + 1 + 0 + 0 + 1 + 2 = 4$\n",
        "\n",
        "$\\sum{x_i^2} = 0^2 + 0^2 + 1^2 + 2^2 + 2^2 + 2^2 = 13$\n",
        "\n",
        "$\\sum{x_iy_i} = (0 \\cdot 0) + (0 \\cdot 1) + (1 \\cdot 0) + (2 \\cdot 0) + (2 \\cdot 1) + (2 \\cdot 2) = 6$\n",
        "\n",
        "$\\sum{y_i^2} = 0^2 + 1^2 + 0^2 + 0^2 + 1^2 + 2^2 = 6$\n",
        "\n",
        "$\\sum{z_i} = 1.42 + 1.85 + 0.78 + 0.18 + 0.60 + 1.05 = 5.88$\n",
        "\n",
        "$\\sum{x_iz_i} = (0 \\cdot 1.42) + (0 \\cdot 1.85) + (1 \\cdot 0.78) + (2 \\cdot 0.18) + (2 \\cdot 0.60) + (2 \\cdot 1.05) = 4.44$\n",
        "\n",
        "\n",
        "$\\sum{y_iz_i} = (0 \\cdot 1.42) + (1 \\cdot 1.85) + (0 \\cdot 0.78) + (0 \\cdot 0.18) + (1 \\cdot 0.60) + (2 \\cdot 1.05) = 4.55$\n",
        "\n",
        "Now, we can set up the normal equations:\n",
        "\n",
        "$\n",
        "\\begin{bmatrix}\n",
        "6 & 7 & 4 \\\\\n",
        "7 & 13 & 6 \\\\\n",
        "4 & 6 & 6 \\\\\n",
        "\\end{bmatrix}\n",
        "\\begin{bmatrix}\n",
        "a \\\\\n",
        "b \\\\\n",
        "c \\\\\n",
        "\\end{bmatrix}\n",
        "=\n",
        "\\begin{bmatrix}\n",
        "5.88 \\\\\n",
        "4.44 \\\\\n",
        "4.55 \\\\\n",
        "\\end{bmatrix}\n",
        "$\n",
        "\n",
        "To solve this system of equations for a, b, and c, one can use matrix algebra or a numerical solver. Solving for\n",
        "$\\begin{bmatrix}\n",
        "a \\\\\n",
        "b \\\\\n",
        "c\n",
        "\\end{bmatrix}$,\n",
        "one'll obtain the values of the coefficients a=1.413, b=-0.621, and c=0.438 for the best-fit plane f(x, y) = 1.413 - 0.621x + 0.438y.\n"
      ],
      "metadata": {
        "id": "JWfqS23vSNwV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Problem -3:***"
      ],
      "metadata": {
        "id": "EmrcnDmwU6sE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Debye’s formula for the heat capacity $C_V$ as a solid is $C_V$ = 9Nkg(u), where\n",
        "\n",
        "\\begin{equation}\n",
        "    g(u)=u^3\\int_{0}^{\\frac{1}{u}} \\frac{x^4e^x}{(e^x-1)^2} \\,dx\n",
        "\\end{equation}\n",
        "\n",
        "The terms in this equation are\n",
        "                      \n",
        "N = number of particles in the solid\n",
        "\n",
        "k = Boltzmann constant\n",
        "\n",
        "$u=\\frac{T}{\\Theta_D}$\n",
        "\n",
        "T = absolute temperature\n",
        "\n",
        "$\\Theta_D$=Debye temperature\n",
        "\n",
        "Compute g(u) from u = 0 to 1.0 in intervals of 0.05 and plot the results.\n",
        "\n"
      ],
      "metadata": {
        "id": "71Uc49HgVUA1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Ans:-***"
      ],
      "metadata": {
        "id": "KIEFwb_LXxzY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "I use  romberg code to plotting this graph"
      ],
      "metadata": {
        "id": "CCy_DOsnX2ed"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def richardson(Rprev, Rincurr0, i):\n",
        "    Rcurr = [Rincurr0]\n",
        "    for j in range(1, i + 1):\n",
        "        val = (4**j * Rcurr[j - 1] - Rprev[j - 1]) / (4**j - 1)\n",
        "        Rcurr.append(val)\n",
        "    return Rcurr\n",
        "\n",
        "def trapezoid(f, a, b, n):\n",
        "    h = (b - a) / (n - 1)\n",
        "    xs = a + np.arange(n) * h\n",
        "    cs = np.ones(n)\n",
        "    cs[0] = 0.5\n",
        "    cs[-1] = 0.5\n",
        "    contribs = cs * f(xs)\n",
        "\n",
        "    contribs = np.where(np.isfinite(contribs), contribs, 0)\n",
        "    return h * np.sum(contribs)\n",
        "\n",
        "\n",
        "def prettyprint(row):\n",
        "    for elem in row:\n",
        "        print(\"{0:1.10f} \".format(elem), end=\"\")\n",
        "    print(\"\")\n",
        "\n",
        "def romberg(f, a, b, imax=20, tol=1.e-8):\n",
        "    n = 2\n",
        "    val = trapezoid(f, a, b, n)\n",
        "    Rprev = [val]\n",
        "    prettyprint(Rprev)\n",
        "    for i in range(1, imax):\n",
        "        nprime = 2 * n - 1\n",
        "        Rincurr0 = trapezoid(f, a, b, nprime)\n",
        "        Rcurr = richardson(Rprev, Rincurr0, i)\n",
        "        prettyprint(Rcurr)\n",
        "        err = abs(Rprev[-1] - Rcurr[-1]) / abs(Rcurr[-1])\n",
        "        valprime = Rcurr[-1]\n",
        "        if err < tol:\n",
        "            return valprime\n",
        "        n = nprime\n",
        "        Rprev = Rcurr[:]\n",
        "    else:\n",
        "        return None\n",
        "    return valprime\n",
        "\n",
        "\n",
        "def integrand(x, u):\n",
        "    return x**4 * np.exp(x) / (np.exp(x) - 1)**2\n",
        "\n",
        "def g(u):\n",
        "    result = u**3 * romberg(lambda x: integrand(x, u), 0, 1/u, tol=1.e-8)\n",
        "    return result\n",
        "\n",
        "# Initialize arrays to store u and g(u) values\n",
        "u_values = np.arange(0.05, 1.05, 0.05)\n",
        "g_values = []\n",
        "\n",
        "# Calculate g(u) for each u value\n",
        "for u in u_values:\n",
        "    g_u = g(u)\n",
        "    g_values.append(g_u)\n",
        "\n",
        "# Plot the results\n",
        "plt.plot(u_values, g_values, marker='o', label='g(u)')\n",
        "plt.xlabel('u')\n",
        "plt.ylabel('g(u)')\n",
        "plt.title('Plot of g(u) vs. u')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "PmnhG_oSYggd",
        "outputId": "9630b4b6-2452-4adb-be1b-a40129963c21"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-15-165827d47fea>:50: RuntimeWarning: invalid value encountered in divide\n",
            "  return x**4 * np.exp(x) / (np.exp(x) - 1)**2\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.0032978458 \n",
            "4.5420541580 6.0549729287 \n",
            "23.6911864018 30.0742304831 31.6755143201 \n",
            "25.9726736748 26.7331694325 26.5104320291 26.4284465959 \n",
            "25.9753171154 25.9761982622 25.9257335175 25.9164525888 25.9144447691 \n",
            "25.9753423809 25.9753508028 25.9752943055 25.9760809847 25.9763148215 25.9763753006 \n",
            "25.9753487903 25.9753509268 25.9753509350 25.9753518339 25.9753489745 25.9753480304 25.9753477795 \n",
            "25.9753503986 25.9753509347 25.9753509352 25.9753509352 25.9753509317 25.9753509336 25.9753509343 25.9753509345 \n",
            "25.9753508010 25.9753509352 25.9753509352 25.9753509352 25.9753509352 25.9753509352 25.9753509352 25.9753509352 25.9753509352 \n",
            "2.2702026175 \n",
            "22.4778290594 29.2137045400 \n",
            "25.1326488429 26.0175887707 25.8045143861 \n",
            "25.2384017813 25.2736527607 25.2240570267 25.2148434178 \n",
            "25.2648114993 25.2736147387 25.2736122039 25.2743987940 25.2746323445 \n",
            "25.2714511671 25.2736643897 25.2736676998 25.2736685807 25.2736657171 25.2736647722 \n",
            "25.2731133957 25.2736674719 25.2736676774 25.2736676770 25.2736676735 25.2736676754 25.2736676761 \n",
            "25.2735290971 25.2736676642 25.2736676770 25.2736676770 25.2736676770 25.2736676770 25.2736676770 25.2736676770 \n",
            "8.4008506265 \n",
            "19.9873557319 23.8495241003 \n",
            "20.7997758515 21.0705825581 20.8853197886 \n",
            "20.9774697933 21.0367011073 21.0344423439 21.0368093686 \n",
            "21.0216043762 21.0363159038 21.0362902236 21.0363195550 21.0363176342 \n",
            "21.0326190694 21.0362906338 21.0362889491 21.0362889289 21.0362888087 21.0362887806 \n",
            "21.0353715449 21.0362890367 21.0362889303 21.0362889300 21.0362889300 21.0362889301 21.0362889301 \n",
            "10.6713638753 \n",
            "14.8495889753 16.2423306753 \n",
            "15.2391084080 15.3689482189 15.3107227218 \n",
            "15.3299872185 15.3602801553 15.3597022844 15.3604797378 \n",
            "15.3523579253 15.3598148275 15.3597838057 15.3597850997 15.3597823756 \n",
            "15.3579291433 15.3597862160 15.3597843086 15.3597843166 15.3597843135 15.3597843154 \n",
            "15.3593206124 15.3597844355 15.3597843168 15.3597843169 15.3597843169 15.3597843169 15.3597843169 \n",
            "9.7307942193 \n",
            "10.6578903974 10.9669224567 \n",
            "10.7160402386 10.7354235190 10.7199902564 \n",
            "10.7281035612 10.7321246687 10.7319047453 10.7320938642 \n",
            "10.7309839255 10.7319440469 10.7319320055 10.7319324382 10.7319318052 \n",
            "10.7316958182 10.7319331158 10.7319323871 10.7319323931 10.7319323929 10.7319323935 \n",
            "10.7318732831 10.7319324381 10.7319323929 10.7319323930 10.7319323930 10.7319323930 10.7319323930 \n",
            "7.8934652093 \n",
            "7.6385880067 7.5536289392 \n",
            "7.5369418124 7.5030597476 7.4996884682 \n",
            "7.5111321890 7.5025289812 7.5024935968 7.5025381227 \n",
            "7.5046618646 7.5025050898 7.5025034970 7.5025036541 7.5025035190 \n",
            "7.5030432591 7.5025037239 7.5025036328 7.5025036350 7.5025036349 7.5025036350 \n",
            "7.5026385451 7.5025036405 7.5025036349 7.5025036349 7.5025036349 7.5025036349 7.5025036349 \n",
            "6.1540864602 \n",
            "5.5434414310 5.3398930879 \n",
            "5.3888537601 5.3373245365 5.3371532997 \n",
            "5.3505297249 5.3377550465 5.3377837472 5.3377937543 \n",
            "5.3409705767 5.3377841939 5.3377861371 5.3377861750 5.3377861453 \n",
            "5.3385821775 5.3377860444 5.3377861678 5.3377861683 5.3377861682 5.3377861683 \n",
            "4.7569535188 \n",
            "4.0959890252 3.8756675273 \n",
            "3.9369881649 3.8839878782 3.8845425682 \n",
            "3.8977040983 3.8846094095 3.8846508449 3.8846525635 \n",
            "3.8879122290 3.8846482726 3.8846508635 3.8846508638 3.8846508571 \n",
            "3.8854660823 3.8846507001 3.8846508619 3.8846508619 3.8846508619 3.8846508619 \n",
            "3.6934933058 \n",
            "3.0856654462 2.8830561597 \n",
            "2.9405760091 2.8922128634 2.8928233103 \n",
            "2.9047257583 2.8927756747 2.8928131954 2.8928130349 \n",
            "2.8957892182 2.8928103715 2.8928126846 2.8928126765 2.8928126751 \n",
            "2.8935567037 2.8928125322 2.8928126763 2.8928126762 2.8928126762 2.8928126762 \n",
            "2.8962466439 \n",
            "2.3687969161 2.1929803402 \n",
            "2.2426561609 2.2006092424 2.2011178359 \n",
            "2.2114580323 2.2010586561 2.2010886170 2.2010881532 \n",
            "2.2036792102 2.2010862695 2.2010881104 2.2010881024 2.2010881022 \n",
            "2.2017357936 2.2010879880 2.2010881026 2.2010881024 2.2010881024 2.2010881024 \n",
            "2.2981298656 \n",
            "1.8507063022 1.7015651144 \n",
            "1.7432546978 1.7074374963 1.7078289885 \n",
            "1.7166489527 1.7077803711 1.7078032294 1.7078028205 \n",
            "1.7100133146 1.7078014353 1.7078028396 1.7078028334 1.7078028334 \n",
            "1.8459277010 \n",
            "1.4693093137 1.3437698512 \n",
            "1.3784591747 1.3481757950 1.3484695246 \n",
            "1.3559398186 1.3484333666 1.3484505380 1.3484502367 \n",
            "1.3503218585 1.3484492051 1.3484502610 1.3484502566 1.3484502566 \n",
            "1.3489181079 1.3484501910 1.3484502567 1.3484502566 1.3484502566 1.3484502566 \n",
            "1.5003722628 \n",
            "1.1835569288 1.0779518175 \n",
            "1.1068192719 1.0812400529 1.0814592686 \n",
            "1.0877796775 1.0814331461 1.0814460189 1.0814458086 \n",
            "1.0830286954 1.0814450348 1.0814458273 1.0814458243 1.0814458244 \n",
            "1.0818415051 1.0814457750 1.0814458244 1.0814458243 1.0814458243 1.0814458243 \n",
            "1.2331991004 \n",
            "0.9659239078 0.8768321769 \n",
            "0.9009522376 0.8792950142 0.8794592033 \n",
            "0.8848183658 0.8794404086 0.8794501016 0.8794499571 \n",
            "0.8807916207 0.8794493723 0.8794499699 0.8794499678 0.8794499678 \n",
            "0.8797853531 0.8794499306 0.8794499679 0.8794499678 0.8794499678 0.8794499678 \n",
            "1.0241732840 \n",
            "0.7976486317 0.7221404142 \n",
            "0.7424115122 0.7239991391 0.7241230541 \n",
            "0.7286849637 0.7241094475 0.7241168014 0.7241167021 \n",
            "0.7252584334 0.7241162566 0.7241167106 0.7241167091 0.7241167092 \n",
            "0.8587561329 \n",
            "0.6657242523 0.6013802921 \n",
            "0.6185283136 0.6027963340 0.6028907368 \n",
            "0.6067926640 0.6028807808 0.6028864105 0.6028863419 \n",
            "0.6038626656 0.6028859995 0.6028863474 0.6028863464 0.6028863464 \n",
            "0.7264186355 \n",
            "0.5609819709 0.5058364161 \n",
            "0.5204400685 0.5069261010 0.5069987467 \n",
            "0.5103535452 0.5069913707 0.5069957221 0.5069956740 \n",
            "0.5078349427 0.5069954085 0.5069956777 0.5069956770 0.5069956770 \n",
            "0.6194593967 \n",
            "0.4768545170 0.4293195571 \n",
            "0.4418385954 0.4301666215 0.4302230924 \n",
            "0.4331228166 0.4302175571 0.4302209528 0.4302209188 \n",
            "0.4309462374 0.4302207110 0.4302209212 0.4302209207 0.4302209207 \n",
            "0.5321842602 \n",
            "0.4085665749 0.3673606798 \n",
            "0.3781608972 0.3680256713 0.3680700041 \n",
            "0.3705895719 0.3680657968 0.3680684718 0.3680684475 \n",
            "0.3686986055 0.3680682834 0.3680684491 0.3680684488 0.3680684488 \n",
            "0.4603367971 \n",
            "0.3525964638 0.3166830194 \n",
            "0.3260566445 0.3172100381 0.3172451727 \n",
            "0.3194456128 0.3172419355 0.3172440620 0.3172440444 \n",
            "0.3177943384 0.3172439136 0.3172440455 0.3172440452 0.3172440452 \n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}