A1_Abhishek_1911007.ipynb

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        "<a href=\"https://colab.research.google.com/github/physicsme1729/Numerical-methods-in-physics/blob/main/0_11_swarup_kumar_Giri_phy_P745.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "# ***Problem-1:***"
      ],
      "metadata": {
        "id": "D5ke9D_5-DVc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Find the minimum of the function $F(x, y, z) = 2x^2 + 3y^2 + z^2 + xy + xz − 2y$\n",
        "\n",
        "and confirm the result analytically."
      ],
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      "cell_type": "markdown",
      "source": [
        "# ***Solution:-***"
      ],
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      "cell_type": "markdown",
      "source": [
        "**Analytical solution:**\n"
      ],
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      "source": [
        "\n",
        "\n",
        "To find the minimum of the function $F(x, y, z) = 2x^2 + 3y^2 + z^2 + xy + xz - 2y$, we can use calculus. The minimum occurs at a point where the gradient of the function is zero. The gradient of the function is a vector of its partial derivatives with respect to each variable:\n",
        "\n",
        "$\n",
        "\\nabla F = \\left(\\frac{\\partial F}{\\partial x}, \\frac{\\partial F}{\\partial y}, \\frac{\\partial F}{\\partial z}\\right)\n",
        "$\n",
        "\n",
        "Let's compute the partial derivatives of \\(F\\) with respect to \\(x\\), \\(y\\), and \\(z\\):\n",
        "\n",
        "$\n",
        "\\frac{\\partial F}{\\partial x} = 4x + y + z\n",
        "$\n",
        "\n",
        "$\n",
        "\\frac{\\partial F}{\\partial y} = 6y + x - 2\n",
        "$\n",
        "\n",
        "$\n",
        "\\frac{\\partial F}{\\partial z} = 2z + x\n",
        "$\n",
        "\n",
        "Now, we can set each of these partial derivatives equal to zero to find the critical points:\n",
        "\n",
        "$\n",
        "\\frac{\\partial F}{\\partial x} = 4x + y + z = 0\n",
        "$\n",
        "\n",
        "$\n",
        "\\frac{\\partial F}{\\partial y} = 6y + x - 2 = 0\n",
        "$\n",
        "\n",
        "$\n",
        "\\frac{\\partial F}{\\partial z} = 2z + x = 0\n",
        "$\n",
        "\n",
        "Solving these equations simultaneously will give us the critical point(s) where the gradient is zero.\n",
        "\n",
        "Let's first solve for \\(x\\) in the third equation:\n",
        "\n",
        "$\n",
        "2z + x = 0 \\implies x = -2z\n",
        "$\n",
        "\n",
        "Now, we can substitute this expression for \\(x\\) into the first and second equations:\n",
        "\n",
        "$\n",
        "4x + y + z = 0 \\implies 4(-2z) + y + z = 0\n",
        "$\n",
        "\n",
        "$\n",
        "-8z + y + z = 0\n",
        "$\n",
        "\n",
        "$\n",
        "-7z + y = 0 \\implies y = 7z\n",
        "$\n",
        "\n",
        "$\n",
        "6y + x - 2 = 0 \\implies 6(7z) + (-2z) - 2 = 0\n",
        "$\n",
        "\n",
        "$\n",
        "42z - 2z - 2 = 0\n",
        "$\n",
        "\n",
        "$\n",
        "40z - 2 = 0\n",
        "$\n",
        "\n",
        "$\n",
        "40z = 2\n",
        "$\n",
        "\n",
        "$\n",
        "z = \\frac{2}{40} = \\frac{1}{20}\n",
        "$\n",
        "\n",
        "Now that we have found values for \\(x\\), \\(y\\), and \\(z\\), we can calculate the corresponding minimum value of \\(F\\):\n",
        "\n",
        "$\n",
        "x = -2z = -2\\left(\\frac{1}{20}\\right) = -\\frac{1}{10}\n",
        "$\n",
        "\n",
        "$\n",
        "y = 7z = 7\\left(\\frac{1}{20}\\right) = \\frac{7}{20}\n",
        "$\n",
        "\n",
        "Now, substitute these values into \\(F\\):\n",
        "\n",
        "$\n",
        "F\\left(-\\frac{1}{10}, \\frac{7}{20}, \\frac{1}{20}\\right) = 2\\left(-\\frac{1}{10}\\right)^2 + 3\\left(\\frac{7}{20}\\right)^2 + \\left(\\frac{1}{20}\\right)^2 - \\frac{1}{10}\\left(\\frac{7}{20}\\right) - \\frac{1}{10}\\left(\\frac{1}{20}\\right) - 2\\left(\\frac{7}{20}\\right)\n",
        "$\n",
        "\n",
        "Now, one can  find the minimum value of \\(F\\) from  above $F\\left(-\\frac{1}{10}, \\frac{7}{20}, \\frac{1}{20}\\right)$ .\n",
        "\n",
        "\n"
      ],
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      "cell_type": "markdown",
      "source": [
        "***solution in python using  \"gradient descent\"***"
      ],
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    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Define the function F(x, y, z)\n",
        "def F(x, y, z):\n",
        "    return 2*x**2 + 3*y**2 + z**2 + x*y + x*z - 2*y\n",
        "\n",
        "# Define the gradient of F(x, y, z)\n",
        "def gradient_F(x, y, z):\n",
        "    df_dx = 4*x + y + z\n",
        "    df_dy = 6*y + x - 2\n",
        "    df_dz = 2*z + x\n",
        "    return np.array([df_dx, df_dy, df_dz])\n",
        "\n",
        "# Gradient descent parameters\n",
        "learning_rate = 0.01\n",
        "num_iterations = 1000\n",
        "initial_point = np.array([1.0, 1.0, 1.0])  # Initial guess\n",
        "\n",
        "# Gradient descent optimization\n",
        "current_point = initial_point\n",
        "for i in range(num_iterations):\n",
        "    gradient = gradient_F(*current_point)\n",
        "    current_point -= learning_rate * gradient\n",
        "\n",
        "# The minimum point is in current_point\n",
        "min_x, min_y, min_z = current_point\n",
        "min_value = F(min_x, min_y, min_z)\n",
        "\n",
        "print(f\"Minimum at (x, y, z) = ({min_x}, {min_y}, {min_z})\")\n",
        "print(f\"Minimum value of F: {min_value}\")\n"
      ],
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          "text": [
            "Minimum at (x, y, z) = (-0.10000003159536985, 0.3500000071008973, 0.050000070291636986)\n",
            "Minimum value of F: -0.34999999999999537\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Problem 2:-***"
      ],
      "metadata": {
        "id": "-ew_bWKbT3IN"
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      "cell_type": "markdown",
      "source": [
        "\n",
        "The following table displays thermal efficiencies of some early steam engines4.\n",
        "Use linear regression to predict the thermal efficiency in the year 2000.\n",
        "\n",
        "| Year | Efficiency (%) | Type             |\n",
        "|------|----------------|------------------|\n",
        "| 1718 | 0.5            | Newcomen         |\n",
        "| 1767 | 0.8            | Smeaton          |\n",
        "| 1774 | 1.4            | Smeaton          |\n",
        "| 1775 | 2.7            | Watt             |\n",
        "| 1792 | 4.5            | Watt             |\n",
        "| 1816 | 7.5            | Woolf compound   |\n",
        "| 1828 | 12.0           | Improved Cornish |\n",
        "| 1834 | 17.0           | Improved Cornish |\n",
        "| 1878 | 17.2           | Corliss compound |\n",
        "| 1906 | 23.0           | Triple expansion |\n",
        "\n",
        "\n"
      ],
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    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Ans:***"
      ],
      "metadata": {
        "id": "SqzH3ylyu9rO"
      }
    },
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      "cell_type": "markdown",
      "source": [
        "To predict the thermal efficiency in the year 2000 using linear regression, one can perform a straight line fit (also known as linear regression) by calculating the slope and intercept of the best-fitting line manually. Here's how one can do it:\n",
        "\n",
        "1.To  Calculate the mean of the year and efficiency values:\n",
        "\n",
        "$\n",
        "\\bar{x} = \\frac{1}{n} \\sum_{i=1}^n x_i \\quad \\text{(mean of years)}\n",
        "$\n",
        "\n",
        "\n",
        "$\n",
        "\\bar{y} = \\frac{1}{n} \\sum_{i=1}^n y_i \\quad \\text{(mean of efficiencies)}\n",
        "$\n",
        "\n",
        "2. To Calculate the slope (\\(m\\)) of the best-fitting line using the formula:\n",
        "\n",
        "$\n",
        "m = \\frac{\\sum_{i=1}^n (x_i - \\bar{x})(y_i - \\bar{y})}{\\sum_{i=1}^n (x_i - \\bar{x})^2}\n",
        "$\n",
        "\n",
        "3. To Calculate the intercept (\\(b\\)) of the best-fitting line using the formula:\n",
        "\n",
        "$\n",
        "b = \\bar{y} - m\\bar{x}\n",
        "$\n",
        "\n",
        "4. Use the equation of the line (\\(y = mx + b\\)) to predict the thermal efficiency in the year 2000 (\\(x = 2000\\)):\n",
        "\n",
        "$\n",
        "\\text{Efficiency}(2000) = m \\cdot 2000 + b\n",
        "$\n",
        "\n",
        "Let's calculate this manually:\n",
        "\n",
        "\\begin{align*}\n",
        "\\text{Data:} \\\\\n",
        "\\text{Years} &= [1718, 1767, 1774, 1775, 1792, 1816, 1828, 1834, 1878, 1906] \\\\\n",
        "\\text{Efficiencies} &= [0.5, 0.8, 1.4, 2.7, 4.5, 7.5, 12.0, 17.0, 17.2, 23.0]\n",
        "\\end{align*}\n",
        "\n",
        "Calculate means:\n",
        "\n",
        "$\n",
        "\\text{Mean Year} = \\frac{\\sum \\text{Years}}{\\text{Number of Years}}\n",
        "$\n",
        "\n",
        "$\n",
        "\\text{Mean Efficiency} = \\frac{\\sum \\text{Efficiencies}}{\\text{Number of Efficiencies}}\n",
        "$\n",
        "\n",
        "Calculate slope (\\(m\\)):\n",
        "\n",
        "$\n",
        "\\text{Numerator} = \\sum_{i=1}^n (x_i - \\bar{x})(y_i - \\bar{y})\n",
        "$\n",
        "\n",
        "$\n",
        "\\text{Denominator} = \\sum_{i=1}^n (x_i - \\bar{x})^2\n",
        "$\n",
        "\n",
        "$\n",
        "\\text{Slope (}m\\text{)} = \\frac{\\text{Numerator}}{\\text{Denominator}}\n",
        "$\n",
        "\n",
        "Calculate intercept (\\(b\\)):\n",
        "\n",
        "$\n",
        "\\text{Intercept (}b\\text{)} = \\text{Mean Efficiency} - \\text{Slope (}m\\text{)} \\times \\text{Mean Year}\n",
        "$\n",
        "\n",
        "\n",
        "$\n",
        "\\text{Predicted Efficiency in 2000} = \\text{Slope (}m\\text{)} \\times \\text{Year 2000} + \\text{Intercept (}b\\text{)}\n",
        "$\n",
        "\n",
        "The predicted thermal efficiency in the year 2000 is approximately found using python code attached below."
      ],
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      "source": [
        "# Data\n",
        "years = [1718, 1767, 1774, 1775, 1792, 1816, 1828, 1834, 1878, 1906]\n",
        "efficiencies = [0.5, 0.8, 1.4, 2.7, 4.5, 7.5, 12.0, 17.0, 17.2, 23.0]\n",
        "\n",
        "# Calculate means\n",
        "mean_x = sum(years) / len(years)\n",
        "mean_y = sum(efficiencies) / len(efficiencies)\n",
        "\n",
        "# Calculate the slope (m) and y-intercept (b)\n",
        "numerator = sum((x - mean_x) * (y - mean_y) for x, y in zip(years, efficiencies))\n",
        "denominator = sum((x - mean_x) ** 2 for x in years)\n",
        "m = numerator / denominator\n",
        "b = mean_y - m * mean_x\n",
        "\n",
        "# Predict Efficiency in the year 2000\n",
        "year_2000 = 2000\n",
        "efficiency_2000 = m * year_2000 + b\n",
        "print (\"mean_x=\",mean_x)\n",
        "print (\"mean_y=\",mean_y)\n",
        "print ('slope_m=',m)\n",
        "print ('intercept_b=',b)\n",
        "print(f\"Predicted Efficiency in the year 2000: {efficiency_2000:.2f}%\")\n",
        "\n",
        "# Plot the data and linear regression line\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.scatter(years, efficiencies, label=\"Data Points\")\n",
        "plt.plot(years, [m * x + b for x in years], color='red', label=\"Linear Regression Line\")\n",
        "plt.xlabel(\"Year\")\n",
        "plt.ylabel(\"Efficiency (%)\")\n",
        "plt.title(\"Thermal Efficiency of Steam Engines\")\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ],
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          "text": [
            "mean_x= 1808.8\n",
            "mean_y= 8.66\n",
            "slope_m= 0.1376889353715669\n",
            "intercept_b= -240.3917463000902\n",
            "Predicted Efficiency in the year 2000: 34.99%\n"
          ]
        },
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          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The predicted efficiency in year 2000 is -240.39 + $0.13769\\times 2000$ = 35.0%"
      ],
      "metadata": {
        "id": "qDclAxWhbuhP"
      }
    }
  ]
}