From 087dd56fbec01adff30030b3b108f887b7feccf1 Mon Sep 17 00:00:00 2001 From: Ulrich <ulrich.kerzel@rwth-aachen.de> Date: Mon, 17 Mar 2025 11:42:00 +0100 Subject: [PATCH] update runtime --- ...n_ContinuousCasting_ConicSteelVessel.ipynb | 600 +++++++----------- .../solutions/Solution_CyclicBoosting.ipynb | 35 +- runtime.txt | 2 +- 3 files changed, 249 insertions(+), 388 deletions(-) diff --git a/datascienceintro/solutions/Solution_ContinuousCasting_ConicSteelVessel.ipynb b/datascienceintro/solutions/Solution_ContinuousCasting_ConicSteelVessel.ipynb index 0861149..2d7a02a 100644 --- a/datascienceintro/solutions/Solution_ContinuousCasting_ConicSteelVessel.ipynb +++ b/datascienceintro/solutions/Solution_ContinuousCasting_ConicSteelVessel.ipynb @@ -1,21 +1,10 @@ { - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } - }, "cells": [ { "cell_type": "markdown", + "metadata": { + "id": "ROkOel9qfsfr" + }, "source": [ "# Continuous Casting with Conic Supply Vessel\n", "\n", @@ -30,13 +19,13 @@ "\n", "N.B. This is the same example as discussed in the lecture \"Numerische Modellierung in der Prozesstechnik\" and we discuss this example here to apply the methods of this course to the same example.\n", "\n" - ], - "metadata": { - "id": "ROkOel9qfsfr" - } + ] }, { "cell_type": "markdown", + "metadata": { + "id": "JvESDWsUhe94" + }, "source": [ "## Torrielli's Law\n", "\n", @@ -76,17 +65,11 @@ "$$\n", "\\frac{dh}{dt} = -\\frac{a}{\\pi \\left[ R_1 + \\left( \\dfrac{R_2 - R_1}{H} \\right) h \\right]^2} \\sqrt{2 g h}\n", "$$\n" - ], - "metadata": { - "id": "JvESDWsUhe94" - } + ] }, { "cell_type": "code", - "source": [ - "# make sure we have the required libraries\n", - "! pip install torchdiffeq" - ], + "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -94,117 +77,19 @@ "id": "fDiLVN2ZjOiZ", "outputId": "84cbf733-5539-4c18-ef5e-c47391669906" }, - "execution_count": null, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - 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nvidia-cudnn-cu12-9.3.0.75:\n", - " Successfully uninstalled nvidia-cudnn-cu12-9.3.0.75\n", - " Attempting uninstall: nvidia-cusolver-cu12\n", - " Found existing installation: nvidia-cusolver-cu12 11.6.3.83\n", - " Uninstalling nvidia-cusolver-cu12-11.6.3.83:\n", - " Successfully uninstalled nvidia-cusolver-cu12-11.6.3.83\n", - "Successfully installed nvidia-cublas-cu12-12.4.5.8 nvidia-cuda-cupti-cu12-12.4.127 nvidia-cuda-nvrtc-cu12-12.4.127 nvidia-cuda-runtime-cu12-12.4.127 nvidia-cudnn-cu12-9.1.0.70 nvidia-cufft-cu12-11.2.1.3 nvidia-curand-cu12-10.3.5.147 nvidia-cusolver-cu12-11.6.1.9 nvidia-cusparse-cu12-12.3.1.170 nvidia-nvjitlink-cu12-12.4.127 torchdiffeq-0.2.5\n" - ] - } + "outputs": [], + "source": [ + "# make sure we have the required libraries\n", + "# ! pip install torchdiffeq" ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "pAfdaw0afrWZ" + }, + "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -219,56 +104,56 @@ "\n", "\n", "from datetime import datetime" - ], - "metadata": { - "id": "pAfdaw0afrWZ" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "markdown", + "metadata": { + "id": "EiNuMdQfkauk" + }, "source": [ "# Plot Height vs Time\n", "\n", "As a first step, we visualise how the height of the molten steel in the conic vessel changes with time.\n", "\n", "We will use $r=2$ cm for this example, though the radius $r$ is the quantity we want to optimise later to make sure we can maintain the required throughput, including the change-over time.\n" - ], - "metadata": { - "id": "EiNuMdQfkauk" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "AcIz5EjClHSh" + }, + "outputs": [], "source": [ "# Geometry of the truncated cone\n", "H = 2.0 # Total height of the vessel (m)\n", "R1 = 0.9 # Radius at the bottom (m)\n", "R2 = 1.2 # Radius at the top (m)\n", "s = (R2 - R1) / H # Slope of the radius as a function of height\n" - ], - "metadata": { - "id": "AcIz5EjClHSh" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "ccZ5IeSUwf4j" + }, + "outputs": [], "source": [ "# assume a fixed radius of the orifice\n", "a = np.pi * (0.02)**2 # Area of the hole at the bottom (m^2)\n", " # assuming r=2cm" - ], - "metadata": { - "id": "ccZ5IeSUwf4j" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "OP5j1PjUlMN8" + }, + "outputs": [], "source": [ "# Time parameters\n", "t0 = 0.0 # Initial time (s)\n", @@ -281,15 +166,13 @@ "\n", "# Physical Constants\n", "g = torch.tensor(scipy.constants.g, dtype=torch.float32)" - ], - "metadata": { - "id": "OP5j1PjUlMN8" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "markdown", + "metadata": { + "id": "ATNqzi02nMgB" + }, "source": [ "This is the differential equation from above, assuming Torricelli's law.\n", "\n", @@ -301,13 +184,15 @@ "\n", "Since the function ```odeint``` does not take additional arguments, we have to specify these outside the scope of the function.\n", "This is not an issue at this stage, but we will see later that this requires us to write the code in a specific way when we want to optimise the radius of the orifice and, hence, the area ```a```." - ], - "metadata": { - "id": "ATNqzi02nMgB" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "RRO687otlxU5" + }, + "outputs": [], "source": [ "# Function defining the differential equation dh/dt\n", "def dhdt(t, h):\n", @@ -323,15 +208,15 @@ " # Handle h = 0 to prevent division by zero\n", " dh = torch.where(h > 0.0, dh, torch.tensor(0.0))\n", " return dh" - ], - "metadata": { - "id": "RRO687otlxU5" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "NJ5soVYNly9b" + }, + "outputs": [], "source": [ "# Solve the ODE using torchdiffeq's odeint function\n", "h_values = odeint(dhdt, h0, t_values, method='dopri5')\n", @@ -341,28 +226,11 @@ "\n", "# Ensure non-negative heights\n", "h_values = torch.clamp(h_values, min=0.0)\n" - ], - "metadata": { - "id": "NJ5soVYNly9b" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "code", - "source": [ - "# Plot the results\n", - "t_np = t_values.numpy()\n", - "h_np = h_values.detach().numpy()\n", - "\n", - "plt.figure(figsize=(8, 5))\n", - "sns.lineplot(x=t_np, y=h_np)\n", - "plt.title('Height of Liquid in Truncated Cone Over Time')\n", - "plt.xlabel('Time (s)')\n", - "plt.ylabel('Height (m)')\n", - "plt.grid(True)\n", - "plt.show()" - ], + "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -371,22 +239,37 @@ "id": "dSd1kx4ql4vC", "outputId": "6de2a73a-cdd2-465b-ddda-a2614079eb91" }, - "execution_count": null, "outputs": [ { - "output_type": "display_data", "data": { + "image/png": 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", "text/plain": [ "<Figure size 800x500 with 1 Axes>" - ], - "image/png": 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\n" + ] }, - "metadata": {} + "metadata": {}, + "output_type": "display_data" } + ], + "source": [ + "# Plot the results\n", + "t_np = t_values.numpy()\n", + "h_np = h_values.detach().numpy()\n", + "\n", + "plt.figure(figsize=(8, 5))\n", + "sns.lineplot(x=t_np, y=h_np)\n", + "plt.title('Height of Liquid in Truncated Cone Over Time')\n", + "plt.xlabel('Time (s)')\n", + "plt.ylabel('Height (m)')\n", + "plt.grid(True)\n", + "plt.show()" ] }, { "cell_type": "markdown", + "metadata": { + "id": "G6dj0FhwosoG" + }, "source": [ "# Optimising Outlet Radius - Differential Equation\n", "\n", @@ -397,25 +280,25 @@ "\n", "N.B. in the following, we will denote the radius of the output orifice for each step of the optimisation as $r_0$ to avoid confusion with values inside each optimisation step.\n", "\n" - ], - "metadata": { - "id": "G6dj0FhwosoG" - } + ] }, { "cell_type": "code", - "source": [ - "# Target emptying time\n", - "t_target = torch.tensor(428.32, dtype=torch.float32) # seconds" - ], + "execution_count": null, "metadata": { "id": "ti5Iu5x6qAhH" }, - "execution_count": null, - "outputs": [] + "outputs": [], + "source": [ + "# Target emptying time\n", + "t_target = torch.tensor(428.32, dtype=torch.float32) # seconds" + ] }, { "cell_type": "markdown", + "metadata": { + "id": "PTwdltLgqDMS" + }, "source": [ "We now define the function that computes the height of the remaining molten steel inside the vessel at the target time ```t_target``` for a given radius $r_0$ of the output orifice.\n", "\n", @@ -429,13 +312,15 @@ "Note:\n", "Unlike earlier, the area of the orifice now depends on the radius $r_0$ that we are changing. Ideally, we would add another argument to the function with the differential equation.\n", "However, the function ```odeint``` of [torchdiffeq](https://github.com/rtqichen/torchdiffeq) does not support this. Therefore, we define the function for the differential equation within the function computing the height at time ```t_target```. Then, for each round, the value of the area $a$ is defined and we, kind-off, side-step the problem." - ], - "metadata": { - "id": "PTwdltLgqDMS" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "GJG0nbEtsSof" + }, + "outputs": [], "source": [ "# Compute the height of the molten steel for a given\n", "# radius of the outlet orifice r_0 after t_target has elapsed\n", @@ -471,38 +356,38 @@ " h_tend = h_values[-1, 0] # Height at t_target\n", "\n", " return h_tend, r_o" - ], - "metadata": { - "id": "GJG0nbEtsSof" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "markdown", + "metadata": { + "id": "bj2N5KIL0CB9" + }, "source": [ "Before we find the optimal value, we can plot the result to get a feeling for our expectation.\n", "\n", "N.B. due to the line ```h = h.clamp(min=0.0)``` we cannot have negative heights in the vessel." - ], - "metadata": { - "id": "bj2N5KIL0CB9" - } + ] }, { "cell_type": "markdown", + "metadata": { + "id": "1dEYfP_s0jWq" + }, "source": [ "**Exercise**\n", "\n", "Plot the function of the height of the remaining steel in the vessel after the target time ```t_target``` has elapsed for the radius in the interval $(0.02, 0.05)$ for 100 steps.\n", "Note that we need PyTorch tensors." - ], - "metadata": { - "id": "1dEYfP_s0jWq" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "V7OcDeyg0umW" + }, + "outputs": [], "source": [ "# Generate x_space and compute y_space\n", "x_space = torch.linspace(0.02, 0.05, steps=50) # Orifice radii from 0.02 m to 0.05 m\n", @@ -530,24 +415,40 @@ "plt.legend()\n", "plt.grid(True)\n", "plt.show()" - ], - "metadata": { - "id": "V7OcDeyg0umW" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "markdown", - "source": [ - "**Solution**" - ], "metadata": { "id": "dELBNAZG1DDu" - } + }, + "source": [ + "**Solution**" + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 568 + }, + "id": "Zd_OZdKyygnx", + "outputId": "f5aee4bf-95b5-464d-812d-aa401712a6a1" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1000x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Generate x_space and compute y_space\n", "x_space = torch.linspace(0.02, 0.05, steps=50) # Orifice radii from 0.02 m to 0.05 m\n", @@ -575,42 +476,26 @@ "plt.legend()\n", "plt.grid(True)\n", "plt.show()\n" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 568 - }, - "id": "Zd_OZdKyygnx", - "outputId": "f5aee4bf-95b5-464d-812d-aa401712a6a1" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "<Figure size 1000x600 with 1 Axes>" - ], - "image/png": 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\n" - }, - "metadata": {} - } ] }, { "cell_type": "markdown", + "metadata": { + "id": "ZpDou3GMspeU" + }, "source": [ "## Newton's Method\n", "\n", "We can find the root of the above function using, for example, Newton's method, and detemine the optimal radius of the outlet orifice." - ], - "metadata": { - "id": "ZpDou3GMspeU" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "T5I5RaEeszoC" + }, + "outputs": [], "source": [ "def newtons_method(f, r_o_init, tol=1e-6, rtol=1e-6, max_iter=20):\n", " r_o = torch.tensor(r_o_init, dtype=torch.float32, requires_grad=True)\n", @@ -644,31 +529,11 @@ "\n", " print(\"Maximum iterations reached without convergence.\")\n", " return r_o.item()" - ], - "metadata": { - "id": "T5I5RaEeszoC" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "code", - "source": [ - "# Define the function f(r_o)\n", - "def f(r_o):\n", - " h_tend, r_o = compute_h_at_tend(r_o)\n", - " return h_tend, r_o\n", - "\n", - "# Initial guess for r_o (in meters)\n", - "r_o_initial = 0.025 # 25 mm\n", - "\n", - "# Run Newton's method\n", - "t_start = datetime.now()\n", - "optimal_r_o = newtons_method(f, r_o_initial, tol=1e-5, rtol=1e-6, max_iter=50)\n", - "t_stop = datetime.now()\n", - "print(f\"\\nOptimal orifice radius found: {optimal_r_o * 1000:.2f} mm\")\n", - "print(f'Time taken: {t_stop - t_start}')" - ], + "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -676,11 +541,10 @@ "id": "W9tlOcaNs2tY", "outputId": "0798d66d-d770-47d3-f5c4-476be420fcc9" }, - "execution_count": null, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Iteration 0: r_o = 0.035460 m, h(t_end) = 0.871790, f'(r_o) = -83.348442, delta_r_o = 0.010460\n", "Iteration 1: r_o = 0.037223 m, h(t_end) = 0.081241, f'(r_o) = -46.081654, delta_r_o = 0.001763\n", @@ -696,21 +560,58 @@ "Time taken: 0:00:01.596860\n" ] } + ], + "source": [ + "# Define the function f(r_o)\n", + "def f(r_o):\n", + " h_tend, r_o = compute_h_at_tend(r_o)\n", + " return h_tend, r_o\n", + "\n", + "# Initial guess for r_o (in meters)\n", + "r_o_initial = 0.025 # 25 mm\n", + "\n", + "# Run Newton's method\n", + "t_start = datetime.now()\n", + "optimal_r_o = newtons_method(f, r_o_initial, tol=1e-5, rtol=1e-6, max_iter=50)\n", + "t_stop = datetime.now()\n", + "print(f\"\\nOptimal orifice radius found: {optimal_r_o * 1000:.2f} mm\")\n", + "print(f'Time taken: {t_stop - t_start}')" ] }, { "cell_type": "markdown", + "metadata": { + "id": "XD0WIuTeuw1y" + }, "source": [ "Now plot the final function of height vs time for the optimal radius\n", "\n", "(remember that we cannot add another argument to the function ```dhdt```, so we need to define it again with the optimal radius).\n" - ], - "metadata": { - "id": "XD0WIuTeuw1y" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 564 + }, + "id": "sMYY2gAvu1mT", + "outputId": "808bc199-cbdc-4707-87dd-8b340e6d7b29" + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1000x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "def dhdt_opt(t, h):\n", " h = h.clamp(min=0.0)\n", @@ -733,31 +634,13 @@ "plt.ylabel('Height (m)')\n", "plt.grid(True)\n", "plt.show()" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 564 - }, - "id": "sMYY2gAvu1mT", - "outputId": "808bc199-cbdc-4707-87dd-8b340e6d7b29" - }, - "execution_count": null, - "outputs": [ - { - "output_type": "display_data", - "data": { - "text/plain": [ - "<Figure size 1000x600 with 1 Axes>" - ], - "image/png": 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\n" - }, - "metadata": {} - } ] }, { "cell_type": "markdown", + "metadata": { + "id": "t1jsBFi-1zF-" + }, "source": [ "# Optimising Outlet Radius - Iterative Approach\n", "\n", @@ -767,13 +650,15 @@ "The remainnig parameters (```R1, R2, initial_height```) specifiy the geometry and initial height of the molten steel in the vessel. We can make these parameters argument to the function here as we are not constrained by the calling function like ```odeint``` earlier.\n", "\n", "N.B. We need to work with PyTorch tensors (or types that are easily converted) to be able to call Newton's method efficiently later on." - ], - "metadata": { - "id": "t1jsBFi-1zF-" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "34g7UoXu2A0I" + }, + "outputs": [], "source": [ "def calculate_height_fixpoint(r: torch.tensor, delta_t: float = 1.0, t_max: float = 100000.0,\n", " R1: float = 0.9, R2: float = 1.2, initial_height: float = 2.0,\n", @@ -835,66 +720,44 @@ " height_at_desired_time = current_height\n", "\n", " return height_at_desired_time" - ], - "metadata": { - "id": "34g7UoXu2A0I" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "markdown", + "metadata": { + "id": "kkMJ_cT9E-H4" + }, "source": [ "**Exercise**\n", "\n", "Use the above function to call the function ```newtons_method``` we defined earlier and find the optimal radius of the output orifice." - ], - "metadata": { - "id": "kkMJ_cT9E-H4" - } + ] }, { "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "ybu1ouSSFQhG" + }, + "outputs": [], "source": [ "##\n", "## your code goes here\n", "##" - ], - "metadata": { - "id": "ybu1ouSSFQhG" - }, - "execution_count": null, - "outputs": [] + ] }, { "cell_type": "markdown", - "source": [ - "**Solution**" - ], "metadata": { "id": "oKGUQSaqFOin" - } + }, + "source": [ + "**Solution**" + ] }, { "cell_type": "code", - "source": [ - "# with Newton's Method above\n", - "\n", - "# Define the function f(r_o)\n", - "def f(r_o):\n", - " h_tend = calculate_height_fixpoint(r_o)\n", - " return h_tend, r_o\n", - "\n", - "# Initial guess for r_o (in meters)\n", - "r_o_initial = 0.025 # 25 mm\n", - "\n", - "# Run Newton's method\n", - "t_start = datetime.now()\n", - "optimal_r_o = newtons_method(f, r_o_initial, tol=1e-5, rtol=1e-6, max_iter=50)\n", - "t_stop = datetime.now()\n", - "print(f\"\\nOptimal orifice radius found: {optimal_r_o * 1000:.2f} mm\")\n", - "print(f'Time taken: {t_stop - t_start}')" - ], + "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -902,11 +765,10 @@ "id": "vKIG_b6d2VcF", "outputId": "8cda474d-9262-4147-9a00-cc371621ad6b" }, - "execution_count": null, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Iteration 0: r_o = 0.035422 m, h(t_end) = 0.870002, f'(r_o) = -83.478127, delta_r_o = 0.010422\n", "Iteration 1: r_o = 0.037166 m, h(t_end) = 0.080678, f'(r_o) = -46.268208, delta_r_o = 0.001744\n", @@ -921,7 +783,39 @@ "Time taken: 0:00:01.100965\n" ] } + ], + "source": [ + "# with Newton's Method above\n", + "\n", + "# Define the function f(r_o)\n", + "def f(r_o):\n", + " h_tend = calculate_height_fixpoint(r_o)\n", + " return h_tend, r_o\n", + "\n", + "# Initial guess for r_o (in meters)\n", + "r_o_initial = 0.025 # 25 mm\n", + "\n", + "# Run Newton's method\n", + "t_start = datetime.now()\n", + "optimal_r_o = newtons_method(f, r_o_initial, tol=1e-5, rtol=1e-6, max_iter=50)\n", + "t_stop = datetime.now()\n", + "print(f\"\\nOptimal orifice radius found: {optimal_r_o * 1000:.2f} mm\")\n", + "print(f'Time taken: {t_stop - t_start}')" ] } - ] -} \ No newline at end of file + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/datascienceintro/solutions/Solution_CyclicBoosting.ipynb b/datascienceintro/solutions/Solution_CyclicBoosting.ipynb index 2bca073..8a3410f 100644 --- a/datascienceintro/solutions/Solution_CyclicBoosting.ipynb +++ b/datascienceintro/solutions/Solution_CyclicBoosting.ipynb @@ -32,40 +32,7 @@ "id": "lqW01yddrFMz", "outputId": "816757bf-085d-40fd-c032-35d027c727c8" }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Requirement already satisfied: cyclic-boosting in /usr/local/lib/python3.11/dist-packages (1.4.0)\n", - "Requirement already satisfied: decorator>=5.1.1 in /usr/local/lib/python3.11/dist-packages (from cyclic-boosting) (5.2.1)\n", - "Requirement already satisfied: hypothesis>=6.70.0 in /usr/local/lib/python3.11/dist-packages (from cyclic-boosting) (6.129.0)\n", - "Requirement already satisfied: matplotlib>=1.5.1 in /usr/local/lib/python3.11/dist-packages (from cyclic-boosting) (3.10.0)\n", - "Requirement already satisfied: numba>=0.56.4 in /usr/local/lib/python3.11/dist-packages (from cyclic-boosting) (0.60.0)\n", - "Requirement already satisfied: numexpr>=2.5.2 in /usr/local/lib/python3.11/dist-packages (from cyclic-boosting) (2.10.2)\n", - "Requirement already satisfied: numpy>=1.12.1 in /usr/local/lib/python3.11/dist-packages (from cyclic-boosting) (1.26.4)\n", - "Requirement already satisfied: pandas>=0.20.3 in /usr/local/lib/python3.11/dist-packages (from cyclic-boosting) (2.2.2)\n", - 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"Requirement already satisfied: tzdata>=2022.7 in /usr/local/lib/python3.11/dist-packages (from pandas>=0.20.3->cyclic-boosting) (2025.1)\n", - "Requirement already satisfied: joblib>=1.2.0 in /usr/local/lib/python3.11/dist-packages (from scikit-learn>=0.18.2->cyclic-boosting) (1.4.2)\n", - "Requirement already satisfied: threadpoolctl>=3.1.0 in /usr/local/lib/python3.11/dist-packages (from scikit-learn>=0.18.2->cyclic-boosting) (3.5.0)\n" - ] - } - ], + "outputs": [], "source": [ "# install the package if not avaialable\n", "# !pip install cyclic-boosting\n" diff --git a/runtime.txt b/runtime.txt index 5509089..67ebc4e 100644 --- a/runtime.txt +++ b/runtime.txt @@ -1 +1 @@ -python-3.10 +python-3.11 -- GitLab