miniproject script
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ME_2016/.ipynb_checkpoints/joblib_demo-checkpoint.ipynb
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ME_2016/.ipynb_checkpoints/joblib_demo-checkpoint.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "33f1ce1d-1a09-46d1-9304-3d02c715903f",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Benchmarking...\n",
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"Single-process execution time: 37.67 seconds\n"
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]
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},
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "e29a55948eae404da54cadb0ff8396ff",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"Running Simulations: 0%| | 0/1000 [00:00<?, ?it/s]"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Parallel execution time: 5.86 seconds\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"from scipy.integrate import odeint\n",
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"from joblib import Parallel, delayed\n",
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"import matplotlib.pyplot as plt\n",
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"import time\n",
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"from tqdm.notebook import tqdm\n",
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"from numba import jit\n",
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"\n",
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"# Accelerate the ODE system using numba\n",
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"@jit(nopython=True)\n",
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"def simple_oscillator(y, t):\n",
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" x, v = y # y[0] = position (x), y[1] = velocity (v)\n",
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" dxdt = v # dx/dt = v\n",
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" dvdt = -x # dv/dt = -x\n",
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" return [dxdt, dvdt]\n",
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"\n",
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"# Function to simulate a batch of initial conditions\n",
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"def simulate_batch(batch):\n",
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" t = np.linspace(0, 1000, 100000) # Larger time steps for benchmarking\n",
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" results = [(t, odeint(simple_oscillator, ic, t, atol=1e-9)) for ic in batch]\n",
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" return results\n",
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"\n",
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"# Function to run simulations using joblib for parallelism\n",
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"def parallel_simulations(initial_conditions_list, batch_size=2):\n",
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" # Split the initial conditions into batches to reduce overhead\n",
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" batches = [\n",
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" initial_conditions_list[i:i + batch_size]\n",
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" for i in range(0, len(initial_conditions_list), batch_size)\n",
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" ]\n",
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" \n",
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" # Run parallel simulations with joblib\n",
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" results = Parallel(n_jobs=-1)(\n",
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" delayed(simulate_batch)(batch) for batch in tqdm(batches, desc=\"Running Simulations\")\n",
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" )\n",
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" \n",
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" # Flatten the list of batches into a single list of results\n",
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" return [item for batch_result in results for item in batch_result]\n",
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"\n",
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"# Benchmarking function\n",
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"def benchmark(initial_conditions_list):\n",
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" print(\"Benchmarking...\")\n",
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"\n",
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" # Single-process execution\n",
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" start_time = time.time()\n",
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" single_process_results = [simulate_batch([ic])[0] for ic in initial_conditions_list]\n",
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" single_process_time = time.time() - start_time\n",
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" print(f\"Single-process execution time: {single_process_time:.2f} seconds\")\n",
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"\n",
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" # Parallel execution with joblib\n",
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" start_time = time.time()\n",
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" parallel_results = parallel_simulations(initial_conditions_list, batch_size=2)\n",
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" parallel_time = time.time() - start_time\n",
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" print(f\"Parallel execution time: {parallel_time:.2f} seconds\")\n",
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"\n",
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" return single_process_results, parallel_results\n",
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"\n",
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"# List of initial conditions for benchmarking\n",
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"initial_conditions_list = [\n",
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" [1.0, 0.0], # Initial position 1.0, velocity 0.0\n",
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" [0.5, 0.5], # Initial position 0.5, velocity 0.5\n",
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" [-1.0, 0.0], # Initial position -1.0, velocity 0.0\n",
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" [0.0, 1.0], # Initial position 0.0, velocity 1.0\n",
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" [2.0, -1.0] # Initial position 2.0, velocity -1.0\n",
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"] * 400 # Increase the workload for meaningful benchmarking\n",
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"\n",
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"# Run the benchmark\n",
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"single_process_results, parallel_results = benchmark(initial_conditions_list)\n",
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"\n",
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"# Plotting all results on the same plot (using the parallel results)\n",
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"plt.figure(figsize=(10, 6))\n",
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"for i, (t, solution) in enumerate(parallel_results):\n",
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" plt.plot(t, solution[:, 0], label=f'Initial Condition {i+1}')\n",
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"\n",
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"# Add labels, title, legend, and grid\n",
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"plt.xlabel('Time (t)')\n",
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"plt.ylabel('Position (x)')\n",
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"plt.title('ODE Simulations: Simple Harmonic Oscillator')\n",
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"plt.legend(loc='upper right', bbox_to_anchor=(1.15, 1))\n",
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"plt.grid(True)\n",
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"\n",
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"# Display the plot\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "367b156c-a843-4fec-9d95-5aeeb2de38c6",
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "03f1d22f-7efa-41de-9c8e-d165213172e2",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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355
ME_2016/.ipynb_checkpoints/miniproject-checkpoint.ipynb
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ME_2016/.ipynb_checkpoints/miniproject-checkpoint.ipynb
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ME_2016/joblib_demo.ipynb
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ME_2016/joblib_demo.ipynb
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355
ME_2016/miniproject.ipynb
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355
ME_2016/miniproject.ipynb
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"execution_count": 10,
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"id": "0766e4d9-1f49-4449-a35d-05de86a3580e",
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"metadata": {},
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"outputs": [
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@ -410,10 +410,10 @@
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{
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"data": {
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"text/latex": [
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"$\\displaystyle - C_{1} = 280000 - 40 C_{2}$"
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"$\\displaystyle C_{1} = 280000 - 400 C_{2}$"
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],
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"text/plain": [
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"Eq(-C_1, 280000 - 40*C_2)"
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"Eq(C_1, 280000 - 400*C_2)"
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]
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},
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"metadata": {},
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"source": [
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"C_1, C_2 = sm.symbols('C_1, C_2')\n",
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"\n",
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"left_BC = sm.Eq(C_1, h_left*(T_left - C_2/k ))\n",
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"left_BC = sm.Eq(C_1, h_left*(T_left - C_2))\n",
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"display('Left BC', left_BC)\n",
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"\n",
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"right_BC = sm.Eq(q_ppprime*x_right + C_1, h_right*(T_right + (q_ppprime*x_right**2/2/k + C_1/k*x_right + C_2)))\n",
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"execution_count": 11,
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"id": "765d2f17-7d1a-43a8-8b46-88ffed3ddaa3",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{C_1: -240714.285714286, C_2: 982.142857142858}"
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"{C_1: -164000.000000000, C_2: 1110.00000000000}"
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]
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},
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"metadata": {},
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"execution_count": 12,
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"id": "736b23d6-b2b3-43fe-bc16-5b1e5ae5c07b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle -997.420634920635$"
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"$\\displaystyle -856.777777777778$"
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],
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"text/plain": [
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"-997.420634920635"
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"-856.777777777778"
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]
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},
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"execution_count": 39,
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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"Just trying some stuff"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"id": "7af1e713-fc89-4679-99aa-f2bbacfb0c8e",
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"metadata": {},
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"outputs": [],
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"source": [
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"x = sm.symbols('x')\n",
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"T = sm.Function('T')(x)\n",
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"gov_eq = sm.Eq(0,T.diff(x)+q_ppprime)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"id": "5edad66f-d4c8-4b51-8c92-343f83f65944",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle T{\\left(x \\right)} = C_{1} - 50000000.0 x$"
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],
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"text/plain": [
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"Eq(T(x), C1 - 50000000.0*x)"
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]
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},
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"execution_count": 36,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sm.dsolve(gov_eq)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "85cf7fed-e3cd-41cf-ab69-c790f972c212",
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"id": "e819cb10-9498-4522-8b69-0f7c46e5b7d7",
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"metadata": {},
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"source": [
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"## Part B"
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": 13,
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"id": "ca0c2b96-652e-4f67-81b0-f98aecfb1707",
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"metadata": {},
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"outputs": [
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"\n",
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"=========FINAL ANSWER=========\n",
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"3C:\n",
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"At the left face: -5550 F \n",
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"At the right face:-10411 F\n",
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"At the left face: 111 F \n",
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"At the right face:-857 F\n",
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"=========FINAL ANSWER=========\n",
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"\n"
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]
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