miniproject script

ME_2016/.ipynb_checkpoints/joblib_demo-checkpoint.ipynb

@@ -0,0 +1,162 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "33f1ce1d-1a09-46d1-9304-3d02c715903f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Benchmarking...\n",
+      "Single-process execution time: 37.67 seconds\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "e29a55948eae404da54cadb0ff8396ff",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Running Simulations:   0%|          | 0/1000 [00:00<?, ?it/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Parallel execution time: 5.86 seconds\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from scipy.integrate import odeint\n",
+    "from joblib import Parallel, delayed\n",
+    "import matplotlib.pyplot as plt\n",
+    "import time\n",
+    "from tqdm.notebook import tqdm\n",
+    "from numba import jit\n",
+    "\n",
+    "# Accelerate the ODE system using numba\n",
+    "@jit(nopython=True)\n",
+    "def simple_oscillator(y, t):\n",
+    "    x, v = y  # y[0] = position (x), y[1] = velocity (v)\n",
+    "    dxdt = v  # dx/dt = v\n",
+    "    dvdt = -x  # dv/dt = -x\n",
+    "    return [dxdt, dvdt]\n",
+    "\n",
+    "# Function to simulate a batch of initial conditions\n",
+    "def simulate_batch(batch):\n",
+    "    t = np.linspace(0, 1000, 100000)  # Larger time steps for benchmarking\n",
+    "    results = [(t, odeint(simple_oscillator, ic, t, atol=1e-9)) for ic in batch]\n",
+    "    return results\n",
+    "\n",
+    "# Function to run simulations using joblib for parallelism\n",
+    "def parallel_simulations(initial_conditions_list, batch_size=2):\n",
+    "    # Split the initial conditions into batches to reduce overhead\n",
+    "    batches = [\n",
+    "        initial_conditions_list[i:i + batch_size]\n",
+    "        for i in range(0, len(initial_conditions_list), batch_size)\n",
+    "    ]\n",
+    "    \n",
+    "    # Run parallel simulations with joblib\n",
+    "    results = Parallel(n_jobs=-1)(\n",
+    "        delayed(simulate_batch)(batch) for batch in tqdm(batches, desc=\"Running Simulations\")\n",
+    "    )\n",
+    "    \n",
+    "    # Flatten the list of batches into a single list of results\n",
+    "    return [item for batch_result in results for item in batch_result]\n",
+    "\n",
+    "# Benchmarking function\n",
+    "def benchmark(initial_conditions_list):\n",
+    "    print(\"Benchmarking...\")\n",
+    "\n",
+    "    # Single-process execution\n",
+    "    start_time = time.time()\n",
+    "    single_process_results = [simulate_batch([ic])[0] for ic in initial_conditions_list]\n",
+    "    single_process_time = time.time() - start_time\n",
+    "    print(f\"Single-process execution time: {single_process_time:.2f} seconds\")\n",
+    "\n",
+    "    # Parallel execution with joblib\n",
+    "    start_time = time.time()\n",
+    "    parallel_results = parallel_simulations(initial_conditions_list, batch_size=2)\n",
+    "    parallel_time = time.time() - start_time\n",
+    "    print(f\"Parallel execution time: {parallel_time:.2f} seconds\")\n",
+    "\n",
+    "    return single_process_results, parallel_results\n",
+    "\n",
+    "# List of initial conditions for benchmarking\n",
+    "initial_conditions_list = [\n",
+    "    [1.0, 0.0],  # Initial position 1.0, velocity 0.0\n",
+    "    [0.5, 0.5],  # Initial position 0.5, velocity 0.5\n",
+    "    [-1.0, 0.0], # Initial position -1.0, velocity 0.0\n",
+    "    [0.0, 1.0],  # Initial position 0.0, velocity 1.0\n",
+    "    [2.0, -1.0]  # Initial position 2.0, velocity -1.0\n",
+    "] * 400  # Increase the workload for meaningful benchmarking\n",
+    "\n",
+    "# Run the benchmark\n",
+    "single_process_results, parallel_results = benchmark(initial_conditions_list)\n",
+    "\n",
+    "# Plotting all results on the same plot (using the parallel results)\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "for i, (t, solution) in enumerate(parallel_results):\n",
+    "    plt.plot(t, solution[:, 0], label=f'Initial Condition {i+1}')\n",
+    "\n",
+    "# Add labels, title, legend, and grid\n",
+    "plt.xlabel('Time (t)')\n",
+    "plt.ylabel('Position (x)')\n",
+    "plt.title('ODE Simulations: Simple Harmonic Oscillator')\n",
+    "plt.legend(loc='upper right', bbox_to_anchor=(1.15, 1))\n",
+    "plt.grid(True)\n",
+    "\n",
+    "# Display the plot\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "367b156c-a843-4fec-9d95-5aeeb2de38c6",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "03f1d22f-7efa-41de-9c8e-d165213172e2",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

NUCE_2100/HW6.ipynb

@@ -394,7 +394,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 10,
    "id": "0766e4d9-1f49-4449-a35d-05de86a3580e",
    "metadata": {},
    "outputs": [
@@ -410,10 +410,10 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle - C_{1} = 280000 - 40 C_{2}$"
+       "$\\displaystyle C_{1} = 280000 - 400 C_{2}$"
       ],
       "text/plain": [
-       "Eq(-C_1, 280000 - 40*C_2)"
+       "Eq(C_1, 280000 - 400*C_2)"
       ]
      },
      "metadata": {},
@@ -444,7 +444,7 @@
    "source": [
     "C_1, C_2 = sm.symbols('C_1, C_2')\n",
     "\n",
-    "left_BC = sm.Eq(C_1, h_left*(T_left - C_2/k ))\n",
+    "left_BC = sm.Eq(C_1, h_left*(T_left - C_2))\n",
     "display('Left BC', left_BC)\n",
     "\n",
     "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",
@@ -461,14 +461,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 11,
    "id": "765d2f17-7d1a-43a8-8b46-88ffed3ddaa3",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{C_1: -240714.285714286, C_2: 982.142857142858}"
+       "{C_1: -164000.000000000, C_2: 1110.00000000000}"
       ]
      },
      "metadata": {},
@@ -490,20 +490,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 12,
    "id": "736b23d6-b2b3-43fe-bc16-5b1e5ae5c07b",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle -997.420634920635$"
+       "$\\displaystyle -856.777777777778$"
       ],
       "text/plain": [
-       "-997.420634920635"
+       "-856.777777777778"
       ]
      },
-     "execution_count": 39,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -521,45 +521,9 @@
     "Just trying some stuff"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "id": "7af1e713-fc89-4679-99aa-f2bbacfb0c8e",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "x = sm.symbols('x')\n",
-    "T = sm.Function('T')(x)\n",
-    "gov_eq = sm.Eq(0,T.diff(x)+q_ppprime)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "id": "5edad66f-d4c8-4b51-8c92-343f83f65944",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/latex": [
-       "$\\displaystyle T{\\left(x \\right)} = C_{1} - 50000000.0 x$"
-      ],
-      "text/plain": [
-       "Eq(T(x), C1 - 50000000.0*x)"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "sm.dsolve(gov_eq)"
-   ]
-  },
   {
    "cell_type": "markdown",
-   "id": "85cf7fed-e3cd-41cf-ab69-c790f972c212",
+   "id": "e819cb10-9498-4522-8b69-0f7c46e5b7d7",
    "metadata": {},
    "source": [
     "## Part B"
@@ -575,7 +539,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 13,
    "id": "ca0c2b96-652e-4f67-81b0-f98aecfb1707",
    "metadata": {},
    "outputs": [
@@ -586,8 +550,8 @@
       "\n",
       "=========FINAL ANSWER=========\n",
       "3C:\n",
-      "At the left face: -5550 F \n",
+      "At the left face: 111 F \n",
-      "At the right face:-10411 F\n",
+      "At the right face:-857 F\n",
       "=========FINAL ANSWER=========\n",
       "\n"
      ]