add final exercise
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README.md
12
README.md
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@ -72,9 +72,17 @@ Setup:
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- … unless of course you plan to mostly loop *across* time series :)
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- watch out when migrating code from MATLAB® or to `pandas.DataFrame` ➔ they store data in memory using the opposite convention, the column-major order!!!
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Notes on the [Python benchmark](benchmark_python/):
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## A final exercise to put it all together
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- fork this repo to your account and clone your fork on the laptop
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- create a branch `ex` and switch to it
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- work on the [exercise](exercise.ipynb)
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- push your solution to yuor fork and create a Pull Request to this repo
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- while running it attached to one core on my laptop, the core was running under a constant load of 100% (almost completely user-time) and at a fixed frequency of 3.8 GHz, where the theoretical max would be 5.2 GHz
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## Notes on the benchmarks
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- while running the benchmarks attached to one core on my laptop, the core was running under a constant load of 100% (almost completely user-time) and at a fixed frequency of 3.8 GHz, where the theoretical max would be 5.2 GHz
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➔ the CPU does not "starve" because it scales its speed down to match the memory throughput? Or I am misinterpreting this? This problem which at first sight should be perfectly memory-bound, becomes CPU-bound, or actually, exactly balanced? From the [Intel documentation](https://lenovopress.lenovo.com/lp1836-tuning-uefi-settings-4th-gen-intel-xeon-scalable-processor):
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> **Energy Efficient Turbo**
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181
exercise.ipynb
Normal file
181
exercise.ipynb
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@ -0,0 +1,181 @@
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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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"metadata": {
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"execution": {
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"iopub.execute_input": "2024-03-04T09:40:28.904Z",
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"iopub.status.busy": "2024-03-04T09:40:28.896Z",
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"iopub.status.idle": "2024-03-04T09:40:28.978Z",
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"shell.execute_reply": "2024-03-04T09:40:28.967Z"
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np"
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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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"metadata": {
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"execution": {
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"iopub.execute_input": "2024-03-04T10:02:39.062Z",
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"iopub.status.busy": "2024-03-04T10:02:39.057Z",
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"iopub.status.idle": "2024-03-04T10:02:39.068Z",
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"shell.execute_reply": "2024-03-04T10:02:39.071Z"
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}
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},
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"outputs": [],
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"source": [
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"n_series = 32\n",
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"len_one_series = 5*2**20\n",
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"time_series = np.random.rand(n_series, len_one_series)\n",
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"gap = 16*2**10"
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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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"metadata": {
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"execution": {
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"iopub.execute_input": "2024-03-04T10:02:41.027Z",
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"iopub.status.busy": "2024-03-04T10:02:41.020Z",
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"iopub.status.idle": "2024-03-04T10:02:41.036Z",
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"shell.execute_reply": "2024-03-04T10:02:41.040Z"
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},
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"scrolled": true
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},
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"outputs": [],
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"source": [
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"print(f'Size of one time series: {int(time_series[0].nbytes/2**20)} M')\n",
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"print(f'Size of collection: {int(time_series.nbytes/2**20)} M')\n",
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"print(f'Gap size: {int(gap*8/2**10)} K')\n",
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"print(f'Gapped series size: {int(time_series[0, ::gap].nbytes/2**10)} K')"
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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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"metadata": {
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"execution": {
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"iopub.execute_input": "2024-03-04T10:06:08.461Z",
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"iopub.status.busy": "2024-03-04T10:06:08.459Z",
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"iopub.status.idle": "2024-03-04T10:06:08.466Z",
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"shell.execute_reply": "2024-03-04T10:06:08.468Z"
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}
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},
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"outputs": [],
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"source": [
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"# compute a Taylor-like series\n",
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"def taylor(time_series, mean, gap):\n",
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" for row, ts in enumerate(time_series):\n",
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" for pwr in range(1,20):\n",
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" mean[row] += (ts[::gap]**pwr).sum()\n",
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" return mean\n",
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" "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Challenge\n",
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"- Can you improve on the above implementation of the `taylor` function?\n",
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"- Change the following `taylor_improved` function and see what you can do\n",
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"- **Remember**: you can't change any other cell in this notebook!"
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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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"metadata": {
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"execution": {
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"iopub.execute_input": "2024-03-04T10:06:08.461Z",
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"iopub.status.busy": "2024-03-04T10:06:08.459Z",
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"iopub.status.idle": "2024-03-04T10:06:08.466Z",
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"shell.execute_reply": "2024-03-04T10:06:08.468Z"
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}
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},
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"outputs": [],
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"source": [
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"def taylor_improved(time_series, mean, gap):\n",
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" for row, ts in enumerate(time_series):\n",
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" for pwr in range(1,20):\n",
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" mean[row] += (ts[::gap]**pwr).sum()\n",
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" return mean"
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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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"metadata": {},
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"outputs": [],
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"source": [
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"# verify that they yield the same results\n",
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"out1 = taylor(time_series, np.zeros(n_series), gap)\n",
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"out2 = taylor_improved(time_series, np.zeros(n_series), gap)\n",
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"np.testing.assert_allclose(out1, out2)"
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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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"metadata": {
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"execution": {
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"iopub.execute_input": "2024-03-04T10:06:14.959Z",
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"iopub.status.busy": "2024-03-04T10:06:14.956Z",
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"iopub.status.idle": "2024-03-04T10:06:17.437Z",
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"shell.execute_reply": "2024-03-04T10:06:17.443Z"
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}
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},
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"outputs": [],
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"source": [
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"mean = np.zeros(n_series, dtype='float64')\n",
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"%timeit taylor(time_series, mean, gap)"
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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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"metadata": {
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"execution": {
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"iopub.execute_input": "2024-03-04T10:06:20.056Z",
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"iopub.status.busy": "2024-03-04T10:06:20.053Z",
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"iopub.status.idle": "2024-03-04T10:06:21.695Z",
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"shell.execute_reply": "2024-03-04T10:06:21.700Z"
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}
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},
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"outputs": [],
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"source": [
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"mean = np.zeros(n_series, dtype='float64')\n",
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"%timeit taylor_improved(time_series, mean, gap)"
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]
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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": "3.12.5"
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},
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"nteract": {
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"version": "0.28.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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