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exercise-my-solution.ipynb
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241
exercise-my-solution.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": 1,
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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": 2,
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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": 3,
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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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Size of one time series: 40 M\n",
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"Size of collection: 1280 M\n",
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"Gap size: 128 K\n",
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"Gapped series size: 2 K\n"
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]
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}
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],
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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": "markdown",
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"metadata": {},
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"source": [
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"The following function implements an approximation of a power series of every `gap` value in our time series.\n",
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"\n",
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"If we define one time series of length `N` to be:\n",
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"\n",
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"$[x_0, x_1, x_2, ..., x_N]$,\n",
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"\n",
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"then the \"gapped\" series with `gap=g` is:\n",
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"\n",
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"$[x_0, x_g, x_{2g}, ..., x_{N/g}]$,\n",
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"\n",
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"where $N/g$ is the number of gaps.\n",
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"\n",
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"The approximation of the power series up to power `30` for our \"gapped\" series is defined as:\n",
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"\n",
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"$$\\mathbf{P} = \\sum_{p=0}^{30} \\sum_i x_i^{p} = \\sum_i x_i^0 + \\sum_i x_i^1 + \\sum_i x_i^2 + ... + \\sum_i x_i^{30} $$\n",
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"\n",
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"where $i \\in [0, g, 2g, ..., N/g]$"
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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": 4,
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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 an approximation of a power series for a collection of gapped timeseries\n",
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"def power(time_series, P, gap):\n",
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" for row in range(time_series.shape[0]):\n",
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" for pwr in range(30):\n",
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" P[row] += (time_series[row, ::gap]**pwr).sum()\n",
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" return P\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 `power` function?\n",
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"- Change the following `power_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": 5,
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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 power_improved(time_series, P, gap):\n",
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" y = time_series[:,::gap].copy()\n",
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" for row in range(time_series.shape[0]):\n",
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" for pwr in range(30):\n",
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" P[row] += (y[row, :]**pwr).sum()\n",
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" return P"
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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": 6,
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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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"P = np.zeros(n_series, dtype='float64')\n",
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"out1 = power(time_series, P, gap)\n",
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"P = np.zeros(n_series, dtype='float64')\n",
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"out2 = power_improved(time_series, P, 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": 7,
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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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"38.9 ms ± 492 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
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]
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}
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],
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"source": [
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"P = np.zeros(n_series, dtype='float64')\n",
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"%timeit power(time_series, P, 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": 8,
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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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"6.79 ms ± 35.2 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
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]
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}
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],
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"source": [
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"P = np.zeros(n_series, dtype='float64')\n",
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"%timeit power_improved(time_series, P, 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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"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": "3.13.5"
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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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