{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-04T09:40:28.904Z",
     "iopub.status.busy": "2024-03-04T09:40:28.896Z",
     "iopub.status.idle": "2024-03-04T09:40:28.978Z",
     "shell.execute_reply": "2024-03-04T09:40:28.967Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-04T10:02:39.062Z",
     "iopub.status.busy": "2024-03-04T10:02:39.057Z",
     "iopub.status.idle": "2024-03-04T10:02:39.068Z",
     "shell.execute_reply": "2024-03-04T10:02:39.071Z"
    }
   },
   "outputs": [],
   "source": [
    "n_series = 32\n",
    "len_one_series = 5*2**20\n",
    "time_series = np.random.rand(n_series, len_one_series)\n",
    "gap = 16*2**10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-04T10:02:41.027Z",
     "iopub.status.busy": "2024-03-04T10:02:41.020Z",
     "iopub.status.idle": "2024-03-04T10:02:41.036Z",
     "shell.execute_reply": "2024-03-04T10:02:41.040Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "print(f'Size of one time series: {int(time_series[0].nbytes/2**20)} M')\n",
    "print(f'Size of collection: {int(time_series.nbytes/2**20)} M')\n",
    "print(f'Gap size: {int(gap*8/2**10)} K')\n",
    "print(f'Gapped series size: {int(time_series[0, ::gap].nbytes/2**10)} K')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-04T10:06:08.461Z",
     "iopub.status.busy": "2024-03-04T10:06:08.459Z",
     "iopub.status.idle": "2024-03-04T10:06:08.466Z",
     "shell.execute_reply": "2024-03-04T10:06:08.468Z"
    }
   },
   "outputs": [],
   "source": [
    "# compute a Taylor-like series\n",
    "def taylor(time_series, mean, gap):\n",
    "    for row, ts in enumerate(time_series):\n",
    "        for pwr in range(1,20):\n",
    "            mean[row] += (ts[::gap]**pwr).sum()\n",
    "    return mean\n",
    "       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-04T10:06:08.461Z",
     "iopub.status.busy": "2024-03-04T10:06:08.459Z",
     "iopub.status.idle": "2024-03-04T10:06:08.466Z",
     "shell.execute_reply": "2024-03-04T10:06:08.468Z"
    }
   },
   "outputs": [],
   "source": [
    "def taylor_improved(time_series, mean, gap):\n",
    "    y = time_series[:,::gap].copy()\n",
    "    for row, ts in enumerate(y):\n",
    "        for pwr in range(1,20):\n",
    "            mean[row] += (ts**pwr).sum()\n",
    "    return mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# verify that they yield the same results\n",
    "out1 = taylor(time_series, np.zeros(n_series), gap)\n",
    "out2 = taylor_improved(time_series, np.zeros(n_series), gap)\n",
    "np.testing.assert_allclose(out1, out2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-04T10:06:14.959Z",
     "iopub.status.busy": "2024-03-04T10:06:14.956Z",
     "iopub.status.idle": "2024-03-04T10:06:17.437Z",
     "shell.execute_reply": "2024-03-04T10:06:17.443Z"
    }
   },
   "outputs": [],
   "source": [
    "mean = np.zeros(n_series, dtype='float64')\n",
    "%timeit taylor(time_series, mean, gap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-04T10:06:20.056Z",
     "iopub.status.busy": "2024-03-04T10:06:20.053Z",
     "iopub.status.idle": "2024-03-04T10:06:21.695Z",
     "shell.execute_reply": "2024-03-04T10:06:21.700Z"
    }
   },
   "outputs": [],
   "source": [
    "mean = np.zeros(n_series, dtype='float64')\n",
    "%timeit taylor_improved(time_series, mean, gap)"
   ]
  }
 ],
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