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lecture_no
| Author | SHA1 | Date | |
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 Tiziano Zito
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165239e433 |
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@ -16,9 +16,6 @@
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Two exercises to activate the body and the mind
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Common goal of both exercises is to sort a deck of tarot cards by value
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Before starting, make yourself acquainted with the meanining and the power of the tarot cards. Carefully read [this booklet](https://aspp.school/wiki/_media/tarot-runic.pdf)
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### First experiment: human sorting
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Setup:
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- 1 volunteer to keep the time spent sorting
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@ -11,7 +11,7 @@
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- `bin(14)` ➔ `'0b1110'`
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- `np.iinfo(np.int32)` ➔ `iinfo(min=-2147483648, max=2147483647, dtype=int32)`
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- Python integers, as opposed to numpy integer types, are represented with a flexible number of bits: `sys.int_info` ➔ `bits_per_digit=30, sizeof_digit=4, default_max_str_digits=4300, str_digits_check_threshold=640`
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- they are called "long" or "sperlong" integers, because they can have arbitrary size. Low level implementation explained:
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- they are called "long" or "superlong" integers, because they can have arbitrary size. Low level implementation explained:
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- [Arpit Bhayani's blog](https://arpitbhayani.me/blogs/long-integers-python/)
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- [Artem Golubin's blog](https://rushter.com/blog/python-integer-implementation/)
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@ -37,7 +37,6 @@
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- UTF8 encoded, flexible width from 1B (byte) to 4B (bytes): 1,112,064 Unicode characters (code points)
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- ASCII: 7 bits (fits in one byte), 127 characters ➔ [ASCII table](https://upload.wikimedia.org/wikipedia/commons/2/26/ASCII_Table_%28suitable_for_printing%29.svg)
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- [visualization](https://sonarsource.github.io/utf8-visualizer/)
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- actually in Python strings (more precisely: unicode objects) are stored in different formats depending on which characters are stored for memory efficiency. Look at the gory details [here](https://docs.python.org/3.14/c-api/unicode.html) ➔ not for the faint-hearted!
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- **hexadecimal notation**:
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- base16 ➔ '0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f'
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@ -1,172 +0,0 @@
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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": "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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" y = time_series[:,::gap].copy()\n",
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" for row, ts in enumerate(y):\n",
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" for pwr in range(1,20):\n",
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" mean[row] += (ts**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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