1277 lines
288 KiB
Plaintext
1277 lines
288 KiB
Plaintext
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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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"nbgrader": {
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"grade": false,
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"grade_id": "cell-654bd336ff003835",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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"outputs": [],
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"source": [
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"# You must run this cell, but you can ignore its contents.\n",
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"\n",
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"import hashlib\n",
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"\n",
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"def ads_hash(ty):\n",
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" \"\"\"Return a unique string for input\"\"\"\n",
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" ty_str = str(ty).encode()\n",
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" m = hashlib.sha256()\n",
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" m.update(ty_str)\n",
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" return m.hexdigest()[:10]"
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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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"nbgrader": {
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"grade": false,
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"grade_id": "cell-7f7c9f7f55486e9b",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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"source": [
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"# numpy"
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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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"nbgrader": {
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"grade": false,
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"grade_id": "cell-e630f56f923f6053",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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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": "markdown",
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"metadata": {
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-da0a17e5d1fbe62c",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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},
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"tags": []
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},
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"source": [
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"## Q1 Create a 1 dimensional numpy array named `x` with 20 elements from 0 to 19.\n",
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"\n",
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"Hint: use the `arange` function of numpy."
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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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"nbgrader": {
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"grade": false,
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"grade_id": "cell-1502b7b220c53c56",
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"locked": false,
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"schema_version": 3,
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"solution": true,
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"task": false
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},
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"tags": []
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,\n",
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" 17, 18, 19])"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"x = np.arange(20)\n",
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"x"
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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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"nbgrader": {
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"grade": true,
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"grade_id": "cell-f67a7b35435b525c",
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"locked": true,
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"points": 0,
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"schema_version": 3,
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"solution": false,
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"task": false
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},
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"tags": []
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},
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"outputs": [],
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"source": [
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"# If this runs without error, it means the answer in your previous cell was correct.\n",
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"assert ads_hash(x)=='7a150607a7'"
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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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"nbgrader": {
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"grade": false,
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"grade_id": "cell-64d2210f9a71e242",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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},
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"tags": []
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},
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"source": [
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"## Q2 Create a 1 dimensional numpy array named `x` with 20 elements from 0 to 38 with an increment of 2.\n",
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"\n",
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"Hint: use the `arange` function of numpy."
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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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"nbgrader": {
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"grade": false,
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"grade_id": "cell-cff3a5e50b06014a",
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"locked": false,
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"schema_version": 3,
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"solution": true,
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"task": false
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},
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"tags": []
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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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"[ 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38]\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"'8bc0a3b6c4'"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"x = np.arange(0, 40, 2)\n",
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"print(x)\n",
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"ads_hash(x)"
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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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"nbgrader": {
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"grade": true,
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"grade_id": "cell-64723536c462a2d1",
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"locked": true,
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"points": 1,
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"schema_version": 3,
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"solution": false,
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"task": false
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},
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"tags": []
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},
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"outputs": [],
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"source": [
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"# If this runs without error, it means the answer in your previous cell was correct.\n",
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"assert ads_hash(x)=='8bc0a3b6c4'"
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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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||
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|
"nbgrader": {
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||
|
|
"grade": false,
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||
|
|
"grade_id": "cell-f439954fdaef75da",
|
||
|
|
"locked": true,
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||
|
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"schema_version": 3,
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||
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"solution": false,
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||
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"task": false
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||
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}
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},
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"source": [
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"## Q3 Create a 2 dimensional numpy array named `x` of shape 5,6."
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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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"nbgrader": {
|
||
|
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"grade": false,
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||
|
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"grade_id": "cell-15f8e74190eecaf8",
|
||
|
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"locked": false,
|
||
|
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"schema_version": 3,
|
||
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"solution": true,
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||
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"task": false
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}
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},
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"outputs": [],
|
||
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"source": [
|
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"# Type your answer here and then run this and the following cell.\n",
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"x = np.arange(30)\n",
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"x.shape = (5,6)"
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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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||
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"nbgrader": {
|
||
|
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"grade": true,
|
||
|
|
"grade_id": "cell-38a672b790c362eb",
|
||
|
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"locked": true,
|
||
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"points": 1,
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|
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"schema_version": 3,
|
||
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"solution": false,
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"task": false
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}
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},
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"outputs": [],
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"source": [
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"# If this runs without error, it means the answer in your previous cell was correct.\n",
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"assert ads_hash(x.shape)=='6510380315'"
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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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"nbgrader": {
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||
|
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"grade": false,
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||
|
|
"grade_id": "cell-681527231f43677f",
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||
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"locked": true,
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||
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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"source": [
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"## Q4 Consider the first 100 integers starting with 0. What is their mean value? Put this in a variable `mean100`."
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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": 9,
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"metadata": {
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"nbgrader": {
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||
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"grade": false,
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||
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"grade_id": "cell-34f66fe8d8b001fb",
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"locked": false,
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||
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"schema_version": 3,
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||
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"solution": true,
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"task": false
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}
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},
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"outputs": [],
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"source": [
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"mean100 = np.mean(np.arange(100))"
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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": 10,
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"metadata": {
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"nbgrader": {
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||
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"grade": true,
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||
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"grade_id": "cell-9ef246cf9714c370",
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||
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"locked": true,
|
||
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"points": 1,
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||
|
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"schema_version": 3,
|
||
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"solution": false,
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||
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"task": false
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||
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}
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},
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"outputs": [],
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"source": [
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"# If this runs without error, it means the answer in your previous cell was correct.\n",
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"assert ads_hash(round(mean100*1000))=='bc8d4a4d1e'"
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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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||
|
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"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-b4c0d9ce0a0e3ec7",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
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"task": false
|
||
|
|
}
|
||
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},
|
||
|
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"source": [
|
||
|
|
"## Q5 Create an array named `x` with every 4th value of the first 100000 integers."
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||
|
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]
|
||
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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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||
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"execution_count": 11,
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||
|
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"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-6b4ee0992aa506c5",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
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}
|
||
|
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},
|
||
|
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"outputs": [
|
||
|
|
{
|
||
|
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"data": {
|
||
|
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"text/plain": [
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||
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"array([ 0, 4, 8, ..., 99988, 99992, 99996])"
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]
|
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},
|
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"execution_count": 11,
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||
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"metadata": {},
|
||
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"output_type": "execute_result"
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||
|
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}
|
||
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],
|
||
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"source": [
|
||
|
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"x = np.arange(100000)[::4]\n",
|
||
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"x"
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]
|
||
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},
|
||
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{
|
||
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"cell_type": "code",
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||
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"execution_count": 12,
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||
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"metadata": {
|
||
|
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"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-6833bfed10c7430c",
|
||
|
|
"locked": true,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
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"source": [
|
||
|
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"# If this runs without error, it means the answer in your previous cell was correct.\n",
|
||
|
|
"assert ads_hash(len(x))=='0812a4ef4e' \n",
|
||
|
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"assert ads_hash(x)=='17e101b2ef'"
|
||
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]
|
||
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},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-34c0aed2a2c992a4",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
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"source": [
|
||
|
|
"## Q6 set the shape of `x` to be (5, 5000)"
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||
|
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]
|
||
|
|
},
|
||
|
|
{
|
||
|
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"cell_type": "code",
|
||
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"execution_count": 13,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e07f245d339e6328",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"x.shape = (5, 5000)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 14,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-190e11601c41f920",
|
||
|
|
"locked": true,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# If this runs without error, it means the answer in your previous cell was correct.\n",
|
||
|
|
"assert ads_hash(len(x))=='ef2d127de3' \n",
|
||
|
|
"assert ads_hash(x)=='3331e0302b'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-1802e3087f27de21",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Q7 Create the variable `y` from the first 3 rows and the first 8 columns of `x`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-ef33bd87060e2253",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"array([[ 0, 4, 8, 12, 16, 20, 24, 28],\n",
|
||
|
|
" [20000, 20004, 20008, 20012, 20016, 20020, 20024, 20028],\n",
|
||
|
|
" [40000, 40004, 40008, 40012, 40016, 40020, 40024, 40028]])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"y = x[:3,:8]\n",
|
||
|
|
"y"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 16,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-38599e5840dfe50f",
|
||
|
|
"locked": true,
|
||
|
|
"points": 0,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# If this runs without error, it means the answer in your previous cell was correct.\n",
|
||
|
|
"assert ads_hash(len(y))=='4e07408562' \n",
|
||
|
|
"assert ads_hash(y)=='b39d640ca0'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-c760334b1b549d83",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Plotting numpy arrays with matplotlib\n",
|
||
|
|
"\n",
|
||
|
|
"Let's start plotting numpy arrays. The `plot()` function in matplotlib's `pyplot` module works differently depending on the number of arguments it was called with. Like your `get_2D_coordinates()` function above, if only one argument is used, it is treated as the `y` coordinates. The `x` coordinates are the integers starting with `0`. If two arguments are used, they are treated as the `x` and `y` coordinates.\n",
|
||
|
|
"\n",
|
||
|
|
"Here we are also going to label our axes to keep track of what we are plotting. We will use the `plt.xlabel()` and `plt.ylabel()` functions."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 17,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-022fd8735aa958ba",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import matplotlib.pyplot as plt"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-efcd917dafccd54c",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"We are going to generate some \"toy\" (artificial, false, fake, made-up) positions of a bee over time. First, we need the times where we have tracking data. We are going to track the bee for 10 seconds. Over these 10 seconds, we have 100 measurements."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 18,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-3acd919556155f8f",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"time_values = np.linspace(0,10,100)\n",
|
||
|
|
"plt.plot(time_values)\n",
|
||
|
|
"plt.ylabel('time (seconds)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-54aa9b963835b42f",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Now we will get the `y` coordinate of the bee over these 10 seconds. Instead of real data, we generate toy data by using the `np.sin()` function. We take the sine of the time value as the `y` coordinate of the bee."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 19,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-d8eefc7a088ab564",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"y = np.sin(time_values)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-44143dbd92ac071d",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Now let's plot the `y` coordinate of the bee over time."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 20,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e1a3bbf4c1b1618c",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(time_values,y)\n",
|
||
|
|
"plt.xlabel('time (seconds)');\n",
|
||
|
|
"plt.ylabel('y (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-de601837bd41103a",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"So our bee was oscillating in `y` over time.\n",
|
||
|
|
"\n",
|
||
|
|
"In addition to a `y` coordinate, our tracking system also gives us `x` coordinates. Let's make some toy data for this, too."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 21,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-9a46e6754a91f190",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"x = 0.5*np.sin(time_values*3.2)+1.1"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 22,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-153b385adbe59ec2",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(time_values,x)\n",
|
||
|
|
"plt.xlabel('time (seconds)');\n",
|
||
|
|
"plt.ylabel('x (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-d5670c1510ca17ff",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"So the bee was also oscillating in `x`, and even faster than in `y`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-65c1964e62b88a11",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Storing multiple dimensions data in single array\n",
|
||
|
|
"\n",
|
||
|
|
"We might want to store our coordinates in a single multi-dimensional numpy array where the columns are time and the rows are the different coordinates (`x`, and `y`).\n",
|
||
|
|
"\n",
|
||
|
|
"```\n",
|
||
|
|
"x0, x1, x2, ..., xn\n",
|
||
|
|
"y0, y1, y2, ..., yn\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"We can use the `np.vstack()` (\"vertical stack\") function for this. It will return a new array whose rows are the given in its input argument."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 23,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-6e94a8443b27f2bf",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"bee_coords = np.vstack((x,y))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-de3884dcd3459ef6",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"By doing these, we can keep the different measurements together. Of course, we can still plot just a single dimension. Here is `x` over time again. In this case, the x axis is simply the index of the array passed to `plot()`:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 24,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-5f3a313fa88f20be",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAGdCAYAAADuR1K7AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAAB970lEQVR4nO29eZhcVZ3//76191K9d7rTSWdjCzshEQRUggoaMI7KCA5qFJh5ZFAWo84YmR84yhiXERlHBb7KMjMiMiwy6jBoWMOmkEDLEiCBbJ2kt+qturu61nt/f9w6995Ob7XcW/eccz+v58nzQHVV9+nT557zPp9V0TRNA0EQBEEQhCT43B4AQRAEQRCEnZC4IQiCIAhCKkjcEARBEAQhFSRuCIIgCIKQChI3BEEQBEFIBYkbgiAIgiCkgsQNQRAEQRBSQeKGIAiCIAipCLg9gEqjqioOHTqEaDQKRVHcHg5BEARBEAWgaRrGxsbQ0dEBn29u24znxM2hQ4fQ2dnp9jAIgiAIgiiB7u5uLF68eM73eE7cRKNRAPrk1NXVuTwagiAIgiAKIR6Po7Oz0zjH58Jz4oa5ourq6kjcEARBEIRgFBJSQgHFBEEQBEFIBYkbgiAIgiCkgsQNQRAEQRBSQeKGIAiCIAipIHFDEARBEIRUkLghCIIgCEIqSNwQBEEQBCEVJG4IgiAIgpAKEjcEQRAEQUiFq+Jm69atWL9+PTo6OqAoCh566KF5P5NKpXDddddh6dKlCIfDOOKII3DHHXc4P1iCIAiCIITA1fYLExMTOPnkk3HppZfiwgsvLOgzF110Efr6+nD77bfjyCOPRH9/P7LZrMMjJQiCIAhCFFwVN+vWrcO6desKfv8jjzyCp556Crt370ZTUxMAYNmyZQ6NjiAIgiAIEREq5ua3v/0t1qxZg+9///tYtGgRjj76aHz1q1/F5OTkrJ9JpVKIx+NT/olGMpPDL57ejR2HxBs7QTA0TcN4iqysTvDEm/145cCI28MgCG4QStzs3r0bzzzzDF577TX85je/wc0334z7778fX/ziF2f9zObNm1FfX2/86+zsrOCI7eFf/vcN3Pi/b+CLv3oJqqq5PRyp+PFju3DOvz6JJ9/qd3soUpNIZ/F3/7kNJ37zD3j+nUG3hyMVrx0cxaV3vYi/vvV5EjgOk1M1bN05gNcOjro9FGIehBI3qqpCURTcfffdOO2003D++efjpptuwl133TWr9WbTpk0YHR01/nV3d1d41OXxh9d78V9/2gcA2BObwHN0MNhGMpPDbU+9gz2xCVx614v40ZadyJF4tJ3hiTQ+/Ys/49E3+qFpwK9e2O/2kKTinvx8prMqvvBf2zEwlnJ5RPIRT2bwi6d34+wfPIENd7yAi257HvFkxu1hEXMglLhZuHAhFi1ahPr6euO1Y489Fpqm4cCBAzN+JhwOo66ubso/UTg0Mol/uP8VAEBzTQgA8Mu80CHKZ+vOAUykcwj5fdA04N8e24VL73oRQxNpt4cmDYdGJvHJ257Hy/tHUBX0AwAe3dGHRJrcU3Ywmc7ht12HAACN1UH0jCbxxbtfQianujwyORhPZfHPv3sdZ25+HDf+7xs4MKxfohPpHJ7eGXN5dMRcCCVuzjrrLBw6dAjj4+PGazt37oTP58PixYtdHJn95FQN197bhdHJDE5aXI//uOw0AMCWN/rQF0+6PDo5+L/XegEAn3n3UvzwkycjEvRh684BrP/3Z8jsbAO7+sZw4S3P4e3+cSysj+B/vnQWljZXYzKTw6NvkBvQDh5+tQdjqSw6m6rw3184A7XhAF7YO4Rv/36H20OTgu/935u489m9GE9lcdSCWmz+xInYcMZSAMBjb/S5PDpiLlwVN+Pj4+jq6kJXVxcAYM+ePejq6sL+/bqZddOmTdiwYYPx/ksuuQTNzc249NJLsWPHDmzduhVf+9rXcNlll6GqqsqNX8ExfvrE23hhzxBqQn78+FOrcMKierxrWSNyqoZfvyCWa41HUtkcHt2hb04XnNSOC1cvxm+uPAvLmqtxcGQSG/+7y90BCk5sPIVP3vY8ekaTOKK1Bg/8/Zk4ui2K9Sd1AAB+95dDLo9QDu59Ud8LLl7TiaPaorj54lMAAP/5/D7c+yK5/8pl664BAMC3P3YC/vjl9+FvTluC809cCAB44q1+cmNzjKviZtu2bVi1ahVWrVoFANi4cSNWrVqF66+/HgDQ09NjCB0AqK2txZYtWzAyMoI1a9bg05/+NNavX48f//jHrozfKbbtHcK/PbYLgP5QLWupAaBbGADdx54ls3NZPLMrhrFUFu11EazqbAQAHLuwDvf//ZkAgJ1944iNU+xCqTz11gBGEhksb6nB/VeciY4G/fKx/uQO4+ujkxSzUA67B8bxwt4h+BTgr1friRIfPK4NX/7g0QCA/++h18kCWQZ98ST2DSagKMBfnaIXmgWA1UsbURcJYDiRQVf3sMujJGbDVXGzdu1aaJo27d9dd90FALjrrrvw5JNPTvnMypUrsWXLFiQSCXR3d+OHP/yhdFab6//ndeRUDR9ftQifONV0t334hHY014TQG0/isTfJrF8O//tqDwB9Tn0+xXi9pTaMIxfUAgC69o+4MTQp6OoeAQB8YOUCNObjxQDgmPYojmmLIp1T8YfXe10anRzcu0232qw9ZgHa6yPG61e9/0isPaYV6ZyKB16aORaRmJ8X9gwBAI5bWIe6SNB4Pej3Ye0xCwAAj5F7lVuEirnxAmPJDHb06PVsvnH+sVO+Fg748ck1+g2NAotLJ51VsSXvkmImZiunLmkAALy0n25lpfJy/ka7aknjtK+tP1mfc3JNlU4mp+KB7QcBABetmVrewudTDPcfWW5K58W9urh517KmaV/7wLEkbniHxA1nvJ4v1NdRH0FrNDzt658+fQkUBXh6Vwx7YxOVHp4UPPt2DGPJLFqjYaxeOv3wPTV/IJO4KY3JdA5v9owBAE7JC0UrH8kfvM+9M0iuvxJ5/M1+xMZTaKkNGQetlZMW6xmlrx2MU1xIiTDLzWnLp4ubs49uhd+n4K2+MXQPJSo9NKIASNxwBrtpnbCofsavdzZV4+yjWwFQvZBSeTjvklp3Qjv8FpcU49S84PlL9yjFNpXAa4dGkVU1tEbD6LC4SxjLWmpw0uJ65FQN/5f/WxDF8d/5QOILT12MoH/6Nr6itRbVIT8mMzm8MzA+7evE3IxOZvBWny7QZ7LcNFSHjIvRE1QAlEtI3HDGfOIGAD5zuh5YfN+2biQzuYqMSxYyORV/zLuk1p0w3SUFAEe21iIaDmAyk8ObvWOVHJ4UsFilVZ0NRhDm4Xz0ZJY1ReKmWHpHk8aBetG7Zq647vcpOKFD30NeOUCuqWLZvm8ImgYsb6mZ0YIO6PFkAKisAaeQuOGMV/Pi5sQ5xM05Kxegoz6C4UQGT++iQlLF8Nw7gxidzKClNjSjuRnQYxaYO+Vlck0VDQsmnsklxbjgJF1YvrB3CD2js/eGI6Zz//ZuqBrwrmWNOKK1dtb3nWi4pkjcFMuf97B4m+luawZzB/7pnUFMUM807iBxwxETqSx25+No5rLc+H0K3r2iGQDwZg810yyGh1/RLQUfOn5mlxRjlRF3M1KJYUkFE4QsxX4mFtZX4bS8uf/3ZL0piq35C401k3ImWNwN9ZsqnheNeJvmWd9zRGstljZXI51T8czbdMnkDRI3HLGjJw5NA9rqwrOaQhlHtUUBALv6yZ9eKJmcij/s0NOPZ8qSskIZU6XRF0/i0GgSPsU8XGfDyJp6hbKmiuHt/DM/l3XX+vXXD8UpdqwIkpmcYUE/bYZ4G4aiKHj/SpY1RdWKeYPEDUe8emB+lxTj6DbdHL2zj2JCCuXFvUMYSWTQVBPC6bO4pBjM6rBvMEEZPUXwct7SdXRbFDXhwJzvPfe4dgC6K5ZixwpjcDyFoYk0FAVzuqQAYFlzDaLhAFJZlS5BRfDy/hFkchra6sLobJq7htoHVrYBAB5/cwAqZaVxBYkbjnjt0PzBxIyjFuiWm90DE3QrK5Ad+TT7d69oQmCGDBMr9dVBo5jfy+S
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(bee_coords[0])\n",
|
||
|
|
"plt.ylabel('x (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-765b4dd8839b4076",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Of course, we can also plot the time value as the x axis and label it correctly:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 25,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-b2b1ea1720798043",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(time_values, bee_coords[0])\n",
|
||
|
|
"plt.xlabel('time (seconds)');\n",
|
||
|
|
"plt.ylabel('x (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-c92b5b7235df5958",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"If `x` and `y` are horizontal positions, we can plot a \"top view\" of the bee position by plotting x against y:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 26,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-8a08ee9348762caf",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(bee_coords[0], bee_coords[1])\n",
|
||
|
|
"plt.xlabel('x (meters)')\n",
|
||
|
|
"plt.ylabel('y (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e2889206cd341445",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Let's now calculate how far the bee is in any moment in time from a particular location. Remember the distance function we made in lecture:\n",
|
||
|
|
"\n",
|
||
|
|
"```python\n",
|
||
|
|
"def compute_dist(a,b):\n",
|
||
|
|
" \"\"\"compute distance between two points, `a` and `b`\n",
|
||
|
|
" \n",
|
||
|
|
" `a` and `b` are each 2D sequences representing the coordinates of the point.\"\"\"\n",
|
||
|
|
" dx = b[0] - a[0]\n",
|
||
|
|
" dy = b[1] - a[1]\n",
|
||
|
|
" return np.sqrt( dx**2 + dy**2 )\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"We wrote this function with the idea that `a` and `b` are each a 2D point. With `a = (xa, ya)` and `b = (xb, yb)`.\n",
|
||
|
|
"\n",
|
||
|
|
"Now we want a a function which returns the distance between a single input point `a` with coordinates `(xa, ya)` and each and every point in an array `bee_coords` which has shape `(2, n)`. So column `i` of `bee_coords` is thus a coordinate `(xi, yi)`.\n",
|
||
|
|
"\n",
|
||
|
|
"Let's build up to this function piece-by-piece.\n",
|
||
|
|
"\n",
|
||
|
|
"## Q8\n",
|
||
|
|
"\n",
|
||
|
|
"First write a function called `compute_dx_squared` with the signature:\n",
|
||
|
|
"\n",
|
||
|
|
"```python\n",
|
||
|
|
"def compute_dx_squared(a,b):\n",
|
||
|
|
" \"\"\"return the x distance squared between `a` and all points in `b`.\n",
|
||
|
|
" \n",
|
||
|
|
" `a` is a length 2 sequence with coordinates `(xa, ya)` and `b` is a numpy array of shape `(2, n)`.\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"This function returns the squared `x` distance between point `a` (a length 2 sequence of the `x`,`y` coordinates of point `a`) and each coordinate in the 2D array `b` with shape `(2,n)`. Thus, for `a=[1.0,2.1]` and `b=np.array([[1,2,3],[4,5,6]])`, this will return `np.array([0., 1., 4.])`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 27,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-68e7d25afb2f1765",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def compute_dx_squared(a, b):\n",
|
||
|
|
" dx = b[0] - a[0]\n",
|
||
|
|
" return dx**2"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 28,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-917fe5138adc3d85",
|
||
|
|
"locked": true,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# If this runs without error, it means the answer in your previous cell was correct.\n",
|
||
|
|
"assert ads_hash(compute_dx_squared([1.0,2.1],np.array([[1,2,3],[4,5,6]])))=='1bacf727ce'\n",
|
||
|
|
"assert ads_hash(compute_dx_squared([1.0,2.1],np.array([[1,2,3,4.2],[4,5,6,8.2]])))=='c9c0596224'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-18f7f59d96101f0c",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Q9\n",
|
||
|
|
"\n",
|
||
|
|
"Now write a function called `compute_dy_squared` with the signature:\n",
|
||
|
|
"\n",
|
||
|
|
"```python\n",
|
||
|
|
"def compute_dy_squared(a,b):\n",
|
||
|
|
" \"\"\"return the y distance squared between `a` and all points in `b`.\n",
|
||
|
|
" \n",
|
||
|
|
" `a` is a length 2 sequence with coordinates `(xa, ya)` and `b` is a numpy array of shape `(2, n)`.\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"This function returns the squared `y` distance between point `a` (a length 2 sequence of the `x`,`y` coordinates of point `a`) and each coordinate in the 2D array `b` with shape `(2,n)`. Thus, for `a=[1.0,2.1]` and `b=np.array([[1,2,3],[4,5,6]])`, this will return `array([ 3.61, 8.41, 15.21])`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 29,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e74d9319eda293c6",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def compute_dy_squared(a, b):\n",
|
||
|
|
" dy = b[1] - a[1]\n",
|
||
|
|
" return dy**2"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 30,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-52b68c1bd8f83a48",
|
||
|
|
"locked": true,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# If this runs without error, it means the answer in your previous cell was correct.\n",
|
||
|
|
"assert ads_hash(compute_dy_squared([1.0, 2.1], np.array([[1,2,3],[4,5,6]])))=='759d96c1e4'\n",
|
||
|
|
"assert ads_hash(compute_dy_squared([1.0, 2.1], np.array([[1,2,3,1.2],[4,5,6,-3]])))=='cb574f3c8e'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-3360812bc0c687c5",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Q10\n",
|
||
|
|
"\n",
|
||
|
|
"Now write a function called `compute_distance` with the signature:\n",
|
||
|
|
"\n",
|
||
|
|
"```python\n",
|
||
|
|
"def compute_distance(a,b):\n",
|
||
|
|
" \"\"\"return the distance between `a` and all points in `b`.\n",
|
||
|
|
" \n",
|
||
|
|
" `a` is a length 2 sequence with coordinates `(xa, ya)` and `b` is a numpy array of shape `(2, n)`.\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"This function returns the distance between point `a` (a length 2 sequence of the `x`,`y` coordinates of point `a`) and each coordinate in the 2D array `b` with shape `(2,n)`. Thus, for `a=[1.0,2.1]` and `b=np.array([[1,2,3],[4,5,6]])`, this will return `array([1.9 , 3.06757233, 4.3829214 ])`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 31,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-cbbcbdf110a030b2",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def compute_distance(a, b):\n",
|
||
|
|
" dx = b[0] - a[0]\n",
|
||
|
|
" dy = b[1] - a[1]\n",
|
||
|
|
" return np.sqrt(dx**2 + dy**2)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 32,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-eb44de204d241fa6",
|
||
|
|
"locked": true,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# If this runs without error, it means the answer in your previous cell was correct.\n",
|
||
|
|
"assert ads_hash(compute_distance([1.0, 2.1], np.array([[1,2,3],[4,5,6]])))=='1e2fc6c5fd'\n",
|
||
|
|
"assert ads_hash(compute_distance([1.0, 2.1], np.array([[1,2,3,10.1],[4,5,6,-2.2]])))=='b7ef5a80ae'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-b084804c3c32a977",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Q11\n",
|
||
|
|
"\n",
|
||
|
|
"Now let's imagine you upgraded your tracking system to work in 3 dimensions and now you collect data in `x`, `y` and `z`. Write a function called `compute_distance_3d` with the signature:\n",
|
||
|
|
"\n",
|
||
|
|
"```python\n",
|
||
|
|
"def compute_distance_3d(a,b):\n",
|
||
|
|
" \"\"\"return the distance between `a` and all points in `b`.\n",
|
||
|
|
" \n",
|
||
|
|
" `a` is a length 3 sequence with coordinates `(xa, ya, za)` and `b` is a numpy array of shape `(3, n)`.\n",
|
||
|
|
" \"\"\"\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"This function returns the distance between point `a` (a length 3 sequence of the `x`,`y`,`z` coordinates of point `a`) and each coordinate in the 2D array `b` with shape `(3,n)`. Thus, for `a=[1.0,2.1,0.0]` and `b=np.array([[1,2,3],[4,5,6],[7,8,9]])`, this will return `np.array([ 7.25327512, 8.56796359, 10.01049449])`.\n",
|
||
|
|
"\n",
|
||
|
|
"Remember that the formula for distance in 3D is:\n",
|
||
|
|
"\n",
|
||
|
|
"```\n",
|
||
|
|
"distance = sqrt( dx**2 + dy**2 + dz**2 )\n",
|
||
|
|
"```\n",
|
||
|
|
"\n",
|
||
|
|
"where `dx` is the distance along the `x` direction, `dy` is the distance along the `y` direction, and `dz` is the distance along the `z` direction, "
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 33,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-d3cd40a661182621",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def compute_distance_3d(a, b):\n",
|
||
|
|
" dx = b[0] - a[0]\n",
|
||
|
|
" dy = b[1] - a[1]\n",
|
||
|
|
" dz = b[2] - a[2]\n",
|
||
|
|
" return np.sqrt(dx**2 + dy**2 + dz**2)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 34,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-f0538c2e9972a4ba",
|
||
|
|
"locked": true,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# If this runs without error, it means the answer in your previous cell was correct.\n",
|
||
|
|
"assert ads_hash(compute_distance_3d([1.0,2.1,0.0], np.array([[1,2,3],[4,5,6],[7,8,9]])))=='6f84b17de0'\n",
|
||
|
|
"assert ads_hash(compute_distance_3d([1.0,2.1,0.1], np.array([[1,2,3,0.0],[4,5,6,1.0],[7,8,9.2,0.0]])))=='0b9c9c17b1'"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"celltoolbar": "Create Assignment",
|
||
|
|
"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": "3.11.10"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|