598 lines
130 KiB
Plaintext
598 lines
130 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-e894ec2378fa46eb",
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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": "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-ada87b3b188b2d39",
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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 also run this cell.\n",
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"\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt"
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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-d7462f8b0f718bef",
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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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"# Exercise - Optimization first steps\n",
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"\n",
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"We are going to take our first steps towards optimization by returning to a bumblebee example.\n",
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"\n",
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"We are going to define the positions of a flower and the flight path of a bumblebee."
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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-78cb75cddd4fc5ef",
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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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"flower = np.array([7.5, 10.3])"
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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": false,
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"grade_id": "cell-ab9736432799913b",
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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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"def make_bee_track(t):\n",
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" pos0 = (-10,3)\n",
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" velocity = (4.0, 0.2)\n",
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" pos_x = pos0[0] + t*velocity[0]\n",
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" pos_y = pos0[1] + t*velocity[1]\n",
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" return np.array([pos_x,pos_y])\n",
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"\n",
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"t = np.linspace(0,15,20)\n",
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"bee_track = make_bee_track(t)"
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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-08928dcd585933a7",
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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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"Here we plot these positions."
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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-4b58d56276437c3a",
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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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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"fig, ax = plt.subplots(nrows=1, ncols=1)\n",
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"ax.plot( [flower[0]], [flower[1]], 'or', label='flower' )\n",
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"ax.plot( bee_track[0], bee_track[1], '.-k', label='bee')\n",
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"ax.axis('equal')\n",
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"ax.legend();"
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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-701acd6a5b4a9581",
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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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"## Q1 Draw a figure as above with, additionally, a blue line between each point on `bee_track` and `flower`.\n",
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"\n",
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"When complete, your figure should look like this:\n",
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"\n",
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"<img src=\"data:image/png;base64,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
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"Hint, draw the flower first. Then, make a for loop which steps through each position of the bee. Inside the for loop, draw a line segment between the bee and the flower."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 6,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-43f8774b1a82b15b",
|
||
|
|
"locked": false,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Your code here. Check it is correct by comparing your figure with the above.\n",
|
||
|
|
"fig, ax = plt.subplots(nrows=1, ncols=1)\n",
|
||
|
|
"ax.plot( [flower[0]], [flower[1]], 'or', label='flower' )\n",
|
||
|
|
"ax.plot( bee_track[0], bee_track[1], '.-k', label='bee')\n",
|
||
|
|
"for i in range(bee_track.shape[1]):\n",
|
||
|
|
" bee_pos = bee_track[:,i]\n",
|
||
|
|
" ax.plot( [flower[0], bee_pos[0]], [flower[1], bee_pos[1]], 'b-' )\n",
|
||
|
|
"ax.axis('equal')\n",
|
||
|
|
"ax.legend();"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-45a057824a59090e",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Q2 write a function called `my_distance` which takes two arguments, each of which is a length 2 sequence of `x`, `y` position and returns the Euclidean distance between these points."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 7,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-9d86e35ff582bf8f",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def my_distance(a,b):\n",
|
||
|
|
" a = np.array(a)\n",
|
||
|
|
" b = np.array(b)\n",
|
||
|
|
" return np.sqrt(np.sum((a-b)**2))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 8,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-d96cb3c1a49758db",
|
||
|
|
"locked": true,
|
||
|
|
"points": 0,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"assert my_distance((0,0),(3,4)) == 5\n",
|
||
|
|
"assert my_distance((3,4), (0,0)) == 5\n",
|
||
|
|
"assert my_distance((13,14), (10,10)) == 5\n",
|
||
|
|
"assert my_distance((10,10), (13,14)) == 5"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-9426c238469156ae",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Q3 compute the distance between each point on `bee_track` and `flower`. Put the results in a 1D numpy array called `distance`.\n",
|
||
|
|
"\n",
|
||
|
|
"Hint: recall the function you wrote in the \"numpy basics\" exercise called `compute_distance`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 9,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-bf78a3429e48b28d",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"array([18.96154002, 16.02203642, 13.18581669, 10.53661864, 8.256474 ,\n",
|
||
|
|
" 6.73148224, 6.5154281 , 7.71901634, 9.83412849, 12.40287921,\n",
|
||
|
|
" 15.19694713, 18.11235632, 21.09886634, 24.13009179, 27.19108233,\n",
|
||
|
|
" 30.27281036, 33.36953095, 36.47742595, 39.59386407, 42.71697555])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"distance = np.zeros(bee_track.shape[1])\n",
|
||
|
|
"for i in range(bee_track.shape[1]):\n",
|
||
|
|
" bee_pos = bee_track[:,i]\n",
|
||
|
|
" distance[i] = my_distance(bee_pos, flower)\n",
|
||
|
|
"display(distance)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 10,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-70fd1e669decb646",
|
||
|
|
"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(np.round(distance*1000).astype(np.int32))=='54f4f2edcb'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Q4 make a plot of the bee track parameter `t` on the X axis and `distance` on the Y axis.\n",
|
||
|
|
"\n",
|
||
|
|
"It should look like this:\n",
|
||
|
|
"\n",
|
||
|
|
"<img src=\"data:image/png;base64,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
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-acdc61a7b1539944",
|
||
|
|
"locked": false,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"Text(0, 0.5, 'distance')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Your code here. Check it is correct by comparing your figure with the above.\n",
|
||
|
|
"fig, ax = plt.subplots(nrows=1, ncols=1)\n",
|
||
|
|
"ax.plot( t, distance )\n",
|
||
|
|
"ax.set_xlabel('t')\n",
|
||
|
|
"ax.set_ylabel('distance')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Q5 Using `calc_distance_func` from the lecture, find the value of `t` that minimizes the distance between the bee and the flower. Save the result in `best_t`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 12,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-23d19427610d2072",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"t: 0.0 -> dist: 18.96154002184422\n",
|
||
|
|
"t: 1.0 -> dist: 15.253196386331622\n",
|
||
|
|
"t: 2.6180339999999998 -> dist: 9.762703375781847\n",
|
||
|
|
"t: 15.908845000462023 -> dist: 46.31882030539557\n",
|
||
|
|
"t: 7.694671914602477 -> dist: 14.474578507642399\n",
|
||
|
|
"t: 4.55713707768905 -> dist: 6.429979961714315\n",
|
||
|
|
"t: 4.606244750761416 -> dist: 6.44546748591665\n",
|
||
|
|
"t: 4.427556823536537 -> dist: 6.417932686426614\n",
|
||
|
|
"t: 3.7363806287215797 -> dist: 7.03303244654773\n",
|
||
|
|
"t: 4.454999062553287 -> dist: 6.416983793293304\n",
|
||
|
|
"t: 4.455122430031719 -> dist: 6.416983777420453\n",
|
||
|
|
"t: 4.455112223273879 -> dist: 6.416983777290153\n",
|
||
|
|
"t: 4.455112157328219 -> dist: 6.416983777290158\n",
|
||
|
|
"t: 4.45511228921954 -> dist: 6.416983777290159\n",
|
||
|
|
" message: \n",
|
||
|
|
" Optimization terminated successfully;\n",
|
||
|
|
" The returned value satisfies the termination criteria\n",
|
||
|
|
" (using xtol = 1.48e-08 )\n",
|
||
|
|
" success: True\n",
|
||
|
|
" fun: 6.416983777290153\n",
|
||
|
|
" x: 4.455112223273879\n",
|
||
|
|
" nit: 10\n",
|
||
|
|
" nfev: 14\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Your code here. \n",
|
||
|
|
"\n",
|
||
|
|
"def compute_distance(a,b):\n",
|
||
|
|
" a = np.array(a)\n",
|
||
|
|
" b = np.array(b)\n",
|
||
|
|
" return np.sqrt(np.sum((a-b)**2))\n",
|
||
|
|
"\n",
|
||
|
|
"def calc_distance_func(t):\n",
|
||
|
|
" x1, y1 = flower\n",
|
||
|
|
" x2, y2 = make_bee_track(t)\n",
|
||
|
|
" dist = compute_distance((x1,y1), (x2,y2))\n",
|
||
|
|
" print(f't: {t} -> dist: {dist}')\n",
|
||
|
|
" return dist\n",
|
||
|
|
"\n",
|
||
|
|
"import scipy.optimize\n",
|
||
|
|
"result = scipy.optimize.minimize_scalar(calc_distance_func)\n",
|
||
|
|
"print(result)\n",
|
||
|
|
"best_t = result.x"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-0a3594afd2952a33",
|
||
|
|
"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(np.round(best_t*1000).astype(np.int32))=='dec1ab2f6d'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 14,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"array([7.82044889, 3.89102244])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 14,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"make_bee_track(best_t)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Q6 What is the position of the bee when it is closest to the flower? Save the result as a numpy array in `best_pos`."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-cac598c7f739d146",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Your code here. \n",
|
||
|
|
"best_pos = make_bee_track(best_t)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 16,
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-9d882991838f0996",
|
||
|
|
"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 type(best_pos)==np.ndarray\n",
|
||
|
|
"assert best_pos.ndim==1\n",
|
||
|
|
"assert best_pos.shape==(2,)\n",
|
||
|
|
"assert ads_hash(np.round(best_pos[0]*1000).astype(np.int32))=='e33b9415bc'\n",
|
||
|
|
"assert ads_hash(np.round(best_pos[1]*1000).astype(np.int32))=='f71cbfce4c'"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"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": "3.11.7"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|