1362 lines
34 KiB
Plaintext
1362 lines
34 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": null,
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"metadata": {
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"deletable": false,
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"editable": false,
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"nbgrader": {
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"cell_type": "code",
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"checksum": "b8a591f5e43fe66ddaf506c4afbac6b5",
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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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"deletable": false,
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"editable": false,
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"nbgrader": {
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"cell_type": "markdown",
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"checksum": "0ace91955d048ca2dad2a2fd7fd23b13",
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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": null,
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"metadata": {
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"deletable": false,
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"editable": false,
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"nbgrader": {
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"cell_type": "code",
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"checksum": "e8f57f43c9d18b610d47e028e6cd28bd",
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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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"deletable": false,
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"editable": false,
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"nbgrader": {
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"cell_type": "markdown",
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"checksum": "c88374b41163058dcfb2d5307b0db2d7",
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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": null,
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"metadata": {
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"deletable": false,
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"nbgrader": {
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"cell_type": "code",
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"checksum": "852192edc9b51f8cbd01be49c694f3a4",
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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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"source": [
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"# YOUR CODE HERE\n",
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"raise NotImplementedError()"
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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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"deletable": false,
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"editable": false,
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"nbgrader": {
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"cell_type": "code",
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"checksum": "d12ac5f0875993c39a482e79089db6d3",
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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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"deletable": false,
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"editable": false,
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"nbgrader": {
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"cell_type": "markdown",
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"checksum": "195c5c3c99efa4e8100572968a6ac996",
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"grade": false,
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"grade_id": "cell-64d2210f9a71e242",
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"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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"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": null,
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"metadata": {
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"deletable": false,
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"nbgrader": {
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|
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"cell_type": "code",
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"checksum": "a92d385dd3e887d40bc84b01db422cfa",
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"grade": false,
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|
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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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"source": [
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|
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"# YOUR CODE HERE\n",
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|
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"raise NotImplementedError()"
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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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"deletable": false,
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"editable": false,
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||
|
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"nbgrader": {
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"cell_type": "code",
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"checksum": "5ea3420f20c13566a89e9e2f9e24d452",
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"grade": true,
|
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"grade_id": "cell-64723536c462a2d1",
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"locked": true,
|
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|
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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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"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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|
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"metadata": {
|
||
|
|
"deletable": false,
|
||
|
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"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
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"cell_type": "markdown",
|
||
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"checksum": "3baffdf43eb0dd45219fba107dbdb539",
|
||
|
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"grade": false,
|
||
|
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"grade_id": "cell-f439954fdaef75da",
|
||
|
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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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"## 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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{
|
||
|
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"cell_type": "code",
|
||
|
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"execution_count": null,
|
||
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"metadata": {
|
||
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"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
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"checksum": "0d0f5fc61512a2356922219f33d9582f",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-15f8e74190eecaf8",
|
||
|
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"locked": false,
|
||
|
|
"schema_version": 3,
|
||
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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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"# YOUR CODE HERE\n",
|
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|
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"raise NotImplementedError()"
|
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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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"deletable": false,
|
||
|
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"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
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"cell_type": "code",
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"checksum": "6d683f118d9eb97c8068c189b2f73188",
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"grade": true,
|
||
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"grade_id": "cell-38a672b790c362eb",
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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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},
|
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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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||
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"deletable": false,
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||
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"editable": false,
|
||
|
|
"nbgrader": {
|
||
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"cell_type": "markdown",
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"checksum": "2a1cf3d973361fa8f60c6c15bae08706",
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"grade": false,
|
||
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"grade_id": "cell-681527231f43677f",
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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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"## 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": null,
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||
|
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"metadata": {
|
||
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"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
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||
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"checksum": "3014f7556d69336f39c1bf0a51d4105b",
|
||
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"grade": false,
|
||
|
|
"grade_id": "cell-34f66fe8d8b001fb",
|
||
|
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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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"outputs": [],
|
||
|
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"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
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},
|
||
|
|
{
|
||
|
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"cell_type": "code",
|
||
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"execution_count": null,
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||
|
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"metadata": {
|
||
|
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"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
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"cell_type": "code",
|
||
|
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"checksum": "dcc4c6d18784c72102da8af214db89d4",
|
||
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"grade": true,
|
||
|
|
"grade_id": "cell-9ef246cf9714c370",
|
||
|
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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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"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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"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "3887513d944274daef5b5860c23e77bc",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-b4c0d9ce0a0e3ec7",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
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}
|
||
|
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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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{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "def98d3a4ff5a4444e78d6884b16a34b",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-6b4ee0992aa506c5",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
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"outputs": [],
|
||
|
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"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "6fa450c5d140a4ab2c21dcce3a621435",
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-6833bfed10c7430c",
|
||
|
|
"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))=='0812a4ef4e' \n",
|
||
|
|
"assert ads_hash(x)=='17e101b2ef'"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "3047231b1742b9a7f70d6335eb0fc54f",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-34c0aed2a2c992a4",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"## Q6 set the shape of `x` to be (5, 5000)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "2c82b4ab20f94362a6d24a4d808a0691",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e07f245d339e6328",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "aee8fd1dd13562ee0917a50a259aa42e",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "8d588e43438e0ad079169fd7f7474666",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "bf27135b61c26a05aea91e1f01349726",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-ef33bd87060e2253",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "8c0873922759ff509513beaece8a2d83",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "6962a55d45696646cb66150fb17292a7",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "181bbd6b82abfdb3eb5c059aadb65133",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "6a4775d495f1a5512fa5dae7549ea9f2",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "c519aba9a18e96655ad371783599635b",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-3acd919556155f8f",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"time_values = np.linspace(0,10,100)\n",
|
||
|
|
"plt.plot(time_values)\n",
|
||
|
|
"plt.ylabel('time (seconds)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "7721645f3a1dd2463328aed14ca9bd53",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "baa830db90f60c4aa74699f4b97be765",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "657471fb5d9fe09f5063b8ad763f51b0",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "958eea9bacbfb559c136f6cd30287279",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e1a3bbf4c1b1618c",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(time_values,y)\n",
|
||
|
|
"plt.xlabel('time (seconds)');\n",
|
||
|
|
"plt.ylabel('y (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "882e42c3d072439e1ed1ad4060ac55ca",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "b0ebba9258ed9c6e02de101ad481179f",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "ede756e28026500ee3dffa5744a78c88",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-153b385adbe59ec2",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(time_values,x)\n",
|
||
|
|
"plt.xlabel('time (seconds)');\n",
|
||
|
|
"plt.ylabel('x (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "ace790d5cadd15eb9e38000bfcabfd7b",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "0f19a80dae475aaca9a80d4e76dab504",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "c0a41e2d3055d4a8d46dc08148090189",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "6e4a851ef99bd3eecee7ac10e7fca08c",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "f9fba2927a0e61aea16248bc91a7f367",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-5f3a313fa88f20be",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(bee_coords[0])\n",
|
||
|
|
"plt.ylabel('x (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "d0ac2bfcddf131514f0af04ddc3a0cb8",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "17c6db774136c7bdd01d470a7bcff60c",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-b2b1ea1720798043",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(time_values, bee_coords[0])\n",
|
||
|
|
"plt.xlabel('time (seconds)');\n",
|
||
|
|
"plt.ylabel('x (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "5a299e560d66a4acfd84839cc037db22",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "cb952d36ae3050e5408a9eb8d1d1dc02",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-8a08ee9348762caf",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"plt.plot(bee_coords[0], bee_coords[1])\n",
|
||
|
|
"plt.xlabel('x (meters)')\n",
|
||
|
|
"plt.ylabel('y (meters)');"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "a608d6fec980934b711d6e6333715291",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "c62b867a4dbcfe7515a1943db943bb31",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-68e7d25afb2f1765",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "9ab00230a2f278b346751df2cd8bd515",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "053967690bf5d021be99d4f204731a64",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "d187a8201410e5f44975535430ba0ed7",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e74d9319eda293c6",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "684ce2fcf426e29c83c3b74a4f734d7b",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "e74e0813d1790618b60dbd94003a0d22",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "e3ad5869bba054247db559e212ff3a59",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-cbbcbdf110a030b2",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "d61620c804e2942937dc11a4b2f94c8f",
|
||
|
|
"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": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"checksum": "a25e6c52be197ecbbcd3019ffd4b68a0",
|
||
|
|
"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": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "3a9d790b24c98c5b0f23899ca9446375",
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-d3cd40a661182621",
|
||
|
|
"locked": false,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# YOUR CODE HERE\n",
|
||
|
|
"raise NotImplementedError()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"deletable": false,
|
||
|
|
"editable": false,
|
||
|
|
"nbgrader": {
|
||
|
|
"cell_type": "code",
|
||
|
|
"checksum": "c3133f6c56e721f29f92c2b9a5f29857",
|
||
|
|
"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": {
|
||
|
|
"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
|
||
|
|
}
|