├── .gitattributes ├── x150.png ├── .DS_Store ├── Media2.wav ├── Raster.png ├── FakeErnst.png ├── TwoLine.png ├── FakeErnst2.png ├── Oldman2000Hz.png ├── .ipynb_checkpoints ├── InClassTest-checkpoint.ipynb ├── W1T1 The Line -checkpoint.ipynb ├── W1T2 Two Lines-checkpoint.ipynb └── W2T4 Frequencies -checkpoint.ipynb ├── LICENSE ├── README.md ├── W1T1 The Line_solutions.ipynb └── W1T1 The Line .ipynb /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | -------------------------------------------------------------------------------- /x150.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/x150.png -------------------------------------------------------------------------------- /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/.DS_Store -------------------------------------------------------------------------------- /Media2.wav: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/Media2.wav -------------------------------------------------------------------------------- /Raster.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/Raster.png -------------------------------------------------------------------------------- /FakeErnst.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/FakeErnst.png -------------------------------------------------------------------------------- /TwoLine.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/TwoLine.png -------------------------------------------------------------------------------- /FakeErnst2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/FakeErnst2.png -------------------------------------------------------------------------------- /Oldman2000Hz.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/john-s-butler-dit/Basic-Introduction-to-Python/HEAD/Oldman2000Hz.png -------------------------------------------------------------------------------- /.ipynb_checkpoints/InClassTest-checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [], 3 | "metadata": {}, 4 | "nbformat": 4, 5 | "nbformat_minor": 5 6 | } 7 | -------------------------------------------------------------------------------- /.ipynb_checkpoints/W1T1 The Line -checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [], 3 | "metadata": {}, 4 | "nbformat": 4, 5 | "nbformat_minor": 4 6 | } 7 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021 John Butler 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Basic Introduction to Maths and Python for Neuroscience 2 | Developed and taught by [John S Butler](https://johnsbutler.netlify.app) 3 | 4 | ## Description of Module 5 | This is a very short introduction into simple mathematical functions that are used in behavourial and neurophysiolgical papers. 6 | The python code below is motivated by data and plots from papers to illusrate the use and power of the line, sigmoid function, and sinewaves to analyse and interpret data. 7 | 8 | 9 | ## Module Content 10 | ## Behavioural Examples 11 | Applying simple examples of the line and a psychometric function used Behavioural and Clinical Neuroscience to illustrate Python functions, the tutorials and solutions open in colab. 12 | ### Tutorial 1 Plotting the line [1]. 13 | 14 | | Tutorial | Solution | 15 | |----------|:-------------:| 16 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T1%20The%20Line%20.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T1%20The%20Line_solutions.ipynb) | 17 | 18 | 19 | ### Tutorial 2 Two lines [1]. 20 | | Tutorial | Solution | 21 | |----------|:-------------:| 22 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T2%20Two%20Lines.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T2%20Two%20Lines_solutions.ipynb) | 23 | 24 | ### Tutorial 3 The Psychometric Function [2]. 25 | 26 | | Tutorial | Solution | 27 | |----------|:-------------:| 28 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T3%20The%20Psychometric%20Function.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T3%20The%20Psychometric%20Function_solution.ipynb) | 29 | 30 | ### Tutorial 4 The Psychometric function for multisensory integration [2]. 31 | 32 | | Tutorial | Solution | 33 | |----------|:-------------:| 34 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T4%20The%20Psychometric%20for%20Multisensory%20Integration.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W1T4%20The%20Psychometric%20for%20Multisensory%20Integration_Solution.ipynb) | 35 | 36 | ## Neurophysiolgical Examples 37 | Using python to implement simple examples of Spike train analysis, tuning functions, frequencies and fast fourier transform. 38 | 39 | ### Tutorial 1 Single Spike Train [3]. 40 | 41 | | Tutorial | Solution | 42 | |----------|:-------------:| 43 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T1%20Simulate%20a%20Spiking%20Neuron.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T1%20Simulate%20a%20Spiking%20Neuron_Solution.ipynb) | 44 | 45 | 46 | ### Tutorial 2 Multiple Spike Trains [3]. 47 | 48 | | Tutorial | Solution | 49 | |----------|:-------------:| 50 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T2%20Simulate%20Spiking%20Trials.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T2%20Simulate%20Spiking%20TrialsSolution.ipynb) | 51 | 52 | 53 | ### Tutorial 3 The Tuning Function [4]. 54 | 55 | | Tutorial | Solution | 56 | |----------|:-------------:| 57 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T3%20Tuning%20Curve.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T3%20Tuning%20CurveSolution.ipynb) | 58 | 59 | ### Tutorial 4 Frequencies [5]. 60 | 61 | | Tutorial | Solution | 62 | |----------|:-------------:| 63 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T4%20Frequencies%20.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T4%20FrequenciesSolution.ipynb) | 64 | 65 | ### Tutorial 5 Fourier Transform [5]. 66 | 67 | | Tutorial | Solution | 68 | |----------|:-------------:| 69 | | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T5%20Fast%20Fourier%20Transform.ipynb) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T5%20Fast%20Fourier%20Transform%20Solution.ipynb) | 70 | 71 | [The sound of different spike patterns [6]](https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2%20Spiking%20Model%20-%20Izhikevch%20Model.ipynb) 72 | 73 | 74 | ## References 75 | 76 | [1] Butler, John S., et al. "Non-parametric bootstrapping method for measuring the temporal discrimination threshold for movement disorders." Journal of neural engineering 12.4 (2015): 046026. 77 | 78 | [2] Ernst, Marc O., and Martin S. Banks. "Humans integrate visual and haptic information in a statistically optimal fashion." Nature 415.6870 (2002): 429-433. 79 | 80 | [3] Meredith, M. A., & Stein, B. E. (1986). Visual, auditory, and somatosensory convergence on cells in superior colliculus results in multisensory integration. Journal of neurophysiology, 56(3), 640-662. 81 | 82 | [4] Britten, Kenneth H., et al. "The analysis of visual motion: a comparison of neuronal and psychophysical performance." Journal of Neuroscience 12.12 (1992): 4745-4765. 83 | 84 | [5] Fiebelkorn, I. C., Foxe, J. J., Butler, J. S., Mercier, M. R., Snyder, A. C., & Molholm, S. (2011). Ready, set, reset: stimulus-locked periodicity in behavioral performance demonstrates the consequences of cross-sensory phase reset. Journal of Neuroscience, 31(27), 9971-9981. 85 | 86 | [6] Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on neural networks, 14(6), 1569-1572. 87 | 88 | ## Supplemental References 89 | Dayan, P., & Abbott, L. F. (2001). Theoretical neuroscience: computational and mathematical modeling of neural systems. Computational Neuroscience Series. 90 | 91 | 92 | ## More Advanced Modules 93 | [Mathematical Tools for Neuroscience by Ella Batty]( 94 | https://github.com/ebatty/MathToolsforNeuroscience) 95 | 96 | Butler, J. (2023, December 14). Numerical Methods and Machine Learning for Differential Equations with Applications in Python. Zenodo. https://doi.org/10.5281/zenodo.10376815 97 | 98 | ## Neuromatch Academy Materials 99 | 't Hart, B. M., Achakulvisut, T., Blohm, G., Kording, K., Peters, M. A. K., Akrami, A., Alicea, B., et al. (2021, February 15). Neuromatch Academy: a 3-week, online summer school in computational neuroscience. OSF Preprints. Retrieved from [https://osf.io/9fp4v/] 100 | 101 | [Neuromatch Academy GitHub Repository](https://github.com/NeuromatchAcademy/course-content) 102 | 103 | [Neuromatch Computational Neuroscience Summer School](https://compneuro.neuromatch.io/tutorials/intro.html) 104 | 105 | [Neuromatch Deep Learning Summer School](https://deeplearning.neuromatch.io/tutorials/intro.html) 106 | 107 | 108 | ## Supplemental Popular Reading List 109 | Lindsay, G. (2021). Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain. Bloomsbury Publishing. 110 | 111 | Strogatz, S. (2004). Sync: The emerging science of spontaneous order. Penguin UK. 112 | 113 | Humphries, M. (2021). The Spike. In The Spike. Princeton University Press. 114 | 115 | -------------------------------------------------------------------------------- /.ipynb_checkpoints/W1T2 Two Lines-checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# The line" 8 | ] 9 | }, 10 | { 11 | "cell_type": "markdown", 12 | "metadata": {}, 13 | "source": [ 14 | "In this notebook we will got show some of the basics of plotting and accessing elements of a vector (array) of numbers using the line." 15 | ] 16 | }, 17 | { 18 | "cell_type": "markdown", 19 | "metadata": {}, 20 | "source": [ 21 | "### Libraries" 22 | ] 23 | }, 24 | { 25 | "cell_type": "code", 26 | "execution_count": 10, 27 | "metadata": {}, 28 | "outputs": [], 29 | "source": [ 30 | "# LIBRARY\n", 31 | "\n", 32 | "import numpy as np # vector manipulation\n", 33 | "\n", 34 | "# THIS IS FOR PLOTTING\n", 35 | "%matplotlib inline\n", 36 | "import matplotlib.pyplot as plt # side-stepping mpl backend\n", 37 | "import warnings\n", 38 | "warnings.filterwarnings(\"ignore\")" 39 | ] 40 | }, 41 | { 42 | "cell_type": "markdown", 43 | "metadata": {}, 44 | "source": [ 45 | "## A Single Line Plot\n", 46 | "\n", 47 | "The code below will plot a line from 20 to 70 on the x axis with a slope of $m=0.3$ and an intercept of $c=10$.\n", 48 | "The formula for the line is\n", 49 | "$$ y=0.3x+10.$$\n", 50 | "We first asign the values:" 51 | ] 52 | }, 53 | { 54 | "cell_type": "code", 55 | "execution_count": 11, 56 | "metadata": {}, 57 | "outputs": [], 58 | "source": [ 59 | "m=0.3\n", 60 | "c=10" 61 | ] 62 | }, 63 | { 64 | "cell_type": "markdown", 65 | "metadata": {}, 66 | "source": [ 67 | "Now we define a range of x values starting at 20 and ending at 69 in unit steps. To do this we use the __numpy__ library function __arange__." 68 | ] 69 | }, 70 | { 71 | "cell_type": "code", 72 | "execution_count": 12, 73 | "metadata": {}, 74 | "outputs": [ 75 | { 76 | "name": "stdout", 77 | "output_type": "stream", 78 | "text": [ 79 | "[20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43\n", 80 | " 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67\n", 81 | " 68 69]\n" 82 | ] 83 | } 84 | ], 85 | "source": [ 86 | "x=np.arange(20,70,1)\n", 87 | "print(x)" 88 | ] 89 | }, 90 | { 91 | "cell_type": "markdown", 92 | "metadata": {}, 93 | "source": [ 94 | "To print the first element of the x range use the comand print(x[0])" 95 | ] 96 | }, 97 | { 98 | "cell_type": "code", 99 | "execution_count": 13, 100 | "metadata": {}, 101 | "outputs": [ 102 | { 103 | "name": "stdout", 104 | "output_type": "stream", 105 | "text": [ 106 | "20\n" 107 | ] 108 | } 109 | ], 110 | "source": [ 111 | "print(x[0])" 112 | ] 113 | }, 114 | { 115 | "cell_type": "markdown", 116 | "metadata": {}, 117 | "source": [ 118 | "We now write the formula for the line\n", 119 | "$$ y=mx+c.$$" 120 | ] 121 | }, 122 | { 123 | "cell_type": "code", 124 | "execution_count": 14, 125 | "metadata": {}, 126 | "outputs": [ 127 | { 128 | "name": "stdout", 129 | "output_type": "stream", 130 | "text": [ 131 | "[16. 16.3 16.6 16.9 17.2 17.5 17.8 18.1 18.4 18.7 19. 19.3 19.6 19.9\n", 132 | " 20.2 20.5 20.8 21.1 21.4 21.7 22. 22.3 22.6 22.9 23.2 23.5 23.8 24.1\n", 133 | " 24.4 24.7 25. 25.3 25.6 25.9 26.2 26.5 26.8 27.1 27.4 27.7 28. 28.3\n", 134 | " 28.6 28.9 29.2 29.5 29.8 30.1 30.4 30.7]\n" 135 | ] 136 | } 137 | ], 138 | "source": [ 139 | "y= m*x+c\n", 140 | "print(y)" 141 | ] 142 | }, 143 | { 144 | "cell_type": "markdown", 145 | "metadata": {}, 146 | "source": [ 147 | "To plot the result we use the __matplotlib__ library function __plt__." 148 | ] 149 | }, 150 | { 151 | "cell_type": "code", 152 | "execution_count": 15, 153 | "metadata": {}, 154 | "outputs": [ 155 | { 156 | "data": { 157 | "image/png": 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\n", 158 | "text/plain": [ 159 | "
" 160 | ] 161 | }, 162 | "metadata": { 163 | "needs_background": "light" 164 | }, 165 | "output_type": "display_data" 166 | } 167 | ], 168 | "source": [ 169 | "fig = plt.figure(figsize=(6,6)) # This setups the size of the figure\n", 170 | "plt.plot(x,y,'-',color='red')\n", 171 | "plt.show() # This plots the figure" 172 | ] 173 | }, 174 | { 175 | "cell_type": "markdown", 176 | "metadata": {}, 177 | "source": [ 178 | "## Problem 1\n", 179 | "Re-do the plot with a slope of 1 and an intercept of -5.\n" 180 | ] 181 | }, 182 | { 183 | "cell_type": "code", 184 | "execution_count": 16, 185 | "metadata": {}, 186 | "outputs": [ 187 | { 188 | "data": { 189 | "image/png": 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\n", 190 | "text/plain": [ 191 | "
" 192 | ] 193 | }, 194 | "metadata": { 195 | "needs_background": "light" 196 | }, 197 | "output_type": "display_data" 198 | } 199 | ], 200 | "source": [ 201 | "##############################################################################\n", 202 | "## INSERT: Update the slope to 1 and intercept to -5\n", 203 | "##############################################################################\n", 204 | "\n", 205 | "\n", 206 | "x=np.arange(20,70,1)\n", 207 | "y= m*x+c\n", 208 | "\n", 209 | "fig = plt.figure(figsize=(6,6))\n", 210 | "plt.plot(x,y,'-',color='red')\n", 211 | "plt.show()" 212 | ] 213 | }, 214 | { 215 | "cell_type": "markdown", 216 | "metadata": {}, 217 | "source": [ 218 | "## Problem 2\n", 219 | "Re-do the plot but with a different coloured line." 220 | ] 221 | }, 222 | { 223 | "cell_type": "code", 224 | "execution_count": 17, 225 | "metadata": {}, 226 | "outputs": [ 227 | { 228 | "data": { 229 | "text/plain": [ 230 | "
" 231 | ] 232 | }, 233 | "metadata": {}, 234 | "output_type": "display_data" 235 | } 236 | ], 237 | "source": [ 238 | "\n", 239 | "fig = plt.figure(figsize=(6,6))\n", 240 | "##############################################################################\n", 241 | "## INSERT: change the plot function to plot a different coloured line.\n", 242 | "##############################################################################\n", 243 | "\n", 244 | "plt.show()" 245 | ] 246 | }, 247 | { 248 | "cell_type": "markdown", 249 | "metadata": {}, 250 | "source": [ 251 | "## Problem 3\n", 252 | "What is the value of the 5th element of the y vector." 253 | ] 254 | }, 255 | { 256 | "cell_type": "code", 257 | "execution_count": 18, 258 | "metadata": {}, 259 | "outputs": [ 260 | { 261 | "name": "stdout", 262 | "output_type": "stream", 263 | "text": [ 264 | "[16. 16.3 16.6 16.9 17.2 17.5 17.8 18.1 18.4 18.7 19. 19.3 19.6 19.9\n", 265 | " 20.2 20.5 20.8 21.1 21.4 21.7 22. 22.3 22.6 22.9 23.2 23.5 23.8 24.1\n", 266 | " 24.4 24.7 25. 25.3 25.6 25.9 26.2 26.5 26.8 27.1 27.4 27.7 28. 28.3\n", 267 | " 28.6 28.9 29.2 29.5 29.8 30.1 30.4 30.7]\n" 268 | ] 269 | } 270 | ], 271 | "source": [ 272 | "print(y)" 273 | ] 274 | }, 275 | { 276 | "cell_type": "code", 277 | "execution_count": null, 278 | "metadata": {}, 279 | "outputs": [], 280 | "source": [] 281 | }, 282 | { 283 | "cell_type": "code", 284 | "execution_count": null, 285 | "metadata": {}, 286 | "outputs": [], 287 | "source": [] 288 | } 289 | ], 290 | "metadata": { 291 | "kernelspec": { 292 | "display_name": "Python 3", 293 | "language": "python", 294 | "name": "python3" 295 | }, 296 | "language_info": { 297 | "codemirror_mode": { 298 | "name": "ipython", 299 | "version": 3 300 | }, 301 | "file_extension": ".py", 302 | "mimetype": "text/x-python", 303 | "name": "python", 304 | "nbconvert_exporter": "python", 305 | "pygments_lexer": "ipython3", 306 | "version": "3.7.9" 307 | } 308 | }, 309 | "nbformat": 4, 310 | "nbformat_minor": 4 311 | } 312 | -------------------------------------------------------------------------------- /W1T1 The Line_solutions.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "kernelspec": { 6 | "display_name": "Python 3", 7 | "language": "python", 8 | "name": "python3" 9 | }, 10 | "language_info": { 11 | "codemirror_mode": { 12 | "name": "ipython", 13 | "version": 3 14 | }, 15 | "file_extension": ".py", 16 | "mimetype": "text/x-python", 17 | "name": "python", 18 | "nbconvert_exporter": "python", 19 | "pygments_lexer": "ipython3", 20 | "version": "3.7.9" 21 | }, 22 | "colab": { 23 | "name": "W1T1 The Line .ipynb", 24 | "provenance": [], 25 | "include_colab_link": true 26 | } 27 | }, 28 | "cells": [ 29 | { 30 | "cell_type": "markdown", 31 | "metadata": { 32 | "id": "view-in-github", 33 | "colab_type": "text" 34 | }, 35 | "source": [ 36 | "\"Open" 37 | ] 38 | }, 39 | { 40 | "cell_type": "markdown", 41 | "metadata": { 42 | "id": "wjw5J2KF9Y_t" 43 | }, 44 | "source": [ 45 | "# The line Week 1, Tutorial 1\n", 46 | "John Butler" 47 | ] 48 | }, 49 | { 50 | "cell_type": "markdown", 51 | "metadata": { 52 | "id": "Q2UwpnGU9Y_z" 53 | }, 54 | "source": [ 55 | "In this notebook we will show some of the basics of plotting and accessing elements of a vector (array) of numbers using the line." 56 | ] 57 | }, 58 | { 59 | "cell_type": "markdown", 60 | "metadata": { 61 | "id": "HIw9sEB39Y_z" 62 | }, 63 | "source": [ 64 | "### Libraries" 65 | ] 66 | }, 67 | { 68 | "cell_type": "code", 69 | "metadata": { 70 | "id": "Z-9U5qbQ9Y_z" 71 | }, 72 | "source": [ 73 | "# LIBRARY\n", 74 | "import numpy as np # vector manipulation\n", 75 | "\n", 76 | "# THIS IS FOR PLOTTING\n", 77 | "%matplotlib inline\n", 78 | "import matplotlib.pyplot as plt # side-stepping mpl backend\n", 79 | "import warnings\n", 80 | "warnings.filterwarnings(\"ignore\")" 81 | ], 82 | "execution_count": 44, 83 | "outputs": [] 84 | }, 85 | { 86 | "cell_type": "markdown", 87 | "metadata": { 88 | "id": "jngXI1dd9Y_0" 89 | }, 90 | "source": [ 91 | "## A Single Line Plot\n", 92 | "\n", 93 | "The code below will plot a line from 20 to 70 on the x axis with a slope of $m=0.3$ and an intercept of $c=10$.\n", 94 | "The formula for the line is\n", 95 | "$$ y=0.3x+10.$$\n", 96 | "We first assign the values for m and c:\n" 97 | ] 98 | }, 99 | { 100 | "cell_type": "code", 101 | "metadata": { 102 | "id": "tt9dMM529Y_0" 103 | }, 104 | "source": [ 105 | "m=0.3 # sets m to be 0.3\n", 106 | "c=10 # sets c to be 10" 107 | ], 108 | "execution_count": 45, 109 | "outputs": [] 110 | }, 111 | { 112 | "cell_type": "markdown", 113 | "metadata": { 114 | "id": "_bytS9jx9Y_0" 115 | }, 116 | "source": [ 117 | "Now we define a range of x values starting at 20 and ending at 69 in unit steps. To do this we use the __numpy__ library function __arange__." 118 | ] 119 | }, 120 | { 121 | "cell_type": "code", 122 | "metadata": { 123 | "id": "SFQXATAv9Y_1", 124 | "outputId": "d700f03a-925d-451b-e4cd-7d3252e8dddb", 125 | "colab": { 126 | "base_uri": "https://localhost:8080/" 127 | } 128 | }, 129 | "source": [ 130 | "x=np.arange(20,70,1) # Start at 20 go to just before 70 in steps of 1 \n", 131 | "print(x)" 132 | ], 133 | "execution_count": 46, 134 | "outputs": [ 135 | { 136 | "output_type": "stream", 137 | "name": "stdout", 138 | "text": [ 139 | "[20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43\n", 140 | " 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67\n", 141 | " 68 69]\n" 142 | ] 143 | } 144 | ] 145 | }, 146 | { 147 | "cell_type": "markdown", 148 | "metadata": { 149 | "id": "u8i76VS_9Y_2" 150 | }, 151 | "source": [ 152 | "To print the first element of the x range use the comand print(x[0])" 153 | ] 154 | }, 155 | { 156 | "cell_type": "code", 157 | "metadata": { 158 | "id": "eiM1EKZ49Y_2", 159 | "outputId": "bbb7534e-9455-4b71-f850-6105fb38f8e4", 160 | "colab": { 161 | "base_uri": "https://localhost:8080/" 162 | } 163 | }, 164 | "source": [ 165 | "print(x[0]) # first element\n", 166 | "print(x[9]) # 10th element\n", 167 | "print(x[-1]) # last\n", 168 | "print(x[2:10])" 169 | ], 170 | "execution_count": 47, 171 | "outputs": [ 172 | { 173 | "output_type": "stream", 174 | "name": "stdout", 175 | "text": [ 176 | "20\n", 177 | "29\n", 178 | "69\n", 179 | "[22 23 24 25 26 27 28 29]\n" 180 | ] 181 | } 182 | ] 183 | }, 184 | { 185 | "cell_type": "markdown", 186 | "metadata": { 187 | "id": "ZB7HOPUY9Y_3" 188 | }, 189 | "source": [ 190 | "We now write the formula for the line\n", 191 | "$$ y=mx+c.$$" 192 | ] 193 | }, 194 | { 195 | "cell_type": "code", 196 | "metadata": { 197 | "id": "Y1hxdDQ39Y_3", 198 | "outputId": "74020a64-8968-4fbc-e470-81db75b0aa85", 199 | "colab": { 200 | "base_uri": "https://localhost:8080/" 201 | } 202 | }, 203 | "source": [ 204 | "y= m*x+c\n", 205 | "print(y)" 206 | ], 207 | "execution_count": 48, 208 | "outputs": [ 209 | { 210 | "output_type": "stream", 211 | "name": "stdout", 212 | "text": [ 213 | "[16. 16.3 16.6 16.9 17.2 17.5 17.8 18.1 18.4 18.7 19. 19.3 19.6 19.9\n", 214 | " 20.2 20.5 20.8 21.1 21.4 21.7 22. 22.3 22.6 22.9 23.2 23.5 23.8 24.1\n", 215 | " 24.4 24.7 25. 25.3 25.6 25.9 26.2 26.5 26.8 27.1 27.4 27.7 28. 28.3\n", 216 | " 28.6 28.9 29.2 29.5 29.8 30.1 30.4 30.7]\n" 217 | ] 218 | } 219 | ] 220 | }, 221 | { 222 | "cell_type": "markdown", 223 | "metadata": { 224 | "id": "FgIwc08F9Y_3" 225 | }, 226 | "source": [ 227 | "To plot the result we use the __matplotlib__ library function __plt__." 228 | ] 229 | }, 230 | { 231 | "cell_type": "code", 232 | "metadata": { 233 | "id": "qE8a3N6e9Y_3", 234 | "outputId": "f35bb16a-617f-4cf2-8b37-95f11ce4572f", 235 | "colab": { 236 | "base_uri": "https://localhost:8080/", 237 | "height": 374 238 | } 239 | }, 240 | "source": [ 241 | "fig = plt.figure(figsize=(6,6)) # This setups the size of the figure\n", 242 | "plt.plot(x,y,'o',color='red')\n", 243 | "plt.show() # This plots the figure" 244 | ], 245 | "execution_count": 49, 246 | "outputs": [ 247 | { 248 | "output_type": "display_data", 249 | "data": { 250 | "image/png": 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\n", 251 | "text/plain": [ 252 | "
" 253 | ] 254 | }, 255 | "metadata": { 256 | "needs_background": "light" 257 | } 258 | } 259 | ] 260 | }, 261 | { 262 | "cell_type": "markdown", 263 | "metadata": { 264 | "id": "OYy_EVh09Y_4" 265 | }, 266 | "source": [ 267 | "# Problems \n", 268 | "There are three simple problem questions to show how to plot a line in python.\n", 269 | "\n" 270 | ] 271 | }, 272 | { 273 | "cell_type": "markdown", 274 | "source": [ 275 | "## Problem 1\n", 276 | "Re-do the plot with a slope of 1 and an intercept of -5.\n" 277 | ], 278 | "metadata": { 279 | "id": "rPZJos9eCRNj" 280 | } 281 | }, 282 | { 283 | "cell_type": "code", 284 | "metadata": { 285 | "id": "ydBiZ2Ar9Y_4", 286 | "outputId": "804b8a76-525b-4a15-9985-a2dca4e7c01a", 287 | "colab": { 288 | "base_uri": "https://localhost:8080/", 289 | "height": 374 290 | } 291 | }, 292 | "source": [ 293 | "##############################################################################\n", 294 | "## INSERT: Update the slope to 1 and intercept to -5\n", 295 | "##############################################################################\n", 296 | "\n", 297 | "#######################ANSWER###############################\n", 298 | "m=1\n", 299 | "c=-5\n", 300 | "#######################################################################\n", 301 | "\n", 302 | "x=np.arange(20,70,1)\n", 303 | "y= m*x+c\n", 304 | "\n", 305 | "fig = plt.figure(figsize=(6,6))\n", 306 | "plt.plot(x,y,'-',color='red')\n", 307 | "plt.show()" 308 | ], 309 | "execution_count": 53, 310 | "outputs": [ 311 | { 312 | "output_type": "display_data", 313 | "data": { 314 | "image/png": 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\n", 315 | "text/plain": [ 316 | "
" 317 | ] 318 | }, 319 | "metadata": { 320 | "needs_background": "light" 321 | } 322 | } 323 | ] 324 | }, 325 | { 326 | "cell_type": "markdown", 327 | "metadata": { 328 | "id": "tkN77Rnu9Y_5" 329 | }, 330 | "source": [ 331 | "## Problem 2\n", 332 | "Re-do the plot but with a different coloured line." 333 | ] 334 | }, 335 | { 336 | "cell_type": "code", 337 | "metadata": { 338 | "id": "uDqN0g7P9Y_5", 339 | "outputId": "34125741-b614-4a28-a5be-957ed6942ba5", 340 | "colab": { 341 | "base_uri": "https://localhost:8080/", 342 | "height": 391 343 | } 344 | }, 345 | "source": [ 346 | "\n", 347 | "fig = plt.figure(figsize=(6,6))\n", 348 | "##############################################################################\n", 349 | "## INSERT: change the plot function to plot a different coloured line.\n", 350 | "##############################################################################\n", 351 | "\n", 352 | "#######################ANSWER###############################\n", 353 | "m=1\n", 354 | "c=-5\n", 355 | "\n", 356 | "x=np.arange(20,70,1)\n", 357 | "y= m*x+c\n", 358 | "\n", 359 | "fig = plt.figure(figsize=(6,6))\n", 360 | "plt.plot(x,y,'--',color=\"hotpink\")\n", 361 | "#######################################################################\n", 362 | "\n", 363 | "plt.show()" 364 | ], 365 | "execution_count": 56, 366 | "outputs": [ 367 | { 368 | "output_type": "display_data", 369 | "data": { 370 | "text/plain": [ 371 | "
" 372 | ] 373 | }, 374 | "metadata": {} 375 | }, 376 | { 377 | "output_type": "display_data", 378 | "data": { 379 | "image/png": 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\n", 380 | "text/plain": [ 381 | "
" 382 | ] 383 | }, 384 | "metadata": { 385 | "needs_background": "light" 386 | } 387 | } 388 | ] 389 | }, 390 | { 391 | "cell_type": "markdown", 392 | "metadata": { 393 | "id": "AQzcrptU9Y_6" 394 | }, 395 | "source": [ 396 | "## Problem 3\n", 397 | "What is the value of the 5th element of the y vector." 398 | ] 399 | }, 400 | { 401 | "cell_type": "code", 402 | "metadata": { 403 | "id": "87iT4icO9Y_6", 404 | "outputId": "d415c841-fbd5-44af-c08d-3e5a93eec511", 405 | "colab": { 406 | "base_uri": "https://localhost:8080/" 407 | } 408 | }, 409 | "source": [ 410 | "########## ANSWER ###################\n", 411 | "print(y[4])" 412 | ], 413 | "execution_count": 58, 414 | "outputs": [ 415 | { 416 | "output_type": "stream", 417 | "name": "stdout", 418 | "text": [ 419 | "19\n" 420 | ] 421 | } 422 | ] 423 | }, 424 | { 425 | "cell_type": "markdown", 426 | "metadata": { 427 | "id": "WzpgliAh9Y_7" 428 | }, 429 | "source": [ 430 | "---\n", 431 | "# Summary\n", 432 | "\n", 433 | "In this tutorial, we learned:\n", 434 | "\n", 435 | "* To plot a line.\n", 436 | "* To access elements of an array." 437 | ] 438 | } 439 | ] 440 | } -------------------------------------------------------------------------------- /W1T1 The Line .ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "kernelspec": { 6 | "display_name": "Python 3", 7 | "language": "python", 8 | "name": "python3" 9 | }, 10 | "language_info": { 11 | "codemirror_mode": { 12 | "name": "ipython", 13 | "version": 3 14 | }, 15 | "file_extension": ".py", 16 | "mimetype": "text/x-python", 17 | "name": "python", 18 | "nbconvert_exporter": "python", 19 | "pygments_lexer": "ipython3", 20 | "version": "3.7.9" 21 | }, 22 | "colab": { 23 | "name": "W1T1 The Line .ipynb", 24 | "provenance": [], 25 | "toc_visible": true, 26 | "include_colab_link": true 27 | } 28 | }, 29 | "cells": [ 30 | { 31 | "cell_type": "markdown", 32 | "metadata": { 33 | "id": "view-in-github", 34 | "colab_type": "text" 35 | }, 36 | "source": [ 37 | "\"Open" 38 | ] 39 | }, 40 | { 41 | "cell_type": "markdown", 42 | "metadata": { 43 | "id": "wjw5J2KF9Y_t" 44 | }, 45 | "source": [ 46 | "# The line Week 1, Tutorial 1" 47 | ] 48 | }, 49 | { 50 | "cell_type": "markdown", 51 | "metadata": { 52 | "id": "Q2UwpnGU9Y_z" 53 | }, 54 | "source": [ 55 | "In this notebook we will show some of the basics of plotting and accessing elements of a vector (array) of numbers using the line." 56 | ] 57 | }, 58 | { 59 | "cell_type": "markdown", 60 | "metadata": { 61 | "id": "HIw9sEB39Y_z" 62 | }, 63 | "source": [ 64 | "### Libraries" 65 | ] 66 | }, 67 | { 68 | "cell_type": "code", 69 | "metadata": { 70 | "id": "Z-9U5qbQ9Y_z" 71 | }, 72 | "source": [ 73 | "# LIBRARY\n", 74 | "import numpy as np # vector manipulation\n", 75 | "\n", 76 | "# THIS IS FOR PLOTTING\n", 77 | "%matplotlib inline\n", 78 | "import matplotlib.pyplot as plt # side-stepping mpl backend\n", 79 | "import warnings\n", 80 | "warnings.filterwarnings(\"ignore\")" 81 | ], 82 | "execution_count": 1, 83 | "outputs": [] 84 | }, 85 | { 86 | "cell_type": "markdown", 87 | "metadata": { 88 | "id": "jngXI1dd9Y_0" 89 | }, 90 | "source": [ 91 | "## A Single Line Plot\n", 92 | "\n", 93 | "The code below will plot a line from 20 to 70 on the x axis with a slope of $m=0.3$ and an intercept of $c=10$.\n", 94 | "The formula for the line is\n", 95 | "$$ y=0.3x+10.$$\n", 96 | "We first assign the values:\n", 97 | "My name is " 98 | ] 99 | }, 100 | { 101 | "cell_type": "code", 102 | "metadata": { 103 | "id": "tt9dMM529Y_0" 104 | }, 105 | "source": [ 106 | "m=0.3\n", 107 | "c=10" 108 | ], 109 | "execution_count": 2, 110 | "outputs": [] 111 | }, 112 | { 113 | "cell_type": "markdown", 114 | "metadata": { 115 | "id": "_bytS9jx9Y_0" 116 | }, 117 | "source": [ 118 | "Now we define a range of x values starting at 20 and ending at 69 in unit steps. To do this we use the __numpy__ library function __arange__." 119 | ] 120 | }, 121 | { 122 | "cell_type": "code", 123 | "metadata": { 124 | "id": "SFQXATAv9Y_1", 125 | "outputId": "56e4adf9-a9bc-4441-8085-f95061fd986c", 126 | "colab": { 127 | "base_uri": "https://localhost:8080/" 128 | } 129 | }, 130 | "source": [ 131 | "x=np.arange(20,70,1)\n", 132 | "print(x)" 133 | ], 134 | "execution_count": 3, 135 | "outputs": [ 136 | { 137 | "output_type": "stream", 138 | "name": "stdout", 139 | "text": [ 140 | "[20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43\n", 141 | " 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67\n", 142 | " 68 69]\n" 143 | ] 144 | } 145 | ] 146 | }, 147 | { 148 | "cell_type": "markdown", 149 | "metadata": { 150 | "id": "u8i76VS_9Y_2" 151 | }, 152 | "source": [ 153 | "To print the first element of the x range use the comand print(x[0])" 154 | ] 155 | }, 156 | { 157 | "cell_type": "code", 158 | "metadata": { 159 | "id": "eiM1EKZ49Y_2", 160 | "outputId": "daa2b44a-3a9f-493d-c11e-05e9bd5c891a", 161 | "colab": { 162 | "base_uri": "https://localhost:8080/" 163 | } 164 | }, 165 | "source": [ 166 | "print(x[0])" 167 | ], 168 | "execution_count": 4, 169 | "outputs": [ 170 | { 171 | "output_type": "stream", 172 | "name": "stdout", 173 | "text": [ 174 | "20\n" 175 | ] 176 | } 177 | ] 178 | }, 179 | { 180 | "cell_type": "markdown", 181 | "metadata": { 182 | "id": "ZB7HOPUY9Y_3" 183 | }, 184 | "source": [ 185 | "We now write the formula for the line\n", 186 | "$$ y=mx+c.$$" 187 | ] 188 | }, 189 | { 190 | "cell_type": "code", 191 | "metadata": { 192 | "id": "Y1hxdDQ39Y_3", 193 | "outputId": "e902a7a9-d4f0-484b-8587-360be1e655f3", 194 | "colab": { 195 | "base_uri": "https://localhost:8080/" 196 | } 197 | }, 198 | "source": [ 199 | "y= m*x+c\n", 200 | "print(y)" 201 | ], 202 | "execution_count": 5, 203 | "outputs": [ 204 | { 205 | "output_type": "stream", 206 | "name": "stdout", 207 | "text": [ 208 | "[16. 16.3 16.6 16.9 17.2 17.5 17.8 18.1 18.4 18.7 19. 19.3 19.6 19.9\n", 209 | " 20.2 20.5 20.8 21.1 21.4 21.7 22. 22.3 22.6 22.9 23.2 23.5 23.8 24.1\n", 210 | " 24.4 24.7 25. 25.3 25.6 25.9 26.2 26.5 26.8 27.1 27.4 27.7 28. 28.3\n", 211 | " 28.6 28.9 29.2 29.5 29.8 30.1 30.4 30.7]\n" 212 | ] 213 | } 214 | ] 215 | }, 216 | { 217 | "cell_type": "markdown", 218 | "metadata": { 219 | "id": "FgIwc08F9Y_3" 220 | }, 221 | "source": [ 222 | "To plot the result we use the __matplotlib__ library function __plt__." 223 | ] 224 | }, 225 | { 226 | "cell_type": "code", 227 | "metadata": { 228 | "id": "qE8a3N6e9Y_3", 229 | "outputId": "dd6e5726-029d-4c7d-f4e5-898c11a6f0d9", 230 | "colab": { 231 | "base_uri": "https://localhost:8080/", 232 | "height": 388 233 | } 234 | }, 235 | "source": [ 236 | "fig = plt.figure(figsize=(6,6)) # This setups the size of the figure\n", 237 | "plt.plot(x,y,'-',color='b')\n", 238 | "plt.xlabel('Age')\n", 239 | "plt.ylabel('Temporal Discrimination (ms)')\n", 240 | "plt.show() # This plots the figure" 241 | ], 242 | "execution_count": 8, 243 | "outputs": [ 244 | { 245 | "output_type": "display_data", 246 | "data": { 247 | "text/plain": [ 248 | "
" 249 | ], 250 | "image/png": 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\n" 251 | }, 252 | "metadata": { 253 | "needs_background": "light" 254 | } 255 | } 256 | ] 257 | }, 258 | { 259 | "cell_type": "markdown", 260 | "metadata": { 261 | "id": "OYy_EVh09Y_4" 262 | }, 263 | "source": [ 264 | "# Problems \n", 265 | "There are three simple problem questions to show how to plot a line in python.\n", 266 | "\n" 267 | ] 268 | }, 269 | { 270 | "cell_type": "markdown", 271 | "source": [ 272 | "## Problem 1\n", 273 | "Re-do the plot with a slope of 1 and an intercept of -5.\n" 274 | ], 275 | "metadata": { 276 | "id": "rPZJos9eCRNj" 277 | } 278 | }, 279 | { 280 | "cell_type": "code", 281 | "metadata": { 282 | "id": "ydBiZ2Ar9Y_4", 283 | "outputId": "0a978e46-2c20-44f6-b80c-b5af569bc35b", 284 | "colab": { 285 | "base_uri": "https://localhost:8080/", 286 | "height": 374 287 | } 288 | }, 289 | "source": [ 290 | "##############################################################################\n", 291 | "## INSERT: Update the slope to 1 and intercept to -5\n", 292 | "##############################################################################\n", 293 | "\n", 294 | "#######################ANSWER###############################\n", 295 | "\n", 296 | "#######################################################################\n", 297 | "\n", 298 | "x=np.arange(20,70,1)\n", 299 | "y= m*x+c\n", 300 | "\n", 301 | "fig = plt.figure(figsize=(6,6))\n", 302 | "plt.plot(x,y,'-',color='red')\n", 303 | "plt.show()" 304 | ], 305 | "execution_count": null, 306 | "outputs": [ 307 | { 308 | "output_type": "display_data", 309 | "data": { 310 | "image/png": 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\n", 311 | "text/plain": [ 312 | "
" 313 | ] 314 | }, 315 | "metadata": { 316 | "tags": [], 317 | "needs_background": "light" 318 | } 319 | } 320 | ] 321 | }, 322 | { 323 | "cell_type": "markdown", 324 | "metadata": { 325 | "id": "tkN77Rnu9Y_5" 326 | }, 327 | "source": [ 328 | "## Problem 2\n", 329 | "Re-do the plot but with a different coloured line." 330 | ] 331 | }, 332 | { 333 | "cell_type": "code", 334 | "metadata": { 335 | "id": "uDqN0g7P9Y_5", 336 | "outputId": "f6a24d18-ed94-4833-9e59-81ee65ec8130", 337 | "colab": { 338 | "base_uri": "https://localhost:8080/", 339 | "height": 391 340 | } 341 | }, 342 | "source": [ 343 | "\n", 344 | "fig = plt.figure(figsize=(6,6))\n", 345 | "##############################################################################\n", 346 | "## INSERT: change the plot function to plot a different coloured line.\n", 347 | "##############################################################################\n", 348 | "\n", 349 | "#######################ANSWER###############################\n", 350 | "m=1\n", 351 | "c=-5\n", 352 | "\n", 353 | "x=np.arange(20,70,1)\n", 354 | "y= m*x+c\n", 355 | "\n", 356 | "fig = plt.figure(figsize=(6,6))\n", 357 | "plt.plot(x,y,'--')\n", 358 | "#######################################################################\n", 359 | "\n", 360 | "plt.show()" 361 | ], 362 | "execution_count": null, 363 | "outputs": [ 364 | { 365 | "output_type": "display_data", 366 | "data": { 367 | "text/plain": [ 368 | "
" 369 | ] 370 | }, 371 | "metadata": { 372 | "tags": [] 373 | } 374 | }, 375 | { 376 | "output_type": "display_data", 377 | "data": { 378 | "image/png": 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\n", 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" 381 | ] 382 | }, 383 | "metadata": { 384 | "tags": [], 385 | "needs_background": "light" 386 | } 387 | } 388 | ] 389 | }, 390 | { 391 | "cell_type": "markdown", 392 | "metadata": { 393 | "id": "AQzcrptU9Y_6" 394 | }, 395 | "source": [ 396 | "## Problem 3\n", 397 | "What is the value of the 5th element of the y vector." 398 | ] 399 | }, 400 | { 401 | "cell_type": "code", 402 | "metadata": { 403 | "id": "87iT4icO9Y_6", 404 | "outputId": "b8de6b3c-bd36-4123-a164-3e5a128b5942", 405 | "colab": { 406 | "base_uri": "https://localhost:8080/" 407 | } 408 | }, 409 | "source": [ 410 | "########## ANSWER ###################\n" 411 | ], 412 | "execution_count": null, 413 | "outputs": [ 414 | { 415 | "output_type": "stream", 416 | "text": [ 417 | "19\n" 418 | ], 419 | "name": "stdout" 420 | } 421 | ] 422 | }, 423 | { 424 | "cell_type": "markdown", 425 | "metadata": { 426 | "id": "WzpgliAh9Y_7" 427 | }, 428 | "source": [ 429 | "---\n", 430 | "# Summary\n", 431 | "\n", 432 | "In this tutorial, we learned:\n", 433 | "\n", 434 | "* To plot a line.\n", 435 | "* To access elements of an array." 436 | ] 437 | } 438 | ] 439 | } -------------------------------------------------------------------------------- /.ipynb_checkpoints/W2T4 Frequencies -checkpoint.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": { 6 | "id": "XFQ4m10G9ZbO" 7 | }, 8 | "source": [ 9 | "# Tuning Curve, Week 2 Tutorial 3" 10 | ] 11 | }, 12 | { 13 | "cell_type": "markdown", 14 | "metadata": { 15 | "id": "lK8n73qF9ZbU" 16 | }, 17 | "source": [ 18 | "In this notebook we will illustrate simple spike analysis for repeated Trials." 19 | ] 20 | }, 21 | { 22 | "cell_type": "markdown", 23 | "metadata": { 24 | "id": "INuPpdSX9ZbV" 25 | }, 26 | "source": [ 27 | "### Libraries" 28 | ] 29 | }, 30 | { 31 | "cell_type": "code", 32 | "execution_count": 1, 33 | "metadata": { 34 | "id": "mi0jlUXN9ZbV" 35 | }, 36 | "outputs": [], 37 | "source": [ 38 | "# LIBRARY\n", 39 | "\n", 40 | "import numpy as np # vector manipulation\n", 41 | "from scipy.stats import norm # Psychometric Function\n", 42 | "from scipy.stats import poisson\n", 43 | "\n", 44 | "# THIS IS FOR PLOTTING\n", 45 | "%matplotlib inline\n", 46 | "import matplotlib.pyplot as plt # side-stepping mpl backend\n", 47 | "import warnings\n", 48 | "warnings.filterwarnings(\"ignore\")" 49 | ] 50 | }, 51 | { 52 | "cell_type": "markdown", 53 | "metadata": { 54 | "id": "8sltgvNI9ZbW" 55 | }, 56 | "source": [ 57 | "## Gaussian Tunning Function\n", 58 | "\n", 59 | "To simulate a single 1000ms trial we generate a matrix of 1000 time 100 trials random numbers between 0 and 1." 60 | ] 61 | }, 62 | { 63 | "cell_type": "code", 64 | "execution_count": 2, 65 | "metadata": {}, 66 | "outputs": [ 67 | { 68 | "data": { 69 | "image/png": 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\n", 70 | "text/plain": [ 71 | "
" 72 | ] 73 | }, 74 | "metadata": { 75 | "needs_background": "light" 76 | }, 77 | "output_type": "display_data" 78 | } 79 | ], 80 | "source": [ 81 | "Orientation=np.arange(-40,40,1)\n", 82 | "Max_Firing=60\n", 83 | "Preferred_Direction=0\n", 84 | "tunning_curve= Max_Firing*norm.pdf(Orientation,Preferred_Direction,10)/max(norm.pdf(Orientation,Preferred_Direction,10))\n", 85 | "fig = plt.figure(figsize=(8,4)) # This setups the size of the figure\n", 86 | "plt.plot(Orientation,tunning_curve,'-',color='black')\n", 87 | "plt.xlabel('Orientation')\n", 88 | "plt.ylabel('Firing Rate (Hz)')\n", 89 | "plt.show() # This plots the figure" 90 | ] 91 | }, 92 | { 93 | "cell_type": "markdown", 94 | "metadata": {}, 95 | "source": [ 96 | "## Sigmoid Tunning Function\n", 97 | "A neuron will only fire if the probability is below the threshold.\n", 98 | "We set the neuron to have 0 spikes at all 1000 time points and 100 trials." 99 | ] 100 | }, 101 | { 102 | "cell_type": "code", 103 | "execution_count": 3, 104 | "metadata": { 105 | "colab": { 106 | "base_uri": "https://localhost:8080/" 107 | }, 108 | "id": "zQTRHlGK9ZbW", 109 | "outputId": "338c674f-d0da-4be9-e6e8-b50bac2de487" 110 | }, 111 | "outputs": [ 112 | { 113 | "data": { 114 | "image/png": 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\n", 115 | "text/plain": [ 116 | "
" 117 | ] 118 | }, 119 | "metadata": { 120 | "needs_background": "light" 121 | }, 122 | "output_type": "display_data" 123 | } 124 | ], 125 | "source": [ 126 | "Disparity=np.arange(-1,1,0.01)\n", 127 | "\n", 128 | "tunning_curve= 40*norm.cdf(Disparity,0,0.2)\n", 129 | "\n", 130 | "\n", 131 | "\n", 132 | "fig = plt.figure(figsize=(8,4)) # This setups the size of the figure\n", 133 | "plt.plot(Disparity,tunning_curve,'-',color='black')\n", 134 | "plt.xlabel('Disparity')\n", 135 | "plt.ylabel('Firing Rate (Hz)')\n", 136 | "plt.show() # This plots the figure" 137 | ] 138 | }, 139 | { 140 | "cell_type": "markdown", 141 | "metadata": { 142 | "id": "DWTnLxR79Zbb" 143 | }, 144 | "source": [ 145 | "## Problem 1\n", 146 | "Plot a gaussian tuning for oriention with a max firing rate of 50Hz at 10 degrees and a baseline firing rate of 10Hz with a standard deviation of 5 degrees.\n" 147 | ] 148 | }, 149 | { 150 | "cell_type": "code", 151 | "execution_count": 4, 152 | "metadata": { 153 | "colab": { 154 | "base_uri": "https://localhost:8080/", 155 | "height": 374 156 | }, 157 | "id": "ll-tN8Nk9Zbb", 158 | "outputId": "09a8b494-fa0f-458f-d31e-13900e20aeef" 159 | }, 160 | "outputs": [ 161 | { 162 | "ename": "ValueError", 163 | "evalue": "x and y must have same first dimension, but have shapes (80,) and (200,)", 164 | "output_type": "error", 165 | "traceback": [ 166 | "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", 167 | "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", 168 | "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0mfig\u001b[0m \u001b[0;34m=\u001b[0m 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{y.shape}\")\n\u001b[1;32m 401\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", 173 | "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (80,) and (200,)" 174 | ] 175 | }, 176 | { 177 | "data": { 178 | "image/png": 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" 181 | ] 182 | }, 183 | "metadata": { 184 | "needs_background": "light" 185 | }, 186 | "output_type": "display_data" 187 | } 188 | ], 189 | "source": [ 190 | "\n", 191 | "\n", 192 | "Orientation=np.arange(-40,40,1)\n", 193 | "##############################################################################\n", 194 | "## INSERT: Plot a gaussian tuning for oriention with a max firing rate of 50Hz at 10 degrees and a baseline firing rate of 10Hz with a standard deviation of 5 degrees.\n", 195 | "\n", 196 | "\n", 197 | "##############################################################################\n", 198 | "#######################ANSWER#################################\n", 199 | "\n", 200 | "\n", 201 | "\n", 202 | "#######################ANSWER#################################\n", 203 | "\n", 204 | "fig = plt.figure(figsize=(8,4)) # This setups the size of the figure\n", 205 | "plt.plot(Orientation,tunning_curve,'-',color='black')\n", 206 | "plt.xlabel('Orientation')\n", 207 | "plt.ylabel('Firing Rate (Hz)')\n", 208 | "plt.show() # This plots the figure" 209 | ] 210 | }, 211 | { 212 | "cell_type": "markdown", 213 | "metadata": { 214 | "id": "6dp5s8jI9Zbe" 215 | }, 216 | "source": [ 217 | "---\n", 218 | "# Summary\n", 219 | "\n", 220 | "In this tutorial, we learned:\n", 221 | "\n", 222 | "* To plot and manipulate a neruonal Tuning function.\n" 223 | ] 224 | }, 225 | { 226 | "cell_type": "code", 227 | "execution_count": null, 228 | "metadata": {}, 229 | "outputs": [], 230 | "source": [] 231 | } 232 | ], 233 | "metadata": { 234 | "colab": { 235 | "include_colab_link": true, 236 | "name": "W1T3 The Psychometric Function.ipynb", 237 | "provenance": [] 238 | }, 239 | "kernelspec": { 240 | "display_name": "Python 3", 241 | "language": "python", 242 | "name": "python3" 243 | }, 244 | "language_info": { 245 | "codemirror_mode": { 246 | "name": "ipython", 247 | "version": 3 248 | }, 249 | "file_extension": ".py", 250 | "mimetype": "text/x-python", 251 | "name": "python", 252 | "nbconvert_exporter": "python", 253 | "pygments_lexer": "ipython3", 254 | "version": "3.8.5" 255 | } 256 | }, 257 | "nbformat": 4, 258 | "nbformat_minor": 1 259 | } 260 | --------------------------------------------------------------------------------