COSC 490 Computational Topology

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1 COSC 490 Computational Topology Dr. Joe Anderson Fall 2018 Salisbury University Course Structure Weeks 1-2: Python and Basic Data Processing Python commonly used in industry & academia Weeks 3-6: Group theory, topology of simple structures Graphs are a natural tool to study the structure of spatial data Group theory generalizes many algebraic notions and can formally capture geometric intuition Weeks 7-14: Algebraic topology, algorithms Deep mathematical modeling of data Usually people use statistics, but we will use geometry! How to write programs to use topological models to make inference 1

2 Course Materials Main point of reference: Helpful textbooks Computational Topology by Edelsbrunner and Harer Topology for Computing by Zomorodian A Short Course in Computation Geometry and Topology by Edelsbrunner Elementary Applied Topology by Ghrist Technology Python w/ scientific computing libraries (via the Anaconda distribution manager - GNU/Linux and C++ with graphics libraries (e.g. trimesh ) Homework 0 Find my office (DH 140) and come say hello Install Python, verify that the example script on the course webpage (pytest.py) runs without error (using the system-provided Python is not recommended) Familiarize with Python 3 functionality, syntax 2

3 Getting Python Highly recommended: the Anaconda Python environment manager On COSC Linux, use install script to install to your own home directory Why? Python is maturing and the community is quite large Has had far more growing pains than a language like C++ because of its widespread usage New and different libraries have come along that do not always interact well together What is Anaconda? A single install that brings along Python, some important libraries (numpy and scipy) for scientific computing A package manager to easily add more Python libraries and tools Python Overview High-level language Many common built-in types, but also uses more abstraction than, e.g. C++ Example: an array in Python is automatically of flexible size, and can hold mixed data values Dynamic Variables are not created with a fixed type, can be re-assigned to any type Everything is (usually) a pointer automatically, no -> notation needed Interpreted Programs are read and executed line-by-line, not compiled Can be programmed interactively see the results of each line before you type the next one 3

4 Python To open the interpreter (on Linux) on the command-line, type python and press Enter You can now type Python code and when you press Enter, the line will be either executed or continued on the next line (in the case of control-flow, like if-statements and for-loops) Some big syntactic differences No semi-colons to end statements, need newlines No brackets to designate blocks, instead blocks are determined by indentation No explicit variable types, return types, or parameter types Python Example highlights: 4

5 Get in and practice! Consult the Python and Numpy documentation frequently! Homework 1 On webpage, practice writing some Python scripts for numerical manipulation Program speed and efficiency count! Solutions should not need more than a few seconds to complete (Computational topology will be much more difficult to solve computationally, better get fast now!) Python for Numerical Manipulation Check out: Key topics: Vectorizing Broadcasting Shaping Slicing Plots 5

6 More Python tools: ipython Very similar environment to Mathematica But Python driven! Can save as Python script easily Comes installed with the Anaconda (hooray!) To access: open a terminal and execute jupyter notebook Errors? Make sure your anaconda folder is added to your PATH environment variable Example: Graph algorithms Graph is a pair G = (V,E) of vertices and edges Questions: 1. How do we represent a graph programmatically? 2. What are the structural properties of the graph? 3. How can we represent and compute the structure? 6

7 Using ipython + Jupyter For graphs: (Sigh) install the graphviz library with pip install graphviz for documentation Computations happen in individual cells like Mathematica To execute a cell, press Shift+Enter The results will be displayed below The environment is persistent across cells! To clear your environment (variables and functions) use the restart the kernel button 7