CIS192 Python Programming
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1 CIS192 Python Programming Scientific Computing Eric Kutschera University of Pennsylvania March 20, 2015 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
2 Course Feedback Let me know what you like/don t Anonymous Really Short The link is also on Piazza Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
3 Outline 1 NumPy and SciPy NumPy SciPy 2 Extra Packages Matplotlib SymPy 3 Data Storage Pickle Pandas PyTables Hdf5 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
4 NumPy NumPy is the base module for scientific computing Like Matlab but with Python! pip install numpy It provides: An effecient Matrix type Basic Matrix operations (Multiplication, Logical And) Linear Algebra (Eigenvectors, Nullspace) Fourier Transforms, Statistical operations, Random matrices Like Matlab, NumPy has an effcient C/C++ implementation vector operations Brodcasting (Vector operations on Matrices) The Numpy ndarray is the standard interface Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
5 Using a NumPy ndarray import numpy as np Create from Python sequence np.array([1, 3, 5, 2]) Create Matlab style np.zeros((2, 3)) np.arrange((1, 5, 0.5)) Be careful to supply tuple arguments. You ll need extra parens Indexing into matrix returns a view over the data x[2] gets the 3 rd element or third row x[1, 3] gets the 2 nd row 4 th column x[1][3] works but is inefficient x[1:5:2,::3] gets rows 1 and 3 with columns 0, 3, 6,... Indexing with an ndarray gives a copy of the data x[np.array([0,5,2])] new ndarray with 1 st, 6 th, 3 rd elements Even more complex indexing if you need it Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
6 NumPy Data Types ndarrays must be homogeneous if using numpy base types You can mix types if you use Python built-ins or NumPy objects C style numeric types bool_ 1 byte bool int_ C long intc C int int8, int16,..., int64 uint8, uint16,..., uint64 float16, float32, float64 complex64, complex128 Specify the data type np.array([0, 1], dtype=np.bool_) Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
7 Iterating Arrays support v for v in array 2 dimensional arrays support v for row in matrix for v in row Create an iterator for arbitrary dimensions with np.nditer Iteration order defaults to order in memory Can specify order with kwarg nditer(a, order= (F/C) ) order= F is Fortran Column Major order= C is C/C++ Row Major it = np.nditer(a, flags=[ multi_index ]) for v in it: v, it.multi_index # value, (row, col,...) Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
8 NumPy Operations Can do element-wise arithmetic with +, -, *, / Matrix dimensions must match or be broadcast Dimension mismatch with one of the inputs having dimension 1: Numpy tries to broadcast the single values Numpy copies that value as many times as necessary Matrix multiplication with np.dot(a, b) Logical operations np.logical_and, np.logical_or,... Returns new array of element-wise results Comparisons np.greater(m1, m2) m1 > m2 Returns new array of element-wise results Don t use in conditional if m1 < m2 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
9 Additional Operations np.fft For discrete and continuous Fourier transforms Linear algebra import numpy.linalg as la la.matrix_power(m, n), la.eig(m), la.norm(v) import numpy.matlib np.matlib.rand(dimens) random matrix from numpy.polynomial.polynomial import Polynomial Polynomial([-6, 1, 1], ) x 2 + x 6 Algebra, roots, least-squares,... Statistics np.percentile, np.median, np.var,... Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
10 Outline 1 NumPy and SciPy NumPy SciPy 2 Extra Packages Matplotlib SymPy 3 Data Storage Pickle Pandas PyTables Hdf5 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
11 SciPy More powerful operations built on top of Numpy Covers basically everything built-in to Matlab Symbolic math in SymPy Graphical Plots in matplotlib pip install scipy Broken into sub-packages Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
12 Integrate from scipy import integrate as inte General purpose numeric integration inte.quad(f, a, b) Numericaly evaluates b a f (x)dx inte.dblquad(f, a, b, g, h) evaluates b a h(x) g(x) f (x, y)dydx inte.tplquad(f, a, b, g, h, q, r) evaluates b h(x) r(x) a g(x) q(x) f (x, y, z)dzdydx Returns a tuple (y, abserr) y is the result err is an upper bound on the absolute value of the error Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
13 Linalg from scipy import linalg linalg.inv(a) A 1 x = linalg.solve(a,b) Ax = b Construct Special Matrices linalg.pascal linalg.hilbert Matrix decomposition linalg.svd(a) Singular Value Decomposition linalg.lu(a) LU factorization Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
14 Stats from scipy import stats as st Lots of random distributions st.norm: normal/gaussian distribution st.poisson: Poisson distribution st.expon: Exponential Random Variable Given a distribution, d d.pdf(x) probability density function d.cdf(x) cumulative distribution function d.pmf(x) probability mass function for DRVs d.mean() d.var() variance Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
15 Outline 1 NumPy and SciPy NumPy SciPy 2 Extra Packages Matplotlib SymPy 3 Data Storage Pickle Pandas PyTables Hdf5 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
16 Matplotlib Built on top of NumPy Intends to emulate Matlab plotting pip install matplotlib import matplotlib.pyplot as plt plt.plot(xs, ys) plt.show() xs and ys are sequences of numbers Omitting xs defaults to range(len(ys)) Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
17 Plot Attributes plt is stateful plt remembers the current figure and settings Change the boundaries plt.axis([xmin, xmax, ymin, ymax]) Label the axis plt.ylabel( Y Label ) plt.xlabel( X Label ) Set line colors with strings plt.plot(x, y, r ) Save plot as image plt.savefig( f_name.ext ) Most of the features of Matlab plotting Multiple figures, grids, histograms, step plots,... Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
18 Outline 1 NumPy and SciPy NumPy SciPy 2 Extra Packages Matplotlib SymPy 3 Data Storage Pickle Pandas PyTables Hdf5 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
19 SymPy Symbolic mathematics (as opposed to numeric solutions) Similar features to Wolfram Mathematica Free and Open Source Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
20 Outline 1 NumPy and SciPy NumPy SciPy 2 Extra Packages Matplotlib SymPy 3 Data Storage Pickle Pandas PyTables Hdf5 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
21 Pickle Pickle is a built-in data serialization protocol Stores a Python data type to a binary file Useful for Saving the results of a computation Communicating data between Python processes A Pickle object supports only full reads Need something more complex to read out partial information Pickle is not a database Pickle is not compressed import pickle will try to import the optimized cpickle falls back to the Python implementation, pickle Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
22 Using Pickle pickle.dump(obj, f_handle) Serializes a Python object into a byte stream Writes that stream to the open file handle The file must be open in binary mode open(f_name, wb ) obj = pickle.load(f_handle) returns a Python object by inverting the Pickling process The file must be open in binary mode open(f_name, rb ) Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
23 What Can Be Pickled Built-ins: None, booleans, numbers lists, tuples, sets, dictionaries Functions and Classes defined at the top-level of a module User defined: Functions and Classes defined at the top-level of a module Instances of Classes defined at the top-level: If that class s dict can be Pickled Functions and classes are Pickled by a fully qualified name The code for the class or function is not pickled Just the name module.function_name The un-pickling environment must have access to those modules The code in the un-pickling environment is used Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
24 Outline 1 NumPy and SciPy NumPy SciPy 2 Extra Packages Matplotlib SymPy 3 Data Storage Pickle Pandas PyTables Hdf5 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
25 Pandas Python Data Analysis Library Goal is to process Large data sets in Python Instead of using R (A Domain Specific Language) It s Fast: Critical Code is written in C Like Relational Databases (SQL): Allows data searching and group-by Can use aggregation functions over queries Unlike Databases: Pandas is optimized for in memory processing Databases are optimized for File-System access Use Pandas if your data fits in RAM Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
26 Using Pandas pip install pandas import pandas as pd Read in data as a DataFrame: Excel: df = pd.read_excel( f_name.xlsx, sheet ) Comma Separated Value: df = pd.read_csv( f_name.csv ) HDF5: df = pd.read_hdf( f_name.h5, data_name ) Sort: df.sort(columns=[ 1st_col_name, 2nd_col ]) Select: df[df.col > 0] Stats: df.mean() The average for each column Transform: df.apply(lambda col: f(col), axis=0) Transform: df.apply(lambda row: f(row), axis=1) Write: df.to_(csv/excel/hdf)(...) Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
27 Outline 1 NumPy and SciPy NumPy SciPy 2 Extra Packages Matplotlib SymPy 3 Data Storage Pickle Pandas PyTables Hdf5 Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
28 PyTables Hdf5 A Python library for the HDF5 API Fast access to data that is too big for RAM Allows for SQL-style queries Faster than Relational SQL Databases Simple design Fast but fewer features Standard interface: Send data between programs (Matlab, Mathematica) Eric Kutschera (University of Pennsylvania) CIS 192 March 20, / 28
Chapter 3 Software Packages to Install How to Set Up Python Eclipse How to Set Up Eclipse... 42
Table of Contents Preface..... 21 About the Authors... 23 Acknowledgments... 24 How This Book is Organized... 24 Who Should Buy This Book?... 24 Where to Find Answers to Review Questions and Exercises...
CIS192 Python Programming
CIS192 Python Programming Introduction Eric Kutschera University of Pennsylvania January 16, 2015 Eric Kutschera (University of Pennsylvania) CIS 192 January 16, 2015 1 / 30 Outline 1 Logistics Rooms and
Review Questions in Introductory Knowledge... 37
Table of Contents Preface..... 17 About the Authors... 19 How This Book is Organized... 20 Who Should Buy This Book?... 20 Where to Find Answers to Review Questions and Exercises... 20 How to Report Errata...
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