Scientific Computing Using Python - PHYS:4905 - Fall 2018

Lecture #02 - 8/23/2018 - Prof. Kaaret


Objects

When you write x = 17 in Python, you might have thought that you were just putting the value 17 into a variable called x, but you are actually creating an integer object and then making the variable x point to that object.  An object in programming terms, is a collection of data and functions.  The object x is an integer object and has a set of functions that are common to all integers in Python.  For example, x.bit_length() is a function that calculates how many binary bits are needed to write the integer and x.__hex__() is a function that prints out a in hexadecimal or base 16 (Python uses 0x at the start of a number to indicate hexadecimal).  Floats and strings are also objects, but come with different sets of functions more appropriate for floats and strings.

When you execute an expression like x = x+3, Python creates a new integer object, extracts the value from x and adds 3, assigns that to be the value of the new integer object, and then makes the variable x point to the new object.  Integers are immutable, once you make an integer object, you can never change its value.  You have to make a new object everytime you want a integer with a new value.

You can check the type of an object using the type function, e.g. type(x) should return int.

Lists

Python has a built in object for lists.  A list is an ordered set of objects.  The objects can be of any type and mixed types, including lists.  You make lists using square brackets, L = [1.0, 1, x, 'Hi', 1+2j, [2, 1]].

You access the elements of lists using square brackets.  This is call slicing.  The first element of a list is element 0, so L[0] returns 1.0 and L[3] returns 'Hi'.
You can get ranges or slices of elements using a colon. L[3:5] returns ['Hi', (1+2j)]. This is a new list with two elements.  When you slice, you start with the first number in the slice, but end with the one less than the last number.  You can also leave out numbers.  L[3:] returns ['Hi', (1+2j), [2, 1]], while L[:5] returns [1.0, 1, 17, 'Hi', (1+2j)], and L[:] returns the whole list.  The latter doesn't seem that useful for one-dimensional lists, but gets useful when you get into more dimensions or if you want to make a copy of a list.

Lists are mutable, meaning that you can change the contents of the list after you make it.  L[1] = 33 changes L to [1.0, 33, 17, 'Hi', (1+2j), [2, 1]].  Changing an element of a list doesn't make a whole new list.


Tuples

Tuples are like lists, but are made using parentheses, t = (1.0, 2, 'three').  If you want to return multiple values from a function, you use tuples.  Also, we'll use tuples when we need a few numbers grouped together, like specifying the size of a two or three dimensional array.

Arrays

Arrays are objects used to store a set of numbers.  Arrays are not lists.  They often look like lists, but there are many numerically oriented operations that you can do with arrays that you cannot do with lists.  Arrays are not built into Python, rather they are defined in the NumPy library and extend Python.  (One of the reasons that Python is so popular is that it lends itself to being extended.) To use arrays, you need to first import NumPy.  I'll assume that you do this via import numpy as np.  If you use from numpy import *, drop the np. in front of all the function calls below.

You can make one and two dimensional arrays using
v = np.array([1.0, 2.0, 3.0])
a = np.zeros(3)
b = np.ones((3,3))
c = np.arange(0.4, 1.8, 0.1)
r = np.random.random(10)
Note the use of a tuple in making the 2D arrays.  If you forget the extra parenthesis that make the argument of zeros into a tuple, you'll get an error.  The arange function makes an array with evenly (linearly) spaced values.  Like slicing, it starts with the first number, but does not reach the second number. The third number is the spacing.  People sometimes prefer np.linspace.

The great thing about how NumPy extends Python to use arrays is that you can write expressions that work on arrays as a whole without having to worry about the individual components.  For example, to multiply each element of v by 3, just type 3*v.  In more typical programming languages such as C and C++, one need to explicitly write out instruction to multiply each element of the array.  NumPy also has lots (and lots and lots) of functions that work on arrays, for example sum, mean, std (standard deviation), min, max, median, sin, cos, tan, ...

You can find the dimensions of an array using shape(b) or b.shape.  In the latter, note that you do not use b.shape(). The shape parameters are data stored in the array object, so you don't need a function with () to access them.  You can change the shape of an array using the reshape method.  The total number of elements in the new shape must be the same as the total number of elements in the array.

You can slice arrays just like you do lists and you can modify individual or groups of elements in arrays just like you do with lists.  You can also use a list to select a disjoint set of elements in an array. 
q = [2, 4, 7]
v[q]
returns array([0.6, 0.8, 1.1]).
You can use a Boolean array to pick out elements of an array that satisfy some condition.  For example
q = (c > 1.0)
c[q]
returns the elements of c with values greater than one.


Strings

Python can manipulate text in the form of strings.  However, this class is mainly devoted to numerical stuff, so the main function that you need to know is str(), which converts a number to a string.  If you want your numbers to look nice, you need to use the format method or the % operator, but it is better to pick one of the two and then learn it when you have an application at hand to focus your mind. 

Assignment

The remainder of today's class will be devoted to learning the basics of Python by working through the second chapter of the textbook.  As you read the chapter, enter the commands in the purple highlights into Spyder and see what you get.  When you are done with the chapter, do the second assignment which will be due at the start of class on Tuesday.  Also, please do the reading for 8/28 before class on Tuesday.

HW #2 is due at the beginning of class on Tuesday, August 28.
https://homepage.physics.uiowa.edu/~pkaaret/2018f_p4905/hw02.html