List comprehensions

Introducing Python and Sage

print(list1_stripped_2)

list2 = []

for val in srange(0.0, 10.0, 1.0): if val % 2 == 0:

list2.append(numerical_approx(val**2, digits=3)) print(list2)

list3 = [numerical_approx(val**2, digits=3) for val in srange(0.0, 10.0, 1.0) if val % 2 == 0]

print(list3)

Run the example. You should get:

What just happened?

This example demonstrated how a list comprehension can be used in place of a for loop to create a list. In the first part of the example, we defined a list of strings, each of which contained whitespace before and/or after the character. First, we defined an empty list and used a for loop to iterate over the list of strings. The string method strip was used to remove the whitespace from each string, and we used the list method append to create a new list of stripped strings. We then used a list comprehension to perform the same operation. The general syntax for a list comprehension is:

new_list = [ operation_on_value for value in existing_list ]

If you are creating a new list, then the existing list can be generated by a function like range or srange. In the second part of the example, we used a for loop with the srange function to generate a list of even floating-point numbers. We used an if clause so that our list

will contain only squares of even numbers. We did this to demonstrate how the if clause works—a better way to generate a list of even numbers would be to give srange a step size of two. We then repeated the operation with a list comprehension. We'll learn more about if statements soon. List comprehensions are somewhat more compact than an equivalent for loop. For more examples of list comprehensions, see http://docs.python.org/ tutorial/datastructures.html#list-comprehensions

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Chapter 4

WhileloopsandtextfileI/O

Lists and loops are the two basic tools we need to access data that is stored in a file. The problem with using a for loop to access a data file is that we don't necessarily know how many iterations will be needed, because we don't always know how many lines are in the file. The solution is to use a while loop.

Timeforaction–savingdatainatextfile

Let's save the results of a calculation to a text file. In the next example, we will get the data back into Sage. When you enter the following code, change the path to the data file so that it gets saved in a convenient location.

from matplotlib import pyplot as plt import os

# Create some data

times = srange(0.0, 10.0, 0.1) data = [sin(t) for t in times]

#Plot the data plt.figure(figsize=(6,4)) plt.plot(times, data) plt.savefig('example2a.png') plt.close()

#Save data to a text file

path = '/Users/cfinch/Documents/Writing/Sage for Beginners/Chapters/ Chapter 4/'

fileName = 'data.txt'

text_file = open(os.path.join(path, fileName), 'w') for i in range(len(data)):

text_file.write('{0}, {1}{2}'.format(times[i], data[i], os.linesep))

text_file.close()

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Introducing Python and Sage

Run the script using one of the methods previously described. A plot of the data is saved to a

PNG file, and the data is saved to a text file with two columns. The plot should look like this:

The first few lines of the text file should look like this:

0.000000000000000, 0.000000000000000 0.100000000000000, 0.0998334166468282 0.200000000000000, 0.198669330795061

What just happened?

We used the srange function to generate a list of time points, and then used a list comprehension to create a list containing the sine of each time point. We plotted the data, using the pyplot interface to matplotlib, like we did in a previous example. The data was then saved to a text file.

The file object is the key component in file operations. A file object is created using the open function:

text_file_object = open('data.txt', 'w')

The first argument to open is a string containing the name of the file. The second argument is a string that indicates in which mode the file should be opened. The first letter of the mode string chooses read, write, or append mode. The letter b can be appended to the mode string to indicate that the file should be opened in binary mode. If the mode string is omitted, the file is opened for reading in text mode.

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Introducing Python and Sage

# Read in the data file times = []

data = []

text_file = open(os.path.join(path, fileName), 'r') line = text_file.readline()

while len(line) > 0: print(line)

#split each line into a list of strings elements = line.split(',')

#Strip newlines and convert strings to real numbers times.append(float(elements[0].strip())) data.append(float(elements[1].strip()))

line = text_file.readline()

text_file.close()

# Plot the data plt.figure() plt.plot(times, data) plt.savefig('example2b.png') plt.close()

The data is plotted to another image file. This plot should be identical to the plot in the previous example. When you run this example in the Notebook interface, Sage will not print every line of the file. When text output gets too long, Sage will truncate the output and provide a link that you can click to see the rest of the output. The result will look like this:

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Chapter 4

What just happened?

This script demonstrated how to open a text file for reading and read in one line at a time. The open function was used to create a file object as previously described. Since we are reading data, the readline method was used to read one line of data from the file and return the line as a string. Once again, we used the os module to handle operations involving paths and newlines.

Whileloops

A while loop is used when we don't know how many iterations will be required. The general syntax for a while loop is:

while conditional_expression: statement 1

statement 2

...

The loop iterates as long as the conditional expression evaluates to the Boolean value True. The loop terminates as soon as the expression evaluates to False. In this example, the loop iterates as long as the string that is read from the file has one or more characters. The readline method returns a string for every line in the file. Even a blank line has a newline character, so the conditional expression will be True for every line in the file. The readline method returns an empty string after reading the last line of the file, which causes the conditional expression to evaluate to False and end the loop. There are two very important things to remember when using a while loop:

1.Make sure the conditional expression can be evaluated before the first iteration of the loop. In the example, the first line is read from the file before the while loop.

2.Make sure that the conditional expression will evaluate to False at some point. Otherwise, the loop will repeat endlessly. The last statement of the loop in the example loads another line from the file. When the end of the file is reached, the conditional expression will evaluate to False.

Parsingstringsandextractingdata

Since each line of the file was read as single string, we had to do some work to extract the numerical data. First, we used the split method of the string object to break the string at the comma:

elements = line.split(',')

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Introducing Python and Sage

The result was a list of strings called elements. The first element of this list is the string that contains the time value. Next, we used the strip method of the string object to remove any unnecessary white space, such as the invisible newline character that is found at the end of every line:

elements[0].strip()

Finally, we used the float function to convert the string to a Python floating-point number, and appended the result to a list. In the example, the parsing operations were combined like this:

times.append(float(elements[0].strip()))

data.append(float(elements[1].strip()))

Finally, the lists are ready to be plotted.

Alternativeapproachtoreadingfromatextfile

A Python file object is iterable, which means that you can iterate over a file object just like you can iterate over a list. This allows you to use the following syntax:

for line in text_file:

#split each line into a list of strings elements = line.split(',')

#Strip newlines and convert strings to real numbers times.append(float(elements[0].strip()))

When using this approach, you should not include a call to text_file.readline() in the loop body.

Haveagohero–defineafunctionforreadingthetextfile

It's good practice to organize your code as you're writing. In the previous example, we should separate the code that reads the data from the file from the code that does the plotting. Define a function that takes a file name as an argument and reads the data. Use a tuple to return a list of time values and a list of data values. Call the function to read the data, and to plot the data.

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