Chapter 6

The file src/files/xy.dat contains two columns of numbers, corresponding to \(x\) and \(y\) coordinates on a curve. The start of the file looks as this: \(\begin{array}{cc}-1.0000 & -0.0000 \\ -0.9933 & -0.0087 \\ -0.9867 & -0.0179 \\ -0.9800 & -0.0274 \\ -0.9733 & -0.0374\end{array}\) Make a program that reads the first column into a list \(\mathrm{x}\) and the second column into a list y. Then convert the lists to arrays, and plot the curve. Print out the maximum and minimum \(y\) coordinates. (Hint: Read the file line by line, split each line into words, convert to float, and append to \(\mathrm{x}\) and y.) Name of program file: read_2columns.py

Files with data in a tabular fashion are very common and so is the operation of the reading the data into arrays. Therefore, the scitools.filetable module offers easy-to-use functions for loading data files with columns of numbers into NumPy arrays. First read about scitools.filetable using pydoc in a terminal window (cf. page 80). Then solve Exercise \(6.1\) using appropriate functions from the scitools.filetable module. Name of program file: read_2columns_filetable.py.

Imagine that a GPS device measures your position at every \(s\) seconds. The positions are stored as \((x, y)\) coordinates in a file src/files/pos.dat with the an \(x\) and \(y\) number on each line, except for the first line which contains the value of \(s\). First, load \(s\) into a float variable and the \(x\) and \(y\) numbers into two arrays and draw a straight line between the points (i.e., plot the \(y\) coordinates versus the \(x\) coordinates). The next task is to compute and plot the velocity of the movements. If \(x(t)\) and \(y(t)\) are the coordinates of the positions as a function of time, we have that the velocity in \(x\) direction is \(v_{x}(t)=d x / d t\), and the velocity in \(y\) direction is \(v_{y}=d y / d t .\) Since \(x\) and \(y\) are only known for some discrete times, \(t_{k}=k s, k=0, \ldots, n-1\), we must use numerical differentation. A simple (forward) formula is \(v_{x}\left(t_{k}\right) \approx \frac{x\left(t_{k+1}\right)-x\left(t_{k}\right)}{s}, \quad v_{y}\left(t_{k}\right) \approx \frac{y\left(t_{k+1}\right)-y\left(t_{k}\right)}{s}, \quad k=0, \ldots, n-2\) Compute arrays vx and vy with velocities based on the formulas above for \(v_{x}\left(t_{k}\right)\) and \(v_{y}\left(t_{k}\right), k=0, \ldots, n-2 .\) Plot vx versus time and vy versus time. Name of program file: position2velocity.py.

The program src/basic/lnsum.py produces, among other things, this output: $$ \begin{aligned} &\text { epsilon: } 1 e-04, \text { exact error: } 8.18 \mathrm{e}-04, \mathrm{n}=55 \\ &\text { epsilon: } 1 \mathrm{e}-06, \text { exact error: } 9.02 \mathrm{e}-06, \mathrm{n}=97 \\ &\text { epsilon: } 1 \mathrm{e}-08, \text { exact error: } 8.70 \mathrm{e}-08, \mathrm{n}=142 \\ &\text { epsilon: } 1 \mathrm{e}-10, \text { exact error: } 9.20 \mathrm{e}-10, \mathrm{n}=187 \\ &\text { epsilon: } 1 \mathrm{e}-12, \text { exact error: } 9.31 \mathrm{e}-12, \mathrm{n}=233 \end{aligned} $$ Redirect the output to a file. Write a Python program that reads the file and extracts the numbers corresponding to epsilon, exact error, and \(\mathrm{n}\). Store the numbers in three arrays and plot epsilon and the exact error versus \(\mathrm{n}\). Use a logarithmic scale on the \(y\) axis, which is enabled by the \(\log =\) ' \(\mathrm{y}\) ' keyword argument to the plot function. Name of program file: read_error.py.

The purpose of this exercise is to tell you how hard it may be to write Python programs in the standard programs that most people use for writing text. Type the following one-line program in either Microsoft Word or OpenOffice: $$ \text { print "Hello, World!" } $$ Both Word and OpenOffice are so "smart" that they automatically edit "print" to "Print" since a sentence should always start with a capital. This is just an example that word processors are made for writing documents, not computer programs. Save the program as a .doc (Word) or .odt (OpenOffice) file. Now try to run this file as a Python program. You will get a message SyntaxError: Non-ASCII character Explain why you get this error. Then save the program as a .txt file. Run this file as a Python program. It may work well if you wrote the program text in Microsoft Word, but with OpenOffice there may still be strange characters in the file. Use a text editor to view the exact contents of the file. Name of program file: office.py.

Writing if a: or while a: in a program, where a is some object, requires evaluation of a in a boolean context. To see the value of an object a in a boolean context, one can call bool (a). Try the following program to learn what values of what objects that are True or False in a boolean context: Write down a rule for the family of Python objects that evaluate to False in a boolean context. \(\diamond\)

Suppose we have measured the oscillation period \(T\) of a simple pendulum with a mass \(m\) at the end of a massless rod of length \(L\). We have varied \(L\) and recorded the corresponding \(T\) value. The measurements are found in a file src/files/pendulum. dat, containing two columns. The first column contains \(L\) values and the second column has the corresponding \(T\) values. Load the \(L\) and \(T\) values into two arrays. Plot \(L\) versus \(T\) using circles for the data points. We shall assume that \(L\) as a function of \(T\) is a polynomial. Use the NumPy utilities polyfit and poly1d, as explained in Exercise 6.4, and experiment with fitting polynomials of degree 1,2 , and 3. Visualize the polynomial curves together with the experimental data. Which polynomial fits the measured data best? Name of program file: fit_pendulum_data.py.

For each of a collection of weather forecast sites, say $$ \begin{aligned} &\text { http://weather.yahoo.com } \\ &\text { http://www.weather.com } \\ &\text { http://www.weatherchannel.com } \\ &\text { http://weather.cnn.com } \\ &\text { http://yr.no } \end{aligned} $$ find the pages corresponding to your favorite location. Study the HTML sources and write a function for each HTML page that downloads the web page and extracts basic forecast information: date, weather type (name of symbol), and temperature. Write out a comparison of different forecasts on the screen. Name of program file: weather_forecast_comparison1.py.