September 7, 2004 --- Class 3  --- Redirection, Axis, AWK, Intro to Euler Method

Activities:

	Filters, Pipelines and Redirection

		UNIX has some wonderful facilities that make it easy to
		combine simple commands together to do complex jobs.  The
		key ideas are "standard input", "standard  output",
		and pipelines.

		Many commands require input to do their work and are
		set up to use the "standard input", which is normally
		the keyboard.  Suppose you have prepared a file with
		the input you want because you know there are a lot of
		commands and you may make a typo.  In UNIX do this:

		command < infile

		This runs "command", but tells it to "redirect" the input
		from the keyboard to the file named infile.  So, the infile
		is used as the input and you don't have to type all the
		input commands.  If the file is setup, so that its output
		goes to the "standard output", you will see the output
		at the screen.  But, what is good for the input, is good
		for the output, so if we type

		command < infile > outfile

		then what would go to the screen instead is redirected to the
		file outfile.

		Any program that takes its input from the standard input
		and sends its output to the standard output is called a filter.
		Think of a red filter.  On the input side is any kind of light.
		On the output is only the red component of the incoming
		light.  With filters, you can then pass the light through
		another filter further modify the light.  In UNIX, a filter
		takes information from the standard input, modifies it and
		sends it to the standard output.  But how do we send the
		output of one filter to the input of another?  We do that with
		a pipeline.

		filter1 <in1 | filter2 > out2

		takes input from in1 and runs command filter1, then it
		takes the output of filter1 and uses is as the input to
		command filter2.  Finally, it puts the results in file out2.
		We will have many opportunities to use this capability.

	axis
		
		axis is a simple graphics program that can make publication
		quality graphs.  You may wish to use it for this class and
		your other work.  There is a color version of axis.  You should
		use
		/usr/local/bin/axis and /usr/local/bin/plot

		The following potential problem has not arisen recently, so
		if /usr/local/bin/axis </dev/null |/usr/local/bin/plot -T x
		works for you, skip to the next paragraph.
		You will also need to make sure that the loader looks in
		/usr/local/lib for the plotting library.  To do this, you
		use the command:
		setenv LD_LIBRARY_PATH /usr/local/lib:$LD_LIBRARY_PATH
		or 
		setenv LD_LIBRARY_PATH /usr/local/lib:/opt/SUNWspro/lib:/usr/dt/lib:/usr/openwin/lib:/usr/lib:/lib

		To plot the data in file data, the command is
		/usr/local/bin/axis <data | /usr/local/bin/plot -T X
		if you want output to come to the screen.  If you
		to print your graph, use 
		/usr/local/bin/axis <data | /usr/local/bin/plot -T ps |lpr
		or 
		/usr/local/bin/axis <data | /usr/local/bin/plot -T ps >data.ps
		lpr data.ps
	
		The axis handout has many more details of how to make a nice
		graph.

	AWK
		If you have \delta t values in a file and you want to have
		\delta t and 0.5*(\delta t)^2 on each line, it is easy to
		do this with an awk command.  Assume the \delta t are in
		a file with one value per line and the file is called col.

		awk '{print $1,0.5*$1*$1}' col
		
		will result in two columns with the desired numbers.  The output
		may be redirected to a file if desired.

		awk may be used to create a list of numbers, as well
		awk 'END{for(i=1;i<$1; ++i) print 0.01*i}'
		can be used and you may interactively type a number and
		then on the next line ^D (which stands for pressing d, while
		holding down the control key).

		AWK is a very versatile pattern matching utility that can be
		used to manipulate files.  Each AWK commands consists or a
		pattern followed by an action.  If the pattern is matched, the
		action is performed.  The action is placed inside curly
		braces.  A very simple awk command is:
		  awk '{print}' file_name
		The single quotes protect the curly braces from being 
		interpreted by the shell as special characters.  In this
		AWK command, there is no pattern to match, so the print
		command is always invoked.
		  awk '/1/ {print}' file_name
		has a pattern that matches any line containing the character 1.
		Only such lines will be printed.
		  awk '/^1/ {print}' file_name
		In this example, "^" is a special character to indicate the 
		beginning of a line.  Thus, only lines that begin with "1"
		will be printed.
		  awk '{print $2}' file_name
		will result in the second word of each line being printed.
		(Words are separated by white space, i.e., spaces or tabs.)
		  awk '{print $2,$1}' file_name
		prints the second word followed by the first word.

		You might like to try to the above examples with the file
		cols that you are welcome to copy from my home directory.

	Tea or coffee cooling problem (CSM, Sec. 2.1)
		This is the problem discussed in chapter 2.  Should you add
		the milk to the tea as soon as it is poured, or just before
		you want to drink it in order to cool it as quickly as possible?
		To solve this problem, we are going to learn to integrate a
		differential equation numerically via the Euler method.

	A simple integral first (CSM, Secs. 2.2-2.5)
		In ~sg/chap2 you will find a file euler.c that you can use
		to do a numerical integral.  It might be set up with the
		function 2*x or 3*x^2.

		To create an executable either type:
		make euler.c
		or
		cc -o euler euler.c

		I looked at two step sizes 0.1 and 0.05.  The numerical output
		is more accurate for smaller step size.

		In the next class, we will:

		1) Make a graph of the result as a function of x.

		2) Try different step sizes and see that the answer varies, but
		converges as the step size decreases.

		3) Create (understand) the script ~sg/chap2/ans_vs_step.csh

		4) Plot the result as a function of step size.

It would be useful if you read Chapter 2 before the next class.  You 
don't have to solve the problems! (Yet)  Some will be assigned for homework.