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<H1>Grace Tutorials</H1>

<H2>Edward Vigmond
<CODE>evigmon@tulane.edu</CODE></H2>for Grace-5.1.4
<P>
<H2><A NAME="toc1">1.</A> <A HREF="Tutorial.html#s1">Introduction</A></H2>

<UL>
<LI><A NAME="toc1.1">1.1</A> <A HREF="Tutorial.html#ss1.1">Purpose</A>
<LI><A NAME="toc1.2">1.2</A> <A HREF="Tutorial.html#ss1.2">Nomenclature</A>
<LI><A NAME="toc1.3">1.3</A> <A HREF="Tutorial.html#ss1.3">Computer System</A>
<LI><A NAME="toc1.4">1.4</A> <A HREF="Tutorial.html#ss1.4">Generalities</A>
<LI><A NAME="toc1.5">1.5</A> <A HREF="Tutorial.html#ss1.5">Disclaimer</A>
</UL>
<P>
<H2><A NAME="toc2">2.</A> <A HREF="Tutorial.html#s2">Making a Simple Graph</A></H2>

<UL>
<LI><A NAME="toc2.1">2.1</A> <A HREF="Tutorial.html#ss2.1">Reading the data from a file</A>
<LI><A NAME="toc2.2">2.2</A> <A HREF="Tutorial.html#ss2.2">Set appearance</A>
<LI><A NAME="toc2.3">2.3</A> <A HREF="Tutorial.html#ss2.3">Labelling the axes using the font tool</A>
<LI><A NAME="toc2.4">2.4</A> <A HREF="Tutorial.html#ss2.4">Graph titles</A>
<LI><A NAME="toc2.5">2.5</A> <A HREF="Tutorial.html#ss2.5">Legends</A>
<LI><A NAME="toc2.6">2.6</A> <A HREF="Tutorial.html#ss2.6">A challenge</A>
</UL>
<P>
<H2><A NAME="toc3">3.</A> <A HREF="Tutorial.html#s3">Block Data</A></H2>

<P>
<H2><A NAME="toc4">4.</A> <A HREF="Tutorial.html#s4">Creating sets within Grace</A></H2>

<UL>
<LI><A NAME="toc4.1">4.1</A> <A HREF="Tutorial.html#ss4.1">By formula</A>
<LI><A NAME="toc4.2">4.2</A> <A HREF="Tutorial.html#ss4.2">In spreadsheet</A>
<LI><A NAME="toc4.3">4.3</A> <A HREF="Tutorial.html#ss4.3">In text editor</A>
<LI><A NAME="toc4.4">4.4</A> <A HREF="Tutorial.html#ss4.4">From block data</A>
</UL>
<P>
<H2><A NAME="toc5">5.</A> <A HREF="Tutorial.html#s5">Batch plotting </A></H2>

<UL>
<LI><A NAME="toc5.1">5.1</A> <A HREF="Tutorial.html#ss5.1">Simple nonGUI printing</A>
<LI><A NAME="toc5.2">5.2</A> <A HREF="Tutorial.html#ss5.2">Multiple graphs</A>
<LI><A NAME="toc5.3">5.3</A> <A HREF="Tutorial.html#ss5.3">Things for which no command line option exists</A>
</UL>
<P>
<H2><A NAME="toc6">6.</A> <A HREF="Tutorial.html#s6">Fitting curves </A></H2>

<UL>
<LI><A NAME="toc6.1">6.1</A> <A HREF="Tutorial.html#ss6.1">Linear Regression</A>
<LI><A NAME="toc6.2">6.2</A> <A HREF="Tutorial.html#ss6.2">Non-linear</A>
</UL>
<P>
<H2><A NAME="toc7">7.</A> <A HREF="Tutorial.html#s7">Transformations </A></H2>

<UL>
<LI><A NAME="toc7.1">7.1</A> <A HREF="Tutorial.html#ss7.1">Graphical </A>
<LI><A NAME="toc7.2">7.2</A> <A HREF="Tutorial.html#ss7.2">Restrictions</A>
</UL>
<P>
<H2><A NAME="toc8">8.</A> <A HREF="Tutorial.html#s8">Using Pipes </A></H2>

<UL>
<LI><A NAME="toc8.1">8.1</A> <A HREF="Tutorial.html#ss8.1">Instead of data files</A>
<LI><A NAME="toc8.2">8.2</A> <A HREF="Tutorial.html#ss8.2">Named pipes</A>
</UL>
<P>
<H2><A NAME="toc9">9.</A> <A HREF="Tutorial.html#s9">Multiple Graphs</A></H2>

<UL>
<LI><A NAME="toc9.1">9.1</A> <A HREF="Tutorial.html#ss9.1">Selecting graphs</A>
<LI><A NAME="toc9.2">9.2</A> <A HREF="Tutorial.html#ss9.2">Overlaying Graphs</A>
</UL>
<P>
<H2><A NAME="toc10">10.</A> <A HREF="Tutorial.html#s10">Hot Links</A></H2>

<UL>
<LI><A NAME="toc10.1">10.1</A> <A HREF="Tutorial.html#ss10.1">File containing a Single Set</A>
<LI><A NAME="toc10.2">10.2</A> <A HREF="Tutorial.html#ss10.2">Multiple sets within a file</A>
<LI><A NAME="toc10.3">10.3</A> <A HREF="Tutorial.html#ss10.3">Updating by hot keys</A>
</UL>

<HR>
<H2><A NAME="s1">1.</A> <A HREF="#toc1">Introduction</A></H2>

<P>These tutorials assumes that you are a new user to Grace but are somewhat
familiar with a windowing system. They are designed to show you some of the
basic operation of Grace as well as a few of its less intuitive features. Please
feel free to go beyond the bounds of the actions described herein and explore
the possibilities of using Grace. After all, you will be the one who benefits.<CODE></CODE></P>
<H2><A NAME="ss1.1">1.1</A> <A HREF="#toc1.1">Purpose</A>
</H2>

<P>The purpose of these tutorials are to give brief examples to show you the
basics of how to do something. Essentials and some of the more esoteric features
of Grace will be demonstrated to give the user an idea of the capabilities
of this program. It is not possible to show everything that Grace is capable
of doing. That knowledge only comes with use and experimentation. I recommend
that you do the tutorial and then by playing around with things, you will begin
to understand them. Finally, when you get stuck, read the user guide to help
you.</P>
<H2><A NAME="ss1.2">1.2</A> <A HREF="#toc1.2">Nomenclature</A>
</H2>

<P>In referring to what item to select, the tutorial will use something of
the form <SF>snaf:/foo/bar/bell </SF>which means that on the snaf popup, select from
the foo menu the submenu bar and from the bar menu, the entry bell. The popup
main is the large one with the graph that pops up when you run xmgrace. If
there is a space in the menu item, it will be replaced by an underscore. So
, if the menu item was actually "Bell jar" instead of bell in the last example,
it would be <SF>snaf:/foo/bar/Bell_jar.</SF></P>
<P>Things that are to be typed in will be presented in a typewriter font,
eg, type <CODE>y = 3*sin(x)</CODE>. </P>
<P>Some of examples require you to input a data file or graph. In such instances,
there should be a file in the tutorial directory named data.N or N.agr where
N is the tutorial number. For example, when doing tutorial 7.1.3, you should
look for a file 7.1.3.agr. It is assumed that each major tutorial section starts
with a clean graph.</P>
<H2><A NAME="ss1.3">1.3</A> <A HREF="#toc1.3">Computer System</A>
</H2>

<P>Some of the following examples require that system commands be run. The
commands may be different on your machine or require a slightly different syntax.
In this tutorial, an attempt will be made to use the most commonly available
UNIX commands. This tutorial was prepared on a Linux machine with kernel 2.0.32.</P>
<H2><A NAME="ss1.4">1.4</A> <A HREF="#toc1.4">Generalities</A>
</H2>

<P>A couple of points should be made about the GUI before we begin to make
life easier.</P>
<P>
<OL>
<LI>It is often possible to select more than one item from a list at a time
(some lists may prevent it when it makes no sense.). Clicking on a list entry
without any keyboard modifier pressed will deselect all other entries and select
only that one. Depressing shift while clicking an entry selects all entries
from a previously selected entry to the currently selected one. Finally, depressing
control allows one to individually toggle the selection of an entry.</LI>
<LI>There are often two buttons on a pop up: Apply and Accept. Changes are
not registered until either of these buttons is pressed. The difference between
them is that Accept also closes the window.</LI>
</OL>
</P>
<H2><A NAME="ss1.5">1.5</A> <A HREF="#toc1.5">Disclaimer</A>
</H2>

<P>Even though I do my best to keep this up to date with the latest release,
I cannot guarantee it. Think of this a perpetual work in progress. Therefore,
if something is wrong, you can notify me and I'll fix it but keep in mind that
I am doing it in my spare time for no money.</P>
<H2><A NAME="s2">2.</A> <A HREF="#toc2">Making a Simple Graph</A></H2>

<P>The object of this tutorial is to do the most basic function of Grace:
read in some data into a graph and then label the graph. Along the way, a few
of the basic Grace commands and widgets will be introduced.</P>
<H2><A NAME="ss2.1">2.1</A> <A HREF="#toc2.1">Reading the data from a file</A>
</H2>

<P>Start by bringing up the set reading widget <EM>Main:Data/Import/ASCII</EM>. Select
the file 2.1.dat (both double clicking and hitting return work). You should
see a black curve drawn on a graph.</P>
<P>Now we would like to add some more sets to the graph, but this time the
data file will be in a slightly different format. Looking at the file "2.1.dat"
(with the program of your choice), you can see that its several columns of
numbers. One way to interpret this file is the first column gives the x-values
and the rest of the columns are y-values. From Grace, again open the "Read Sets"
widget. This time, check the "NXY" button. Now select the file "2.1.dat". At this
point you will have several differently coloured curves.</P>
<P>You should now have 2 copies of the first set since you've read the file
twice. It would be nice to eliminate one copy. This is most easily accomplished
by bringing up a popup which lists all the sets. Selecting <EM>Main:Edit/Data_sets...</EM>bring up the Data set props popup. It lists all the sets and for the selected
set, its type and a few statistics. To eliminate a set, select it and then
press the right mouse button. A menu should appear from which you can select
kill. You'll note that there is a kill and kill data. The former totally eliminates
everything associated with a set while the latter eliminates the data but keeps
the settings for it so that if new data is read into the set, it will have
the same properties like colouring and line width, etc. Kill set 0 for now.</P>
<H2><A NAME="ss2.2">2.2</A> <A HREF="#toc2.2">Set appearance</A>
</H2>

<P>We would now like style the sets. Practically all aspects of the curves
are configurable including colour, line thickness, symbols, drop lines, fills,
etc. These operations are available under the "Set appearance" widget which is
invoked by selecting <EM>Main:Plot/Set appearance...</EM> or by double clicking near
the target set within the graph frame.</P>
<P>When the widget comes up, there will be a list of the sets with their number
(eg. G0.S1 refers to set 1 in graph 0). Later operations will require you to
know the number. Like the data sets pop up, clicking on mouse button 3 in the
set list will bring up the menu of set operations.</P>
<H3>Colouring all sets differently</H3>

<P>The simplest way to colour all sets differently is from Set_Appearance:Data/All
colors. First select the sets which you wish to recolour and then select Set_Appearance:Data/All
colors. Do this now to your graph.</P>
<H3>Customizing each set</H3>

<P>When a set in the list is highlighted, the widgets change to reflect the
settings. Practically all aspects are configurable. Experiment by changing
the line colours and widths, placing a symbol at each data point, not connecting
data points and fill the space between the x-axis and the curve. Don't forget
to try out what is available under the other tabs besides Main. To see the
effect of a change, you have to hit the "Apply" button. <B>N.B</B>.: Things are drawn
in numerical order so if there is overlap, the highest numbered item will be
on top. This applies to graphs and sets within each graph.</P>
<H2><A NAME="ss2.3">2.3</A> <A HREF="#toc2.3">Labelling the axes using the font tool</A>
</H2>

<P>Aspects of the axes are controlled by the axes popup which is called from
<EM>Main:Plot/Axis properties</EM> or by double clicking the graph frame. All aspects
of the axes can be changed like the title, the font, colour, whether or not
to draw grid lines, or user defined tick marks and labels. There are many settings
and the best thing to do is to experiment to see what each setting does.</P>
<P>For now, let's start by labelling the axes. Suppose these curves represent
the number of tasks a processor runs as the function of the number of users.
To make it more interesting, assume we are doing this in Quebec. That means
we want to plot "Nombre de tâches vs. nombre d'usagers". Note the importance
of having the accent over the a in tâches or we would end up plotting the number
of stains which is entirely another case. Bring up the Axes pop up, select
the Y axis, and click in the space to enter the label string of the axis label.
Start typing Nombre de t. At this point we need to enter a accented letter,
so we bring up the font tool by pressing <CODE>Control-E. </CODE>You will now see what we
have typed in the Cstring widget. Move the cursor to where you want to place
the accented letter and click on the letter. It should now appear in the string.
You can either finish the string here or hit accept and keep editing. Label
the x axis as well. This font tool is available wherever text needs to be entered.</P>
<P>All the attributes regarding the axis labels like size, colour, font, position
are changeable. </P>
<H2><A NAME="ss2.4">2.4</A> <A HREF="#toc2.4">Graph titles</A>
</H2>

<P>Our next exercise will be to title the graph so other. Operation pertaining
to this are found in the "Graph appearance" widget which we open by selecting
<EM>Main:Plot/Graph appearance</EM> or by double clicking just above the graph frame.</P>
<P>We can now fill in the title of the graph and by clicking on the "Titles"
tab, the font and size and colour can be chosen. The Viewport box under the
"Main" tab defines the 4 corners of the graph frame. You can type them in or
use the mouse to move them by first double clicking on them.</P>
<P>Other things which can be controlled in this widget are the frame drawn
around the graph, whether or not the graph background is coloured and the legends.
Legends will be dealt with a little later. </P>
<H2><A NAME="ss2.5">2.5</A> <A HREF="#toc2.5">Legends</A>
</H2>

<P>Since we have several lines in our graph, it makes sense that we label
them with a legend so that other people can figure out what they mean. The
first thing to do is to give each set a label. This is done by entering a legend
string for each set in the Set appearance popup. Now, from the Main form in
the Graph appearance popup, click on "Display legend" to see the legend box.
The location and appearance of the box is controlled by clicking on the "Leg.
box" tab. The appearance and spacing of the legend entries is controlled by
the "Legends" tab. For simplicity, label the sets alphabetically and then play
with the appearance, etc. to get something you like. </P>
<P>Specifying the placement of the graph by entering the coordinates can be
painful, especially the fine tuning. To alleviate this problem, a graphical
method is also available, although not readily apparent. After a legend appears,
it may be dragged to a new location. To do this, press Ctrl-L with your mouse
on the main canvas. You should see the arrow cursor turn into a hand. If this
doesn't work, double click on the main canvas (to get its attention) and then
press Ctrl-L. Click on the legend and drag it. To cancel the legend drag mode
(as with all other modes), click on mouse button 3. </P>
<H2><A NAME="ss2.6">2.6</A> <A HREF="#toc2.6">A challenge</A>
</H2>

<P>I got bored so I took the data files and produced my own, albeit ugly,
graph. See if you can copy 
<A HREF="mygraph.png">mygraph.png</A> </P>
<H2><A NAME="s3">3.</A> <A HREF="#toc3">Block Data</A></H2>

<P>A block of data is a table of number which are interpreted as columns of
numbers. How sets are created from the columns depends on the information you
want to extract from the file. </P>
<P>We first need to read in a block of data. We do this from <EM>Main:Data/Import/ASCII</EM>.
Select the file "3.dat" and Load as "Block data". If the read was successful, a
window should pop up asking you to create a set from the block data. At the
top it will list how many columns of data were read.</P>
<P>First we choose the type of set we would like. For now we'll stick with
xy.</P>
<P>Next we choose which column of data contains the x-ordinate. If there is
no column, we can select "index" which will use the index into the column as
the x ordinate starting from one.</P>
<P>The values Y1 through Y4 are used for selecting error bars as may be needed
by other set types.</P>
<P>The last thing to specify is the graph into which to load the set if we
have more than 1 set.</P>
<P>Finally, hitting accept will create the set.</P>
<P>If you close this window, it can reopened by bringing up a set list (eg.
<EM>Main:Edit/Data_sets</EM>) and then selecting Create_new/From_block_data from the
menu brought up by right clicking on the set list. </P>
<P>Try creating a new set of type XYdY. This is an XY curve with error bars.
Try X, Y, and Y1(the error) from different columns.</P>
<H2><A NAME="s4">4.</A> <A HREF="#toc4">Creating sets within Grace</A></H2>

<P>Besides reading in data files, Grace has an extensive scripting language
with a large number of math functions built in, These function include the
basic add, multiply, square root, etc, and also the cephes library of higher
order math functions like Bessel functions and the gamma function. Hence, functions
in Grace are basically unlimited. See the user guide for more details. In addition,
users can dynamically add libraries to Grace with any desired function. As
well, points may be added manually to a set by the use of editors. To begin,
choose <EM>Main:Edit/Data sets</EM>. To create a set, press mouse button 3 (the rightmost
one for right handed people) anywhere within the data set list (which may be
empty) and select Create new. A menu with 4 different ways of creating new
sets will be presented. We'll go through them one by one.</P>
<H2><A NAME="ss4.1">4.1</A> <A HREF="#toc4.1">By formula</A>
</H2>

<P>The load and evaluate window will pop up when this is selected.</P>
<P>
<OL>
<LI>The first step is to set up the parameter mesh which will determine the
range and sampling of the variable $t. Most often, $t will simply
be the abscissa.</LI>
<LI>Next, choose the type of set you would like to produce.</LI>
<LI>Using the syntax of the command language, an expression for x is entered
which uses $t as the independent variable. This can be an extremely
complicated function.</LI>
<LI>Likewise, an expression for y is entered and for any other expressions
that may be needed. Fields after y are labelled y1, y2, y3 and y4. For example,
if the set type xydxdy is chosen, y1 will hold dx and y2 will hold dy and it
will be necessary to enter expressions for them.</LI>
<LI>Pressing apply or accept will perform the calculations and create the new
set. You may have to autoscale to see the new set.</LI>
</OL>
</P>
<P>Below are a few samples:</P>
<P>
<OL>
<LI>To plot one cycle of a sine wave: Load: Set X, Start load at: <CODE>0</CODE>, Stop load
at: <CODE>2*pi</CODE>, Length: <CODE>100</CODE>, X=$t, Y=<CODE>sin($t)</CODE></LI>
<LI>A unit circle by parameterization: Start at:<CODE>0</CODE>, Stop at: <CODE>2*pi</CODE>, Length: <CODE>100</CODE>,
X=cos($t), Y=sin($t)</LI>
</OL>
</P>
<H2><A NAME="ss4.2">4.2</A> <A HREF="#toc4.2">In spreadsheet</A>
</H2>

<P>If your system has the Xbae widget set, this choice brings up a spreadsheet
like editor to allow one to enter the points of the set by hand. Initially,
it just has the point ( 0, 0 ). Clicking on add will insert a copy of the currently
selected row immediately below the selected row. Clicking delete will delete
the row which contains the cursor. This method is best suited to examining
or modifying existing sets or creating very small sets. The sets gets updated
after one hits enter or leaves the cell.</P>
<H2><A NAME="ss4.3">4.3</A> <A HREF="#toc4.3">In text editor</A>
</H2>

<P>If your system doesn't have the Xbae widget set or you want the power of
your favourite external editor, a text editor of your choice may be used to
enter data. The editor is selected by the GRACE_EDITOR environment variable.
If the set is new, it will contain only the point (0,0). During editing, no
other operations are possible. After the editor is closed, the set will be
updated.</P>
<H2><A NAME="ss4.4">4.4</A> <A HREF="#toc4.4">From block data</A>
</H2>

<P>This creates a new set from a block of data which has been read in. See
section 3.</P>
<H2><A NAME="s5">5.</A> <A HREF="#toc5">Batch plotting </A></H2>

<P>Grace supports a large number of command line options which allow the user
to control the appearance and placement of graphs. This can be very useful
if you want to use it to quickly print something without going through the
GUI, use it within a script to automatically generate graphs, or have a plot
come up already configured which can be much quicker than going through the
GUI menus. </P>
<H2><A NAME="ss5.1">5.1</A> <A HREF="#toc5.1">Simple nonGUI printing</A>
</H2>

<P>Invoking Grace with the command "grbatch"from the command line will cause
Grace to start, produce a plot, send it to the printer (unless a file is specified)
and then exit. In its simplest form, to produce a plot of the file a.agr, type</P>
<P>gracebat a.agr</P>
<P>If gracebat is unavailable on your system, the hardcopy option to xmgrace
will do the same thing. Assuming the hardcopy device is a postscript printer,
one could also type</P>
<P>xmgrace -hdevice PostScript -hardcopy a.agr</P>
<H2><A NAME="ss5.2">5.2</A> <A HREF="#toc5.2">Multiple graphs</A>
</H2>

<P>Often, one wishes to plot several graphs with each graph having different
characteristics. This is easily accomplished from the command line. Options
specified on the command line are parsed in order and stay in effect until
overridden by specifying them again.</P>
<P>
<OL>
<LI>The first step in plotting multiple graphs is usually telling Grace how
many graphs we have and how to arrange them. The interpreter command "arrange"
will do this. For example, if we want 4 graphs arranged in a simple 2x2 table,
we specify 
-pexec "arrange ( 2, 2, .1, .1,.1,ON,ON,ON)"
The exact meaning of
all the options is explained in the reference manual.</LI>
<LI>Specify any global options. </LI>
<LI>Specify for each graph, the data to plot and any options. Options should
be specified in the following order:
<OL>
<LI>"-graph g" where g is the graph number starting at 0. This says to apply
all following options to this graph.</LI>
<LI>Set any autoscaling options. Autoscaling is performed when the file is
read; ergo, the autoscaling must be specified BEFORE the file is read. Remember,
this setting is persistent.</LI>
<LI>Set the set type. This is also a persistent setting.</LI>
<LI>Specify the graph type and the input file.</LI>
<LI>If reading in block data, create the sets with the "-bxy" option.</LI>
<LI>Specify any world scaling. It is important to do this AFTER sets are read
(unless autoscaling is off) as the graph gets rescaled when data is read in.</LI>
<LI>Specify anything else</LI>
</OL>
</LI>
</OL>
</P>
<H3>An example</H3>

<P>Let's try an example. We will assume 5 plots, the first 4 of which are
to be stacked vertically, and the fifth inset into the fourth. We wish to plot
the files a.dat, b.dat, c.dat and d.dat with the inset graph being a magnified
portion of d.dat. Assume a.dat contains multiple columns of data, b.dat is
a block of data from which we wish to make a curve from columns 2 and 4 with
the error given by column 3, c.dat is to be represented as a bar graph, and
for the inset graph, we wish to graph to region (0,0) to (1,1). This can be
accomplished by</P>
<P>gracebat -pexec "arrange (4,1,.1,.1,.1,ON,ON,ON)" -nxy a.dat -graph 1 -block
b.dat -settype xydy -bxy 2:4:3 -graph 2 -settype bar c.dat -graph 3 -settype
xy d.dat -graph 4 d.dat -world 0 0 1 1 -viewport .15 .3 .8 .88</P>
<P>Note that the graph numbers start at 0 and that 0 is the default so it
does not have to be specified for the first graph.</P>
<H2><A NAME="ss5.3">5.3</A> <A HREF="#toc5.3">Things for which no command line option exists</A>
</H2>

<P>Undoubtedly, you will reach a point where you want to do something for
which no command line option exists. (We have been doing this with the arrange
command.) This is where Grace's parameter file language is vital. The option
"-pexec" will execute the next argument as if it had read it from a parameter
file or excuted on the command line. If you want to do something more complicated
than one command, you can use several pexec's or put the commands in a file
and run the file with the "-batch" option.</P>
<H3>Pexec example</H3>

<P>To read in the files foo.dat and bar.dat and scale foo.dat in Y by 1000,
the simplest way is</P>
<P>xmgrace foo.dat bar.dat -pexec "s0.y = s0.y * 1000"</P>
<H3>Batch example</H3>

<P>To do the same as the previous example but also label the axes and recolour
the curves, make a file called "bfile" with the Grace commands</P>
<P>
<HR>
<PRE>
#Obligatory descriptive comment
s0.y = s0.y * 1000
s0 line color 3
s1 line color 4
title "A Gnasty Graph"
xaxis label "Time ( s )"
yaxis label "Gnats ( 1000's  )"
autoscale 
</PRE>
<HR>
</P>
<P>and then run xmgrace with</P>
<P>xmgrace foo.dat bar.dat -batch bfile</P>
<H2><A NAME="s6">6.</A> <A HREF="#toc6">Fitting curves </A></H2>

<P>This tutorial will explain some of Grace's curve fitting abilities. Grace
can perform two types of fittings. The first type is regression or linear fitting
where optimization is done on a linear equation or an equation which can be
expressed in a linear form. This includes fitting polynomials and certain forms
of equations. The other type of fitting is nonlinear and allows for arbitrary
user supplied functions.</P>
<P>Let's take a curve and see how each type of fitting works. To begin, create
a curve of the function <CODE>y = sqrt(x) + exp(x)/3 -1</CODE> over the range 0 to 3 with
100 points.</P>
<H2><A NAME="ss6.1">6.1</A> <A HREF="#toc6.1">Linear Regression</A>
</H2>

<P>Choosing <EM>Main:Data/Transformations/Regression</EM> will pop up the Regression
window. </P>
<P>
<OL>
<LI>Select the set you just created</LI>
<LI>Select the type of fit. For now, pick Linear.</LI>
<LI>We will load the fitted value for now.</LI>
<LI>Press the accept button to see the results of the fit. A window will pop
up which will give you the results of the fit including the final expression.
You might have to scroll back a bit to see it.</LI>
<LI>See how high of a polynomial is needed to get an acceptable fit and try
fitting other types of functions. Note that for the non-polynomial fits, <B></B><B><EM>A</EM></B><EM></EM>
and <B></B><B><EM>B</EM></B><EM></EM> are the fitting parameters of the equation.</LI>
<LI>Now, we are not limited to computing our fitted curve at the points of
the original function. Suppose these data are quarterly sales and we wish to
predict our next quarter. Choose the type of fit which you found to work best.
Instead of loading fitted values,<EM> Load: Function.</EM> Now the bottom of the widget
will become active. We wish to extrapolate over the next quarter, so we would
like to start at 0 and end at 4 and choose 100 points. Press accept to see
the extrapolation.</LI>
</OL>
</P>
<H2><A NAME="ss6.2">6.2</A> <A HREF="#toc6.2">Non-linear</A>
</H2>

<P>We pop up the widget by selecting <EM>Main:Data/Transformations/Non-linear
curve fitting</EM>. You may want to kill all the sets except the original function
and the extrapolated function at this point.</P>
<P>
<OL>
<LI>Begin by selecting the set to optimize, the original function.</LI>
<LI>Next, we write a function of the form we wish to fit. The unknown parameters
are labelled a0..a9. You must start with a0 and work your way up. In this case,
since you know the form of the equation already, so try: <CODE>y = a0*sqrt(x) + a1*exp(x)
+ a2</CODE>.</LI>
<LI>Next we must specify that we have three parameters to fit which are a0,
a1 and a2 and the tolerance of the solution.</LI>
<LI>You must specify initial values for the parameters and put any bounds on
them if necessary. Depending on the function you are optimizing, different
initial conditions may lead to drastically different optima.</LI>
<LI>The solution process is iterative and you must click on a button to run
a certain number of iterations. You should see the parameters change and a
curve created with these parameters. In this example, the exact solution is
reached within 5 steps. More parameters and more difficult functions may require
more steps in which case you may choose to run 20 or 100 or more steps. The
newly created optimized curve should converge with an increasing number of
steps.</LI>
<LI>As in linear curve fitting, you can choose to load the fit function at
the points of the original curve, over an arbitrary range or load the error
at each point. For comparison, load the fitted curve over the range (3,4) by
selecting Nonlinear:Options/Load/Function and filling in the bottom of the
widget. How does the true answer compare to your previous extrapolation?</LI>
<LI>Fitting arbitrary curves can be a tricky business. Initial conditions are
very important. If you don't get a good fit, you may have to experiment a lot
with the initial parameters values.</LI>
<LI>Finally, note that the fitted curve does not get added until the accept
button is pressed. This allows you to "fool around" until you get a good fit
without creating a lot of garbage sets.</LI>
</OL>
</P>
<H2><A NAME="s7">7.</A> <A HREF="#toc7">Transformations </A></H2>

<H2><A NAME="ss7.1">7.1</A> <A HREF="#toc7.1">Graphical </A>
</H2>

<H3>Simple Geometrical</H3>

<P>You can rotate sets around an arbitrary axis perpendicular to the canvas
(e.g. the Z-axis). Also it is possible to scale sets and translate them.</P>
<H3>Mathematical operations between sets</H3>

<P>It is possible to perform operations between sets. With many operations,
however, it is required that the 2 sets have the identical abscissa, i.e.,
the x values of both sets are the exact same. This is necessary since most
operations are performed on a point by point basis. Eg. multiplying 2 sets
is done by multiplying the Y values of the 2 sets together to produce a new
Y value. About the only operations that don't do this are filtering and convolution.
Fortunately, Grace has a function to help out when the abscissas differ. It
is called interpolation which interpolates a set over the domain of another
set to produce a new curve.</P>
<P>Let us now add the cosine of a set to the sine of another set to create
a new curve. However, we will complicate this example by having different domains
with different sampling:</P>
<P>
<OL>
<LI>Read in 7.1.2.agr</LI>
<LI>Note how the abscissa are different. We begin by using interpolate to produce
a third set which is the second set sampled at the x values of the first. Call
up the Interpolate popup from <EM>Main:Data/Transformations/Interpolation/splines ...</EM></LI>
<LI>Select S1 as the source set but don't specify a destination set. A set
will automatically be made. Use the Strict, linear method, Sampling:Abscissas
of another set and use S0 as the Sampling set. Pressing Apply should produce
a curve which is S1 interpolated at the points of S0. Note that the new curve
only exists over the portion of the x axis common to both curves.</LI>
<LI>We still have a problem since set 2 is sampled the same as set 0 but has
a smaller domain. We can perform the computation only over the common region
so we now interpolate on set 0 at points from set 2 to produce set 3. Now set
2 and set 3 have the exact same abscissas.</LI>
<LI>Call up the command interpreter from <EM>Main:Window/Commands</EM> ...</LI>
<LI>We need to create a set to hold the result, S4. We can either make a copy
(using <EM>Main:Edit/Set_operations...</EM>) of S2 which will be guaranteed to have
the proper size to hold out result or we can use type a command: <CODE>s4 length
s2.length</CODE></LI>
<LI>We have to break up the computation into an x part and a y part. In this
instance, we simply wish to keep the same x values. The final result will be
put into set 4, so we issue the command: <CODE>s4.x = s2.x</CODE></LI>
<LI>Now we can perform the math between our interpolated copies of sets 0 and
1: <CODE>s4.y = cos(s3.y) + sin(s2.y)</CODE>. </LI>
<LI>So where is the new set? It's there but it's hidden. Since we already have
the command window open, we can unhide the set by typing: <CODE>S4 on</CODE>. For the GUI
minded (no offense intended), bring up a set list with the set operations menu
(eg. <EM>Main:Edit/Data_sets</EM> or <EM>Main:Plot/Set_appearance</EM>),
select set 4 and unhide it by selecting show from the operation menu (mouse button 3). </LI>
</OL>
</P>
<P>N.B. If the abscissas of the original curves had been the same, we could
have started at step 5. If the sampling had been the same we could have skipped
step 4.</P>
<H3>Feature extraction </H3>

<P>Feature extraction is a way of creating one curve from a family of curves.
It generates one data point from each curve by measuring a characteristic of
the curve. For example, one might have a series of curves which plot the gnat
population as a function of time. Each curve is produced by varying some condition,
like the number of gnus in the environment. Using feature extraction, one could
use this family of curves to produce a new curve of the peak number of gnats
as a function of gnus or the time of the peak number of gnats as a function
of the number of gnus. This is most often useful with more than one graph.</P>
<P>
<OL>
<LI>Read in graph 7.1.3.agr</LI>
<LI>Bring up the feature extraction form by clicking on
<EM>Main:Data/Transformations/Feature_extraction</EM>.
 </LI>
<LI>Select Results to graph 1.</LI>
<LI>Select the feature you are interested in. Choose Y maximum.</LI>
<LI>Select what will determine the x value of the data point. The value of
the characteristic determines the Y value. The X value can be determined by
the set number. The x or y values of a specified set can also be used to produce
the abscissa. Finally, the legend entry of the curve itself can be used to
produce the x value. In this case, the legend entry must be specified as a
single number. Choose index for now.</LI>
<LI>Press accept, click on graph 1 and then click on the autoscale button to
see your results.</LI>
<LI>Choose another feature, like frequency, this time and get X values from
the legend. Make sure that graph 0 has the focus when you hit accept. </LI>
</OL>
</P>
<H2><A NAME="ss7.2">7.2</A> <A HREF="#toc7.2">Restrictions</A>
</H2>

<P>Often we only wish to examine part of a data set or perform transformations
only on a portion of one. Restrictions allow us to define a region of the graph
on which to perform operations. </P>
<H3>Defining a region</H3>

<P>There are several ways a region may be defined. It may be defined by a
straight line (left of, right of, above, below), by a polygon (inside or outside),
or by a range ( in x, out of x, in y, out of y). Call the define region popup
from <EM>Main:Edit/Regions/Define</EM>. Choose which one of the regions you would like
to define, and press the define button. </P>
<P>
<DL>
<DT><B>Line type</B><DD>
<P>Define the ends of the line by clicking with mouse button
1.</P>
<DT><B>Polygon type</B><DD>
<P>From the define region popup, choose a polygon type and
then the define button. Use mouse button 1 to pick the vertices of the polygon
and then mouse button 3 when you are done.</P>
<DT><B>Range type</B><DD>
<P>From the define region popup, choose a range type and then
pick 2 points which define the range.</P>
</DL>
</P>
<H3>Using regions</H3>

<P>Regions may be only be used to restrict an expression evaluation. Bring
up the evaluateExpressions popup (<EM>Main:Data/Transformations/Evaluate_expression</EM>).
Choose the source and destination sets and specify the formula to apply to
the region of interest. Not specifying an expression is equivalent to the identity
transformation. Choose the region you wish to use. By checking negate, the
complement of the specified region is used. </P>
<P>Click on Apply to perform the operation. The resultant set will be the
expression evaluated only on points contained in the specified region. Thus,
if no expression was specified, the effect is to produce a new set of only
those points contained in the region. Conversely, to delete points in a region,
leave the expression empty, and negate the region selection.</P>
<H2><A NAME="s8">8.</A> <A HREF="#toc8">Using Pipes </A></H2>

<P>Pipes are a way of capturing the output of a running process without the
intermediary step of pacing the output in a file. Instead, the executing program
puts the data in one end of the pipe, and Grace reads it from the other end
of the pipe.</P>
<H2><A NAME="ss8.1">8.1</A> <A HREF="#toc8.1">Instead of data files</A>
</H2>

<P>On certain popups, e.g. <EM>Main:Data/Import/ASCII</EM>, the option to read from
a file or pipe can be specified. If a pipe is chosen, the command in the selection
widget will be run and the stdout will be captured and treated as though it
was data which was read from a file. </P>
<H2><A NAME="ss8.2">8.2</A> <A HREF="#toc8.2">Named pipes</A>
</H2>

<P>A named pipe is a special case of the pipe previously described. In the
previous case, after the program has finished execution and the output had
been read, the pipe was destroyed. A named pipe is a static structure with
the property that multiple processes can write to and/or read from it. The
purpose of using a named pipe with Grace is to start up a Grace window and
then control Grace by sending commands and data through a named pipe. This
is very powerful and lets you do practically anything you can do directly from
the GUI. To use this feature, try the following:</P>
<P>
<OL>
<LI>Start a named pipe (you will have to find the command specific to your
operating system. For example, it could be <EM>mkfifo</EM> or <EM>mknod</EM>): <CODE>mkfifo pvc</CODE>. If
you do a directory listing, you should see the file pvc.</LI>
<LI>Start up Grace in the background using the named pipe option: <CODE>xmgrace</CODE><CODE><EM> -</EM>npipe</CODE><EM></EM><EM><CODE></CODE></EM><CODE>p</CODE><CODE><EM>v</EM>c</CODE>&amp;. Grace is now monitoring the pipe for any data which might be sent
to it. It will interpret things as though they were entered using the command
interpreter. </LI>
<LI>For a simple test, we will create a simple graph over the pipe. From your
command line, type: <CODE>echo "read \"8.2.dat\"" &gt; pvc</CODE><B>. </B>(The back slashes
are needed to escape the quotation marks so that Grace really received the
command :read "8.2.dat".) This just told Grace to read the file data. Now we
would like to autoscale. We could simply click on the button but the point
is to use a named pipe. This time we type <CODE>echo</CODE><EM> </EM><EM><CODE></CODE></EM><CODE>autoscale &gt; pvc</CODE><EM> </EM>followed
by<EM> </EM><EM><CODE></CODE></EM><CODE>echo redraw &gt; pvc</CODE><EM>.</EM> Your graph should now have autoscaled and redrawn.
Exit Grace with <CODE>echo</CODE><CODE><EM> </EM>exit</CODE><CODE><EM> &gt; </EM>pvc</CODE>. You should also clean up by removing pvc.</LI>
<LI>The true power in named pipes lies in driving Grace using another program.
The controlling program can open a named pipe for writing, which is treated
as an ordinary file. It can be opened with the <EM>fopen()</EM> function or whatever
other I/O function you prefer. Commands and data are then written to the file
where they are interpreted by Grace.</LI>
</OL>
</P>
<H2><A NAME="s9">9.</A> <A HREF="#toc9">Multiple Graphs</A></H2>

<H2><A NAME="ss9.1">9.1</A> <A HREF="#toc9.1">Selecting graphs</A>
</H2>

<P>When multiple graphs are present, a graph is selected by clicking inside
the graph frame. In cases where graph frames overlap, clicking will cycle among
the overlapping graphs.</P>
<P>It might be annoying if one is trying to work in a region of overlapping
graphs. If will not be possible to double click on something because the each
click will be interpreted as a single click and you will only end up changing
the graph focus. In such an instance, turning off the graph selection by clicking
might be desirable. Choose <EM>Main:Edit/Preferences</EM> and then set
<EM>Misc:Graph_focus</EM> to "As set". This means one must explicitly set
the focus. Simply bring up a graph list (eg. <EM>Main:Edit/Overlay_graphs</EM>
is but one), select the graph you  want to work on and then, using the menu under
mouse button 3, choose "Focus to".</P>
<H3>Arranging a tableau of graphs</H3>

<P>Placing a large number of regularly spaced graphs is easily done with
<EM>Main:Edit/Arrange_graphs</EM>. This will automatically calculate the layout:</P>
<P>
<OL>
<LI>Choose 3 rows and 3 columns and Apply. You should now see 9 graphs. The
Order button refers to the way the graphs are numbered. The beginning of the
line on the diagram of the button shows which graph is numbered 0 and how the
numbers increase, by row or column.</LI>
<LI>You realize you need horizontal packing, i.e. no horizontal gap between
graphs. Click on the Pack button beside the Hgap/width input and then Apply.</LI>
<LI>Suddenly, you realize you only need 6 graphs and not 9. Choose 2 rows and
press Apply. There is a slight problem as graphs 6, 7 an 8 are still visible.
This is a feature since you don't want to accidentally kill a graph. You can
kill the extra graphs by clicking on the "Kill extra graphs" check box. Now,
any graphs other than the explicitly arranged ones will be automatically killed.</LI>
<LI>The margins are controlled by the Page Offsets, and the intergraph spacing
by the Hgap and Vgap inputs.</LI>
<LI>Press close to remove the window.</LI>
</OL>
</P>
<P>
<BLOCKQUOTE>
Note that only graphs which are selected are taken into consideration.
So, if you wish to reorganize your existing graphs, make sure they are selected
or new ones may be created.
</BLOCKQUOTE>
</P>
<H3>Arranging individual graphs</H3>

<P>Arranging individual graphs may either be done (1) exactly, by specifying
the viewport coordinates from <EM>Main:Plot/Graph_appearance</EM> or
using the previously explained Arrange graphs popup, or (2) roughly,
by double clicking a graph focus marker and then moving it.</P>
<H2><A NAME="ss9.2">9.2</A> <A HREF="#toc9.2">Overlaying Graphs</A>
</H2>

<P>Overlaying one graph onto another is useful for creating a graph with two
different x axes and/or y axes. For example, you may wish to have a graph which
on the x axis has the month of the year. There could be 2 curves on it, one
using the left y axis which is number of gnus sold and one using the right
y-axis which is the number of gnats exported on a logarithmic scale. Likewise,
if one is plotting spectral data, one could have one x axis in Hz and another
one in wavelength. Let's proceed with an example:data</P>
<P>
<OL>
<LI>Begin by selecting <EM>Main:Edit/Overlay graphs</EM> to bring up the Overlay widget.
 </LI>
<LI>Select the graph numbers with which we would like to deal. In this example,
we will overlay graph 1 onto graph 0. At this point, only graph 0 is visible.
We cannot see Graph 1 to select since it does not exist at this point. We need
to create simply by pressing mouse button 3 in a graph list window and selecting
create new. </LI>
<LI>The overlay type is determined by what is common among the overlayed graphs.
In our example, the x axis is common so we will select <EM>X-axes same, Y-axes
different. </EM>This is important because we don't want to alter any axes of the
Overlay graph which we set the same as the underlay graph. In this example,
we don't want to alter the x-axis of graph 1.</LI>
<LI>We are now ready to label the graph axes and read the data. One thing we
must be careful to do is to always make sure that we are working on the intended
graph. Seeing as the graphs are overlain, clicking within the frame is ambiguous
as to what graph is selected. The rule is that in a region of overlay, clicking
will cycle between the graphs. Hence, if graph 1 is selecting, clicking within
the frame will toggle to graph 0.</LI>
<LI>Making sure that graph 0 is active, bring up the Axis properties widget.
Now set the y axis title to Gnus.</LI>
<LI>Select graph 1 as active as set the title as Gnats. Notice how it overlaps
the Gnus. We want to put this on the right side. From the axis label and bar
tab, select label Properties/Side=Opposite.</LI>
<LI>Label the x axis to label it. If graph 1 is the current graph, noticed
how it is greyed out because only 1 x axis need be active. Select graph 0 and
you should now be able to alter the axis label.</LI>
<LI>You are ready to read in data. Just make sure the graph that is active
when you read in the data (or create your set) is the one in which you intend
it to go.</LI>
</OL>
</P>
<H2><A NAME="s10">10.</A> <A HREF="#toc10">Hot Links</A></H2>

<P>Hot links are a way of of updating a set without having to delete it first
and then reread it. The Hot Links window is opened available under <EM>Main:Data/Hot
links</EM>.</P>
<H2><A NAME="ss10.1">10.1</A> <A HREF="#toc10.1">File containing a Single Set</A>
</H2>

<P>The simplest hot link is to a file containing just one set. To make a hot
link to a single set, we must first select the set we want to get updated and
then specify the file. We may also link to a pipe in which case we must specify
it is a pipe to which we are linking. A command may also be entered which will
be run every time the hot link is updated. A common command might be autoscale
which will make sure that the entire set can be seen if it changes size. It's
possible you may want to execute more commands than one. One could, for example,
have a set that is a function of 2 sets that needs to be recomputed if either
set is updated. If this is the case, put your commands in a file and then use
the "READ BATCH" command.</P>
<P>Pressing the Link button will now create the link and if the update button
is pressed, the set will be updated with the current contents of the file you
linked and the contents of the Command widget will be executed.</P>
<P>For a simple example, read in the set 10.1.dat and set up the hot link.
Now, run the command shiftdata.sh and update the hotlink. You should have seen
the peak in the graph shift. Try repeating this a couple of more times.</P>
<H2><A NAME="ss10.2">10.2</A> <A HREF="#toc10.2">Multiple sets within a file</A>
</H2>

<P>Sometimes a data file may contain multiple columns of data and we would
like to be able to link to all or some of those columns. To specify this, select
as many sets as there are xy columns of data in the file. The "x y1 y2" format
is assumed. Choose the file the data and <EM>link</EM>. Now in the link list, the links
will show the file name with an appended colon and number. The number tells
what column of data the link refers to. Any unwanted columns may be selected
and unlinked at this point. When the update button is selected, all sets in
the graph will be updated.</P>
<H2><A NAME="ss10.3">10.3</A> <A HREF="#toc10.3">Updating by hot keys</A>
</H2>

<P>Instead of having to keep the Hot links window open all the time, the update
action is bound to alt-u. If you find that alt-u has no effect, try double
clicking inside the graph you want to update and close the window that pops
up. This will "alert" the canvas to process future hot key strokes.</P>
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