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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<title>Gri: contour plots</title>
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<br>
Chapters:
<br>
&nbsp;&nbsp;<a href="Introduction.html">1: Introduction</a><br>
&nbsp;&nbsp;<a href="SimpleExample.html">2: Simple example</a><br>
&nbsp;&nbsp;<a href="InvokingGri.html">3: Invocation</a><br>
&nbsp;&nbsp;<a href="GettingMoreControl.html">4: Finer Control</a><br>
&nbsp;&nbsp;<a href="X-Y.html">5: X-Y Plots</a><br>
&nbsp;&nbsp;<a href="ContourPlots.html">6: Contour Plots</a><br>
&nbsp;&nbsp;<a href="Images.html">7: Image Plots</a><br>
&nbsp;&nbsp;<a href="Examples.html">8: Examples</a><br>
&nbsp;&nbsp;<a href="Commands.html">9: Gri Commands</a><br>
&nbsp;&nbsp;<a href="Programming.html">10: Programming</a><br>
&nbsp;&nbsp;<a href="Environment.html">11: Environment</a><br>
&nbsp;&nbsp;<a href="Emacs.html">12: Emacs Mode</a><br>
&nbsp;&nbsp;<a href="History.html">13: History</a><br>
&nbsp;&nbsp;<a href="Installation.html">14: Installation</a><br>
&nbsp;&nbsp;<a href="Bugs.html">15: Gri Bugs</a><br>
&nbsp;&nbsp;<a href="TestSuite.html">16: Test Suite</a><br>
&nbsp;&nbsp;<a href="GriInThePress.html">17: Gri in Press</a><br>
&nbsp;&nbsp;<a href="Acknowledgments.html">18: Acknowledgments</a><br>
&nbsp;&nbsp;<a href="License.html">19: License</a><br>
<br>
Indices:<br>
&nbsp;&nbsp;<a href="ConceptIndex.html"><i>Concepts</i></a><br>
&nbsp;&nbsp;<a href="CommandIndex.html"><i>Commands</i></a><br>
&nbsp;&nbsp;<a href="BuiltinIndex.html"><i>Variables</i></a><br>
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<h1>6: Contour Plots</h1>

Contour plots can be done with either pregridded data or randomly
distributed (ie, ungridded) data.
<UL>
<LI><a href="ContourPlots.html#Pre-griddedData">Pre-gridded Data</a>: Contouring f(x1, y1, x2, y2, ...)
<LI><a href="ContourPlots.html#UngriddedData">Ungridded Data</a>: Contouring f(x, y) where (x,y) are not on a grid
</UL>
<p>
<!-- @node   Pre-gridded Data, Ungridded Data, Contour Plots, Contour Plots -->
<a name="Pre-griddedData" ></a>
<h2>6.1: Pre-gridded Data</h2>

This section presents two examples of contouring pre-gridded data, the
first example illustrating a boilerplate program to contour data
stored in a simple matrix form in a file, the second example
illustrating a case with more control of the details (e.g., a nonuniform
grid).
<p>

<h3>6.1.1: Simple example</h3>

This example was hardwired to know the size of the grid, etc.  Here's 
an example which is more general, in that it determines the dimensions
of the grid data from using unix system commands.  Note that the grid is
set to run from 0 to 1 in both x and y; you'll most likely want
to change that after you see the initial plot, but this should get you 
started.
<p>

<TABLE SUMMARY="Example" BORDER="0" BGCOLOR="#efefef" WIDTH="100%">
<TR>
<TD>
<PRE>
<font color="#82140F">
\file = "somefile.dat"
\rows = system wc \file      | awk '{print $1}'
\cols = system head -1 \file | awk '{print NF}'
set x grid 0 1 /\cols
set y grid 0 1 /\rows
open \file
read grid data \rows \cols
close
draw contour
</font></PRE>
</TD>
</TR>
</TABLE>
<p>

<h3>6.1.2: Complicated example</h3>

To get a simple contour graph based on pre-gridded
data, with full control of axes, etc, do something like this:
<p>
<A HREF="example4.png"> 
<IMG ALT="Example 4" SRC="example4-tiny.png" 
ALIGN=top> 
</A> 
<A HREF="example4.html">The command-file.</A> <P> 





Here several new things have been introduced.
<p>
First, you've got to define a grid in xy space.  This example uses a
non-uniform x-grid, and reads it in from the commandfile.  In this form,
the blank line is essential; it tells Gri that the end of data has been
located; if you like, you can specify the number of lines to read, as in
`<font color="#82140F"><code>read grid x 3</code></font>'.
<p>
The y-grid for this example is uniform, however, so it may be specified
with the `<font color="#82140F"><code>set y grid</code></font>' command.  It obtains values (10, 12.5, 15,
17.5, 20).  The `<font color="#82140F"><code>set x|y grid</code></font>' commands accept negative increments.
Furthermore, it is possible to specify the number of steps, rather than
the increment size, by putting `<font color="#82140F"><code>/</code></font>' before the third number; thus
`<font color="#82140F"><code>set x grid 0 1 /5</code></font>' and `<font color="#82140F"><code>set x grid 0 1 0.2</code></font>' are equivalent.
<p>
Having defined a grid, it is time to read in the gridded data.  Here this
is done with the `<font color="#82140F"><code>read grid data</code></font>' command.  Since Gri already knows
the grid dimensions, it will read the data appropriately.  You could
also have told it (`<font color="#82140F"><code>read grid data 3 5</code></font>').  
<p>
The first dataline is the top of the y-grid.  In other words, the data
appear in the file just as they would on the graph, assuming that the
x-grid and y-grid both increase.  
<p>
Sometimes you want to read in the transpose of a matrix.  Gri lets you
do that.  If the `<font color="#82140F"><code>bycolumns</code></font>' keyword is present at the end of the
`<font color="#82140F"><code>read grid</code></font>' command, the first dataline will contain the first
<b>column</b>, of the data.
<p>
If you have an extraneous column of data to the left of your data
matrix, do `<font color="#82140F"><code>read grid data * 2 3</code></font>'
<p>
Now Gri has the grid in its head.  We tell it to draw some contours
with the `<font color="#82140F"><code>draw contour</code></font>' command.   As the comments in the example
show, the contour values will be selected automatically, but you can
alter that.
<p>




<!-- @node   Ungridded Data, Images, Pre-gridded Data, Contour Plots     -->
<a name="UngriddedData" ></a>
<h2>6.2: Ungridded data</h2>

When you have f=f(x,y) points at random x and y, you must cast them onto
a grid to contour them.  This is a difficult problem.  There are many
ways to grid data, and all have both good and bad features.  You should
try various methods, and various settings of the parameters of the
methods.  If you have a favorite gridding method that you prefer, you
should probably pre-grid the data yourself.  If not, Gri can do it for
you.  Gri has two methods for doing this, the ``boxcar'' method and the
``objective analysis'' method.  Each method puts holes in the grid
wherever there are too few data to map to grid points, unless you
specifically ask to fill in the whole grid.
<p>
The next two sections show first an example, then a discussion of the
methods and how to use them.
<p>
<h3>6.2.1: Example</h3>

This example uses data taken from Figure 5 of S. E.  Koch and M.
DesJardins and P. J. Kocin, 1983.  ``An interactive Barnes objective map
anlaysis scheme for use with satellite and conventional data,'', J.
Climate Appl.  Met., vol 22, p. 1487-1503.  Readers should compare
Figures 5 and 6 of that paper to the results shown here.
<p>
<A HREF="example5.png"> 
<IMG ALT="Example 5" SRC="example5-tiny.png" 
ALIGN=top> 
</A> 
<A HREF="example5.html">The command-file.</A> <P> 







<h3>6.2.2: Discussion of Methods</h3>

The various commands for converting columns to a grid are given in
(see <a href="Convert.html#ConvertColumnsToGrid">Convert Columns To Grid</a>).  Generally, the Barnes method is best.
<p>

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