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<HTML>
<HEAD>
<TITLE>Matrix data</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000">
<P><font size="+2" color="green">Matrix data</font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="644">
<TR>
<TD width="14%" valign="top"><B>Syntax</B>:</TD>
<TD width="86%" valign="top"><CODE>
CONTOUR { x y } v nctr { min { incr }}<br />
CONTOUR\COLOURS colr { x y } v nctr { min { incr }}<br />
CONTOUR\INTERPSIZE ntrp { x y } v num { min { incr }}<br />
CONTOUR\INTERPSIZE\COLOURS colr ntrp { x y } v num { min { incr }}<br />
CONTOUR\SPECIFIC { x y } v lvls<br />
CONTOUR\SPECIFIC\COLOURS colr { x y } v lvls<br />
CONTOUR\SPECIFIC\INTERPSIZE ntrp { x y } v lvls<br />
CONTOUR\SPECIFIC\INTERPSIZE\COLOURS colr ntrp { x y } v lvls</CODE>
</TD></TR>
<TR>
<TD width="14%" valign="top"><B>Qualifiers:</B></TD>
<TD width="86%" valign="top"><CODE>
\SPECIFIC, \INTERPSIZE, \POLAR, \LEGEND, \COLOURS, \PARTIAL, \RESET,
\BORDER, \AXES, \COORDINATES, \AREAS, \VOLUMES</CODE>
</TD></TR>
<TR>
<TD valign="top"><B>Defaults:</B></TD>
<TD valign="top"><CODE>
X=[1;2;3;...], y=[1;2;3;...], \-SPECIFIC, \-INTERPSIZE, \-POLAR, \-LEGEND, \-COLOURS,
\-RESET, \-AREAS, \-VOLUMES, \BORDER, \-COORDINATES, \AXES</CODE>
</TD></TR>
</TABLE>
<P>
Suppose that <CODE>v</CODE> is a matrix which has <i>n</i> columns and <i>m</i> rows. The vectors
<CODE>x</CODE> and <CODE>y</CODE> are optional, and if entered, are used for scaling the axes.
Each matrix element, <code>v[i,j]</code>, is associated with the coordinates
<code>(x[j],y[i])</code>. The length of <CODE>x</CODE> must be greater than or equal to <i>n</i>
and the length of <CODE>y</CODE> must be greater than or equal to <i>m</i>.</P>
<P>
If <CODE>x</CODE> and <CODE>y</CODE> are not entered, <CODE>x</CODE> defaults to the set
<CODE>[1;2;3;...;<i>n</i>]</CODE>, and <CODE>y</CODE> defaults to the set
<CODE>[1;2;3;...;<i>m</i>]</CODE>, so that matrix element <code><i>m</i>[i,j]</code> is
associated with the coordinates <code>(j,i)</code>.</P>
<P>
<font size="+1" color="green">Minimum and maximum contour coordinates</font></P>
<P>
The minimum and maximum <i>x</i> value for each contour are automatically
stored in vectors named <CODE><font color="orange">CXMIN</font></CODE> and
<CODE><font color="orange">CXMAX</font></CODE>; the minimum and maximum
<i>y</i> value for each contour are automatically stored in vectors named
<CODE><font color="orange">CYMIN</font></CODE> and
<CODE><font color="orange">CYMAX</font></CODE>. These vectors are then
available to the user for plotting and/or manipulation. Each time the
<CODE>CONTOUR</CODE> command is entered, these
vectors are emptied and replaced, so if you wish to keep them, they should
be renamed or copied into other vectors.</P>
<P>
<font size="+1" color="green">Volume</font></P>
<P>
If the <CODE>\VOLUMES</CODE> qualifier is used, the volume contained within each contour is
calculated as a percentage of the total volume. The volume percentages are automatically stored
in a vector named <CODE><font color="orange">CVOLM</font></CODE>. Each time the
<CODE>CONTOUR</CODE> command is entered, this vector is emptied and replaced, so if you wish to
keep it, it should be renamed or copied into another vector.</P>
<P>
<font size="+1" color="green">Area</font></P>
<P>
If the <CODE>\AREAS</CODE> qualifier is used, the area contained within each contour is calculated
as a percentage of the total area. The area percentages are automatically stored in a vector
named <CODE><font color="orange">CAREA</font></CODE>. Each time the
<CODE>CONTOUR</CODE> command is entered, this vector is emptied and replaced, so if you wish to
keep it, it should be renamed or copied into another vector.</P>
<P>
<font size="+1" color="green">Area and volume calculation</font></P>
<P>
The areas and volumes are calculated in the following way. Two
dimensional, four point linear interpolation is used to calculate a fine
mesh overlayed on the matrix, see the figure below.
Suppose the matrix has <i>n</i> columns and <i>m</i> rows and the size of the
fine mesh is <i>n<sub>1</sub></i> columns by <i>m<sub>1</sub></i> rows. The
total area is <i>n<sub>1</sub>·m<sub>1</sub></i> and the total volume
is the sum of the interpolated values. Each point of the fine mesh is
tested against the contour levels, and if a mesh point has a value greater
than the contour level, a one is binned for the area vector and the mesh
point value is binned for the volume vector. Finally, the area and volume
vectors are normalized by conversion to percentages.</P>
<P>
<center><IMG SRC="img1.gif"><BR />
Interpolating a fine mesh on the contours of a matrix</center></P>
<P>
<font size="+1" color="green">Interpolation size</font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="644">
<TR>
<TD width="14%" valign="top"><B>Syntax</B>:</TD>
<TD width="86%" valign="top"><CODE>
CONTOUR\INTERPSIZE ntrp { x y } v num { min { incr }}<br />
CONTOUR\INTERPSIZE\COLOURS colr ntrp { x y } v num { min { incr }}<br />
CONTOUR\SPECIFIC\INTERPSIZE ntrp { x y } v lvls<br />
CONTOUR\SPECIFIC\INTERPSIZE/COLOURS colr ntrp { x y } v lvls</CODE>
</TD></TR>
</TABLE>
<P>
Suppose the matrix has <i>n</i> columns and <i>m</i> rows. The total size
of the fine mesh, <i>n<sub>1</sub></i> columns by <i>m<sub>1</sub></i> rows,
is defined by the following:</P>
<P>
<CODE><i>n</i><sub>1</sub> = (<i>n</i>-1)<i>i<sub>x</sub></i> + 1</CODE><br />
<CODE><i>m</i><sub>1</sub> = (<i>m</i>-1)<i>i<sub>y</sub></i> + 1</CODE></P>
<P>
where <CODE><i>i<sub>x</sub></i>-1</CODE> is the number of interpolation
points between matrix points in the <i>x</i>-direction, and
<CODE><i>i<sub>y</sub></i>-1</CODE> is the number of interpolation points
between matrix points in the <i>y</i>-direction. The defaults are as
below:</P>
<p>
<table cols="2" border="1">
<tr>
<td><table cols="7" border="0" cellspacing="0">
<tr><td align="center"><i>i<sub>x</sub></i></td><td colspan="6"></td></tr>
<tr><td align="right">10</td><td> if </td>
<td></td><td></td><td><i>n</i></td><td><</td><td>20</td></tr>
<tr><td align="right">5</td><td> if </td>
<td>20</td><td>≤</td><td><i>n</i></td><td><</td><td>50</td></tr>
<tr><td align="right">3</td><td> if </td>
<td>50</td><td>≤</td><td><i>n</i></td><td><</td><td>100 </td></tr>
<tr><td align="right">2</td><td> if </td>
<td>100</td><td>≤</td><td><i>n</i></td><td></td><td></td></tr>
</table></td>
<td><table cols="7" border="0" cellspacing="0">
<tr><td align="center"><i>i<sub>y</sub></i></td><td colspan="6"></td></tr>
<tr><td align="right">10</td><td> if </td>
<td></td><td></td><td><i>m</i></td><td><</td><td>20</td></tr>
<tr><td align="right">5</td><td> if </td>
<td>20</td><td>≤</td><td><i>m</i></td><td><</td><td>50</td></tr>
<tr><td align="right">3</td><td> if </td>
<td>50</td><td>≤</td><td><i>m</i></td><td><</td><td>100</td></tr>
<tr><td align="right">2</td><td> if </td>
<td>100</td><td>≤</td><td><i>m</i></td><td></td><td></td></tr>
</table></td></tr>
</table>
<P>
To over-ride these defaults, use the <CODE>\INTERPSIZE</CODE> qualifier, and
enter <CODE>ntrp</CODE> as the first parameter. Both <i>i<sub>x</sub></i> and <i>i<sub>y</sub></i>
will be set to <CODE>ntrp</CODE>.</P>
<P>
<font size="+1" color="green">Matrix boundary</font></P>
<P>
By default, the boundary of the matrix is outlined within the axes. If this
boundary is not desired, use the <CODE>\-BORDER</CODE> qualifier.</P>
<P>
<a href="scattered.htm"><img src="../shadow_left.gif">
<font size="+1" color="olive">Scattered data</font></a><br />
<a href="example.htm"><img src="../shadow_right.gif">
<font size="+1" color="olive">Example</font></a></P>
</BODY>
</HTML>
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