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Chapters:
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<a href="Introduction.html">1: Introduction</a><br>
<a href="SimpleExample.html">2: Simple example</a><br>
<a href="InvokingGri.html">3: Invocation</a><br>
<a href="GettingMoreControl.html">4: Finer Control</a><br>
<a href="X-Y.html">5: X-Y Plots</a><br>
<a href="ContourPlots.html">6: Contour Plots</a><br>
<a href="Images.html">7: Image Plots</a><br>
<a href="Examples.html">8: Examples</a><br>
<a href="Commands.html">9: Gri Commands</a><br>
<a href="Programming.html">10: Programming</a><br>
<a href="Environment.html">11: Environment</a><br>
<a href="Emacs.html">12: Emacs Mode</a><br>
<a href="History.html">13: History</a><br>
<a href="Installation.html">14: Installation</a><br>
<a href="Bugs.html">15: Gri Bugs</a><br>
<a href="TestSuite.html">16: Test Suite</a><br>
<a href="Acknowledgments.html">17: Acknowledgments</a><br>
<a href="License.html">18: License</a><br>
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Indices:</br>
<a href="ConceptIndex.html"><i>Concepts</i></a><br>
<a href="CommandIndex.html"><i>Commands</i></a><br>
<a href="BuiltinIndex.html"><i>Variables</i></a><br>
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<h3>9.3.44: `<font color="#82140F"><code>smooth</code></font>'</h3>
<!-- latex: \index{smooth} -->
All these smoothing commands ignore the <b>location</b> of the data. For
equispaced data these algorithms have the standard interpretation in
terms of digital filters. For non-equispaced data, the interpretation
is up to the user.
<p>
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<PRE>
<font color="#82140F">
`smooth {x [.n.]} \
| {y [.n.]} \
| {grid data [.f.|{along x|y}]}'
</font></PRE>
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<p>
The `<font color="#82140F"><code>smooth x</code></font>' command does smoothing by the following formula
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<font color="#82140F">
x[i-1] x[i] x[i+1]
------ + ---- + ------
4 2 4
</font></PRE>
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<p>
The `<font color="#82140F"><code>smooth x .n.</code></font>' command does boxcar smoothing with centred
boxcars `<font color="#82140F"><code>.n.</code></font>' points wide. The `<font color="#82140F"><code>smooth y</code></font>' command does the
same as `<font color="#82140F"><code>smooth x</code></font>', but on the `<font color="#82140F"><code>y</code></font>' column.
<p>
<!-- latex: \index{smooth grid data} -->
There are several methods of smoothing grid data. Note that isolated
missing values are filled in by each method. (Let the author know if
you'd like that `feature' to be an option.)
<p>
The `<font color="#82140F"><code>smooth grid data</code></font>' command smooths gridded data, by weighted
average in a plus-shaped window about each gridpoint. The smoothing
algorithm replaces each interior gridpoint value `<font color="#82140F"><code>z[i][j]</code></font>' by
<p>
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<font color="#82140F">
z[i][j] z[i-1][j] + z[i+1][j] + z[i][j-1] + z[i][j+1]
------- + ---------------------------------------------
2 8
</font></PRE>
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<p>
Points along the edges are smoothed by the same formula, after
inventing image points outside the domain by planar extrapolation.
<p>
The `<font color="#82140F"><code>smooth grid data .f.</code></font>' command performs partial smoothing. A
temporary fully-smoothed grid `<font color="#82140F"><code>zSMOOTH[i][h]</code></font>' is constructed as
above, and a linear combination of this grid and the original grid is
used as the replacement grid:
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z[i][j] = (1-f) * z[i][j] + f * zSMOOTH[i][j]
</font></PRE>
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<p>
where `<font color="#82140F"><code>f</code></font>' is the value indicated on the command line.
Thus, `<font color="#82140F"><code>smooth grid data 0</code></font>' performs no smoothing at all, while
`<font color="#82140F"><code>smooth grid data 1</code></font>' is equivalent to `<font color="#82140F"><code>smooth grid data</code></font>'.
<p>
The `<font color="#82140F"><code>smooth grid data along x</code></font>' command smooths the grid data
across `<font color="#82140F"><code>x</code></font>' (i.e., horizontally), by replacing each value
`<font color="#82140F"><code>z[i][j]</code></font>' with the value
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<font color="#82140F">
z[i][j] z[i-1][j] + z[i+1][j]
------- + ---------------------
2 4
</font></PRE>
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<p>
Points along the edges are smoothed by the same formula, after
inventing image points outside the domain by linear extrapolation.
<p>
The `<font color="#82140F"><code>smooth grid data along y</code></font>' command does the same thing as
`<font color="#82140F"><code>smooth grid data along x</code></font>', but the smoothing is along `<font color="#82140F"><code>y</code></font>'.
<p>
<b>See also</b> see <a href="Filter.html#Filter">Filter</a>, a generalization of `<font color="82140F"><code>smooth x|y</code></font>'
which allows for more sophisticated filters.
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