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<a name="Module:Scientific.Functions.Interpolation"><h1>Module Scientific.Functions.Interpolation</h1></a>
<hr width=70%>
<a name="Class:Scientific.Functions.Interpolation.InterpolatingFunction"><h2>Class InterpolatingFunction: Function defined by values on a grid using interpolation</h2></a>
<p>An interpolating function of n variables with m-dimensional values
is defined by an (n+m)-dimensional array of values and n
one-dimensional arrays that define the variables values
corresponding to the grid points. The grid does not have to be
equidistant.</p>
<p>Constructor: InterpolatingFunction(<i>axes</i>, <i>values</i>, <i>default</i>=None)</p>
<p><dl>
<dt><i>axes</i></dt>
<dd><p>
a sequence of one-dimensional arrays, one for each
variable, specifying the values of the variables at
the grid points</p></dd>
<dt><i>values</i></dt>
<dd><p>
an array containing the function values on the grid</p></dd>
<dt><i>default</i></dt>
<dd><p>
the value of the function outside the grid. A value
of <tt>None</tt> means that the function is undefined outside
the grid and that any attempt to evaluate it there
yields an exception.</p></dd>
</dl>
</p>
<p>Evaluation: <tt>function(x1, x2, ...)</tt> yields the function value
obtained by linear interpolation.</p>
<p>Indexing: all array indexing operations except for the
NexAxis operator are supported.
</p>
<b>Methods:</b><br>
<ul>
<li> <b><i>selectInterval</i></b>(<i>first</i>, <i>last</i>, <i>variable</i>=<tt>0</tt>)
<p>Returns a new InterpolatingFunction whose grid is restricted
to the interval from <i>first</i> to <i>last</i> along the variable
whose number is <i>variable</i>.
</p>
<li> <b><i>derivative</i></b>(<i>variable</i>=<tt>0</tt>)
<p>Returns a new InterpolatingFunction describing the derivative
with respect to <i>variable</i> (an integer).
</p>
<li> <b><i>integral</i></b>(<i>variable</i>=<tt>0</tt>)
<p>Returns a new InterpolatingFunction describing the integral
with respect to <i>variable</i> (an integer). The integration constant
is defined in such a way that the value of the integral at the
first grid point along <i>variable</i> is zero.</p>
<li> <b><i>definiteIntegral</i></b>(<i>variable</i>=<tt>0</tt>)
<p>Returns a new InterpolatingFunction describing the definite integral
with respect to <i>variable</i> (an integer). The integration constant
is defined in such a way that the value of the integral at the
first grid point along <i>variable</i> is zero. In the case of a
function of one variable, the definite integral is a number.</p>
<li> <b><i>fitPolynomial</i></b>(<i>order</i>)
<p>Returns a polynomial of <i>order</i> with parameters obtained from
a least-squares fit to the grid values.</p>
</ul>
<hr width=70%>
<a name="Class:Scientific.Functions.Interpolation.NetCDFInterpolatingFunction"><h2>Class NetCDFInterpolatingFunction: Function defined by values on a grid in a netCDF file</h2></a>
<p>A subclass of InterpolatingFunction.</p>
<p>Constructor: NetCDFInterpolatingFunction(<i>filename</i>, <i>axesnames</i>,
<i>variablename</i>,
<i>default</i>=None)</p>
<p><dl>
<dt><i>filename</i></dt>
<dd><p>
the name of the netCDF file</p></dd>
<dt><i>axesnames</i></dt>
<dd><p>
the names of the netCDF variables that contain the
axes information</p></dd>
<dt><i>variablename</i></dt>
<dd><p>
the name of the netCDF variable that contains
the data values</p></dd>
<dt><i>default</i></dt>
<dd><p>
the value of the function outside the grid. A value
of <tt>None</tt> means that the function is undefined outside
the grid and that any attempt to evaluate it there
yields an exception.</p></dd>
</dl>
</p>
<p>Evaluation: <tt>function(x1, x2, ...)</tt> yields the function value
obtained by linear interpolation.
</p>
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