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<a name="lsqcurvefit"></a>
<div class="header">
<p>
Next: <a href="nlinfit.html#nlinfit" accesskey="n" rel="next">nlinfit</a>, Previous: <a href="lsqnonlin.html#lsqnonlin" accesskey="p" rel="prev">lsqnonlin</a>, Up: <a href="Compatibility-functions.html#Compatibility-functions" accesskey="u" rel="up">Compatibility functions</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Curve-fitting"></a>
<h3 class="section">7.4 Curve fitting</h3>
<a name="index-lsqcurvefit-5"></a>
<p>This function is for Matlab compatibility. It attempts to work like
<code>lsqcurvefit</code> by calling <a href="nonlin_005fcurvefit.html#nonlin_005fcurvefit">nonlin_curvefit</a>.
</p>
<a name="XREFlsqcurvefit"></a><dl>
<dt><a name="index-lsqcurvefit"></a>Function File: <em></em> <strong>lsqcurvefit</strong> <em>(<var>fun</var>, <var>x0</var>, <var>xdata</var>, <var>ydata</var>)</em></dt>
<dt><a name="index-lsqcurvefit-1"></a>Function File: <em></em> <strong>lsqcurvefit</strong> <em>(<var>fun</var>, <var>x0</var>, <var>xdata</var>, <var>ydata</var>, <var>lb</var>, <var>ub</var>)</em></dt>
<dt><a name="index-lsqcurvefit-2"></a>Function File: <em></em> <strong>lsqcurvefit</strong> <em>(<var>fun</var>, <var>x0</var>, <var>xdata</var>, <var>ydata</var>, <var>lb</var>, <var>ub</var>, <var>options</var>)</em></dt>
<dt><a name="index-lsqcurvefit-3"></a>Function File: <em></em> <strong>lsqcurvefit</strong> <em>(<var>problem</var>)</em></dt>
<dt><a name="index-lsqcurvefit-4"></a>Function File: <em>[<var>x</var>, <var>resnorm</var>, <var>residual</var>, <var>exitflag</var>, <var>output</var>, <var>lambda</var>, <var>jacobian</var>] =</em> <strong>lsqcurvefit</strong> <em>(…)</em></dt>
<dd><p>Solve nonlinear least-squares (nonlinear data-fitting) problems
</p><div class="example">
<pre class="example">min [EuclidianNorm (f(x, xdata) - ydata)] .^ 2
x
</pre></div>
<p>The first four input arguments must be provided with non-empty
initial guess <var>x0</var>. For a given input <var>xdata</var>, <var>ydata</var>
is the observed output. <var>ydata</var> must be the same size as the
vector (or matrix) returned by <var>fun</var>. The optional bounds
<var>lb</var> and <var>ub</var> should be the same size as <var>x0</var>.
</p>
<p><code>lsqcurvefit</code> may also be called with a single structure
argument with the fields <code>fun</code>, <code>x0</code>, <code>xdata</code>,
<code>ydata</code>, <code>lb</code>, <code>ub</code>, and <code>options</code>, resembling
the separate input arguments above. For compatibility reasons,
field <code>fun</code> may also be called <code>objective</code>. Additionally,
the structure must have the field <code>solver</code>, set to
<code>"lsqcurvefit"</code>.
</p>
<p><var>options</var> can be set with <code>optimset</code>.
Follwing Matlab compatible options
are recognized:
</p>
<p><code>Algorithm</code>
String specifying backend algorithm. Currently available "lm_svd_feasible"
only.
</p>
<p><code>TolFun</code>
Minimum fractional improvement in objective function in an iteration
(termination criterium). Default: 1e-6.
</p>
<p><code>TypicalX</code>
Typical values of x. Default: 1.
</p>
<p><code>MaxIter</code>
Maximum number of iterations allowed. Default: 20.
</p>
<p><code>Jacobian</code>
If set to "on", the function <var>fun</var> must return a second output
containing a user-specified Jacobian. The Jacobian is computed using
finite differences otherwise. Default: "off"
</p>
<p><code>FinDiffType</code>
"centered" or "forward" (Default) type finite differences estimation.
</p>
<p><code>FinDiffRelStep</code>
Step size factor. The default is sqrt(eps) for forward finite differences,
and eps^(1/3) for central finite differences
</p>
<p><code>OutputFcn</code>
One or more user-defined functions, either as a function handle or as a
cell array of function handles that an optimization function calls at each
iteration. The function definition has the following form:
</p>
<p><code>stop = outfun(x, optimValues, state)</code>
</p>
<p><code>x</code> is the point computed at the current iteration.
<code>optimValues</code> is a structure containing data from the current
iteration in the following fields:
"iteration"- number of current iteration.
"residual"- residuals.
<code>state</code> is the state of the algorithm: "init" at start,
"iter" after each iteration and "done" at the end.
</p>
<p><code>Display</code>
String indicating the degree of verbosity. Default: "off".
Currently only supported values are "off" (no messages) and "iter"
(some messages after each iteration).
</p>
<p>Returned values:
</p>
<dl compact="compact">
<dt><var>x</var></dt>
<dd><p>Coefficients to best fit the nonlinear function fun(x,xdata) to the observed values ydata.
</p>
</dd>
<dt><var>resnorm</var></dt>
<dd><p>Scalar value of objective as squared EuclidianNorm(f(x)).
</p>
</dd>
<dt><var>residual</var></dt>
<dd><p>Value of solution residuals f(x).
</p>
</dd>
<dt><var>exitflag</var></dt>
<dd><p>Status of solution:
</p>
<dl compact="compact">
<dt><code>0</code></dt>
<dd><p>Maximum number of iterations reached.
</p>
</dd>
<dt><code>2</code></dt>
<dd><p>Change in x was less than the specified tolerance.
</p>
</dd>
<dt><code>3</code></dt>
<dd><p>Change in the residual was less than the specified tolerance.
</p>
</dd>
<dt><code>-1</code></dt>
<dd><p>Output function terminated the algorithm.
</p></dd>
</dl>
</dd>
<dt><var>output</var></dt>
<dd><p>Structure with additional information, currently the only field is
<code>iterations</code>, the number of used iterations.
</p>
</dd>
<dt><var>lambda</var></dt>
<dd><p>Structure containing Lagrange multipliers at the solution <var>x</var> sepatared by constraint type (<var>lb</var> and <var>ub</var>).
</p>
</dd>
<dt><var>jacobian</var></dt>
<dd><p>m-by-n matrix, where <var>jacobian</var>(i,j) is the partial derivative of <var>fun(i)</var> with respect to <var>x(j)</var>
If <code>Jacobian</code> is set to "on" in <var>options</var> then <var>fun</var> must return a second argument providing a user-sepcified Jacobian. Otherwise, lsqnonlin approximates the Jacobian using finite differences.
</p></dd>
</dl>
<p>This function is a compatibility wrapper. It calls the more general <code>nonlin_curvefit</code> function internally.
</p>
<p><strong>See also:</strong> <a href="lsqnonlin.html#XREFlsqnonlin">lsqnonlin</a>, <a href="nonlin_005fresidmin.html#XREFnonlin_005fresidmin">nonlin_residmin</a>, <a href="nonlin_005fcurvefit.html#XREFnonlin_005fcurvefit">nonlin_curvefit</a>.
</p></dd></dl>
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Next: <a href="nlinfit.html#nlinfit" accesskey="n" rel="next">nlinfit</a>, Previous: <a href="lsqnonlin.html#lsqnonlin" accesskey="p" rel="prev">lsqnonlin</a>, Up: <a href="Compatibility-functions.html#Compatibility-functions" accesskey="u" rel="up">Compatibility functions</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
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