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Previous: <a href="Nonlinear-Programming.html" accesskey="p" rel="prev">Nonlinear Programming</a>, Up: <a href="Optimization.html" accesskey="u" rel="up">Optimization</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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<hr>
<h3 class="section" id="Linear-Least-Squares-1"><span>25.4 Linear Least Squares<a class="copiable-link" href="#Linear-Least-Squares-1"> ¶</a></span></h3>
<p>Octave also supports linear least squares minimization. That is,
Octave can find the parameter <em class="math">b</em> such that the model
<em class="math">y = x*b</em>
fits data <em class="math">(x,y)</em> as well as possible, assuming zero-mean
Gaussian noise. If the noise is assumed to be isotropic the problem
can be solved using the ‘<samp class="samp">\</samp>’ or ‘<samp class="samp">/</samp>’ operators, or the <code class="code">ols</code>
function. In the general case where the noise is assumed to be anisotropic
the <code class="code">gls</code> is needed.
</p>
<a class="anchor" id="XREFols"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-ols"><span><code class="def-type">[<var class="var">beta</var>, <var class="var">sigma</var>, <var class="var">r</var>] =</code> <strong class="def-name">ols</strong> <code class="def-code-arguments">(<var class="var">y</var>, <var class="var">x</var>)</code><a class="copiable-link" href="#index-ols"> ¶</a></span></dt>
<dd><p>Ordinary least squares (OLS) estimation.
</p>
<p>OLS applies to the multivariate model
<em class="math"><var class="var">y</var> = <var class="var">x</var>*<var class="var">b</var> + <var class="var">e</var></em><!-- /@w -->
where
<em class="math"><var class="var">y</var></em> is a <em class="math">t</em>-by-<em class="math">p</em> matrix, <em class="math"><var class="var">x</var></em> is a
<em class="math">t</em>-by-<em class="math">k</em> matrix, <var class="var">b</var> is a <em class="math">k</em>-by-<em class="math">p</em> matrix, and
<var class="var">e</var> is a <em class="math">t</em>-by-<em class="math">p</em> matrix.
</p>
<p>Each row of <var class="var">y</var> is a <em class="math">p</em>-variate observation in which each column
represents a variable. Likewise, the rows of <var class="var">x</var> represent
<em class="math">k</em>-variate observations or possibly designed values. Furthermore,
the collection of observations <var class="var">x</var> must be of adequate rank, <em class="math">k</em>,
otherwise <var class="var">b</var> cannot be uniquely estimated.
</p>
<p>The observation errors, <var class="var">e</var>, are assumed to originate from an
underlying <em class="math">p</em>-variate distribution with zero mean and
<em class="math">p</em>-by-<em class="math">p</em> covariance matrix <var class="var">S</var>, both constant conditioned
on <var class="var">x</var>. Furthermore, the matrix <var class="var">S</var> is constant with respect to
each observation such that
<code class="code">mean (<var class="var">e</var>) = 0</code> and
<code class="code">cov (vec (<var class="var">e</var>)) = kron (<var class="var">s</var>, <var class="var">I</var>)</code>.
(For cases
that don’t meet this criteria, such as autocorrelated errors, see
generalized least squares, gls, for more efficient estimations.)
</p>
<p>The return values <var class="var">beta</var>, <var class="var">sigma</var>, and <var class="var">r</var> are defined as
follows.
</p>
<dl class="table">
<dt><var class="var">beta</var></dt>
<dd><p>The OLS estimator for matrix <var class="var">b</var>.
<var class="var">beta</var> is calculated directly via
<code class="code">inv (<var class="var">x</var>'*<var class="var">x</var>) * <var class="var">x</var>' * <var class="var">y</var></code> if the matrix
<code class="code"><var class="var">x</var>'*<var class="var">x</var></code> is of full rank.
Otherwise, <code class="code"><var class="var">beta</var> = pinv (<var class="var">x</var>) * <var class="var">y</var></code> where
<code class="code">pinv (<var class="var">x</var>)</code> denotes the pseudoinverse of <var class="var">x</var>.
</p>
</dd>
<dt><var class="var">sigma</var></dt>
<dd><p>The OLS estimator for the matrix <var class="var">s</var>,
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"><var class="var">sigma</var> = (<var class="var">y</var>-<var class="var">x</var>*<var class="var">beta</var>)' * (<var class="var">y</var>-<var class="var">x</var>*<var class="var">beta</var>) / (<em class="math">t</em>-rank(<var class="var">x</var>))
</pre></div></div>
</dd>
<dt><var class="var">r</var></dt>
<dd><p>The matrix of OLS residuals, <code class="code"><var class="var">r</var> = <var class="var">y</var> - <var class="var">x</var>*<var class="var">beta</var></code>.
</p></dd>
</dl>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFgls">gls</a>, <a class="ref" href="Basic-Matrix-Functions.html#XREFpinv">pinv</a>.
</p></dd></dl>
<a class="anchor" id="XREFgls"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-gls"><span><code class="def-type">[<var class="var">beta</var>, <var class="var">v</var>, <var class="var">r</var>] =</code> <strong class="def-name">gls</strong> <code class="def-code-arguments">(<var class="var">y</var>, <var class="var">x</var>, <var class="var">o</var>)</code><a class="copiable-link" href="#index-gls"> ¶</a></span></dt>
<dd><p>Generalized least squares (GLS) model.
</p>
<p>Perform a generalized least squares estimation for the multivariate model
<em class="math"><var class="var">y</var> = <var class="var">x</var>*<var class="var">B</var> + <var class="var">E</var></em><!-- /@w -->
where
<var class="var">y</var> is a <em class="math">t</em>-by-<em class="math">p</em> matrix, <var class="var">x</var> is a
<em class="math">t</em>-by-<em class="math">k</em> matrix, <var class="var">b</var> is a <em class="math">k</em>-by-<em class="math">p</em> matrix
and <var class="var">e</var> is a <em class="math">t</em>-by-<em class="math">p</em> matrix.
</p>
<p>Each row of <var class="var">y</var> is a <em class="math">p</em>-variate observation in which each column
represents a variable. Likewise, the rows of <var class="var">x</var> represent
<em class="math">k</em>-variate observations or possibly designed values. Furthermore,
the collection of observations <var class="var">x</var> must be of adequate rank, <em class="math">k</em>,
otherwise <var class="var">b</var> cannot be uniquely estimated.
</p>
<p>The observation errors, <var class="var">e</var>, are assumed to originate from an
underlying <em class="math">p</em>-variate distribution with zero mean but possibly
heteroscedastic observations. That is, in general,
<code class="code"><em class="math">mean (<var class="var">e</var>) = 0</em></code> and
<code class="code"><em class="math">cov (vec (<var class="var">e</var>)) = (<em class="math">s</em>^2)*<var class="var">o</var></em></code>
in which <em class="math">s</em> is a scalar and <var class="var">o</var> is a
<em class="math">t*p</em>-by-<em class="math">t*p</em>
matrix.
</p>
<p>The return values <var class="var">beta</var>, <var class="var">v</var>, and <var class="var">r</var> are
defined as follows.
</p>
<dl class="table">
<dt><var class="var">beta</var></dt>
<dd><p>The GLS estimator for matrix <var class="var">b</var>.
</p>
</dd>
<dt><var class="var">v</var></dt>
<dd><p>The GLS estimator for scalar <em class="math">s^2</em>.
</p>
</dd>
<dt><var class="var">r</var></dt>
<dd><p>The matrix of GLS residuals, <em class="math"><var class="var">r</var> = <var class="var">y</var> - <var class="var">x</var>*<var class="var">beta</var></em>.
</p></dd>
</dl>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFols">ols</a>.
</p></dd></dl>
<a class="anchor" id="XREFlsqnonneg"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-lsqnonneg"><span><code class="def-type"><var class="var">x</var> =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(<var class="var">c</var>, <var class="var">d</var>)</code><a class="copiable-link" href="#index-lsqnonneg"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lsqnonneg-1"><span><code class="def-type"><var class="var">x</var> =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(<var class="var">c</var>, <var class="var">d</var>, <var class="var">x0</var>)</code><a class="copiable-link" href="#index-lsqnonneg-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lsqnonneg-2"><span><code class="def-type"><var class="var">x</var> =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(<var class="var">c</var>, <var class="var">d</var>, <var class="var">x0</var>, <var class="var">options</var>)</code><a class="copiable-link" href="#index-lsqnonneg-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lsqnonneg-3"><span><code class="def-type">[<var class="var">x</var>, <var class="var">resnorm</var>] =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-lsqnonneg-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lsqnonneg-4"><span><code class="def-type">[<var class="var">x</var>, <var class="var">resnorm</var>, <var class="var">residual</var>] =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-lsqnonneg-4"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lsqnonneg-5"><span><code class="def-type">[<var class="var">x</var>, <var class="var">resnorm</var>, <var class="var">residual</var>, <var class="var">exitflag</var>] =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-lsqnonneg-5"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lsqnonneg-6"><span><code class="def-type">[<var class="var">x</var>, <var class="var">resnorm</var>, <var class="var">residual</var>, <var class="var">exitflag</var>, <var class="var">output</var>] =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-lsqnonneg-6"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lsqnonneg-7"><span><code class="def-type">[<var class="var">x</var>, <var class="var">resnorm</var>, <var class="var">residual</var>, <var class="var">exitflag</var>, <var class="var">output</var>, <var class="var">lambda</var>] =</code> <strong class="def-name">lsqnonneg</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-lsqnonneg-7"> ¶</a></span></dt>
<dd>
<p>Minimize <code class="code">norm (<var class="var">c</var>*<var class="var">x</var> - <var class="var">d</var>)</code> subject to
<code class="code"><var class="var">x</var> >= 0</code>.
</p>
<p><var class="var">c</var> and <var class="var">d</var> must be real matrices.
</p>
<p><var class="var">x0</var> is an optional initial guess for the solution <var class="var">x</var>.
</p>
<p><var class="var">options</var> is an options structure to change the behavior of the
algorithm (see <a class="pxref" href="#XREFoptimset"><code class="code">optimset</code></a>). <code class="code">lsqnonneg</code>
recognizes these options: <code class="code">"MaxIter"</code>, <code class="code">"TolX"</code>.
</p>
<p>Outputs:
</p>
<dl class="table">
<dt><var class="var">resnorm</var></dt>
<dd><p>The squared 2-norm of the residual: <code class="code">norm (<var class="var">c</var>*<var class="var">x</var>-<var class="var">d</var>)^2</code>
</p>
</dd>
<dt><var class="var">residual</var></dt>
<dd><p>The residual: <code class="code"><var class="var">d</var>-<var class="var">c</var>*<var class="var">x</var></code>
</p>
</dd>
<dt><var class="var">exitflag</var></dt>
<dd><p>An indicator of convergence. 0 indicates that the iteration count was
exceeded, and therefore convergence was not reached; >0 indicates that the
algorithm converged. (The algorithm is stable and will converge given
enough iterations.)
</p>
</dd>
<dt><var class="var">output</var></dt>
<dd><p>A structure with two fields:
</p>
<ul class="itemize mark-bullet">
<li><code class="code">"algorithm"</code>: The algorithm used (<code class="code">"nnls"</code>)
</li><li><code class="code">"iterations"</code>: The number of iterations taken.
</li></ul>
</dd>
<dt><var class="var">lambda</var></dt>
<dd><p>Lagrange multipliers. If these are nonzero, the corresponding <var class="var">x</var>
values should be zero, indicating the solution is pressed up against a
coordinate plane. The magnitude indicates how much the residual would
improve if the <code class="code"><var class="var">x</var> >= 0</code> constraints were relaxed in that
direction.
</p>
</dd>
</dl>
<p><strong class="strong">See also:</strong> <a class="ref" href="Quadratic-Programming.html#XREFpqpnonneg">pqpnonneg</a>, <a class="ref" href="#XREFlscov">lscov</a>, <a class="ref" href="#XREFoptimset">optimset</a>.
</p></dd></dl>
<a class="anchor" id="XREFlscov"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-lscov"><span><code class="def-type"><var class="var">x</var> =</code> <strong class="def-name">lscov</strong> <code class="def-code-arguments">(<var class="var">A</var>, <var class="var">b</var>)</code><a class="copiable-link" href="#index-lscov"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lscov-1"><span><code class="def-type"><var class="var">x</var> =</code> <strong class="def-name">lscov</strong> <code class="def-code-arguments">(<var class="var">A</var>, <var class="var">b</var>, <var class="var">V</var>)</code><a class="copiable-link" href="#index-lscov-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lscov-2"><span><code class="def-type"><var class="var">x</var> =</code> <strong class="def-name">lscov</strong> <code class="def-code-arguments">(<var class="var">A</var>, <var class="var">b</var>, <var class="var">V</var>, <var class="var">alg</var>)</code><a class="copiable-link" href="#index-lscov-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-lscov-3"><span><code class="def-type">[<var class="var">x</var>, <var class="var">stdx</var>, <var class="var">mse</var>, <var class="var">S</var>] =</code> <strong class="def-name">lscov</strong> <code class="def-code-arguments">(…)</code><a class="copiable-link" href="#index-lscov-3"> ¶</a></span></dt>
<dd>
<p>Compute a generalized linear least squares fit.
</p>
<p>Estimate <var class="var">x</var> under the model <var class="var">b</var> = <var class="var">A</var><var class="var">x</var> + <var class="var">w</var>, where
the noise <var class="var">w</var> is assumed to follow a normal distribution with covariance
matrix <em class="math">{\sigma^2} V</em>.
</p>
<p>If the size of the coefficient matrix <var class="var">A</var> is n-by-p, the size of the
vector/array of constant terms <var class="var">b</var> must be n-by-k.
</p>
<p>The optional input argument <var class="var">V</var> may be an n-element vector of positive
weights (inverse variances), or an n-by-n symmetric positive semi-definite
matrix representing the covariance of <var class="var">b</var>. If <var class="var">V</var> is not supplied,
the ordinary least squares solution is returned.
</p>
<p>The <var class="var">alg</var> input argument, a guidance on solution method to use, is
currently ignored.
</p>
<p>Besides the least-squares estimate matrix <var class="var">x</var> (p-by-k), the function
also returns <var class="var">stdx</var> (p-by-k), the error standard deviation of estimated
<var class="var">x</var>; <var class="var">mse</var> (k-by-1), the estimated data error covariance scale
factors (<em class="math">\sigma^2</em>); and <var class="var">S</var> (p-by-p, or p-by-p-by-k if k > 1),
the error covariance of <var class="var">x</var>.
</p>
<p>Reference: Golub and Van Loan (1996),
<cite class="cite">Matrix Computations (3rd Ed.)</cite>, Johns Hopkins, Section 5.6.3
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFols">ols</a>, <a class="ref" href="#XREFgls">gls</a>, <a class="ref" href="#XREFlsqnonneg">lsqnonneg</a>.
</p></dd></dl>
<a class="anchor" id="XREFoptimset"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-optimset"><span><strong class="def-name">optimset</strong> <code class="def-code-arguments">()</code><a class="copiable-link" href="#index-optimset"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-optimset-1"><span><code class="def-type"><var class="var">options</var> =</code> <strong class="def-name">optimset</strong> <code class="def-code-arguments">()</code><a class="copiable-link" href="#index-optimset-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-optimset-2"><span><code class="def-type"><var class="var">options</var> =</code> <strong class="def-name">optimset</strong> <code class="def-code-arguments">(<var class="var">par</var>, <var class="var">val</var>, …)</code><a class="copiable-link" href="#index-optimset-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-optimset-3"><span><code class="def-type"><var class="var">options</var> =</code> <strong class="def-name">optimset</strong> <code class="def-code-arguments">(<var class="var">old</var>, <var class="var">par</var>, <var class="var">val</var>, …)</code><a class="copiable-link" href="#index-optimset-3"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-optimset-4"><span><code class="def-type"><var class="var">options</var> =</code> <strong class="def-name">optimset</strong> <code class="def-code-arguments">(<var class="var">old</var>, <var class="var">new</var>)</code><a class="copiable-link" href="#index-optimset-4"> ¶</a></span></dt>
<dd><p>Create options structure for optimization functions.
</p>
<p>When called without any input or output arguments, <code class="code">optimset</code> prints
a list of all valid optimization parameters.
</p>
<p>When called with one output and no inputs, return an options structure with
all valid option parameters initialized to <code class="code">[]</code>.
</p>
<p>When called with a list of parameter/value pairs, return an options
structure with only the named parameters initialized.
</p>
<p>When the first input is an existing options structure <var class="var">old</var>, the values
are updated from either the <var class="var">par</var>/<var class="var">val</var> list or from the options
structure <var class="var">new</var>.
</p>
<p>If <var class="var">par</var> does not exactly match the name of a standard parameter,
<code class="code">optimset</code> will attempt to match <var class="var">par</var> to a standard parameter
and will set the value of that parameter if a match is found. Matching is
case insensitive and is based on character matching at the start of the
parameter name. <code class="code">optimset</code> produces an error if it finds multiple
ambiguous matches. If no standard parameter matches are found a warning is
issued and the non-standard parameter is created.
</p>
<p>Standard list of valid parameters:
</p>
<dl class="table">
<dt>AutoScaling</dt>
<dt>ComplexEqn</dt>
<dt>Display</dt>
<dd><p>Request verbose display of results from optimizations. Values are:
</p>
<dl class="table">
<dt><code class="code">"off"</code> [default]</dt>
<dd><p>No display.
</p>
</dd>
<dt><code class="code">"iter"</code></dt>
<dd><p>Display intermediate results for every loop iteration.
</p>
</dd>
<dt><code class="code">"final"</code></dt>
<dd><p>Display the result of the final loop iteration.
</p>
</dd>
<dt><code class="code">"notify"</code></dt>
<dd><p>Display the result of the final loop iteration if the function has
failed to converge.
</p></dd>
</dl>
</dd>
<dt>FinDiffType</dt>
<dt>FunValCheck</dt>
<dd><p>When enabled, display an error if the objective function returns an invalid
value (a complex number, NaN, or Inf). Must be set to <code class="code">"on"</code> or
<code class="code">"off"</code> [default]. Note: the functions <code class="code">fzero</code> and
<code class="code">fminbnd</code> correctly handle Inf values and only complex values or NaN
will cause an error in this case.
</p>
</dd>
<dt>GradObj</dt>
<dd><p>When set to <code class="code">"on"</code>, the function to be minimized must return a
second argument which is the gradient, or first derivative, of the
function at the point <var class="var">x</var>. If set to <code class="code">"off"</code> [default], the
gradient is computed via finite differences.
</p>
</dd>
<dt>Jacobian</dt>
<dd><p>When set to <code class="code">"on"</code>, the function to be minimized must return a
second argument which is the Jacobian, or first derivative, of the
function at the point <var class="var">x</var>. If set to <code class="code">"off"</code> [default], the
Jacobian is computed via finite differences.
</p>
</dd>
<dt>MaxFunEvals</dt>
<dd><p>Maximum number of function evaluations before optimization stops.
Must be a positive integer.
</p>
</dd>
<dt>MaxIter</dt>
<dd><p>Maximum number of algorithm iterations before optimization stops.
Must be a positive integer.
</p>
</dd>
<dt>OutputFcn</dt>
<dd><p>A user-defined function executed once per algorithm iteration.
</p>
</dd>
<dt>TolFun</dt>
<dd><p>Termination criterion for the function output. If the difference in the
calculated objective function between one algorithm iteration and the next
is less than <code class="code">TolFun</code> the optimization stops. Must be a positive
scalar.
</p>
</dd>
<dt>TolX</dt>
<dd><p>Termination criterion for the function input. If the difference in <var class="var">x</var>,
the current search point, between one algorithm iteration and the next is
less than <code class="code">TolX</code> the optimization stops. Must be a positive scalar.
</p>
</dd>
<dt>TypicalX</dt>
<dt>Updating</dt>
</dl>
<p>This list can be extended by the user or other loaded Octave packages. An
updated valid parameters list can be queried using the no-argument form of
<code class="code">optimset</code>.
</p>
<p>Note 1: Only parameter names from the standard list are considered when
matching short parameter names, and <var class="var">par</var> will always be expanded
to match a standard parameter even if an exact non-standard match exists.
The value of a non-standard parameter that is ambiguous with one or more
standard parameters cannot be set by <code class="code">optimset</code> and can only be set
using <code class="code">setfield</code> or dot notation for structs.
</p>
<p>Note 2: The optimization options structure is primarily intended for
manipulation of known parameters by <code class="code">optimset</code> and <code class="code">optimget</code>.
Unpredictable behavior on future calls to <code class="code">optimset</code> or
<code class="code">optimget</code> can result from creating non-standard or ambiguous
parameters or from loading/unloading packages that change the known
parameter list after creation of an optimization options structure.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFoptimget">optimget</a>.
</p></dd></dl>
<a class="anchor" id="XREFoptimget"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-optimget"><span><code class="def-type"><var class="var">val</var> =</code> <strong class="def-name">optimget</strong> <code class="def-code-arguments">(<var class="var">options</var>, <var class="var">par</var>)</code><a class="copiable-link" href="#index-optimget"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-optimget-1"><span><code class="def-type"><var class="var">val</var> =</code> <strong class="def-name">optimget</strong> <code class="def-code-arguments">(<var class="var">options</var>, <var class="var">par</var>, <var class="var">default</var>)</code><a class="copiable-link" href="#index-optimget-1"> ¶</a></span></dt>
<dd><p>Return the value of the specific parameter <var class="var">par</var> from the optimization
options structure <var class="var">options</var> created by <code class="code">optimset</code>.
</p>
<p>If <var class="var">par</var> is not defined then return the <var class="var">default</var> value if
supplied, otherwise return an empty matrix.
</p>
<p>If <var class="var">par</var> does not exactly match the name of a standard parameter,
<code class="code">optimget</code> will attempt to match <var class="var">par</var> to a standard parameter
and will return that parameter’s value if a match is found. Matching is
case insensitive and is based on character matching at the start of the
parameter name. <code class="code">optimget</code> produces an error if it finds multiple
ambiguous matches. If no standard parameter matches are found a warning is
issued. See <code class="code">optimset</code> for information about the standard options
list.
</p>
<p>Note: Only parameter names from the standard list are considered when
matching short parameter names, and <var class="var">par</var> will always be expanded to
match a standard parameter even if an exact non-standard match exists. The
value of a non-standard parameter that is ambiguous with one or more
standard parameters cannot be returned by <code class="code">optimget</code> and can only be
accessed using <code class="code">getfield</code> or dot notation for structs.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFoptimset">optimset</a>.
</p></dd></dl>
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