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diff --git a/help/en_US/lsqnonlin.xml b/help/en_US/lsqnonlin.xml new file mode 100644 index 0000000..d7b8110 --- /dev/null +++ b/help/en_US/lsqnonlin.xml @@ -0,0 +1,199 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * + * This help file was generated from lsqnonlin.sci using help_from_sci(). + * + --> + +<refentry version="5.0-subset Scilab" xml:id="lsqnonlin" xml:lang="en" + xmlns="http://docbook.org/ns/docbook" + xmlns:xlink="http://www.w3.org/1999/xlink" + xmlns:svg="http://www.w3.org/2000/svg" + xmlns:ns3="http://www.w3.org/1999/xhtml" + xmlns:mml="http://www.w3.org/1998/Math/MathML" + xmlns:scilab="http://www.scilab.org" + xmlns:db="http://docbook.org/ns/docbook"> + + <refnamediv> + <refname>lsqnonlin</refname> + <refpurpose>Solves a non linear data fitting problems.</refpurpose> + </refnamediv> + + +<refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + xopt = lsqnonlin(fun,x0) + xopt = lsqnonlin(fun,x0,lb,ub) + xopt = lsqnonlin(fun,x0,lb,ub,options) + [xopt,resnorm] = lsqnonlin( ... ) + [xopt,resnorm,residual] = lsqnonlin( ... ) + [xopt,resnorm,residual,exitflag] = lsqnonlin( ... ) + [xopt,resnorm,residual,exitflag,output,lambda,gradient] = lsqnonlin( ... ) + + </synopsis> +</refsynopsisdiv> + +<refsection> + <title>Parameters</title> + <variablelist> + <varlistentry><term>fun :</term> + <listitem><para> a function, representing the objective function and gradient (if given) of the problem</para></listitem></varlistentry> + <varlistentry><term>x0 :</term> + <listitem><para> a vector of double, contains initial guess of variables.</para></listitem></varlistentry> + <varlistentry><term>lb :</term> + <listitem><para> a vector of double, contains lower bounds of the variables.</para></listitem></varlistentry> + <varlistentry><term>ub :</term> + <listitem><para> a vector of double, contains upper bounds of the variables.</para></listitem></varlistentry> + <varlistentry><term>options :</term> + <listitem><para> a list containing the parameters to be set.</para></listitem></varlistentry> + <varlistentry><term>xopt :</term> + <listitem><para> a vector of double, the computed solution of the optimization problem.</para></listitem></varlistentry> + <varlistentry><term>resnorm :</term> + <listitem><para> a double, objective value returned as the scalar value i.e. sum(fun(x).^2).</para></listitem></varlistentry> + <varlistentry><term>residual :</term> + <listitem><para> a vector of double, solution of objective function i.e. fun(x).</para></listitem></varlistentry> + <varlistentry><term>exitflag :</term> + <listitem><para> The exit status. See below for details.</para></listitem></varlistentry> + <varlistentry><term>output :</term> + <listitem><para> The structure consist of statistics about the optimization. See below for details.</para></listitem></varlistentry> + <varlistentry><term>lambda :</term> + <listitem><para> The structure consist of the Lagrange multipliers at the solution of problem. See below for details.</para></listitem></varlistentry> + <varlistentry><term>gradient :</term> + <listitem><para> a vector of doubles, containing the Objective's gradient of the solution.</para></listitem></varlistentry> + </variablelist> +</refsection> + +<refsection> + <title>Description</title> + <para> +Search the minimum of a constrained non-linear least square problem specified by : + </para> + <para> +<latex> +\begin{eqnarray} +&\mbox{min}_{x} +& (f_1(x)^2 + f_2(x)^2 + ... + f_n(x)^2) \\ +& lb \leq x \leq ub \\ +\end{eqnarray} +</latex> + </para> + <para> +The routine calls fmincon which calls Ipopt for solving the non-linear least square problem, Ipopt is a library written in C++. + </para> + <para> +The options allows the user to set various parameters of the Optimization problem. +It should be defined as type "list" and contains the following fields. +<itemizedlist> +<listitem>Syntax : options= list("MaxIter", [---], "CpuTime", [---],"GradObj", "on");</listitem> +<listitem>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</listitem> +<listitem>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</listitem> +<listitem>GradObj : a string, representing the gradient function is on or off.</listitem> +<listitem>Default Values : options = list("MaxIter", [3000], "CpuTime", [600], "GradObj", "off");</listitem> +</itemizedlist> + </para> + <para> +The exitflag allows to know the status of the optimization which is given back by Ipopt. +<itemizedlist> +<listitem>exitflag=0 : Optimal Solution Found </listitem> +<listitem>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</listitem> +<listitem>exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal.</listitem> +<listitem>exitflag=3 : Stop at Tiny Step.</listitem> +<listitem>exitflag=4 : Solved To Acceptable Level.</listitem> +<listitem>exitflag=5 : Converged to a point of local infeasibility.</listitem> +</itemizedlist> + </para> + <para> +For more details on exitflag see the ipopt documentation, go to http://www.coin-or.org/Ipopt/documentation/ + </para> + <para> +The output data structure contains detailed informations about the optimization process. +It has type "struct" and contains the following fields. +<itemizedlist> +<listitem>output.iterations: The number of iterations performed during the search</listitem> +<listitem>output.constrviolation: The max-norm of the constraint violation.</listitem> +</itemizedlist> + </para> + <para> +The lambda data structure contains the Lagrange multipliers at the end +of optimization. In the current version the values are returned only when the the solution is optimal. +It has type "struct" and contains the following fields. +<itemizedlist> +<listitem>lambda.lower: The Lagrange multipliers for the lower bound constraints.</listitem> +<listitem>lambda.upper: The Lagrange multipliers for the upper bound constraints.</listitem> +</itemizedlist> + </para> + <para> +</para> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//A simple non-linear least square example taken from leastsq default present in scilab +function y=yth(t, x) +y = x(1)*exp(-x(2)*t) +endfunction +// we have the m measures (ti, yi): +m = 10; +tm = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5]'; +ym = [0.79, 0.59, 0.47, 0.36, 0.29, 0.23, 0.17, 0.15, 0.12, 0.08]'; +// measure weights (here all equal to 1...) +wm = ones(m,1); +// and we want to find the parameters x such that the model fits the given +// data in the least square sense: +// +// minimize f(x) = sum_i wm(i)^2 ( yth(tm(i),x) - ym(i) )^2 +// initial parameters guess +x0 = [1.5 ; 0.8]; +// in the first examples, we define the function fun and dfun +// in scilab language +function y=myfun(x, tm, ym, wm) +y = wm.*( yth(tm, x) - ym ) +endfunction +// the simplest call +[xopt,resnorm,residual,exitflag,output,lambda,gradient] = lsqnonlin(myfun,x0) +// Press ENTER to continue + + ]]></programlisting> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//A basic example taken from leastsq default present in scilab with gradient +function y=yth(t, x) +y = x(1)*exp(-x(2)*t) +endfunction +// we have the m measures (ti, yi): +m = 10; +tm = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5]'; +ym = [0.79, 0.59, 0.47, 0.36, 0.29, 0.23, 0.17, 0.15, 0.12, 0.08]'; +// measure weights (here all equal to 1...) +wm = ones(m,1); +// and we want to find the parameters x such that the model fits the given +// data in the least square sense: +// +// minimize f(x) = sum_i wm(i)^2 ( yth(tm(i),x) - ym(i) )^2 +// initial parameters guess +x0 = [1.5 ; 0.8]; +// in the first examples, we define the function fun and dfun +// in scilab language +function [y,dy]=myfun(x, tm, ym, wm) +y = wm.*( yth(tm, x) - ym ) +v = wm.*exp(-x(2)*tm) +dy = [v , -x(1)*tm.*v] +endfunction +options = list("GradObj", "on") +[xopt,resnorm,residual,exitflag,output,lambda,gradient] = lsqnonlin(myfun,x0,[],[],options) + ]]></programlisting> +</refsection> + +<refsection> + <title>Authors</title> + <simplelist type="vert"> + <member>Harpreet Singh</member> + </simplelist> +</refsection> +</refentry> |