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diff --git a/help/en_US/lsqlin.xml b/help/en_US/lsqlin.xml new file mode 100644 index 0000000..92dbd91 --- /dev/null +++ b/help/en_US/lsqlin.xml @@ -0,0 +1,156 @@ +<?xml version="1.0" encoding="UTF-8"?> + +<!-- + * + * This help file was generated from lsqlin.sci using help_from_sci(). + * + --> + +<refentry version="5.0-subset Scilab" xml:id="lsqlin" 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>lsqlin</refname> + <refpurpose>Solves a linear quadratic problem.</refpurpose> + </refnamediv> + + +<refsynopsisdiv> + <title>Calling Sequence</title> + <synopsis> + x = lsqlin(C,d,A,b) + x = lsqlin(C,d,A,b,Aeq,beq) + x = lsqlin(C,d,A,b,Aeq,beq,lb,ub) + x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0) + x = lsqlin(C,d,A,b,Aeq,beq,lb,ub,x0,param) + [xopt,resnorm,residual,exitflag,output,lambda] = lsqlin( ... ) + + </synopsis> +</refsynopsisdiv> + +<refsection> + <title>Parameters</title> + <variablelist> + <varlistentry><term>C :</term> + <listitem><para> a matrix of doubles, represents the multiplier of the solution x in the expression C*x - d. C is M-by-N, where M is the number of equations, and N is the number of elements of x.</para></listitem></varlistentry> + <varlistentry><term>d :</term> + <listitem><para> a vector of doubles, represents the additive constant term in the expression C*x - d. d is M-by-1, where M is the number of equations.</para></listitem></varlistentry> + <varlistentry><term>A :</term> + <listitem><para> a vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry> + <varlistentry><term>b :</term> + <listitem><para> a vector of doubles, represents the linear coefficients in the inequality constraints</para></listitem></varlistentry> + <varlistentry><term>Aeq :</term> + <listitem><para> a matrix of doubles, represents the linear coefficients in the equality constraints</para></listitem></varlistentry> + <varlistentry><term>beq :</term> + <listitem><para> a vector of doubles, represents the linear coefficients in the equality constraints</para></listitem></varlistentry> + <varlistentry><term>LB :</term> + <listitem><para> a vector of doubles, where n is number of variables, contains lower bounds of the variables.</para></listitem></varlistentry> + <varlistentry><term>UB :</term> + <listitem><para> a vector of doubles, where n is number of variables, contains upper bounds of the variables.</para></listitem></varlistentry> + <varlistentry><term>x0 :</term> + <listitem><para> a vector of doubles, contains initial guess of variables.</para></listitem></varlistentry> + <varlistentry><term>param :</term> + <listitem><para> a list containing the the parameters to be set.</para></listitem></varlistentry> + <varlistentry><term>xopt :</term> + <listitem><para> a vector of doubles, the computed solution of the optimization problem.</para></listitem></varlistentry> + <varlistentry><term>fopt :</term> + <listitem><para> a double, the function value at x.</para></listitem></varlistentry> + <varlistentry><term>exitflag :</term> + <listitem><para> Integer identifying the reason the algorithm terminated.</para></listitem></varlistentry> + <varlistentry><term>output :</term> + <listitem><para> Structure containing information about the optimization.</para></listitem></varlistentry> + <varlistentry><term>lambda :</term> + <listitem><para> Structure containing the Lagrange multipliers at the solution x (separated by constraint type).</para></listitem></varlistentry> + </variablelist> +</refsection> + +<refsection> + <title>Description</title> + <para> +Search the minimum of a constrained linear least square problem specified by : +find the minimum of f(x) such that + </para> + <para> +<latex> +\begin{eqnarray} +&\mbox{min}_{x} +& 1/2||C*x - d||_2^2 \\ +& \text{subject to} & A.x \leq b \\ +& & Aeq.x \leq beq \\ +& & lb \leq x \leq ub \\ +\end{eqnarray} +</latex> + </para> + <para> +We are calling IPOpt for solving the linear least square problem, IPOpt is a library written in C++. The code has been written by Andreas Wächter and Carl Laird. + </para> + <para> +</para> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +//A simple linear least square example +C = [0.9501 0.7620 0.6153 0.4057 +0.2311 0.4564 0.7919 0.9354 +0.6068 0.0185 0.9218 0.9169 +0.4859 0.8214 0.7382 0.4102 +0.8912 0.4447 0.1762 0.8936]; +d = [0.0578 +0.3528 +0.8131 +0.0098 +0.1388]; +A = [0.2027 0.2721 0.7467 0.4659 +0.1987 0.1988 0.4450 0.4186 +0.6037 0.0152 0.9318 0.8462]; +b = [0.5251 +0.2026 +0.6721]; +[xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b) + + ]]></programlisting> +</refsection> + +<refsection> + <title>Examples</title> + <programlisting role="example"><![CDATA[ +C = [0.9501 0.7620 0.6153 0.4057 +0.2311 0.4564 0.7919 0.9354 +0.6068 0.0185 0.9218 0.9169 +0.4859 0.8214 0.7382 0.4102 +0.8912 0.4447 0.1762 0.8936]; +d = [0.0578 +0.3528 +0.8131 +0.0098 +0.1388]; +A =[0.2027 0.2721 0.7467 0.4659 +0.1987 0.1988 0.4450 0.4186 +0.6037 0.0152 0.9318 0.8462]; +b =[0.5251 +0.2026 +0.6721]; +Aeq = [3 5 7 9]; +beq = 4; +lb = -0.1*ones(4,1); +ub = 2*ones(4,1); +[xopt,resnorm,residual,exitflag,output,lambda] = lsqlin(C,d,A,b,Aeq,beq,lb,ub) + + ]]></programlisting> +</refsection> + +<refsection> + <title>Authors</title> + <simplelist type="vert"> + <member>Harpreet Singh</member> + </simplelist> +</refsection> +</refentry> |