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143 lines
3.9 KiB
C++
143 lines
3.9 KiB
C++
#ifndef FILE_OPTI
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#define FILE_OPTI
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/**************************************************************************/
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/* File: opti.hpp */
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/* Author: Joachim Schoeberl */
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/* Date: 01. Jun. 95 */
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/**************************************************************************/
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namespace netgen
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{
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/**
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Function to be minimized.
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*/
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class MinFunction
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{
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public:
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///
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virtual double Func (const Vector & x) const;
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///
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virtual void Grad (const Vector & x, Vector & g) const;
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/// function and gradient
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virtual double FuncGrad (const Vector & x, Vector & g) const;
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/// directional derivative
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virtual double FuncDeriv (const Vector & x, const Vector & dir, double & deriv) const;
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/// if |g| < gradaccuray, then stop bfgs
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virtual double GradStopping (const Vector & /* x */) const { return 0; }
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///
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virtual void ApproximateHesse (const Vector & /* x */,
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DenseMatrix & /* hesse */) const;
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};
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class OptiParameters
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{
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public:
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int maxit_linsearch;
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int maxit_bfgs;
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double typf;
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double typx;
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OptiParameters ()
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{
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maxit_linsearch = 100;
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maxit_bfgs = 100;
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typf = 1;
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typx = 1;
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}
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};
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/** Implementation of BFGS method.
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Efficient method for non-linear minimiztion problems.
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@param x initial value and solution
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@param fun function to be minimized
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*/
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extern double BFGS (Vector & x, const MinFunction & fun,
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const OptiParameters & par,
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double eps = 1e-8);
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/** Steepest descent method.
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Simple method for non-linear minimization problems.
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@param x initial value and solution
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@param fun function to be minimized
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*/
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void SteepestDescent (Vector & x, const MinFunction & fun,
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const OptiParameters & par);
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extern void lines (
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Vector & x, // i: Ausgangspunkt der Liniensuche
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Vector & xneu, // o: Loesung der Liniensuche bei Erfolg
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Vector & p, // i: Suchrichtung
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double & f, // i: Funktionswert an der Stelle x
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// o: Funktionswert an der Stelle xneu, falls ifail = 0
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Vector & g, // i: Gradient an der Stelle x
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// o: Gradient an der Stelle xneu, falls ifail = 0
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const MinFunction & fun, // function to minmize
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const OptiParameters & par, // parameters
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double & alphahat, // i: Startwert f<>r alpha_hat
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// o: Loesung falls ifail = 0
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double fmin, // i: untere Schranke f<>r f
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double mu1, // i: Parameter mu_1 aus Alg.2.1
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double sigma, // i: Parameter sigma aus Alg.2.1
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double xi1, // i: Parameter xi_1 aus Alg.2.1
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double xi2, // i: Parameter xi_1 aus Alg.2.1
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double tau, // i: Parameter tau aus Alg.2.1
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double tau1, // i: Parameter tau_1 aus Alg.2.1
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double tau2, // i: Parameter tau_2 aus Alg.2.1
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int & ifail); // o: 0 bei erfolgreicher Liniensuche
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// -1 bei Abbruch wegen Unterschreiten von fmin
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// 1 bei Abbruch, aus sonstigen Gr<47>nden
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/**
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Solver for linear programming problem.
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\begin{verbatim}
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min c^t x
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A x <= b
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\end{verbatim}
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*/
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extern void LinearOptimize (const DenseMatrix & a, const Vector & b,
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const Vector & c, Vector & x);
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#ifdef NONE
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/**
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Simple projection iteration.
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find $u = argmin_{v >= 0} 0.5 u A u - f u$
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*/
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extern void ApproxProject (const BaseMatrix & a, Vector & u,
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const Vector & f,
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double tau, int its);
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/**
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CG Algorithm for quadratic programming problem.
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See: Dostal ...
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d ... diag(A) ^{-1}
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*/
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extern void ApproxProjectCG (const BaseMatrix & a, Vector & x,
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const Vector & b, const class DiagMatrix & d,
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double gamma, int & steps, int & changes);
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#endif
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}
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#endif
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