mirror of
https://github.com/NGSolve/netgen.git
synced 2024-11-14 10:08:32 +05:00
350 lines
7.4 KiB
C++
350 lines
7.4 KiB
C++
/***************************************************************************/
|
|
/* */
|
|
/* Problem: Liniensuche */
|
|
/* */
|
|
/* Programmautor: Joachim Schöberl */
|
|
/* Matrikelnummer: 9155284 */
|
|
/* */
|
|
/* Algorithmus nach: */
|
|
/* */
|
|
/* Optimierung I, Gfrerer, WS94/95 */
|
|
/* Algorithmus 2.1: Liniensuche Problem (ii) */
|
|
/* */
|
|
/***************************************************************************/
|
|
|
|
|
|
|
|
#include <mystdlib.h>
|
|
|
|
#include <myadt.hpp> // min, max, sqr
|
|
|
|
#include <linalg.hpp>
|
|
#include "opti.hpp"
|
|
|
|
|
|
namespace netgen
|
|
{
|
|
const double eps0 = 1E-15;
|
|
|
|
// Liniensuche
|
|
|
|
|
|
double MinFunction :: Func (const Vector & /* x */) const
|
|
{
|
|
cerr << "Func of MinFunction called" << endl;
|
|
return 0;
|
|
}
|
|
|
|
void MinFunction :: Grad (const Vector & /* x */, Vector & /* g */) const
|
|
{
|
|
cerr << "Grad of MinFunction called" << endl;
|
|
}
|
|
|
|
double MinFunction :: FuncGrad (const Vector & x, Vector & g) const
|
|
{
|
|
cerr << "Grad of MinFunction called" << endl;
|
|
return 0;
|
|
/*
|
|
int n = x.Size();
|
|
|
|
Vector xr(n);
|
|
Vector xl(n);
|
|
|
|
double eps = 1e-6;
|
|
double fl, fr;
|
|
|
|
for (int i = 1; i <= n; i++)
|
|
{
|
|
xr.Set (1, x);
|
|
xl.Set (1, x);
|
|
|
|
xr.Elem(i) += eps;
|
|
fr = Func (xr);
|
|
|
|
xl.Elem(i) -= eps;
|
|
fl = Func (xl);
|
|
|
|
g.Elem(i) = (fr - fl) / (2 * eps);
|
|
}
|
|
|
|
double f = Func(x);
|
|
// (*testout) << "f = " << f << " grad = " << g << endl;
|
|
return f;
|
|
*/
|
|
}
|
|
|
|
|
|
double MinFunction :: FuncDeriv (const Vector & x, const Vector & dir, double & deriv) const
|
|
{
|
|
Vector g(x.Size());
|
|
double f = FuncGrad (x, g);
|
|
deriv = (g * dir);
|
|
|
|
// (*testout) << "g = " << g << ", dir = " << dir << ", deriv = " << deriv << endl;
|
|
return f;
|
|
}
|
|
|
|
void MinFunction :: ApproximateHesse (const Vector & x,
|
|
DenseMatrix & hesse) const
|
|
{
|
|
int n = x.Size();
|
|
int i, j;
|
|
|
|
static Vector hx;
|
|
hx.SetSize(n);
|
|
|
|
double eps = 1e-6;
|
|
double f, f11, f12, f21, f22;
|
|
|
|
for (i = 0; i < n; i++)
|
|
{
|
|
for (j = 0; j < i; j++)
|
|
{
|
|
hx = x;
|
|
hx(i) = x(i) + eps;
|
|
hx(j) = x(j) + eps;
|
|
f11 = Func(hx);
|
|
hx(i) = x(i) + eps;
|
|
hx(j) = x(j) - eps;
|
|
f12 = Func(hx);
|
|
hx(i) = x(i) - eps;
|
|
hx(j) = x(j) + eps;
|
|
f21 = Func(hx);
|
|
hx(i) = x(i) - eps;
|
|
hx(j) = x(j) - eps;
|
|
f22 = Func(hx);
|
|
|
|
hesse(i, j) = hesse(j, i) =
|
|
(f11 + f22 - f12 - f21) / (2 * eps * eps);
|
|
}
|
|
|
|
hx = x;
|
|
f = Func(x);
|
|
hx(i) = x(i) + eps;
|
|
f11 = Func(hx);
|
|
hx(i) = x(i) - eps;
|
|
f22 = Func(hx);
|
|
|
|
hesse(i, i) = (f11 + f22 - 2 * f) / (eps * eps);
|
|
}
|
|
// (*testout) << "hesse = " << hesse << endl;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/// Line search, modified Mangasarien conditions
|
|
void lines (Vector & x, // i: initial point of line-search
|
|
Vector & xneu, // o: solution, if successful
|
|
Vector & p, // i: search direction
|
|
double & f, // i: function-value at x
|
|
// o: function-value at xneu, iff ifail = 0
|
|
Vector & g, // i: gradient at x
|
|
// o: gradient at xneu, iff ifail = 0
|
|
const MinFunction & fun, // function to minimize
|
|
const OptiParameters & par,
|
|
double & alphahat, // i: initial value for alpha_hat
|
|
// o: solution alpha iff ifail = 0
|
|
double fmin, // i: lower bound for f
|
|
double mu1, // i: Parameter mu_1 of Alg.2.1
|
|
double sigma, // i: Parameter sigma of Alg.2.1
|
|
double xi1, // i: Parameter xi_1 of Alg.2.1
|
|
double xi2, // i: Parameter xi_1 of Alg.2.1
|
|
double tau, // i: Parameter tau of Alg.2.1
|
|
double tau1, // i: Parameter tau_1 of Alg.2.1
|
|
double tau2, // i: Parameter tau_2 of Alg.2.1
|
|
int & ifail) // o: 0 on success
|
|
// -1 bei termination because lower limit fmin
|
|
// 1 bei illegal termination due to different reasons
|
|
|
|
{
|
|
double phi0, phi0prime, phi1, phi1prime, phihatprime;
|
|
double alpha1, alpha2, alphaincr, c;
|
|
char flag = 1;
|
|
long it;
|
|
|
|
alpha1 = 0;
|
|
alpha2 = 1e50;
|
|
phi0 = phi1 = f;
|
|
|
|
phi0prime = g * p;
|
|
|
|
if (phi0prime > 0)
|
|
{
|
|
ifail = 1;
|
|
return;
|
|
}
|
|
|
|
ifail = 1; // Markus
|
|
|
|
phi1prime = phi0prime;
|
|
|
|
// (*testout) << "phi0prime = " << phi0prime << endl;
|
|
|
|
// it = 100000l;
|
|
it = 0;
|
|
|
|
while (it++ <= par.maxit_linsearch)
|
|
{
|
|
|
|
xneu.Set2 (1, x, alphahat, p);
|
|
|
|
|
|
// f = fun.FuncGrad (xneu, g);
|
|
// f = fun.Func (xneu);
|
|
f = fun.FuncDeriv (xneu, p, phihatprime);
|
|
|
|
// (*testout) << "lines, f = " << f << " phip = " << phihatprime << endl;
|
|
|
|
if (f < fmin)
|
|
{
|
|
ifail = -1;
|
|
break;
|
|
}
|
|
|
|
|
|
if (alpha2 - alpha1 < eps0 * alpha2)
|
|
{
|
|
ifail = 0;
|
|
break;
|
|
}
|
|
|
|
// (*testout) << "i = " << it << " al = " << alphahat << " f = " << f << " fprime " << phihatprime << endl;;
|
|
|
|
if (f - phi0 > mu1 * alphahat * phi1prime + eps0 * fabs (phi0))
|
|
|
|
{
|
|
|
|
flag = 0;
|
|
alpha2 = alphahat;
|
|
|
|
c =
|
|
(f - phi1 - phi1prime * (alphahat-alpha1)) /
|
|
sqr (alphahat-alpha1);
|
|
|
|
alphahat = alpha1 - 0.5 * phi1prime / c;
|
|
|
|
if (alphahat > alpha2)
|
|
alphahat = alpha1 + 1/(4*c) *
|
|
( (sigma+mu1) * phi0prime - 2*phi1prime
|
|
+ sqrt (sqr(phi1prime - mu1 * phi0prime) -
|
|
4 * (phi1 - phi0 - mu1 * alpha1 * phi0prime) * c));
|
|
|
|
alphahat = max2 (alphahat, alpha1 + tau * (alpha2 - alpha1));
|
|
alphahat = min2 (alphahat, alpha2 - tau * (alpha2 - alpha1));
|
|
|
|
// (*testout) << " if-branch" << endl;
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
/*
|
|
f = fun.FuncGrad (xneu, g);
|
|
phihatprime = g * p;
|
|
*/
|
|
f = fun.FuncDeriv (xneu, p, phihatprime);
|
|
|
|
if (phihatprime < sigma * phi0prime * (1 + eps0))
|
|
|
|
{
|
|
if (phi1prime < phihatprime)
|
|
// Approximationsfunktion ist konvex
|
|
|
|
alphaincr = (alphahat - alpha1) * phihatprime /
|
|
(phi1prime - phihatprime);
|
|
|
|
else
|
|
alphaincr = 1e99; // MAXDOUBLE;
|
|
|
|
if (flag)
|
|
{
|
|
alphaincr = max2 (alphaincr, xi1 * (alphahat-alpha1));
|
|
alphaincr = min2 (alphaincr, xi2 * (alphahat-alpha1));
|
|
}
|
|
else
|
|
{
|
|
alphaincr = max2 (alphaincr, tau1 * (alpha2 - alphahat));
|
|
alphaincr = min2 (alphaincr, tau2 * (alpha2 - alphahat));
|
|
}
|
|
|
|
alpha1 = alphahat;
|
|
alphahat += alphaincr;
|
|
phi1 = f;
|
|
phi1prime = phihatprime;
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
ifail = 0; // Erfolg !!
|
|
break;
|
|
}
|
|
|
|
// (*testout) << " else, " << endl;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
// (*testout) << "linsearch: it = " << it << " ifail = " << ifail << endl;
|
|
|
|
fun.FuncGrad (xneu, g);
|
|
|
|
|
|
if (it < 0)
|
|
ifail = 1;
|
|
|
|
// (*testout) << "fail = " << ifail << endl;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
void SteepestDescent (Vector & x, const MinFunction & fun,
|
|
const OptiParameters & par)
|
|
{
|
|
int it, n = x.Size();
|
|
Vector xnew(n), p(n), g(n), g2(n);
|
|
double val, alphahat;
|
|
int fail;
|
|
|
|
val = fun.FuncGrad(x, g);
|
|
|
|
alphahat = 1;
|
|
// testout << "f = ";
|
|
for (it = 0; it < 10; it++)
|
|
{
|
|
// testout << val << " ";
|
|
|
|
// p = -g;
|
|
p.Set (-1, g);
|
|
|
|
lines (x, xnew, p, val, g, fun, par, alphahat, -1e5,
|
|
0.1, 0.1, 1, 10, 0.1, 0.1, 0.6, fail);
|
|
|
|
x = xnew;
|
|
}
|
|
// testout << endl;
|
|
}
|
|
}
|