mirror of
https://github.com/NGSolve/netgen.git
synced 2024-09-23 02:02:49 +05:00
410 lines
8.4 KiB
C++
410 lines
8.4 KiB
C++
/***************************************************************************/
|
|
/* */
|
|
/* Vorlesung Optimierung I, Gfrerer, WS94/95 */
|
|
/* BFGS-Verfahren zur Lösung freier nichtlinearer Optimierungsprobleme */
|
|
/* */
|
|
/* Programmautor: Joachim Schöberl */
|
|
/* Matrikelnummer: 9155284 */
|
|
/* */
|
|
/***************************************************************************/
|
|
|
|
#include <mystdlib.h>
|
|
#include <myadt.hpp>
|
|
|
|
#include <linalg.hpp>
|
|
#include "opti.hpp"
|
|
|
|
|
|
namespace netgen
|
|
{
|
|
|
|
void Cholesky (const DenseMatrix & a,
|
|
DenseMatrix & l, Vector & d)
|
|
{
|
|
// Factors A = L D L^T
|
|
|
|
double x;
|
|
|
|
int n = a.Height();
|
|
|
|
// (*testout) << "a = " << a << endl;
|
|
|
|
l = a;
|
|
|
|
for (int i = 1; i <= n; i++)
|
|
{
|
|
for (int j = i; j <= n; j++)
|
|
{
|
|
x = l.Get(i, j);
|
|
|
|
for (int k = 1; k < i; k++)
|
|
x -= l.Get(i, k) * l.Get(j, k) * d(k-1);
|
|
|
|
if (i == j)
|
|
{
|
|
d(i-1) = x;
|
|
}
|
|
else
|
|
{
|
|
l.Elem(j, i) = x / d(i-1);
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int i = 1; i <= n; i++)
|
|
{
|
|
l.Elem(i, i) = 1;
|
|
for (int j = i+1; j <= n; j++)
|
|
l.Elem(i, j) = 0;
|
|
}
|
|
|
|
/*
|
|
// Multiply:
|
|
(*testout) << "multiplied factors: " << endl;
|
|
for (i = 1; i <= n; i++)
|
|
for (j = 1; j <= n; j++)
|
|
{
|
|
x = 0;
|
|
for (k = 1; k <= n; k++)
|
|
x += l.Get(i, k) * l.Get(j, k) * d.Get(k);
|
|
(*testout) << x << " ";
|
|
}
|
|
(*testout) << endl;
|
|
*/
|
|
}
|
|
|
|
|
|
void MultLDLt (const DenseMatrix & l, const Vector & d, const Vector & g, Vector & p)
|
|
{
|
|
/*
|
|
int i, j, n;
|
|
double val;
|
|
|
|
n = l.Height();
|
|
p = g;
|
|
for (i = 1; i <= n; i++)
|
|
{
|
|
val = 0;
|
|
for (j = i; j <= n; j++)
|
|
val += p.Get(j) * l.Get(j, i);
|
|
p.Set(i, val);
|
|
}
|
|
for (i = 1; i <= n; i++)
|
|
p.Elem(i) *= d.Get(i);
|
|
|
|
for (i = n; i >= 1; i--)
|
|
{
|
|
val = 0;
|
|
for (j = 1; j <= i; j++)
|
|
val += p.Get(j) * l.Get(i, j);
|
|
p.Set(i, val);
|
|
}
|
|
*/
|
|
|
|
|
|
|
|
double val;
|
|
|
|
int n = l.Height();
|
|
p = g;
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
val = 0;
|
|
for (int j = i; j < n; j++)
|
|
val += p(j) * l(j, i);
|
|
p(i) = val;
|
|
}
|
|
|
|
for (int i = 0; i < n; i++)
|
|
p(i) *= d(i);
|
|
|
|
for (int i = n-1; i >= 0; i--)
|
|
{
|
|
val = 0;
|
|
for (int j = 0; j <= i; j++)
|
|
val += p(j) * l(i, j);
|
|
p(i) = val;
|
|
}
|
|
}
|
|
|
|
void SolveLDLt (const DenseMatrix & l, const Vector & d, const Vector & g, Vector & p)
|
|
{
|
|
double val;
|
|
|
|
int n = l.Height();
|
|
p = g;
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
val = 0;
|
|
for (int j = 0; j < i; j++)
|
|
val += p(j) * l(i,j);
|
|
p(i) -= val;
|
|
}
|
|
|
|
for (int i = 0; i < n; i++)
|
|
p(i) /= d(i);
|
|
|
|
for (int i = n-1; i >= 0; i--)
|
|
{
|
|
val = 0;
|
|
for (int j = i+1; j < n; j++)
|
|
val += p(j) * l(j, i);
|
|
p(i) -= val;
|
|
}
|
|
}
|
|
|
|
int LDLtUpdate (DenseMatrix & l, Vector & d, double a, const Vector & u)
|
|
{
|
|
// Bemerkung: Es wird a aus R erlaubt
|
|
// Rueckgabewert: 0 .. D bleibt positiv definit
|
|
// 1 .. sonst
|
|
|
|
int n = l.Height();
|
|
|
|
Vector v(n);
|
|
double t, told, xi;
|
|
|
|
told = 1;
|
|
v = u;
|
|
|
|
for (int j = 1; j <= n; j++)
|
|
{
|
|
t = told + a * sqr (v(j-1)) / d(j-1);
|
|
|
|
if (t <= 0)
|
|
{
|
|
(*testout) << "update err, t = " << t << endl;
|
|
return 1;
|
|
}
|
|
|
|
xi = a * v(j-1) / (d(j-1) * t);
|
|
|
|
d(j-1) *= t / told;
|
|
|
|
for (int i = j + 1; i <= n; i++)
|
|
{
|
|
v(i-1) -= v(j-1) * l.Elem(i, j);
|
|
l.Elem(i, j) += xi * v(i-1);
|
|
}
|
|
|
|
told = t;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
|
|
double BFGS (
|
|
Vector & x, // i: Startwert
|
|
// o: Loesung, falls IFAIL = 0
|
|
const MinFunction & fun,
|
|
const OptiParameters & par,
|
|
double eps
|
|
)
|
|
|
|
|
|
{
|
|
int n = x.Size();
|
|
long it;
|
|
char a1crit, a3acrit;
|
|
|
|
|
|
Vector d(n), g(n), p(n), temp(n), bs(n), xneu(n), y(n), s(n), x0(n);
|
|
DenseMatrix l(n);
|
|
DenseMatrix hesse(n);
|
|
|
|
double /* normg, */ alphahat, hd, fold;
|
|
double a1, a2;
|
|
const double mu1 = 0.1, sigma = 0.1, xi1 = 1, xi2 = 10;
|
|
const double tau = 0.1, tau1 = 0.1, tau2 = 0.6;
|
|
|
|
Vector typx(x.Size()); // i: typische Groessenordnung der Komponenten
|
|
double f, f0;
|
|
double typf; // i: typische Groessenordnung der Loesung
|
|
double fmin = -1e5; // i: untere Schranke fuer Funktionswert
|
|
// double eps = 1e-8; // i: Abbruchschranke fuer relativen Gradienten
|
|
double tauf = 0.1; // i: Abbruchschranke fuer die relative Aenderung der
|
|
// Funktionswerte
|
|
int ifail; // o: 0 .. Erfolg
|
|
// -1 .. Unterschreitung von fmin
|
|
// 1 .. kein Erfolg bei Liniensuche
|
|
// 2 .. Überschreitung von itmax
|
|
|
|
typx = par.typx;
|
|
typf = par.typf;
|
|
|
|
|
|
l = 0;
|
|
for (int i = 1; i <= n; i++)
|
|
l.Elem(i, i) = 1;
|
|
|
|
f = fun.FuncGrad (x, g);
|
|
f0 = f;
|
|
x0 = x;
|
|
|
|
it = 0;
|
|
do
|
|
{
|
|
// Restart
|
|
// cout << "it " << it << "f = " << f << endl;
|
|
if (it % (5 * n) == 0)
|
|
{
|
|
|
|
for (int i = 1; i <= n; i++)
|
|
d(i-1) = typf/ sqr (typx(i-1)); // 1;
|
|
for (int i = 2; i <= n; i++)
|
|
for (int j = 1; j < i; j++)
|
|
l.Elem(i, j) = 0;
|
|
|
|
/*
|
|
hesse = 0;
|
|
for (i = 1; i <= n; i++)
|
|
hesse.Elem(i, i) = typf / sqr (typx.Get(i));
|
|
|
|
fun.ApproximateHesse (x, hesse);
|
|
|
|
Cholesky (hesse, l, d);
|
|
*/
|
|
}
|
|
|
|
it++;
|
|
if (it > par.maxit_bfgs)
|
|
{
|
|
ifail = 2;
|
|
break;
|
|
}
|
|
|
|
|
|
// Solve with factorized B
|
|
|
|
SolveLDLt (l, d, g, p);
|
|
|
|
// (*testout) << "l " << l << endl
|
|
// << "d " << d << endl
|
|
// << "g " << g << endl
|
|
// << "p " << p << endl;
|
|
|
|
|
|
p *= -1;
|
|
y = g;
|
|
|
|
fold = f;
|
|
|
|
// line search
|
|
|
|
alphahat = 1;
|
|
lines (x, xneu, p, f, g, fun, par, alphahat, fmin,
|
|
mu1, sigma, xi1, xi2, tau, tau1, tau2, ifail);
|
|
|
|
if(ifail == 1)
|
|
(*testout) << "no success with linesearch" << endl;
|
|
|
|
/*
|
|
// if (it > par.maxit_bfgs/2)
|
|
{
|
|
(*testout) << "x = " << x << endl;
|
|
(*testout) << "xneu = " << xneu << endl;
|
|
(*testout) << "f = " << f << endl;
|
|
(*testout) << "g = " << g << endl;
|
|
}
|
|
*/
|
|
|
|
// (*testout) << "it = " << it << " f = " << f << endl;
|
|
// if (ifail != 0) break;
|
|
|
|
s.Set2 (1, xneu, -1, x);
|
|
y *= -1;
|
|
y.Add (1,g); // y += g;
|
|
|
|
x = xneu;
|
|
|
|
// BFGS Update
|
|
|
|
MultLDLt (l, d, s, bs);
|
|
|
|
a1 = y * s;
|
|
a2 = s * bs;
|
|
|
|
if (a1 > 0 && a2 > 0)
|
|
{
|
|
if (LDLtUpdate (l, d, 1 / a1, y) != 0)
|
|
{
|
|
// cerr << "BFGS update error1" << endl;
|
|
(*testout) << "BFGS update error1" << endl;
|
|
(*testout) << "l " << endl << l << endl
|
|
<< "d " << d << endl;
|
|
ifail = 1;
|
|
break;
|
|
}
|
|
|
|
if (LDLtUpdate (l, d, -1 / a2, bs) != 0)
|
|
{
|
|
// cerr << "BFGS update error2" << endl;
|
|
(*testout) << "BFGS update error2" << endl;
|
|
(*testout) << "l " << endl << l << endl
|
|
<< "d " << d << endl;
|
|
ifail = 1;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// Calculate stop conditions
|
|
|
|
hd = eps * max2 (typf, fabs (f));
|
|
a1crit = 1;
|
|
for (int i = 1; i <= n; i++)
|
|
if ( fabs (g(i-1)) * max2 (typx(i-1), fabs (x(i-1))) > hd)
|
|
a1crit = 0;
|
|
|
|
|
|
a3acrit = (fold - f <= tauf * max2 (typf, fabs (f)));
|
|
|
|
// testout << "g = " << g << endl;
|
|
// testout << "a1crit, a3crit = " << int(a1crit) << ", " << int(a3acrit) << endl;
|
|
|
|
/*
|
|
// Output for tests
|
|
|
|
normg = sqrt (g * g);
|
|
|
|
testout << "it =" << setw (5) << it
|
|
<< " f =" << setw (12) << setprecision (5) << f
|
|
<< " |g| =" << setw (12) << setprecision (5) << normg;
|
|
|
|
testout << " x = (" << setw (12) << setprecision (5) << x.Elem(1);
|
|
for (i = 2; i <= n; i++)
|
|
testout << "," << setw (12) << setprecision (5) << x.Elem(i);
|
|
testout << ")" << endl;
|
|
*/
|
|
|
|
//(*testout) << "it = " << it << " f = " << f << " x = " << x << endl
|
|
// << " g = " << g << " p = " << p << endl << endl;
|
|
|
|
// (*testout) << "|g| = " << g.L2Norm() << endl;
|
|
|
|
if (g.L2Norm() < fun.GradStopping (x)) break;
|
|
|
|
}
|
|
while (!a1crit || !a3acrit);
|
|
|
|
/*
|
|
(*testout) << "it = " << it << " g = " << g << " f = " << f
|
|
<< " fail = " << ifail << endl;
|
|
*/
|
|
if (f0 < f || (ifail == 1))
|
|
{
|
|
(*testout) << "fail, f = " << f << " f0 = " << f0 << endl;
|
|
f = f0;
|
|
x = x0;
|
|
}
|
|
|
|
// cout << endl;
|
|
|
|
// (*testout) << "x = " << x << ", x0 = " << x0 << endl;
|
|
return f;
|
|
}
|
|
|
|
}
|