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// CppNumericalSolver
#ifndef MORETHUENTE_H_
#define MORETHUENTE_H_
#include "../meta.h"
#include <cmath>
namespace cppoptlib {
template<typename ProblemType, int Ord>
class MoreThuente {
public:
using Scalar = typename ProblemType::Scalar;
using TVector = typename ProblemType::TVector;
/**
* @brief use MoreThuente Rule for (strong) Wolfe conditiions
* @details [long description]
*
* @param searchDir search direction for next update step
* @param objFunc handle to problem
*
* @return step-width
*/
static Scalar linesearch(const TVector &x, const TVector &searchDir, ProblemType &objFunc, const Scalar alpha_init = 1.0) {
// assume step width
Scalar ak = alpha_init;
Scalar fval = objFunc.value(x);
TVector g = x.eval();
objFunc.gradient(x, g);
TVector s = searchDir.eval();
TVector xx = x.eval();
cvsrch(objFunc, xx, fval, g, ak, s);
return ak;
}
static int cvsrch(ProblemType &objFunc, TVector &x, Scalar f, TVector &g, Scalar &stp, TVector &s) {
// we rewrite this from MIN-LAPACK and some MATLAB code
int info = 0;
int infoc = 1;
const Scalar xtol = 1e-15;
const Scalar ftol = 1e-4;
const Scalar gtol = 1e-2;
const Scalar stpmin = 1e-15;
const Scalar stpmax = 1e15;
const Scalar xtrapf = 4;
const int maxfev = 20;
int nfev = 0;
Scalar dginit = g.dot(s);
if (dginit >= 0.0) {
// no descent direction
// TODO: handle this case
return -1;
}
bool brackt = false;
bool stage1 = true;
Scalar finit = f;
Scalar dgtest = ftol * dginit;
Scalar width = stpmax - stpmin;
Scalar width1 = 2 * width;
TVector wa = x.eval();
Scalar stx = 0.0;
Scalar fx = finit;
Scalar dgx = dginit;
Scalar sty = 0.0;
Scalar fy = finit;
Scalar dgy = dginit;
Scalar stmin;
Scalar stmax;
while (true) {
// make sure we stay in the interval when setting min/max-step-width
if (brackt) {
stmin = std::min(stx, sty);
stmax = std::max(stx, sty);
} else {
stmin = stx;
stmax = stp + xtrapf * (stp - stx);
}
// Force the step to be within the bounds stpmax and stpmin.
stp = std::max(stp, stpmin);
stp = std::min(stp, stpmax);
// Oops, let us return the last reliable values
if (
(brackt && ((stp <= stmin) || (stp >= stmax)))
|| (nfev >= maxfev - 1 ) || (infoc == 0)
|| (brackt && ((stmax - stmin) <= (xtol * stmax)))) {
stp = stx;
}
// test new point
x = wa + stp * s;
f = objFunc.value(x);
objFunc.gradient(x, g);
nfev++;
Scalar dg = g.dot(s);
Scalar ftest1 = finit + stp * dgtest;
// all possible convergence tests
if ((brackt & ((stp <= stmin) | (stp >= stmax))) | (infoc == 0))
info = 6;
if ((stp == stpmax) & (f <= ftest1) & (dg <= dgtest))
info = 5;
if ((stp == stpmin) & ((f > ftest1) | (dg >= dgtest)))
info = 4;
if (nfev >= maxfev)
info = 3;
if (brackt & (stmax - stmin <= xtol * stmax))
info = 2;
if ((f <= ftest1) & (fabs(dg) <= gtol * (-dginit)))
info = 1;
// terminate when convergence reached
if (info != 0)
return -1;
if (stage1 & (f <= ftest1) & (dg >= std::min(ftol, gtol)*dginit))
stage1 = false;
if (stage1 & (f <= fx) & (f > ftest1)) {
Scalar fm = f - stp * dgtest;
Scalar fxm = fx - stx * dgtest;
Scalar fym = fy - sty * dgtest;
Scalar dgm = dg - dgtest;
Scalar dgxm = dgx - dgtest;
Scalar dgym = dgy - dgtest;
cstep( stx, fxm, dgxm, sty, fym, dgym, stp, fm, dgm, brackt, stmin, stmax, infoc);
fx = fxm + stx * dgtest;
fy = fym + sty * dgtest;
dgx = dgxm + dgtest;
dgy = dgym + dgtest;
} else {
// this is ugly and some variables should be moved to the class scope
cstep( stx, fx, dgx, sty, fy, dgy, stp, f, dg, brackt, stmin, stmax, infoc);
}
if (brackt) {
if (fabs(sty - stx) >= 0.66 * width1)
stp = stx + 0.5 * (sty - stx);
width1 = width;
width = fabs(sty - stx);
}
}
return 0;
}
static int cstep(Scalar& stx, Scalar& fx, Scalar& dx, Scalar& sty, Scalar& fy, Scalar& dy, Scalar& stp,
Scalar& fp, Scalar& dp, bool& brackt, Scalar& stpmin, Scalar& stpmax, int& info) {
info = 0;
bool bound = false;
// Check the input parameters for errors.
if ((brackt & ((stp <= std::min(stx, sty) ) | (stp >= std::max(stx, sty)))) | (dx * (stp - stx) >= 0.0)
| (stpmax < stpmin)) {
return -1;
}
Scalar sgnd = dp * (dx / fabs(dx));
Scalar stpf = 0;
Scalar stpc = 0;
Scalar stpq = 0;
if (fp > fx) {
info = 1;
bound = true;
Scalar theta = 3. * (fx - fp) / (stp - stx) + dx + dp;
Scalar s = std::max(theta, std::max(dx, dp));
Scalar gamma = s * sqrt((theta / s) * (theta / s) - (dx / s) * (dp / s));
if (stp < stx)
gamma = -gamma;
Scalar p = (gamma - dx) + theta;
Scalar q = ((gamma - dx) + gamma) + dp;
Scalar r = p / q;
stpc = stx + r * (stp - stx);
stpq = stx + ((dx / ((fx - fp) / (stp - stx) + dx)) / 2.) * (stp - stx);
if (fabs(stpc - stx) < fabs(stpq - stx))
stpf = stpc;
else
stpf = stpc + (stpq - stpc) / 2;
brackt = true;
} else if (sgnd < 0.0) {
info = 2;
bound = false;
Scalar theta = 3 * (fx - fp) / (stp - stx) + dx + dp;
Scalar s = std::max(theta, std::max(dx, dp));
Scalar gamma = s * sqrt((theta / s) * (theta / s) - (dx / s) * (dp / s));
if (stp > stx)
gamma = -gamma;
Scalar p = (gamma - dp) + theta;
Scalar q = ((gamma - dp) + gamma) + dx;
Scalar r = p / q;
stpc = stp + r * (stx - stp);
stpq = stp + (dp / (dp - dx)) * (stx - stp);
if (fabs(stpc - stp) > fabs(stpq - stp))
stpf = stpc;
else
stpf = stpq;
brackt = true;
} else if (fabs(dp) < fabs(dx)) {
info = 3;
bound = 1;
Scalar theta = 3 * (fx - fp) / (stp - stx) + dx + dp;
Scalar s = std::max(theta, std::max( dx, dp));
Scalar gamma = s * sqrt(std::max(static_cast<Scalar>(0.), (theta / s) * (theta / s) - (dx / s) * (dp / s)));
if (stp > stx)
gamma = -gamma;
Scalar p = (gamma - dp) + theta;
Scalar q = (gamma + (dx - dp)) + gamma;
Scalar r = p / q;
if ((r < 0.0) & (gamma != 0.0)) {
stpc = stp + r * (stx - stp);
} else if (stp > stx) {
stpc = stpmax;
} else {
stpc = stpmin;
}
stpq = stp + (dp / (dp - dx)) * (stx - stp);
if (brackt) {
if (fabs(stp - stpc) < fabs(stp - stpq)) {
stpf = stpc;
} else {
stpf = stpq;
}
} else {
if (fabs(stp - stpc) > fabs(stp - stpq)) {
stpf = stpc;
} else {
stpf = stpq;
}
}
} else {
info = 4;
bound = false;
if (brackt) {
Scalar theta = 3 * (fp - fy) / (sty - stp) + dy + dp;
Scalar s = std::max(theta, std::max(dy, dp));
Scalar gamma = s * sqrt((theta / s) * (theta / s) - (dy / s) * (dp / s));
if (stp > sty)
gamma = -gamma;
Scalar p = (gamma - dp) + theta;
Scalar q = ((gamma - dp) + gamma) + dy;
Scalar r = p / q;
stpc = stp + r * (sty - stp);
stpf = stpc;
} else if (stp > stx)
stpf = stpmax;
else {
stpf = stpmin;
}
}
if (fp > fx) {
sty = stp;
fy = fp;
dy = dp;
} else {
if (sgnd < 0.0) {
sty = stx;
fy = fx;
dy = dx;
}
stx = stp;
fx = fp;
dx = dp;
}
stpf = std::min(stpmax, stpf);
stpf = std::max(stpmin, stpf);
stp = stpf;
if (brackt & bound) {
if (sty > stx) {
stp = std::min(stx + static_cast<Scalar>(0.66) * (sty - stx), stp);
} else {
stp = std::max(stx + static_cast<Scalar>(0.66) * (sty - stx), stp);
}
}
return 0;
}
};
}
#endif /* MORETHUENTE_H_ */
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