abacus-develop/source/source_relax/line_search.cpp at develop · deepmodeling/abacus-develop · GitHub

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#include "line_search.h"

#include "source_base/global_function.h"

#include "source_base/global_variable.h"

#include <algorithm>

#include <cmath>

#include <ostream>

bool Line_Search::line_search(const bool restart,

const double x, // current point

const double y, // function value at current point

const double f, // derivative at current point

double& xnew, // the next point that we want to try

const double conv_thr,

std::ofstream& ofs_running)

{

if (restart)

{

ls_step = 0;

}

if (ls_step == 0) // first point: make a trial step into trial direction

{

return this->first_order(x, y, f, xnew);

}

if (ls_step == 1) // second point: third order extrapolation/interpolation

{

return this->third_order(x, y, f, xnew, conv_thr);

}

// if still not converging after 2 steps: start Brent

if (ls_step == 2)

{

this->init_brent(x, y, f);

}

if (ls_step >= 3)

{

this->update_brent(x, y, f);

}

if (ls_step >= 2)

{

return this->brent(x, y, f, xnew, conv_thr, ofs_running);

}

ModuleBase::WARNING_QUIT("line_search", "ls_step <0");

__builtin_unreachable();

}

bool Line_Search::first_order(const double x, const double y, const double f, double& xnew)

{

xa = x; // set the first endpoint

ya = y;

fa = f;

xnew = x + 1; // move one step towards trial direction

ls_step++;

return false;

}

bool Line_Search::third_order(const double x, const double y, const double f, double& xnew, const double conv_thr)

{

double dmove = 0.0;

double dmoveh = 0.0;

double dmove1 = 0.0;

double dmove2 = 0.0;

xb = x; // set the second endpoint

yb = y;

fb = f;

double ffin = yb - ya;

double fab = (fa + fb) / 2.0;

double k3 = 3.0 * (fb + fa - 2.0 * ffin);

double k2 = fb + 2.0 * fa - 3.0 * ffin;

double k1 = fa;

double tmp = k1 * k3 / k2 / k2;

// cubic extrapolation

if (std::abs(k3 / k1) < 1.0e-2 || std::abs(k3) < 2.4e-5 || tmp > 1.0) // harmonic case

{

dmove = -fa / (fab - fa) / 2.0;

if (dmove < 0)

{

dmove = 4.0;

}

else // anharmonic case

{

dmove1 = k2 / k3 * (1.0 - std::sqrt(1.0 - tmp));

dmove2 = k2 / k3 * (1.0 + std::sqrt(1.0 - tmp));

double dy1 = -(k1 - (k2 - k3 * dmove1 / 3.0) * dmove1) * dmove1;

double dy2 = -(k1 - (k2 - k3 * dmove2 / 3.0) * dmove2) * dmove2;

if (dy1 > dy2)

{

dmove = dmove1;

}

else

{

dmove = dmove2;

}

dmoveh = -fa / (fab - fa) / 2.0;

if (dmoveh < 0)

{

dmoveh = 4.0;

}

if (dmove > 2.0 * dmoveh || dmoveh > 2.0 * dmove || (fa * fb > 0 && dmove < 1.0)

|| (fa * fb < 0 && dmove > 1.0))

{

dmove = dmoveh;

}

} // end anharmonic case

if (dmove > 4.0)

{

dmove = 4.0;

}

xnew = dmove + xa;

double dy = (fb + (fab - fb) / (xa - xb) * (dmove - xb)) * (dmove - xb);

if (std::abs(dy) < conv_thr)

{

return true;

}

ls_step++;

return false;

}

void Line_Search::init_brent(const double x, const double y, const double f)

{

bracked = true;

if (x > xb) // x > b, start interval [b,x]

{

xa = xb;

ya = yb;

fa = fb;

xb = x;

yb = y;

fb = f;

if (fa * fb > 0)

{

bracked = false;

}

fstart = fa;

}

else // x < b

{

if (fa * f <= 0) // minimum between [a,x]

{

xb = x;

yb = y;

fb = f;

}

else if (fb * f <= 0) // minimum between [x,b]

{

xa = xb;

ya = yb;

fa = fb;

xb = x;

yb = y;

fb = f;

}

else // problematic case, no minimum between [a,b]

{

xa = xb;

ya = yb;

fa = fb;

xb = x;

yb = y;

fb = f;

bracked = false;

}

xc = xb;

fc = fb;

}

void Line_Search::update_brent(const double x, const double y, const double f)

{

xb = x;

yb = y;

fb = f;

if (!bracked && fstart * f < 0)

{

bracked = true;

xc = xb;

fc = fb;

}

bool Line_Search::brent(const double x, const double y, const double f, double& xnew, const double conv_thr, std::ofstream& ofs_running)

{

ls_step++;

double xd = 0.0;

double xe = 0.0;

double xm = 0.0;

// if no zero is between xa and xb

if (!bracked)

{

if (std::abs(fc) <= std::abs(fb) || (xa - xc) < (xb - xa))

{

xc = xa;

fc = fa;

xd = xb - xa;

xe = xb - xa;

}

double tol1 = 2.0 * e8 * std::abs(xb) + 0.5 * e8;

xm = 0.5 * (xc - xb);

if (!(xc <= xa && xa <= xb))

{

ModuleBase::WARNING_QUIT("Brent", "something wrong with Brent line search!");

}

if (std::abs(xm) <= tol1 || fb == 0.0)

{

return true;

}

if (std::abs(xe) >= tol1 && std::abs(fa) > std::abs(fb))

{

double s = fb / fa;

double p = 0.0;

double qq = 0.0;

if (xa == xc)

{

p = 2.0 * xm * s;

qq = 1.0 - s;

}

else

{

qq = fa / fc;

double r = fb / fc;

p = s * (2.0 * xm * qq * (qq - r) - (xb - xa) * (r - 1.0));

qq = (qq - 1.0) * (r - 1.0) * (s - 1.0);

}

if (p > 0.0)

{

qq = -qq;

}

p = std::abs(p);

if (p < std::min(2.0 * (xb - xa) * qq - std::abs(tol1 * qq), std::abs(xe * qq) / 2.0))

{

xe = xd;

xd = p / qq;

}

else

{

xd = 2.0 * (xb - xa);

xe = xd;

}

else

{

xd = 2.0 * (xb - xa);

xe = xd;

}

double fab = (fa + fb) / 2.0;

double dy = (fb + (fab - fb) / (xa - xb) * xd) * xd;

xc = xa;

fc = fa;

xa = xb;

fa = fb;

if (std::abs(xd) > tol1)

{

xb = xb + xd;

}

else

{

xb = xb + tol1;

}

xnew = xb;

if (std::abs(dy) < conv_thr)

{

return true;

}

if (ls_step == 4) // I'm not sure if this is a good choice, but the idea is there should not be so many line

// search steps I feel if the line search does not converge, we'd better change the direction

// and restart line search

{

ofs_running << "Too many Brent steps, let's do next CG step" << std::endl;

return true;

// ModuleBase::WARNING_QUIT("Brent","too many steps in line search, something wrong");

}

return false;

} // end bracked

else

{

if (!((xa <= xb && xb <= xc) || (xc <= xb && xb <= xa)))

{

ModuleBase::WARNING_QUIT("Brent", "something wrong with Brent line search!");

}

if ((fb > 0 && fc > 0) || (fb < 0 && fc < 0))

{

xc = xa;

fc = fa;

xd = xb - xa;

xe = xd;

}

if (std::abs(fc) < std::abs(fb)) // rearrange b,c so that abs(fc)>=abs(fb)

{

xa = xb;

xb = xc;

xc = xa;

fa = fb;

fb = fc;

fc = fa;

}

double tol1 = 2.0 * e8 * std::abs(xb) + 0.5 * e8;

xm = 0.5 * (xc - xb);

if (std::abs(xm) <= tol1 || fb == 0.0)

{

return true;

}

if (std::abs(xe) >= tol1 && std::abs(fa) > std::abs(fb))

{

double s = fb / fa;

double p = 0.0;

double qq = 0.0;

if (xa == xc)

{

p = 2.0 * xm * s;

qq = 1.0 - s;

}

else

{

qq = fa / fc;

double r = fb / fc;

p = s * (2.0 * xm * qq * (qq - r) - (xb - xa) * (r - 1.0));

qq = (qq - 1.0) * (r - 1.0) * (s - 1.0);

}

if (p > 0.0)

{

qq = -qq;

}

p = std::abs(p);

if (2.0 * p < std::min(3.0 * xm * qq - std::abs(tol1 * qq), std::abs(xe * qq)))

{

xe = xd;

xd = p / qq;

}

else

{

xd = xm;

xe = xd;

}

else

{

xd = xm;

xe = xd;

}

double fab = (fa + fb) / 2.0;

double dy = (fb + (fab - fb) / (xa - xb) * xd) * xd;

xa = xb;

fa = fb;

ya = yb;

if (std::abs(xc) > tol1)

{

xb = xb + xd;

}

else

{

if (xm > 0)

{

xb = xb + tol1;

}

else

{

xb = xb - tol1;

}

xnew = xb;

if (std::abs(dy) < conv_thr)

{

return true;

}

if (ls_step == 4)

{

ofs_running << "Too many Brent steps, let's do next CG step" << std::endl;

return true;

}

return false;

} // end ibrack

}

abacus-develop/source/source_relax/line_search.cpp at develop · deepmodeling/abacus-develop · GitHub

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