abacus-develop/source/source_base/opt_CG.cpp at develop · AroundPeking/abacus-develop · GitHub

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#include "opt_CG.h"

#include <vector>

namespace ModuleBase

{

Opt_CG::Opt_CG()

{

}

Opt_CG::~Opt_CG()

{

delete[] this->pb_;

delete[] this->pdirect_old_;

delete[] this->pgradient_old_;

}

/**

* @brief Initialize b before solving Ax = b.

* @param pinp_b b in the linear equation Ax = b

void Opt_CG::init_b(double* pinp_b)

{

if (this->pb_ != nullptr)

delete[] this->pb_;

this->pb_ = new double[this->nx_];

for (int i = 0; i < this->nx_; ++i)

this->pb_[i] = pinp_b[i];

}

/**

* @brief Allocate the space for pdirect_old and pgradient_old.

* @param nx length of the solution array x

void Opt_CG::allocate(int nx)

{

this->nx_ = nx;

delete[] this->pdirect_old_;

delete[] this->pgradient_old_;

this->pdirect_old_ = new double[this->nx_];

this->pgradient_old_ = new double[this->nx_];

ModuleBase::GlobalFunc::ZEROS(this->pdirect_old_, this->nx_);

ModuleBase::GlobalFunc::ZEROS(this->pgradient_old_, this->nx_);

}

void Opt_CG::set_para(double dV)

{

this->dV_ = dV;

}

/**

* @brief Refresh the class.

* If nx changes, reallocate space. If b is provided, initialize it.

* @param nx_new length of new x, default 0 means the length doesn't change

* @param pinp_b new b in Ax = b, default nullptr means we are dealing with general case

void Opt_CG::refresh(int nx_new, double* pinp_b)

{

this->iter_ = 0;

this->alpha_ = 0.;

this->beta_ = 0.;

if (nx_new != 0)

{

this->allocate(nx_new);

}

else

{

ModuleBase::GlobalFunc::ZEROS(this->pdirect_old_, this->nx_);

ModuleBase::GlobalFunc::ZEROS(this->pgradient_old_, this->nx_);

}

if (pinp_b != nullptr)

this->init_b(pinp_b);

}

/**

* @brief Get the next optimization direction.

* @param [in] pgradient Ad for linear equaiont Ax=b, and gradient for general case

* @param [in] label 0 for solve Ax=b, 1 for PR form, 2 for HZ form.

* @param [in, out] rdirect the next optimization direction

void Opt_CG::next_direct(double* pgradient, int label, double* rdirect)

{

if (label == 0) // standard CG to solve Ap=x

{

this->stantard_CGdirect(pgradient, rdirect);

}

else if (label == 1 or label == 2) // FR formula or HZ form

{

if (this->iter_ == 0) // if iter == 0, d = -g

{

for (int i = 0; i < this->nx_; ++i)

{

rdirect[i] = -pgradient[i];

this->pgradient_old_[i] = pgradient[i];

this->pdirect_old_[i] = rdirect[i];

}

else // d = -g + beta * d

{

if (label == 1)

{

this->PR_beta(pgradient);

}

else if (label == 2)

{

this->HZ_beta(pgradient);

}

for (int i = 0; i < this->nx_; ++i)

{

rdirect[i] = -pgradient[i] + this->beta_ * this->pdirect_old_[i];

this->pgradient_old_[i] = pgradient[i];

this->pdirect_old_[i] = rdirect[i];

}

this->iter_++;

}

/**

* @brief Get the step length, only work for standard CG

* @param pAd Ad for Ax=b

* @param pdirect direction

* @param ifPD 0 if positive definite, -1, -2 when not

* @return the step length alpha

double Opt_CG::step_length(double* pAd, double* pdirect, int& ifPD)

{

double dAd = this->inner_product(pdirect, pAd, this->nx_);

Parallel_Reduce::reduce_all(dAd);

ifPD = 0;

// check for positive-definiteness, very important for convergence

if (dAd == 0)

{

this->alpha_ = 0;

return 0;

}

else if (dAd < 0)

{

if (this->iter_ == 1)

{

ifPD = -1;

}

else

{

ifPD = -2;

}

this->alpha_ = this->gg_ / dAd;

return this->alpha_;

}

/**

* @brief Get the next optimization direction with standard CG workflow.

* @param [in] pAd Ad for Ax=b

* @param [out] rdirect the next direction

void Opt_CG::stantard_CGdirect(double* pAd, double* rdirect)

{

if (this->iter_ == 0)

{

for (int i = 0; i < this->nx_; ++i)

{

this->pgradient_old_[i] = -this->pb_[i];

rdirect[i] = this->pb_[i];

this->pdirect_old_[i] = this->pb_[i];

}

else

{

std::vector<double> temp_gradient(this->nx_);

for (int i = 0; i < this->nx_; ++i)

{

temp_gradient[i] = this->pgradient_old_[i] + this->alpha_ * pAd[i];

}

this->beta_ = this->inner_product(temp_gradient.data(), temp_gradient.data(), this->nx_) / this->gg_;

Parallel_Reduce::reduce_all(this->beta_);

for (int i = 0; i < this->nx_; ++i)

{

this->pgradient_old_[i] = temp_gradient[i];

rdirect[i] = -this->pgradient_old_[i] + this->beta_ * this->pdirect_old_[i];

this->pdirect_old_[i] = rdirect[i];

}

this->gg_ = this->inner_product(this->pgradient_old_, this->pgradient_old_, this->nx_);

Parallel_Reduce::reduce_all(this->gg_);

this->iter_++;

}

/**

* @brief Get the beta in PR form.

* beta_k = max{0, <g_k, g_k-g_{k-1}>/<g_{k-1}, g_{k-1}>}

* <> means inner product.

* @param pgradient df(x)/dx

void Opt_CG::PR_beta(double* pgradient)

{

double temp_beta = 0.;

temp_beta = this->inner_product(pgradient, pgradient, this->nx_);

temp_beta -= this->inner_product(pgradient, this->pgradient_old_, this->nx_);

Parallel_Reduce::reduce_all(temp_beta);

double gg_old = this->inner_product(this->pgradient_old_, this->pgradient_old_, this->nx_);

Parallel_Reduce::reduce_all(gg_old);

// temp_beta /= this->inner_product(this->pgradient_old_, this->pgradient_old_, this->nx_);

temp_beta /= gg_old;

this->beta_ = std::max(0., temp_beta);

}

/**

* @brief Get the beta in HZ form.

* See formula in

* Hager W W, Zhang H. SIAM Journal on optimization, 2005, 16(1): 170-192

* @param pgradient df(x)/dx

void Opt_CG::HZ_beta(double* pgradient)

{

double* y = new double[this->nx_];

for (int i = 0; i < this->nx_; ++i)

y[i] = pgradient[i] - this->pgradient_old_[i];

double py = this->inner_product(this->pdirect_old_, y, this->nx_);

Parallel_Reduce::reduce_all(py);

double yy = this->inner_product(y, y, this->nx_);

Parallel_Reduce::reduce_all(yy);

double pg = this->inner_product(this->pdirect_old_, pgradient, this->nx_);

Parallel_Reduce::reduce_all(pg);

double yg = this->inner_product(y, pgradient, this->nx_);

Parallel_Reduce::reduce_all(yg);

double temp_beta = (yg - 2 * pg * yy / py) / py;

double pp = this->inner_product(this->pdirect_old_, this->pdirect_old_, this->nx_);

Parallel_Reduce::reduce_all(pp);

double gg = this->inner_product(this->pgradient_old_, this->pgradient_old_, this->nx_);

Parallel_Reduce::reduce_all(gg);

double temp_eta = -1 / (sqrt(pp) * std::min(this->eta_, sqrt(gg)));

this->beta_ = std::max(temp_beta, temp_eta);

delete[] y;

}

} // namespace ModuleBase

abacus-develop/source/source_base/opt_CG.cpp at develop · AroundPeking/abacus-develop · GitHub

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