adiis.cc

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/*
 *            Copyright 2009-2020 The VOTCA Development Team
 *                       (http://www.votca.org)
 *
 *      Licensed under the Apache License, Version 2.0 (the "License")
 *
 * You may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *              http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 */
 
// Third party includes
#include <boost/format.hpp>
 
// Local VOTCA includes
#include "votca/xtp/adiis.h"
#include "votca/xtp/adiis_costfunction.h"
#include "votca/xtp/bfgs_trm.h"
#include "votca/xtp/logger.h"
 
namespace votca {
namespace xtp {

 
// Restricted ADIIS coefficients. The minimization is carried out for the
// approximate energy functional
//
//   E(c) = sum_i c_i D_iF + 1/2 sum_ij c_i c_j D_iF_j,
//
// under the simplex constraints c_i >= 0 and sum_i c_i = 1. The latter is
// enforced through the squared optimizer parameters followed by
// renormalization.
Eigen::VectorXd ADIIS::CalcCoeff(const std::vector<Eigen::MatrixXd>& dmathist,
                                 const std::vector<Eigen::MatrixXd>& mathist) {
  success = true;
  Index size = dmathist.size();
 
  const Eigen::MatrixXd& dmat = dmathist.back();
  const Eigen::MatrixXd& H = mathist.back();
  Eigen::VectorXd DiF = Eigen::VectorXd::Zero(size);
  Eigen::MatrixXd DiFj = Eigen::MatrixXd::Zero(size, size);
 
  for (Index i = 0; i < size; i++) {
    DiF(i) = ((dmathist[i]) - dmat).cwiseProduct(H).sum();
  }
 
  for (Index i = 0; i < size; i++) {
    for (Index j = 0; j < size; j++) {
      DiFj(i, j) = ((dmathist[i]) - dmat).cwiseProduct((mathist[j]) - H).sum();
    }
  }
 
  ADIIS_costfunction a_cost = ADIIS_costfunction(DiF, DiFj);
  BFGSTRM optimizer = BFGSTRM(a_cost);
  Logger log;
  optimizer.setLog(&log);
  optimizer.setNumofIterations(1000);
  optimizer.setTrustRadius(0.01);
  // Starting point: equal weights on all matrices
  Eigen::VectorXd coeffs = Eigen::VectorXd::Constant(size, 1.0 / double(size));
  optimizer.Optimize(coeffs);
  success = optimizer.Success();
  coeffs = optimizer.getParameters().cwiseAbs2();
  double xnorm = coeffs.sum();
  coeffs /= xnorm;
 
  if (std::abs(coeffs.tail(1).value()) < 0.001) {
    success = false;
  }
  return coeffs;
}
 
// Unrestricted ADIIS variant. The same quadratic surrogate is assembled, but
// with alpha and beta traces added so that the objective approximates the spin-
// summed SCF energy change.
Eigen::VectorXd ADIIS::CalcCoeff(
    const std::vector<Eigen::MatrixXd>& dmathist_alpha,
    const std::vector<Eigen::MatrixXd>& dmathist_beta,
    const std::vector<Eigen::MatrixXd>& mathist_alpha,
    const std::vector<Eigen::MatrixXd>& mathist_beta) {
 
  success = true;
  Index size = dmathist_alpha.size();
 
  const Eigen::MatrixXd& dmat_alpha = dmathist_alpha.back();
  const Eigen::MatrixXd& dmat_beta = dmathist_beta.back();
  const Eigen::MatrixXd& H_alpha = mathist_alpha.back();
  const Eigen::MatrixXd& H_beta = mathist_beta.back();
 
  Eigen::VectorXd DiF = Eigen::VectorXd::Zero(size);
  Eigen::MatrixXd DiFj = Eigen::MatrixXd::Zero(size, size);
 
  for (Index i = 0; i < size; ++i) {
    DiF(i) = (dmathist_alpha[i] - dmat_alpha).cwiseProduct(H_alpha).sum() +
             (dmathist_beta[i] - dmat_beta).cwiseProduct(H_beta).sum();
  }
 
  for (Index i = 0; i < size; ++i) {
    for (Index j = 0; j < size; ++j) {
      DiFj(i, j) = (dmathist_alpha[i] - dmat_alpha)
                       .cwiseProduct(mathist_alpha[j] - H_alpha)
                       .sum() +
                   (dmathist_beta[i] - dmat_beta)
                       .cwiseProduct(mathist_beta[j] - H_beta)
                       .sum();
    }
  }
 
  ADIIS_costfunction a_cost(DiF, DiFj);
  BFGSTRM optimizer(a_cost);
  Logger log;
  optimizer.setLog(&log);
  optimizer.setNumofIterations(1000);
  optimizer.setTrustRadius(0.01);
 
  Eigen::VectorXd coeffs = Eigen::VectorXd::Constant(size, 1.0 / double(size));
  optimizer.Optimize(coeffs);
  success = optimizer.Success();
 
  coeffs = optimizer.getParameters().cwiseAbs2();
  double xnorm = coeffs.sum();
  coeffs /= xnorm;
 
  if (std::abs(coeffs.tail(1).value()) < 0.001) {
    success = false;
  }
  return coeffs;
}
 
}  // namespace xtp
}  // namespace votca