bse_operator_uks.cc

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/*
 *            Copyright 2009-2026 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.
 *
 */
 
#include "votca/xtp/bse_operator_uks.h"
#include "votca/xtp/bse_operator_kernels.h"
 
namespace votca {
namespace xtp {
 
template <Index cqp, Index cx, Index cd, Index cd2>
void BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::setup_block(SpinBlockInfo& blk,
                                                     Index homo, Index offset) {
  blk.homo = homo;
  blk.vmin_rpa = opt_.vmin - opt_.rpamin;
  blk.cmin_rpa = homo + 1 - opt_.rpamin;
  blk.vtotal = homo - opt_.vmin + 1;
  blk.ctotal = opt_.cmax - (homo + 1) + 1;
  blk.size = blk.vtotal * blk.ctotal;
  blk.offset = offset;
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
void BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::configure(BSEOperatorUKS_Options opt) {
  opt_ = opt;
  setup_block(alpha_, opt_.homo_alpha, 0);
  setup_block(beta_, opt_.homo_beta, alpha_.size);
  size_total_ = alpha_.size + beta_.size;
  this->set_size(size_total_);
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
void BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::add_qp_block(
    Eigen::MatrixXd& y, const Eigen::MatrixXd& x, const SpinBlockInfo& blk,
    const Eigen::MatrixXd& Hqp) const {
  if (cqp == 0) {
    return;
  }
  y += ApplyBSEQuasiparticle(Hqp, blk.vtotal, blk.ctotal, x,
                             static_cast<double>(cqp));
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
void BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::add_exchange_block(
    Eigen::MatrixXd& y, const Eigen::MatrixXd& x, const SpinBlockInfo& out_blk,
    const SpinBlockInfo& in_blk, const TCMatrix_gwbse& Mout,
    const TCMatrix_gwbse& Min, double prefactor) const {
  if (cx == 0 || prefactor == 0.0) {
    return;
  }
  const BSEWindow out{out_blk.vmin_rpa, out_blk.cmin_rpa, out_blk.vtotal,
                      out_blk.ctotal};
  const BSEWindow in{in_blk.vmin_rpa, in_blk.cmin_rpa, in_blk.vtotal,
                     in_blk.ctotal};
  y += ApplyBSEExchange(Mout, out, Min, in, x, prefactor);
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
void BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::add_direct_block(
    Eigen::MatrixXd& y, const Eigen::MatrixXd& x, const SpinBlockInfo& out_blk,
    const SpinBlockInfo& in_blk, const TCMatrix_gwbse& Mout,
    const TCMatrix_gwbse& Min, double prefactor) const {
  if (cd == 0 || prefactor == 0.0) {
    return;
  }
 
  const Eigen::DiagonalMatrix<double, Eigen::Dynamic> eps =
      epsilon_0_inv_.asDiagonal();
 
  for (Index v1 = 0; v1 < out_blk.vtotal; ++v1) {
    for (Index c1 = 0; c1 < out_blk.ctotal; ++c1) {
 
      // rows correspond to c2, columns correspond to v2
      const Eigen::MatrixXd left =
          prefactor * Mout[c1 + out_blk.cmin_rpa].middleRows(in_blk.cmin_rpa,
                                                             in_blk.ctotal);
 
      const Eigen::MatrixXd right =
          Min[v1 + out_blk.vmin_rpa].middleRows(in_blk.vmin_rpa, in_blk.vtotal);
 
      // (ctotal_in x naux) * (naux x vtotal_in) = (ctotal_in x vtotal_in)
      const Eigen::MatrixXd block = left * eps * right.transpose();
 
      // Flattening column-major yields index order v2*ctotal + c2
      const Eigen::VectorXd row =
          Eigen::Map<const Eigen::VectorXd>(block.data(), block.size());
 
      const Index out_idx = v1 * out_blk.ctotal + c1;
      y.row(out_idx) += row.transpose() * x;
    }
  }
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
void BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::add_direct2_block(
    Eigen::MatrixXd& y, const Eigen::MatrixXd& x, const SpinBlockInfo& out_blk,
    const SpinBlockInfo& in_blk, const TCMatrix_gwbse& Mout,
    const TCMatrix_gwbse& Min, double prefactor) const {
  if (cd2 == 0 || prefactor == 0.0) {
    return;
  }
 
  const Eigen::DiagonalMatrix<double, Eigen::Dynamic> eps =
      epsilon_0_inv_.asDiagonal();
 
  for (Index c1 = 0; c1 < out_blk.ctotal; ++c1) {
    const Eigen::MatrixXd left =
        prefactor *
        Mout[c1 + out_blk.cmin_rpa].middleRows(in_blk.vmin_rpa, in_blk.vtotal);
 
    for (Index v1 = 0; v1 < out_blk.vtotal; ++v1) {
      const Eigen::MatrixXd right =
          Min[v1 + out_blk.vmin_rpa].middleRows(in_blk.cmin_rpa, in_blk.ctotal);
 
      const Eigen::MatrixXd block = left * eps * right.transpose();
 
      Eigen::VectorXd row(in_blk.vtotal * in_blk.ctotal);
      for (Index v2 = 0; v2 < in_blk.vtotal; ++v2) {
        for (Index c2 = 0; c2 < in_blk.ctotal; ++c2) {
          const Index idx = v2 * in_blk.ctotal + c2;
          row(idx) = block(v2, c2);
        }
      }
 
      const Index out_idx = v1 * out_blk.ctotal + c1;
      y.row(out_idx) += row.transpose() * x;
    }
  }
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
Eigen::MatrixXd BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::matmul(
    const Eigen::MatrixXd& input) const {
 
  static_assert(!(cd != 0 && cd2 != 0),
                "Hamiltonian cannot contain Hd and Hd2 at the same time");
 
  Eigen::MatrixXd y = Eigen::MatrixXd::Zero(size_total_, input.cols());
 
  const Eigen::MatrixXd x_alpha = input.topRows(alpha_.size);
  const Eigen::MatrixXd x_beta = input.bottomRows(beta_.size);
 
  Eigen::MatrixXd y_alpha = Eigen::MatrixXd::Zero(alpha_.size, input.cols());
  Eigen::MatrixXd y_beta = Eigen::MatrixXd::Zero(beta_.size, input.cols());
 
  // Same-spin alpha-alpha
  add_qp_block(y_alpha, x_alpha, alpha_, Hqp_alpha_);
  add_exchange_block(y_alpha, x_alpha, alpha_, alpha_, Mmn_.alpha, Mmn_.alpha,
                     static_cast<double>(cx));
  add_direct_block(y_alpha, x_alpha, alpha_, alpha_, Mmn_.alpha, Mmn_.alpha,
                   -static_cast<double>(cd));
  add_direct2_block(y_alpha, x_alpha, alpha_, alpha_, Mmn_.alpha, Mmn_.alpha,
                    -static_cast<double>(cd2));
 
  // Same-spin beta-beta
  add_qp_block(y_beta, x_beta, beta_, Hqp_beta_);
  add_exchange_block(y_beta, x_beta, beta_, beta_, Mmn_.beta, Mmn_.beta,
                     static_cast<double>(cx));
  add_direct_block(y_beta, x_beta, beta_, beta_, Mmn_.beta, Mmn_.beta,
                   -static_cast<double>(cd));
  add_direct2_block(y_beta, x_beta, beta_, beta_, Mmn_.beta, Mmn_.beta,
                    -static_cast<double>(cd2));
 
  // Cross-spin coupling. In the spin-unrestricted kernel
  //   A(ia s, jb s') = delta_ss' (e_a - e_i) + (ia|jb) - delta_ss' W(ij,ab)
  //   B(ia s, jb s') = (ia|bj) - delta_ss' W(ib,aj)
  // the bare exchange couples all spin blocks, while the screened direct
  // terms act within one spin only. So the alpha-beta blocks of A and of B
  // are both the bare exchange (ia|jb), with the same prefactor as the
  // same-spin exchange. For a closed-shell reference this reproduces the
  // singlet and triplet spectra of the restricted BSE.
  add_exchange_block(y_alpha, x_beta, alpha_, beta_, Mmn_.alpha, Mmn_.beta,
                     static_cast<double>(cx));
  add_exchange_block(y_beta, x_alpha, beta_, alpha_, Mmn_.beta, Mmn_.alpha,
                     static_cast<double>(cx));
 
  y.topRows(alpha_.size) = y_alpha;
  y.bottomRows(beta_.size) = y_beta;
  return y;
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
Eigen::MatrixXd BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::dense_matrix() const {
  Eigen::MatrixXd dense = Eigen::MatrixXd::Zero(rows(), cols());
  for (Index i = 0; i < cols(); ++i) {
    Eigen::MatrixXd e = Eigen::MatrixXd::Zero(rows(), 1);
    e(i, 0) = 1.0;
    dense.col(i) = matmul(e);
  }
  return dense;
}
 
template <Index cqp, Index cx, Index cd, Index cd2>
Eigen::VectorXd BSE_OPERATOR_UKS<cqp, cx, cd, cd2>::diagonal() const {
  static_assert(!(cd != 0 && cd2 != 0),
                "Hamiltonian cannot contain Hd and Hd2 at the same time");
 
  Eigen::VectorXd result = Eigen::VectorXd::Zero(size_total_);
 
  const Eigen::DiagonalMatrix<double, Eigen::Dynamic> eps =
      epsilon_0_inv_.asDiagonal();
 
  // alpha block
  for (Index v = 0; v < alpha_.vtotal; ++v) {
    for (Index c = 0; c < alpha_.ctotal; ++c) {
      double entry = 0.0;
 
      if (cx != 0) {
        entry += cx * Mmn_.alpha[v + alpha_.vmin_rpa]
                          .row(alpha_.cmin_rpa + c)
                          .squaredNorm();
      }
      if (cqp != 0) {
        Index cmin_qp = alpha_.vtotal;
        entry += Hqp_alpha_(c + cmin_qp, c + cmin_qp) - Hqp_alpha_(v, v);
      }
      if (cd != 0) {
        entry -=
            (Mmn_.alpha[c + alpha_.cmin_rpa].row(alpha_.cmin_rpa + c) * eps *
             Mmn_.alpha[v + alpha_.vmin_rpa]
                 .row(alpha_.vmin_rpa + v)
                 .transpose())
                .value();
      }
      if (cd2 != 0) {
        entry -=
            (Mmn_.alpha[c + alpha_.cmin_rpa].row(alpha_.vmin_rpa + v) * eps *
             Mmn_.alpha[v + alpha_.vmin_rpa]
                 .row(alpha_.cmin_rpa + c)
                 .transpose())
                .value();
      }
 
      result(alpha_.offset + v * alpha_.ctotal + c) = entry;
    }
  }
 
  // beta block
  for (Index v = 0; v < beta_.vtotal; ++v) {
    for (Index c = 0; c < beta_.ctotal; ++c) {
      double entry = 0.0;
 
      if (cx != 0) {
        entry +=
            cx *
            Mmn_.beta[v + beta_.vmin_rpa].row(beta_.cmin_rpa + c).squaredNorm();
      }
      if (cqp != 0) {
        Index cmin_qp = beta_.vtotal;
        entry += Hqp_beta_(c + cmin_qp, c + cmin_qp) - Hqp_beta_(v, v);
      }
      if (cd != 0) {
        entry -=
            (Mmn_.beta[c + beta_.cmin_rpa].row(beta_.cmin_rpa + c) * eps *
             Mmn_.beta[v + beta_.vmin_rpa].row(beta_.vmin_rpa + v).transpose())
                .value();
      }
      if (cd2 != 0) {
        entry -=
            (Mmn_.beta[c + beta_.cmin_rpa].row(beta_.vmin_rpa + v) * eps *
             Mmn_.beta[v + beta_.vmin_rpa].row(beta_.cmin_rpa + c).transpose())
                .value();
      }
 
      result(beta_.offset + v * beta_.ctotal + c) = entry;
    }
  }
 
  return result;
}
 
template class BSE_OPERATOR_UKS<1, 1, 1, 0>;
template class BSE_OPERATOR_UKS<0, 1, 0, 1>;
template class BSE_OPERATOR_UKS<0, 0, 1, 0>;
template class BSE_OPERATOR_UKS<0, 0, 0, 1>;
 
template class BSE_OPERATOR_UKS<1, 0, 0, 0>;
template class BSE_OPERATOR_UKS<0, 1, 0, 0>;
 
}  // namespace xtp
}  // namespace votca