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376 lines
18 KiB
C++
376 lines
18 KiB
C++
# include <iostream>
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# include <array>
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# include <numbers>
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# include <numeric>
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# include <fstream>
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# include <optional>
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# include <array>
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# include <utility>
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# include <yaml-cpp/yaml.h>
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# include <eigen3/Eigen/Dense>
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# include <concurrencpp/concurrencpp.h>
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# include <fmt/format.h>
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# include <highfive/H5File.hpp>
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// # include <highfive/H5Easy.hpp>
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using namespace std::literals;
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struct PhonopyComplex { double r, i; };
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HighFive::CompoundType create_compound_complex()
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{ return {{"r", HighFive::AtomicType<double>{}}, {"i", HighFive::AtomicType<double>{}}}; }
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HIGHFIVE_REGISTER_TYPE(PhonopyComplex, create_compound_complex)
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// 在相位中, 约定为使用 $\exp (2 \pi i \vec{q} \cdot \vec{r})$ 来表示原子的运动状态
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// (而不是 $\exp (-2 \pi i \vec{q} \cdot \vec{r})$)
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// 一些书定义的倒格矢中包含了 $2 \pi$ 的部分, 我们这里约定不包含这部分.
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// 也就是说, 正格子与倒格子的转置相乘, 得到单位矩阵.
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struct Input
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{
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// 单胞的三个格矢，每行表示一个格矢的坐标，单位为埃
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Eigen::Matrix3d PrimativeCell;
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// 单胞到超胞的格矢转换时用到的矩阵
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// SuperCellMultiplier 是一个三维列向量且各个元素都是整数，表示单胞在各个方向扩大到多少倍之后，可以得到和超胞一样的体积
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// SuperCellDeformation 是一个行列式为 1 的矩阵，它表示经过 SuperCellMultiplier 扩大后，还需要怎样的变换才能得到超胞
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// SuperCell = (SuperCellDeformation * SuperCellMultiplier.asDiagonal()) * PrimativeCell
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// ReciprocalPrimativeCell = (SuperCellDeformation * SuperCellMultiplier.asDiagonal()).transpose()
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// * ReciprocalSuperCell
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// Position = PositionToCell(line vector) * Cell
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// InversePosition = InversePositionToCell(line vector) * ReciprocalCell
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// PositionToSuperCell(line vector) * SuperCell = PositionToPrimativeCell(line vector) * PrimativeCell
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// ReciprocalPositionToSuperCell(line vector) * ReciprocalSuperCell
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// = ReciprocalPositionToPrimativeCell(line vector) * ReciprocalPrimativeCell
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Eigen::Vector<unsigned, 3> SuperCellMultiplier;
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Eigen::Matrix<double, 3, 3> SuperCellDeformation;
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// 在单胞内取几个平面波的基矢
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Eigen::Vector<unsigned, 3> PrimativeCellBasisNumber;
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// 超胞中原子的坐标，每行表示一个原子的坐标，单位为埃
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Eigen::MatrixX3d AtomPosition;
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// 如果打开调试，就不会合并相近的模式，不过滤权重过小的模式，也不会限制浮点的精度
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std::optional<bool> Debug;
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// 关于各个 Q 点的数据
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struct QPointDataType_
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{
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// Q 点的坐标，单位为超胞的倒格矢
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Eigen::Vector3d QPoint;
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// 关于这个 Q 点上各个模式的数据
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struct ModeDataType_
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{
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// 模式的频率，单位为 THz
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double Frequency;
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// 模式中各个原子的运动状态
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// 这个数据是这样得到的: phonopy 输出的动态矩阵的 eigenvector 乘以 $\exp(-2 \pi i \vec q \cdot \vec r)$
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// 这个数据可以认为是原子位移中, 关于超胞有周期性的那一部分, 再乘以原子质量的开方.
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// 这个数据在读入后不会被立即归一化.
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Eigen::MatrixX3cd AtomMovement;
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};
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std::vector<ModeDataType_> ModeData;
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};
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std::vector<QPointDataType_> QPointData;
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Input(std::string yaml_file, std::optional<std::string> hdf5_file);
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};
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struct Output
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{
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// 关于各个 Q 点的数据
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struct QPointDataType_
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{
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// Q 点的坐标，单位为单胞的倒格矢
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Eigen::Vector3d QPoint;
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// 来源于哪个 Q 点, 单位为超胞的倒格矢
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Eigen::Vector3d Source;
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// 关于这个 Q 点上各个模式的数据
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struct ModeDataType_
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{
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// 模式的频率，单位为 THz
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double Frequency;
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// 模式的权重
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double Weight;
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};
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std::vector<ModeDataType_> ModeData;
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};
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std::vector<QPointDataType_> QPointData;
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};
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concurrencpp::generator<std::pair<Eigen::Vector<unsigned, 3>, unsigned>>
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triplet_sequence(Eigen::Vector<unsigned, 3> range)
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{
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for (unsigned x = 0; x < range[0]; x++)
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for (unsigned y = 0; y < range[1]; y++)
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for (unsigned z = 0; z < range[2]; z++)
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co_yield
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{
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Eigen::Vector<unsigned, 3>{{x}, {y}, {z}},
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x * range[1] * range[2] + y * range[2] + z
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};
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}
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int main(int argc, const char** argv)
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{
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if (argc < 3 || argc > 5)
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throw std::runtime_error("Usage: " + std::string(argv[0]) + " input.yaml [input.hdf5] output.yaml");
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std::cerr << "Reading input file..." << std::flush;
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Input input(argv[1], argc > 3 ? std::make_optional(argv[2]) : std::nullopt);
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std::cerr << "Done." << std::endl;
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// 反折叠的原理: 将超胞中的原子运动状态, 投影到一组平面波构成的基矢中.
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// 每一个平面波的波矢由两部分相加得到: 一部分是单胞倒格子的整数倍, 所取的个数有一定任意性, 论文中建议取大约单胞中原子个数那么多个;
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// 对于没有缺陷的情况, 取一个应该就足够了.
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// 另一部分是超胞倒格子的整数倍, 取 n 个, n 为超胞对应的单胞的倍数, 其实也就是倒空间中单胞对应倒格子中超胞的格点.
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// 只要第一部分取得足够多, 那么单胞中原子的状态就可以完全被这些平面波描述.
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// 将超胞中原子的运动状态投影到这些基矢上, 计算出投影的系数, 就可以将超胞的原子运动状态分解到单胞中的多个 q 点上.
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// 构建基
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// 每个 q 点对应的一组 sub qpoint。不同的 q 点所对应的 sub qpoint 是不一样的，但 sub qpoint 与 q 点的相对位置一致。
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// 这里 xyz_of_diff_of_sub_qpoint 即表示这个相对位置。
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// 由于基只与这个相对位置有关（也就是说，不同 q 点的基是一样的），因此可以先计算出所有的基，这样降低计算量。
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// 外层下标对应超胞倒格子的整数倍那部分(第二部分), 也就是不同的 sub qpoint
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// 内层下标对应单胞倒格子的整数倍那部分(第一部分), 也就是 sub qpoint 上的不同平面波（取的数量越多，结果越精确）
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std::cerr << "Calculating basis..." << std::flush;
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std::vector<std::vector<Eigen::VectorXcd>> basis(input.SuperCellMultiplier.prod());
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// 每个 q 点对应的一组 sub qpoint。不同的 q 点所对应的 sub qpoint 是不一样的，但 sub qpoint 与 q 点的相对位置一致。
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// 这里 xyz_of_diff_of_sub_qpoint 即表示这个相对位置，单位为超胞的倒格矢
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for (auto [xyz_of_diff_of_sub_qpoint_by_reciprocal_super_cell, i_of_diff_of_sub_qpoint]
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: triplet_sequence(input.SuperCellMultiplier))
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{
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basis[i_of_diff_of_sub_qpoint].resize(input.PrimativeCellBasisNumber.prod());
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for (auto [xyz_of_basis, i_of_basis] : triplet_sequence(input.PrimativeCellBasisNumber))
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{
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// 计算 q 点的坐标, 单位为单胞的倒格矢
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auto diff_of_sub_qpoint_by_reciprocal_primative_cell = xyz_of_basis.cast<double>()
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+ input.SuperCellMultiplier.cast<double>().cwiseInverse().asDiagonal()
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* xyz_of_diff_of_sub_qpoint_by_reciprocal_super_cell.cast<double>();
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// 将 q 点坐标转换为埃^-1
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auto qpoint = (diff_of_sub_qpoint_by_reciprocal_primative_cell.transpose()
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* (input.PrimativeCell.transpose().inverse())).transpose();
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// 计算基矢
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basis[i_of_diff_of_sub_qpoint][i_of_basis]
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= (2i * std::numbers::pi_v<double> * (input.AtomPosition * qpoint)).array().exp();
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}
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}
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std::cerr << "Done." << std::endl;
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// 计算投影的结果
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// 最外层下标对应反折叠前的 q 点, 第二层下标对应不同模式, 第三层下标对应这个模式在反折叠后的 q 点(sub qpoint)
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std::vector<std::vector<std::vector<double>>> projection_coefficient(input.QPointData.size());
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for (unsigned i_of_qpoint = 0; i_of_qpoint < input.QPointData.size(); i_of_qpoint++)
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{
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std::cerr << fmt::format("\rCalculating projection coefficient for qpoint {}/{}...",
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i_of_qpoint, input.QPointData.size()) << std::flush;
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projection_coefficient[i_of_qpoint].resize(input.QPointData[i_of_qpoint].ModeData.size());
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for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_qpoint].ModeData.size(); i_of_mode++)
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{
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auto& _ = projection_coefficient[i_of_qpoint][i_of_mode];
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_.resize(input.SuperCellMultiplier.prod());
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for (unsigned i_of_sub_qpoint = 0; i_of_sub_qpoint < input.SuperCellMultiplier.prod(); i_of_sub_qpoint++)
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// 对于 basis 中, 对应于单胞倒格子的部分, 以及对应于不同方向的部分, 分别求内积, 然后求模方和
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for (unsigned i_of_basis = 0; i_of_basis < input.PrimativeCellBasisNumber.prod(); i_of_basis++)
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_[i_of_sub_qpoint] +=
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(
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basis[i_of_sub_qpoint][i_of_basis].transpose().conjugate()
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* input.QPointData[i_of_qpoint].ModeData[i_of_mode].AtomMovement
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).array().abs2().sum();
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// 如果是严格地将向量分解到一组完备的基矢上, 那么不需要对计算得到的权重再做归一化处理
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// 但这里并不是这样一个严格的概念. 因此对分解到各个 sub qpoint 上的权重做归一化处理
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auto sum = std::accumulate(_.begin(), _.end(), 0.);
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for (auto& __ : _)
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__ /= sum;
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}
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}
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std::cerr << "Done." << std::endl;
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// 填充输出对象
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std::cerr << "Filling output object..." << std::flush;
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Output output;
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for (unsigned i_of_qpoint = 0; i_of_qpoint < input.QPointData.size(); i_of_qpoint++)
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for (auto [xyz_of_diff_of_sub_qpoint_by_reciprocal_super_cell, i_of_sub_qpoint]
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: triplet_sequence(input.SuperCellMultiplier))
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{
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auto& _ = output.QPointData.emplace_back();
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auto reciprocal_super_cell =
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(input.SuperCellDeformation * input.SuperCellMultiplier.cast<double>().asDiagonal() * input.PrimativeCell)
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.inverse().transpose();
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// sub qpoint 的坐标，单位为埃^-1
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auto sub_qpoint =
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((xyz_of_diff_of_sub_qpoint_by_reciprocal_super_cell.cast<double>() + input.QPointData[i_of_qpoint].QPoint)
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.transpose() * reciprocal_super_cell).transpose();
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// 将坐标转换为相对于单胞的倒格矢的坐标并写入
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// 由 sub_qpoint.transpose() = sub_qpoint_by_reciprocal_primative_cell.transpose()
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// * PrimativeCell.transpose().inverse()
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// 得到 sub_qpoint_by_reciprocal_primative_cell = PrimativeCell * sub_qpoint
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_.QPoint = input.PrimativeCell * sub_qpoint;
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_.Source = input.QPointData[i_of_qpoint].QPoint;
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if (!input.Debug.value_or(false))
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{
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// 从小到大枚举所有的模式，并将相近的模式（相差小于 0.01 THz）合并
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std::map<double, double> frequency_to_weight;
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for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_qpoint].ModeData.size(); i_of_mode++)
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{
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auto frequency = input.QPointData[i_of_qpoint].ModeData[i_of_mode].Frequency;
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auto weight = projection_coefficient[i_of_qpoint][i_of_mode][i_of_sub_qpoint];
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auto it_lower = frequency_to_weight.lower_bound(frequency - 0.01);
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auto it_upper = frequency_to_weight.upper_bound(frequency + 0.01);
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if (it_lower == it_upper)
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frequency_to_weight[frequency] = weight;
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else
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{
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auto frequency_sum = std::accumulate(it_lower, it_upper, 0.,
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[](const auto& a, const auto& b) { return a + b.first * b.second; });
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auto weight_sum = std::accumulate(it_lower, it_upper, 0.,
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[](const auto& a, const auto& b) { return a + b.second; });
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frequency_sum += frequency * weight;
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weight_sum += weight;
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frequency_to_weight.erase(it_lower, it_upper);
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frequency_to_weight[frequency_sum / weight_sum] = weight_sum;
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}
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}
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// 仅保留权重大于 0.01 的模式
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for (auto& mode : frequency_to_weight)
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if (mode.second > 0.01)
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{
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auto& __ = _.ModeData.emplace_back();
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__.Frequency = mode.first;
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__.Weight = mode.second;
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}
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}
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else
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for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_qpoint].ModeData.size(); i_of_mode++)
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{
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auto& __ = _.ModeData.emplace_back();
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__.Frequency = input.QPointData[i_of_qpoint].ModeData[i_of_mode].Frequency;
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__.Weight = projection_coefficient[i_of_qpoint][i_of_mode][i_of_sub_qpoint];
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}
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}
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std::cerr << "Done." << std::endl;
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// std::ofstream(argv[2]) << YAML::Node(output);
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// YAML 输出得太丑了，我来自己写
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std::cerr << "Writing output file..." << std::flush;
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std::ofstream(argv[2]) << [&]
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{
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std::stringstream print;
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auto format = input.Debug.value_or(false) ? 10 : 3;
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print << "QPointData:\n";
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for (auto& qpoint: output.QPointData)
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{
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print << fmt::format(" - QPoint: [ {1:.{0}f}, {2:.{0}f}, {3:.{0}f} ]\n",
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format, qpoint.QPoint[0], qpoint.QPoint[1], qpoint.QPoint[2]);
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print << fmt::format(" Source: [ {1:.{0}f}, {2:.{0}f}, {3:.{0}f} ]\n",
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format, qpoint.Source[0], qpoint.Source[1], qpoint.Source[2]);
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print << " ModeData:\n";
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for (auto& mode: qpoint.ModeData)
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print << fmt::format(" - {{ Frequency: {1:.{0}f}, Weight: {2:.{0}f} }}\n",
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format, mode.Frequency, mode.Weight);
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}
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return print.str();
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}();
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std::cerr << "Done." << std::endl;
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}
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// 从文件中读取输入, 文件中应当包含: (大多数据可以直接从 phonopy 的输出中复制)
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// 单胞的格矢: lattice 单位为埃 直接从 phonopy 的输出中复制
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// 超胞的倍数: SuperCellMultiplier 手动输入, 为一个包含三个整数的数组
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// 平面波的基矢个数: PrimativeCellBasisNumber 手动输入, 为一个包含三个整数的数组
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// 超胞中原子的坐标: points[*].coordinates 单位为超胞的格矢 直接从 phonopy 的输出中复制
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// 各个 Q 点的坐标: phonon[*].q-position 单位为超胞的倒格子的格矢 直接从 phonopy 的输出中复制
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// 各个模式的频率: phonon[*].band[*].frequency 单位为 THz 直接从 phonopy 的输出中复制
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// 各个模式的原子运动状态: phonon[*].band[*].eigenvector 直接从 phonopy 的输出中复制
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// 文件中可以有多余的项目, 多余的项目不管.
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Input::Input(std::string yaml_file, std::optional<std::string> hdf5_file)
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{
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auto node = YAML::LoadFile(yaml_file);
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for (unsigned i = 0; i < 3; i++)
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for (unsigned j = 0; j < 3; j++)
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PrimativeCell(i, j) = node["lattice"][i][j].as<double>();
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for (unsigned i = 0; i < 3; i++)
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SuperCellMultiplier(i) = node["SuperCellMultiplier"][i].as<int>();
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for (unsigned i = 0; i < 3; i++)
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for (unsigned j = 0; j < 3; j++)
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SuperCellDeformation(i, j) = node["SuperCellDeformation"][i][j].as<double>();
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for (unsigned i = 0; i < 3; i++)
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PrimativeCellBasisNumber(i) = node["PrimativeCellBasisNumber"][i].as<int>();
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if (auto value = node["Debug"])
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Debug = value.as<bool>();
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auto points = node["points"].as<std::vector<YAML::Node>>();
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auto atom_position_to_super_cell = Eigen::MatrixX3d(points.size(), 3);
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for (unsigned i = 0; i < points.size(); i++)
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for (unsigned j = 0; j < 3; j++)
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atom_position_to_super_cell(i, j) = points[i]["coordinates"][j].as<double>();
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AtomPosition = atom_position_to_super_cell
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* (SuperCellDeformation * SuperCellMultiplier.cast<double>().asDiagonal() * PrimativeCell);
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if (hdf5_file)
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{
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HighFive::File file(*hdf5_file, HighFive::File::ReadOnly);
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auto size = file.getDataSet("/frequency").getDimensions();
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auto frequency = file.getDataSet("/frequency")
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.read<std::vector<std::vector<std::vector<double>>>>();
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auto eigenvector_vector = file.getDataSet("/eigenvector")
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.read<std::vector<std::vector<std::vector<std::vector<PhonopyComplex>>>>>();
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auto path = file.getDataSet("/path")
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.read<std::vector<std::vector<std::vector<double>>>>();
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QPointData.resize(size[0] * size[1]);
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for (unsigned i = 0; i < size[0]; i++)
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for (unsigned j = 0; j < size[1]; j++)
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{
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QPointData[i * size[1] + j].QPoint = Eigen::Vector3d(path[i][j].data());
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QPointData[i * size[1] + j].ModeData.resize(size[2]);
|
||
for (unsigned k = 0; k < size[2]; k++)
|
||
{
|
||
QPointData[i * size[1] + j].ModeData[k].Frequency = frequency[i][j][k];
|
||
Eigen::MatrixX3cd eigenvectors(AtomPosition.rows(), 3);
|
||
for (unsigned l = 0; l < AtomPosition.rows(); l++)
|
||
for (unsigned m = 0; m < 3; m++)
|
||
eigenvectors(l, m)
|
||
= eigenvector_vector[i][j][k][l * 3 + m].r + eigenvector_vector[i][j][k][l * 3 + m].i * 1i;
|
||
QPointData[i * size[1] + j].ModeData[k].AtomMovement = eigenvectors / eigenvectors.norm();
|
||
}
|
||
}
|
||
}
|
||
else
|
||
{
|
||
auto phonon = node["phonon"].as<std::vector<YAML::Node>>();
|
||
QPointData.resize(phonon.size());
|
||
for (unsigned i = 0; i < phonon.size(); i++)
|
||
{
|
||
QPointData[i].QPoint.resize(3);
|
||
for (unsigned j = 0; j < 3; j++)
|
||
QPointData[i].QPoint(j) = phonon[i]["q-position"][j].as<double>();
|
||
auto band = phonon[i]["band"].as<std::vector<YAML::Node>>();
|
||
QPointData[i].ModeData.resize(band.size());
|
||
for (unsigned j = 0; j < band.size(); j++)
|
||
{
|
||
QPointData[i].ModeData[j].Frequency = band[j]["frequency"].as<double>();
|
||
auto eigenvector_vectors = band[j]["eigenvector"]
|
||
.as<std::vector<std::vector<std::vector<double>>>>();
|
||
Eigen::MatrixX3cd eigenvectors(AtomPosition.rows(), 3);
|
||
for (unsigned k = 0; k < AtomPosition.rows(); k++)
|
||
for (unsigned l = 0; l < 3; l++)
|
||
eigenvectors(k, l)
|
||
= eigenvector_vectors[k][l][0] + 1i * eigenvector_vectors[k][l][1];
|
||
// 需要对读入的原子运动状态作相位转换, 使得它们与我们的约定一致(对超胞周期性重复)
|
||
// 这里还要需要做归一化处理 (指将数据简单地作为向量处理的归一化)
|
||
auto& AtomMovement = QPointData[i].ModeData[j].AtomMovement;
|
||
// AtomMovement = eigenvectors.array().colwise() * (-2 * std::numbers::pi_v<double> * 1i
|
||
// * (atom_position_to_super_cell * input.QPointData[i].QPoint)).array().exp();
|
||
// AtomMovement /= AtomMovement.norm();
|
||
// phonopy 似乎已经进行了相位的转换！为什么？
|
||
AtomMovement = eigenvectors / eigenvectors.norm();
|
||
}
|
||
}
|
||
}
|
||
}
|