mirror of
https://github.com/CHN-beta/ufo.git
synced 2024-10-23 04:08:45 +08:00
330 lines
15 KiB
C++
330 lines
15 KiB
C++
# include <iostream>
|
||
# include <array>
|
||
# include <numbers>
|
||
# include <numeric>
|
||
# include <fstream>
|
||
# include <optional>
|
||
# include <array>
|
||
# include <utility>
|
||
# include <yaml-cpp/yaml.h>
|
||
# include <eigen3/Eigen/Dense>
|
||
# include <concurrencpp/concurrencpp.h>
|
||
# include <fmt/format.h>
|
||
|
||
using namespace std::literals;
|
||
|
||
// 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
|
||
// (而不是 $\exp (-2 \pi i \vec{q} \cdot \vec{r})$)
|
||
// 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.
|
||
// 也就是说, 正格子与倒格子的转置相乘, 得到单位矩阵.
|
||
|
||
struct Input
|
||
{
|
||
// 单胞的三个格矢，每行表示一个格矢的坐标，单位为埃
|
||
Eigen::Matrix3d PrimativeCell;
|
||
// 超胞在各个方向上是单胞的多少倍，这是一个对角矩阵
|
||
// 暂时不考虑不是对角矩阵的情况
|
||
Eigen::Matrix<unsigned, 3, 3> SuperCellMultiplier;
|
||
// 在单胞内取几个平面波的基矢
|
||
Eigen::Vector<unsigned, 3> PrimativeCellBasisNumber;
|
||
// 超胞中原子的坐标，每行表示一个原子的坐标，单位为埃
|
||
Eigen::MatrixX3d AtomPosition;
|
||
|
||
// 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
|
||
std::optional<bool> Debug;
|
||
|
||
// 关于各个 Q 点的数据
|
||
struct QPointDataType_
|
||
{
|
||
// Q 点的坐标，单位为超胞的倒格矢
|
||
Eigen::Vector3d QPoint;
|
||
|
||
// 关于这个 Q 点上各个模式的数据
|
||
struct ModeDataType_
|
||
{
|
||
// 模式的频率，单位为 THz
|
||
double Frequency;
|
||
// 模式中各个原子的运动状态
|
||
// 这个数据是这样得到的: phonopy 输出的动态矩阵的 eigenvector 乘以 $\exp(-2 \pi i \vec q \cdot \vec r)$
|
||
// 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.
|
||
// 这个数据在读入后不会被立即归一化.
|
||
Eigen::MatrixX3cd AtomMovement;
|
||
};
|
||
std::vector<ModeDataType_> ModeData;
|
||
};
|
||
std::vector<QPointDataType_> QPointData;
|
||
};
|
||
|
||
struct Output
|
||
{
|
||
// 关于各个 Q 点的数据
|
||
struct QPointDataType_
|
||
{
|
||
// Q 点的坐标，单位为超胞的倒格矢
|
||
Eigen::Vector3d QPoint;
|
||
|
||
// 来源于哪个 Q 点, 单位为超胞的倒格矢
|
||
Eigen::Vector3d Source;
|
||
|
||
// 关于这个 Q 点上各个模式的数据
|
||
struct ModeDataType_
|
||
{
|
||
// 模式的频率，单位为 THz
|
||
double Frequency;
|
||
// 模式的权重
|
||
double Weight;
|
||
};
|
||
std::vector<ModeDataType_> ModeData;
|
||
};
|
||
std::vector<QPointDataType_> QPointData;
|
||
};
|
||
|
||
template<> struct YAML::convert<Input> { static bool decode(const Node& node, Input& input); };
|
||
template<> struct YAML::convert<Output> { static Node encode(const Output& output); };
|
||
|
||
concurrencpp::generator<std::pair<Eigen::Vector<unsigned, 3>, unsigned>>
|
||
triplet_sequence(Eigen::Vector<unsigned, 3> range)
|
||
{
|
||
for (unsigned x = 0; x < range[0]; x++)
|
||
for (unsigned y = 0; y < range[1]; y++)
|
||
for (unsigned z = 0; z < range[2]; z++)
|
||
co_yield
|
||
{
|
||
Eigen::Vector<unsigned, 3>{{x}, {y}, {z}},
|
||
x * range[1] * range[2] + y * range[2] + z
|
||
};
|
||
}
|
||
|
||
int main(int argc, const char** argv)
|
||
{
|
||
if (argc != 3)
|
||
throw std::runtime_error("Usage: " + std::string(argv[0]) + " input.yaml output.yaml");
|
||
|
||
auto input = YAML::LoadFile(argv[1]).as<Input>();
|
||
|
||
// 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.
|
||
// 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;
|
||
// 对于没有缺陷的情况, 取一个应该就足够了.
|
||
// 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.
|
||
// 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.
|
||
// 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.
|
||
|
||
// 构建基
|
||
// 外层下标对应超胞倒格子的整数倍那部分(第二部分), 也就是对应不同反折叠后的 q 点(sub qpoint)
|
||
// 内层下标对应单胞倒格子的整数倍那部分(第一部分), 也就是对应同一个反折叠后的 q 点上的不同平面波
|
||
std::vector<std::vector<Eigen::VectorXcd>> basis;
|
||
basis.resize(input.SuperCellMultiplier.diagonal().prod());
|
||
for (auto [xyz_of_sub_qpoint, i_of_sub_qpoint]
|
||
: triplet_sequence(input.SuperCellMultiplier.diagonal()))
|
||
{
|
||
basis[i_of_sub_qpoint].resize(input.PrimativeCellBasisNumber.prod());
|
||
for (auto [xyz_of_basis, i_of_basis] : triplet_sequence(input.PrimativeCellBasisNumber))
|
||
{
|
||
// 计算 q 点的坐标, 单位为单胞的倒格矢
|
||
auto qpoint_relative_to_primative_cell = xyz_of_basis.cast<double>()
|
||
+ input.SuperCellMultiplier.cast<double>().inverse() * xyz_of_sub_qpoint.cast<double>();
|
||
// 将 q 点坐标转换为埃^-1
|
||
auto qpoint = (qpoint_relative_to_primative_cell.transpose() * (input.PrimativeCell.transpose().inverse()))
|
||
.transpose();
|
||
// 计算基矢
|
||
basis[i_of_sub_qpoint][i_of_basis]
|
||
= (-2 * std::numbers::pi_v<double> * 1i * (input.AtomPosition * qpoint)).array().exp();
|
||
}
|
||
}
|
||
|
||
// 计算投影的结果
|
||
// 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
|
||
std::vector<std::vector<std::vector<double>>> projection_coefficient;
|
||
projection_coefficient.resize(input.QPointData.size());
|
||
for (unsigned i_of_folded_qpoint = 0; i_of_folded_qpoint < input.QPointData.size(); i_of_folded_qpoint++)
|
||
{
|
||
auto num_of_mode = input.QPointData[i_of_folded_qpoint].ModeData.size();
|
||
projection_coefficient[i_of_folded_qpoint].resize(num_of_mode);
|
||
for (unsigned i_of_mode = 0; i_of_mode < num_of_mode; i_of_mode++)
|
||
{
|
||
auto num_of_sub_qpoint = input.SuperCellMultiplier.diagonal().prod();
|
||
auto& _ = projection_coefficient[i_of_folded_qpoint][i_of_mode];
|
||
_.resize(num_of_sub_qpoint);
|
||
for (unsigned i_of_sub_qpoint = 0; i_of_sub_qpoint < num_of_sub_qpoint; i_of_sub_qpoint++)
|
||
// 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, 然后求绝对值, 然后求和
|
||
for (unsigned i_of_basis = 0; i_of_basis < input.PrimativeCellBasisNumber.prod(); i_of_basis++)
|
||
_[i_of_sub_qpoint] +=
|
||
(
|
||
basis[i_of_sub_qpoint][i_of_basis].transpose()
|
||
* input.QPointData[i_of_folded_qpoint].ModeData[i_of_mode].AtomMovement
|
||
).array().abs2().sum();
|
||
|
||
// 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
|
||
// 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
|
||
auto sum = std::accumulate(_.begin(), _.end(), 0.);
|
||
for (auto& __ : _)
|
||
__ /= sum;
|
||
}
|
||
}
|
||
|
||
// 填充输出对象
|
||
Output output;
|
||
for (unsigned i_of_folded_qpoint = 0; i_of_folded_qpoint < input.QPointData.size(); i_of_folded_qpoint++)
|
||
for (auto [xyz_of_sub_qpoint, i_of_sub_qpoint]
|
||
: triplet_sequence(input.SuperCellMultiplier.diagonal()))
|
||
{
|
||
auto& sub_qpoint = output.QPointData.emplace_back();
|
||
sub_qpoint.QPoint = input.SuperCellMultiplier.cast<double>().inverse() *
|
||
(input.QPointData[i_of_folded_qpoint].QPoint + xyz_of_sub_qpoint.cast<double>());
|
||
sub_qpoint.Source = input.QPointData[i_of_folded_qpoint].QPoint;
|
||
|
||
if (!input.Debug.value_or(false))
|
||
{
|
||
// 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
|
||
std::map<double, double> frequency_to_weight;
|
||
for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_folded_qpoint].ModeData.size(); i_of_mode++)
|
||
{
|
||
auto frequency = input.QPointData[i_of_folded_qpoint].ModeData[i_of_mode].Frequency;
|
||
auto weight = projection_coefficient[i_of_folded_qpoint][i_of_mode][i_of_sub_qpoint];
|
||
auto it_lower = frequency_to_weight.lower_bound(frequency - 0.01);
|
||
auto it_upper = frequency_to_weight.upper_bound(frequency + 0.01);
|
||
if (it_lower == it_upper)
|
||
frequency_to_weight[frequency] = weight;
|
||
else
|
||
{
|
||
auto frequency_sum = std::accumulate(it_lower, it_upper, 0.,
|
||
[](const auto& a, const auto& b) { return a + b.first * b.second; });
|
||
auto weight_sum = std::accumulate(it_lower, it_upper, 0.,
|
||
[](const auto& a, const auto& b) { return a + b.second; });
|
||
frequency_sum += frequency * weight;
|
||
weight_sum += weight;
|
||
frequency_to_weight.erase(it_lower, it_upper);
|
||
frequency_to_weight[frequency_sum / weight_sum] = weight_sum;
|
||
}
|
||
}
|
||
// 仅保留权重大于 0.01 的模式
|
||
for (auto& mode : frequency_to_weight)
|
||
if (mode.second > 0.01)
|
||
{
|
||
auto& _ = sub_qpoint.ModeData.emplace_back();
|
||
_.Frequency = mode.first;
|
||
_.Weight = mode.second;
|
||
}
|
||
}
|
||
else
|
||
for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_folded_qpoint].ModeData.size(); i_of_mode++)
|
||
{
|
||
auto& _ = sub_qpoint.ModeData.emplace_back();
|
||
_.Frequency = input.QPointData[i_of_folded_qpoint].ModeData[i_of_mode].Frequency;
|
||
_.Weight = projection_coefficient[i_of_folded_qpoint][i_of_mode][i_of_sub_qpoint];
|
||
}
|
||
}
|
||
|
||
// std::ofstream(argv[2]) << YAML::Node(output);
|
||
// YAML 输出得太丑了，我来自己写
|
||
std::ofstream(argv[2]) << [&]
|
||
{
|
||
std::stringstream print;
|
||
auto format = input.Debug.value_or(false) ? 10 : 3;
|
||
print << "QPointData:\n";
|
||
for (auto& qpoint: output.QPointData)
|
||
{
|
||
print << fmt::format(" - QPoint: [ {1:.{0}f}, {2:.{0}f}, {3:.{0}f} ]\n",
|
||
format, qpoint.QPoint[0], qpoint.QPoint[1], qpoint.QPoint[2]);
|
||
print << fmt::format(" Source: [ {1:.{0}f}, {2:.{0}f}, {3:.{0}f} ]\n",
|
||
format, qpoint.Source[0], qpoint.Source[1], qpoint.Source[2]);
|
||
print << " ModeData:\n";
|
||
for (auto& mode: qpoint.ModeData)
|
||
print << fmt::format(" - {{ Frequency: {1:.{0}f}, Weight: {2:.{0}f} }}\n",
|
||
format, mode.Frequency, mode.Weight);
|
||
}
|
||
return print.str();
|
||
}();
|
||
}
|
||
|
||
// 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)
|
||
// 单胞的格矢: lattice 单位为埃 直接从 phonopy 的输出中复制
|
||
// 超胞的倍数: SuperCellMultiplier 手动输入, 为一个包含三个整数的数组
|
||
// 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
|
||
// 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
|
||
// 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
|
||
// 各个模式的频率: phonon[*].band[*].frequency 单位为 THz 直接从 phonopy 的输出中复制
|
||
// 各个模式的原子运动状态: phonon[*].band[*].eigenvector 直接从 phonopy 的输出中复制
|
||
// 文件中可以有多余的项目, 多余的项目不管.
|
||
bool YAML::convert<Input>::decode(const Node& node, Input& input)
|
||
{
|
||
for (unsigned i = 0; i < 3; i++)
|
||
for (unsigned j = 0; j < 3; j++)
|
||
input.PrimativeCell(i, j) = node["lattice"][i][j].as<double>();
|
||
|
||
input.SuperCellMultiplier.setZero();
|
||
for (unsigned i = 0; i < 3; i++)
|
||
input.SuperCellMultiplier(i, i) = node["SuperCellMultiplier"][i].as<int>();
|
||
|
||
for (unsigned i = 0; i < 3; i++)
|
||
input.PrimativeCellBasisNumber(i) = node["PrimativeCellBasisNumber"][i].as<int>();
|
||
|
||
if (auto value = node["Debug"])
|
||
input.Debug = value.as<bool>();
|
||
|
||
auto points = node["points"].as<std::vector<YAML::Node>>();
|
||
auto atom_position_to_super_cell = Eigen::MatrixX3d(points.size(), 3);
|
||
for (unsigned i = 0; i < points.size(); i++)
|
||
for (unsigned j = 0; j < 3; j++)
|
||
atom_position_to_super_cell(i, j) = points[i]["coordinates"][j].as<double>();
|
||
input.AtomPosition = atom_position_to_super_cell * (input.SuperCellMultiplier.cast<double>() * input.PrimativeCell);
|
||
|
||
auto phonon = node["phonon"].as<std::vector<YAML::Node>>();
|
||
input.QPointData.resize(phonon.size());
|
||
for (unsigned i = 0; i < phonon.size(); i++)
|
||
{
|
||
input.QPointData[i].QPoint.resize(3);
|
||
for (unsigned j = 0; j < 3; j++)
|
||
input.QPointData[i].QPoint(j) = phonon[i]["q-position"][j].as<double>();
|
||
auto band = phonon[i]["band"].as<std::vector<YAML::Node>>();
|
||
input.QPointData[i].ModeData.resize(band.size());
|
||
for (unsigned j = 0; j < band.size(); j++)
|
||
{
|
||
input.QPointData[i].ModeData[j].Frequency = band[j]["frequency"].as<double>();
|
||
auto eigenvector_vectors = band[j]["eigenvector"]
|
||
.as<std::vector<std::vector<std::vector<double>>>>();
|
||
auto eigenvectors = Eigen::MatrixX3cd(input.AtomPosition.rows(), 3);
|
||
for (unsigned k = 0; k < input.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 = input.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();
|
||
}
|
||
}
|
||
|
||
return true;
|
||
}
|
||
|
||
// auto YAML::convert<Output>::encode(const Output& output) -> Node
|
||
// {
|
||
// Node node;
|
||
// node["QPointData"] = Node(NodeType::Sequence);
|
||
// for (unsigned i = 0; i < output.QPointData.size(); i++)
|
||
// {
|
||
// node["QPointData"][i]["QPoint"] =
|
||
// ({
|
||
// auto& _ = output.QPointData[i].QPoint;
|
||
// std::vector<double>(_.data(), _.data() + _.size());
|
||
// });
|
||
// node["QPointData"][i]["ModeData"] = Node(NodeType::Sequence);
|
||
// for (unsigned j = 0; j < output.QPointData[i].ModeData.size(); j++)
|
||
// {
|
||
// node["QPointData"][i]["ModeData"][j]["Frequency"] = output.QPointData[i].ModeData[j].Frequency;
|
||
// node["QPointData"][i]["ModeData"][j]["Weight"] = output.QPointData[i].ModeData[j].Weight;
|
||
// node["QPointData"][i]["ModeData"][j]["Source"] =
|
||
// ({
|
||
// auto& _ = output.QPointData[i].ModeData[j].Source;
|
||
// std::vector<double>(_.data(), _.data() + _.size());
|
||
// });
|
||
// }
|
||
// }
|
||
// return node;
|
||
// }
|