mirror of
https://github.com/CHN-beta/ufo.git
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add xmake
整理文件树
This commit is contained in:
parent
b535d9bc27
commit
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2
.gitignore
vendored
2
.gitignore
vendored
@ -5,3 +5,5 @@ main
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plot
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out.yaml
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.ccls-cache
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.xmake/
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build/
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31
flake.lock
31
flake.lock
@ -807,11 +807,11 @@
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"touchix": "touchix"
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},
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"locked": {
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"lastModified": 1695465859,
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"narHash": "sha256-nauD552M00PmcpDkKqoYC0ql8QFaFyfKpIYm2qyRKEQ=",
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"lastModified": 1695648380,
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"narHash": "sha256-8zQct7OdcAtzwsvyPy07wImEtO6v0Rz//grrDtol+Jo=",
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"owner": "CHN-beta",
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"repo": "nixos",
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"rev": "ad7be5bc2b22a47baf34eebb913b93c11482fb37",
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"rev": "e21c7a916a66de6894c3e785a3a0d5f621458272",
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"type": "github"
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},
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"original": {
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@ -951,11 +951,11 @@
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},
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"nixpkgs-unstable": {
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"locked": {
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"lastModified": 1695275987,
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"narHash": "sha256-DjfwcdkKY7Hom5Nk8fR2fJInRf93uyeAvX+GoA1rqKo=",
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"lastModified": 1695562663,
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"narHash": "sha256-cnPZFTKQGldgFHWC9LHt8mDtJVTmj4WJxvKHF5uw5qA=",
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"owner": "CHN-beta",
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"repo": "nixpkgs",
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"rev": "1523dd436e6f9baf1ab789131b4394b3502de789",
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"rev": "82e02a1546fc59bc496f859e446ddcd412f09849",
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"type": "github"
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},
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"original": {
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@ -1013,6 +1013,22 @@
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"type": "github"
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}
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},
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"nixpkgs_5": {
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"locked": {
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"lastModified": 1695360818,
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"narHash": "sha256-JlkN3R/SSoMTa+CasbxS1gq+GpGxXQlNZRUh9+LIy/0=",
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"owner": "NixOS",
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"repo": "nixpkgs",
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"rev": "e35dcc04a3853da485a396bdd332217d0ac9054f",
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"type": "github"
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},
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"original": {
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"owner": "NixOS",
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"ref": "nixos-unstable",
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"repo": "nixpkgs",
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"type": "github"
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}
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},
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"nur": {
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"locked": {
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"lastModified": 1695048039,
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@ -1143,7 +1159,8 @@
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},
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"root": {
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"inputs": {
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"nixos": "nixos"
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"nixos": "nixos",
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"nixpkgs": "nixpkgs_5"
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}
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},
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"sops-nix": {
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30
flake.nix
30
flake.nix
@ -1,16 +1,26 @@
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{
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inputs.nixos.url = "github:CHN-beta/nixos";
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inputs.nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
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outputs = inputs: let pkgs = inputs.nixos.nixosConfigurations.pc.pkgs; in
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{
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devShell.x86_64-linux = pkgs.mkShell.override { stdenv = pkgs.genericPackages.gcc13Stdenv; }
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outputs = inputs:
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let
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pkgs = inputs.nixpkgs.legacyPackages.x86_64-linux;
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localPackages = inputs.nixos.nixosConfigurations.pc.pkgs.localPackages;
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in
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{
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buildInputs = with pkgs;
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[
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yaml-cpp eigen fmt (localPackages.concurrencpp.override { stdenv = genericPackages.gcc13Stdenv; }) highfive
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hdf5.dev tbb (localPackages.matplotplusplus.override { stdenv = genericPackages.gcc13Stdenv; })
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];
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hardeningDisable = [ "all" ];
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devShell.x86_64-linux = pkgs.mkShell.override { stdenv = pkgs.stdenvNoCC; }
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{
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packages = with pkgs; [ xmake gcc13 pkg-config cmake ];
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inputsFrom = with pkgs;
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[
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yaml-cpp eigen fmt localPackages.concurrencpp highfive
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hdf5.dev tbb_2021_8.dev localPackages.matplotplusplus
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localPackages.zpp-bits
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];
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PKG_CONFIG_PATH = "${pkgs.tbb_2021_8.dev}/lib/pkgconfig:${pkgs.yaml-cpp}/share/pkgconfig";
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yaml-cpp_DIR = "${pkgs.yaml-cpp}/share/cmake/yaml-cpp";
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hardeningDisable = [ "all" ];
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NIX_DEBUG = "1";
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};
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};
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};
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}
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142
include/ufo/ufo.hpp
Normal file
142
include/ufo/ufo.hpp
Normal file
@ -0,0 +1,142 @@
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# 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 <execution>
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# include <syncstream>
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# include <any>
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# include <map>
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# include <vector>
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# include <span>
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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 <fmt/std.h>
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# include <highfive/H5File.hpp>
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# include <zpp_bits.h>
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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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HIGHFIVE_REGISTER_TYPE(PhonopyComplex, create_compound_complex)
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namespace Eigen
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{
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constexpr inline auto serialize(auto & archive, Eigen::Matrix3d& matrix)
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{ return archive(std::span<double, 9>(matrix.data(), 9)); }
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}
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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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std::optional<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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// 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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struct InputOutputFile_
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{
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std::string FileName;
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std::string Format;
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std::map<std::string, std::any> ExtraParameters;
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};
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// 从哪个文件读入 AtomPosition, 以及这个文件的格式, 格式可选值包括 "yaml"
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InputOutputFile_ AtomPositionInputFile;
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// 从哪个文件读入 QPointData, 以及这个文件的格式, 格式可选值包括 "yaml" 和 "hdf5"
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InputOutputFile_ QPointDataInputFile;
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// 输出到哪些文件, 以及使用怎样的格式, 格式可选值包括:
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// yaml: 使用 yaml 格式输出
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// yaml-human-readable: 使用 yaml 格式输出, 但是输出的结果更适合人类阅读, 包括合并相近的模式, 去除权重过小的模式, 限制输出的小数位数.
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// zpp: 使用 zpp-bits 序列化, 可以直接被 plot.cpp 读取
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std::vector<InputOutputFile_> QPointDataOutputFile;
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// 从文件中读取输入 (包括一个较小的配置文件, 和一个 hdf5 或者一个 yaml 文件), 文件中应当包含:
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// 单胞的格矢: PrimativeCell 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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// 超胞的变形: SuperCellDeformation 手动输入, 为一个三阶方阵
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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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// 另外还有一个文件, 直接将 phonopy 的输出复制过来即可, 如果是 yaml, 应该包含下面的内容:
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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(std::string filename);
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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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std::size_t SourceIndex_;
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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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void write(std::string filename, std::string format, unsigned percision = 10);
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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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213
include/ufo/ufo.impl.hpp
Normal file
213
include/ufo/ufo.impl.hpp
Normal file
@ -0,0 +1,213 @@
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# include <ufo/ufo.hpp>
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inline HighFive::CompoundType create_compound_complex()
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{ return {{"r", HighFive::AtomicType<double>{}}, {"i", HighFive::AtomicType<double>{}}}; }
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inline Input::Input(std::string filename)
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{
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// read main input file
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{
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auto node = YAML::LoadFile(filename);
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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["PrimativeCell"][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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if (auto value = node["SuperCellDeformation"])
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{
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SuperCellDeformation.emplace();
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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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}
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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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AtomPositionInputFile.FileName = node["AtomPositionInputFile"]["FileName"].as<std::string>();
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AtomPositionInputFile.Format = node["AtomPositionInputFile"]["Format"].as<std::string>();
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if (!std::set<std::string>{"yaml"}.contains(AtomPositionInputFile.Format))
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throw std::runtime_error(fmt::format
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("Unknown format: {}, should be \"yaml\".", AtomPositionInputFile.Format));
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QPointDataInputFile.FileName = node["QPointDataInputFile"]["FileName"].as<std::string>();
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QPointDataInputFile.Format = node["QPointDataInputFile"]["Format"].as<std::string>();
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if (!std::set<std::string>{"yaml", "hdf5"}.contains(QPointDataInputFile.Format))
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throw std::runtime_error(fmt::format
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("Unknown format: {}, should be \"yaml\" or \"hdf5\".", QPointDataInputFile.Format));
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if (auto value = node["QPointDataOutputFile"])
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for (unsigned i = 0; i < value.size(); i++)
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||||
{
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auto& _ = QPointDataOutputFile.emplace_back();
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_.FileName = value[i]["FileName"].as<std::string>();
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_.Format = value[i]["Format"].as<std::string>();
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if (!std::set<std::string>{"yaml", "hdf5"}.contains(_.Format))
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throw std::runtime_error(fmt::format
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("Unknown format: {}, should be \"yaml\" or \"hdf5\".", _.Format));
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}
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}
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if (AtomPositionInputFile.Format == "yaml")
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{
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auto node = YAML::LoadFile(AtomPositionInputFile.FileName);
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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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auto super_cell = SuperCellDeformation.value_or(Eigen::Matrix3d::Identity())
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* SuperCellMultiplier.cast<double>().asDiagonal() * PrimativeCell;
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AtomPosition = atom_position_to_super_cell * super_cell;
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||||
}
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if (QPointDataInputFile.Format == "yaml")
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||||
{
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||||
auto node = YAML::LoadFile(QPointDataInputFile.FileName);
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auto phonon = node["phonon"].as<std::vector<YAML::Node>>();
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||||
QPointData.resize(phonon.size());
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for (unsigned i = 0; i < phonon.size(); i++)
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||||
{
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||||
QPointData[i].QPoint.resize(3);
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for (unsigned j = 0; j < 3; j++)
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||||
QPointData[i].QPoint(j) = phonon[i]["q-position"][j].as<double>();
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||||
auto band = phonon[i]["band"].as<std::vector<YAML::Node>>();
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QPointData[i].ModeData.resize(band.size());
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||||
for (unsigned j = 0; j < band.size(); j++)
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||||
{
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||||
QPointData[i].ModeData[j].Frequency = band[j]["frequency"].as<double>();
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auto eigenvector_vectors = band[j]["eigenvector"]
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.as<std::vector<std::vector<std::vector<double>>>>();
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Eigen::MatrixX3cd eigenvectors(AtomPosition.rows(), 3);
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for (unsigned k = 0; k < AtomPosition.rows(); k++)
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for (unsigned l = 0; l < 3; l++)
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eigenvectors(k, l)
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= eigenvector_vectors[k][l][0] + 1i * eigenvector_vectors[k][l][1];
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// 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)
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||||
// 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)
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||||
auto& AtomMovement = QPointData[i].ModeData[j].AtomMovement;
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// AtomMovement = eigenvectors.array().colwise() * (-2 * std::numbers::pi_v<double> * 1i
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// * (atom_position_to_super_cell * input.QPointData[i].QPoint)).array().exp();
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// AtomMovement /= AtomMovement.norm();
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// phonopy 似乎已经进行了相位的转换！为什么？
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||||
AtomMovement = eigenvectors / eigenvectors.norm();
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||||
}
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||||
}
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||||
}
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||||
else if (QPointDataInputFile.Format == "hdf5")
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||||
{
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||||
HighFive::File file(QPointDataInputFile.FileName, 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")
|
||||
.read<std::vector<std::vector<std::vector<double>>>>();
|
||||
QPointData.resize(size[0] * size[1]);
|
||||
for (unsigned i = 0; i < size[0]; i++)
|
||||
for (unsigned j = 0; j < size[1]; j++)
|
||||
{
|
||||
QPointData[i * size[1] + j].QPoint = Eigen::Vector3d(path[i][j].data());
|
||||
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][l * 3 + m][k].r + eigenvector_vector[i][j][l * 3 + m][k].i * 1i;
|
||||
QPointData[i * size[1] + j].ModeData[k].AtomMovement = eigenvectors / eigenvectors.norm();
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
inline void Output::write(std::string filename, std::string format, unsigned percision)
|
||||
{
|
||||
if (format == "yaml")
|
||||
std::ofstream(filename) << [&]
|
||||
{
|
||||
std::stringstream print;
|
||||
print << "QPointData:\n";
|
||||
for (auto& qpoint: QPointData)
|
||||
{
|
||||
print << fmt::format(" - QPoint: [ {1:.{0}f}, {2:.{0}f}, {3:.{0}f} ]\n",
|
||||
percision, qpoint.QPoint[0], qpoint.QPoint[1], qpoint.QPoint[2]);
|
||||
print << fmt::format(" Source: [ {1:.{0}f}, {2:.{0}f}, {3:.{0}f} ]\n",
|
||||
percision, 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",
|
||||
percision, mode.Frequency, mode.Weight);
|
||||
}
|
||||
return print.str();
|
||||
}();
|
||||
else if (format == "yaml-human-readable")
|
||||
{
|
||||
Output output;
|
||||
std::map<unsigned, std::vector<decltype(QPointData)::const_iterator>>
|
||||
meta_qpoint_to_sub_qpoint_iterators;
|
||||
for (auto it = QPointData.begin(); it != QPointData.end(); it++)
|
||||
meta_qpoint_to_sub_qpoint_iterators[it->SourceIndex_].push_back(it);
|
||||
for (auto [meta_qpoint_index, sub_qpoint_iterators] : meta_qpoint_to_sub_qpoint_iterators)
|
||||
for (auto& qpoint : sub_qpoint_iterators)
|
||||
{
|
||||
std::map<double, double> frequency_to_weight;
|
||||
for (unsigned i_of_mode = 0; i_of_mode < qpoint->ModeData.size(); i_of_mode++)
|
||||
{
|
||||
auto frequency = qpoint->ModeData[i_of_mode].Frequency;
|
||||
auto weight = qpoint->ModeData[i_of_mode].Weight;
|
||||
auto it_lower = frequency_to_weight.lower_bound(frequency - 0.1);
|
||||
auto it_upper = frequency_to_weight.upper_bound(frequency + 0.1);
|
||||
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;
|
||||
}
|
||||
auto& _ = output.QPointData.emplace_back();
|
||||
_.QPoint = qpoint->QPoint;
|
||||
_.Source = qpoint->Source;
|
||||
_.SourceIndex_ = qpoint->SourceIndex_;
|
||||
for (auto [frequency, weight] : frequency_to_weight)
|
||||
if (weight > 0.1)
|
||||
{
|
||||
auto& __ = _.ModeData.emplace_back();
|
||||
__.Frequency = frequency;
|
||||
__.Weight = weight;
|
||||
}
|
||||
}
|
||||
}
|
||||
output.write(filename, "yaml", 3);
|
||||
}
|
||||
else if (format == "zpp")
|
||||
{
|
||||
auto [data, out] = zpp::bits::data_out();
|
||||
std::basic_ofstream<std::byte>(filename, std::ios::binary)
|
||||
<< std::basic_string_view{data.data(), data.size()};
|
||||
}
|
||||
}
|
||||
|
||||
inline 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
|
||||
};
|
||||
}
|
||||
440
main.cpp
440
main.cpp
@ -1,440 +0,0 @@
|
||||
# include <iostream>
|
||||
# include <array>
|
||||
# include <numbers>
|
||||
# include <numeric>
|
||||
# include <fstream>
|
||||
# include <optional>
|
||||
# include <array>
|
||||
# include <utility>
|
||||
# include <execution>
|
||||
# include <syncstream>
|
||||
# include <yaml-cpp/yaml.h>
|
||||
# include <eigen3/Eigen/Dense>
|
||||
# include <concurrencpp/concurrencpp.h>
|
||||
# include <fmt/format.h>
|
||||
# include <highfive/H5File.hpp>
|
||||
|
||||
using namespace std::literals;
|
||||
|
||||
struct PhonopyComplex { double r, i; };
|
||||
HighFive::CompoundType create_compound_complex()
|
||||
{ return {{"r", HighFive::AtomicType<double>{}}, {"i", HighFive::AtomicType<double>{}}}; }
|
||||
HIGHFIVE_REGISTER_TYPE(PhonopyComplex, create_compound_complex)
|
||||
|
||||
// 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;
|
||||
// 单胞到超胞的格矢转换时用到的矩阵
|
||||
// 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
|
||||
// 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
|
||||
// SuperCell = (SuperCellDeformation * SuperCellMultiplier.asDiagonal()) * PrimativeCell
|
||||
// ReciprocalPrimativeCell = (SuperCellDeformation * SuperCellMultiplier.asDiagonal()).transpose()
|
||||
// * ReciprocalSuperCell
|
||||
// Position = PositionToCell(line vector) * Cell
|
||||
// InversePosition = InversePositionToCell(line vector) * ReciprocalCell
|
||||
// PositionToSuperCell(line vector) * SuperCell = PositionToPrimativeCell(line vector) * PrimativeCell
|
||||
// ReciprocalPositionToSuperCell(line vector) * ReciprocalSuperCell
|
||||
// = ReciprocalPositionToPrimativeCell(line vector) * ReciprocalPrimativeCell
|
||||
Eigen::Vector<unsigned, 3> SuperCellMultiplier;
|
||||
Eigen::Matrix<double, 3, 3> SuperCellDeformation;
|
||||
// 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;
|
||||
|
||||
// 是否调整输出结果, 使得结果中的模式适合人类阅读. 默认为 true.
|
||||
// 这包括合并相近的模式, 去除权重过小的模式, 限制输出的小数位数.
|
||||
// 如果想用结果来进一步画图, 则建议关闭.
|
||||
std::optional<bool> Filter;
|
||||
|
||||
// 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;
|
||||
|
||||
Input(std::string yaml_file, std::optional<std::string> hdf5_file);
|
||||
};
|
||||
|
||||
struct Output
|
||||
{
|
||||
// 关于各个 Q 点的数据
|
||||
struct QPointDataType_
|
||||
{
|
||||
// Q 点的坐标，单位为单胞的倒格矢
|
||||
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;
|
||||
};
|
||||
|
||||
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 || argc > 5)
|
||||
throw std::runtime_error("Usage: " + std::string(argv[0]) + " input.yaml [input.hdf5] output.yaml");
|
||||
|
||||
std::cerr << "Reading input file..." << std::flush;
|
||||
Input input(argv[1], argc > 3 ? std::make_optional(argv[2]) : std::nullopt);
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
// 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
|
||||
// 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。
|
||||
// 这里 xyz_of_diff_of_sub_qpoint 即表示这个相对位置。
|
||||
// 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。
|
||||
// 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
|
||||
// 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）
|
||||
std::cerr << "Calculating basis..." << std::flush;
|
||||
std::vector<std::vector<Eigen::VectorXcd>> basis(input.SuperCellMultiplier.prod());
|
||||
// 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。
|
||||
// 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
|
||||
for (auto [xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell, i_of_sub_qpoint]
|
||||
: triplet_sequence(input.SuperCellMultiplier))
|
||||
{
|
||||
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 diff_of_sub_qpoint_by_reciprocal_primative_cell = xyz_of_basis.cast<double>()
|
||||
+ input.SuperCellMultiplier.cast<double>().cwiseInverse().asDiagonal()
|
||||
* xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell.cast<double>();
|
||||
// 将 q 点坐标转换为埃^-1
|
||||
auto qpoint = (diff_of_sub_qpoint_by_reciprocal_primative_cell.transpose()
|
||||
* (input.PrimativeCell.transpose().inverse())).transpose();
|
||||
// 计算基矢
|
||||
basis[i_of_sub_qpoint][i_of_basis]
|
||||
= (2i * std::numbers::pi_v<double> * (input.AtomPosition * qpoint)).array().exp();
|
||||
}
|
||||
}
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
// 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(sub qpoint)
|
||||
std::vector<std::vector<std::vector<double>>> projection_coefficient(input.QPointData.size());
|
||||
std::atomic<unsigned> finished_qpoint(0);
|
||||
// 对每个 q 点并行
|
||||
std::transform
|
||||
(
|
||||
std::execution::par, input.QPointData.begin(), input.QPointData.end(),
|
||||
projection_coefficient.begin(), [&](const auto& qpoint_data)
|
||||
{
|
||||
std::osyncstream(std::cerr) << fmt::format("\rCalculating projection coefficient...({}/{})",
|
||||
finished_qpoint, input.QPointData.size()) << std::flush;
|
||||
std::vector<std::vector<double>> projection_coefficient(qpoint_data.ModeData.size());
|
||||
// 这里, qpoint_data 和 projection_coefficient 均指对应于一个 q 点的数据
|
||||
for (unsigned i_of_mode = 0; i_of_mode < qpoint_data.ModeData.size(); i_of_mode++)
|
||||
{
|
||||
auto& _ = projection_coefficient[i_of_mode];
|
||||
_.resize(input.SuperCellMultiplier.prod());
|
||||
for (unsigned i_of_sub_qpoint = 0; i_of_sub_qpoint < input.SuperCellMultiplier.prod(); 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, 然后求模方和
|
||||
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().conjugate() * qpoint_data.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;
|
||||
}
|
||||
finished_qpoint++;
|
||||
std::osyncstream(std::cerr) << fmt::format("\rCalculating projection coefficient...({}/{})",
|
||||
finished_qpoint, input.QPointData.size()) << std::flush;
|
||||
return projection_coefficient;
|
||||
});
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
// 填充输出对象
|
||||
std::cerr << "Filling output object..." << std::flush;
|
||||
Output output;
|
||||
for (unsigned i_of_qpoint = 0; i_of_qpoint < input.QPointData.size(); i_of_qpoint++)
|
||||
{
|
||||
// 当 SuperCellDeformation 不是单位矩阵时, input.QPointData[i_of_qpoint].QPoint 不一定在 reciprocal_primative_cell 中
|
||||
// 需要首先将 q 点平移数个周期, 进入不包含 SuperCellDeformation 的超胞的倒格子中
|
||||
auto qpoint_by_reciprocal_super_cell_in_modified_reciprocal_super_cell = [&]
|
||||
{
|
||||
auto current_qpoint = input.QPointData[i_of_qpoint].QPoint;
|
||||
// 给一个 q 点打分
|
||||
// 计算这个 q 点以 modified_reciprocal_supre_cell 为单位的坐标, 依次考虑每个维度, 总分为每个维度之和.
|
||||
// 如果这个坐标大于 0 小于 1, 则打 0 分.
|
||||
// 如果这个坐标小于 0, 则打这个坐标的相反数分.
|
||||
// 如果这个坐标大于 1, 则打这个坐标减去 1 的分.
|
||||
auto score = [&](Eigen::Vector3d qpoint_by_reciprocal_super_cell)
|
||||
{
|
||||
// SuperCell = SuperCellDeformation * SuperCellMultiplier.asDiagonal() * PrimativeCell
|
||||
// ModifiedSuperCell = SuperCellMultiplier.asDiagonal() * PrimativeCell
|
||||
// ReciprocalSuperCell = SuperCell.inverse().transpose()
|
||||
// ReciprocalModifiedSuperCell = ModifiedSuperCell.inverse().transpose()
|
||||
// qpoint.transpose() = qpoint_by_reciprocal_super_cell.transpose() * ReciprocalSuperCell
|
||||
// qpoint.transpose() = qpoint_by_reciprocal_modified_super_cell.transpose() * ReciprocalModifiedSuperCell
|
||||
auto qpoint_by_reciprocal_modified_super_cell =
|
||||
(input.SuperCellDeformation.inverse() * qpoint_by_reciprocal_super_cell).eval();
|
||||
double score = 0;
|
||||
for (unsigned i = 0; i < 3; i++)
|
||||
{
|
||||
auto coordinate = qpoint_by_reciprocal_modified_super_cell[i];
|
||||
if (coordinate < 0)
|
||||
score -= coordinate;
|
||||
else if (coordinate > 1)
|
||||
score += coordinate - 1;
|
||||
}
|
||||
return score;
|
||||
};
|
||||
while (score(current_qpoint) > 0)
|
||||
{
|
||||
double min_score = std::numeric_limits<double>::max();
|
||||
Eigen::Vector3d min_score_qpoint;
|
||||
for (int x = -1; x <= 1; x++)
|
||||
for (int y = -1; y <= 1; y++)
|
||||
for (int z = -1; z <= 1; z++)
|
||||
{
|
||||
auto this_qpoint = (current_qpoint
|
||||
+ Eigen::Matrix<int, 3, 1>{{x}, {y}, {z}}.cast<double>()).eval();
|
||||
auto this_score = score(this_qpoint);
|
||||
if (this_score < min_score)
|
||||
{
|
||||
min_score = this_score;
|
||||
min_score_qpoint = this_qpoint;
|
||||
}
|
||||
}
|
||||
current_qpoint = min_score_qpoint;
|
||||
}
|
||||
return current_qpoint;
|
||||
}();
|
||||
for (auto [xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell, i_of_sub_qpoint]
|
||||
: triplet_sequence(input.SuperCellMultiplier))
|
||||
{
|
||||
auto& _ = output.QPointData.emplace_back();
|
||||
// 这一步推导过程在计算 score 的函数中
|
||||
auto qpoint_by_reciprocal_modified_super_cell_in_modified_reciprocal_super_cell =
|
||||
input.SuperCellDeformation.inverse() * qpoint_by_reciprocal_super_cell_in_modified_reciprocal_super_cell;
|
||||
auto reciprocal_modified_super_cell =
|
||||
(input.SuperCellMultiplier.cast<double>().asDiagonal() * input.PrimativeCell).inverse().transpose();
|
||||
// sub qpoint 的坐标，单位为埃^-1
|
||||
auto sub_qpoint = ((xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell.cast<double>()
|
||||
+ qpoint_by_reciprocal_modified_super_cell_in_modified_reciprocal_super_cell)
|
||||
.transpose() * reciprocal_modified_super_cell).transpose();
|
||||
// 将坐标转换为相对于单胞的倒格矢的坐标并写入
|
||||
// 由 sub_qpoint.transpose() = sub_qpoint_by_reciprocal_primative_cell.transpose()
|
||||
// * PrimativeCell.transpose().inverse()
|
||||
// 得到 sub_qpoint_by_reciprocal_primative_cell = PrimativeCell * sub_qpoint
|
||||
_.QPoint = input.PrimativeCell * sub_qpoint;
|
||||
_.Source = input.QPointData[i_of_qpoint].QPoint;
|
||||
if (input.Filter.value_or(true))
|
||||
{
|
||||
// 从小到大枚举所有的模式，并将相近的模式（相差小于 0.1 THz）合并
|
||||
std::map<double, double> frequency_to_weight;
|
||||
for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_qpoint].ModeData.size(); i_of_mode++)
|
||||
{
|
||||
auto frequency = input.QPointData[i_of_qpoint].ModeData[i_of_mode].Frequency;
|
||||
auto weight = projection_coefficient[i_of_qpoint][i_of_mode][i_of_sub_qpoint];
|
||||
auto it_lower = frequency_to_weight.lower_bound(frequency - 0.1);
|
||||
auto it_upper = frequency_to_weight.upper_bound(frequency + 0.1);
|
||||
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 0.1 的模式
|
||||
for (auto& mode : frequency_to_weight)
|
||||
if (mode.second > 0.1)
|
||||
{
|
||||
auto& __ = _.ModeData.emplace_back();
|
||||
__.Frequency = mode.first;
|
||||
__.Weight = mode.second;
|
||||
}
|
||||
}
|
||||
else
|
||||
for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_qpoint].ModeData.size(); i_of_mode++)
|
||||
{
|
||||
auto& __ = _.ModeData.emplace_back();
|
||||
__.Frequency = input.QPointData[i_of_qpoint].ModeData[i_of_mode].Frequency;
|
||||
__.Weight = projection_coefficient[i_of_qpoint][i_of_mode][i_of_sub_qpoint];
|
||||
}
|
||||
}
|
||||
}
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
// YAML 输出得太丑了，我来自己写
|
||||
std::cerr << "Writing output file..." << std::flush;
|
||||
std::ofstream(argc > 3 ? argv[3] : argv[2]) << [&]
|
||||
{
|
||||
std::stringstream print;
|
||||
auto format = input.Filter.value_or(true) ? 3 : 10;
|
||||
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();
|
||||
}();
|
||||
std::cerr << "Done." << std::endl;
|
||||
}
|
||||
|
||||
// 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.
|
||||
Input::Input(std::string yaml_file, std::optional<std::string> hdf5_file)
|
||||
{
|
||||
auto node = YAML::LoadFile(yaml_file);
|
||||
for (unsigned i = 0; i < 3; i++)
|
||||
for (unsigned j = 0; j < 3; j++)
|
||||
PrimativeCell(i, j) = node["lattice"][i][j].as<double>();
|
||||
|
||||
for (unsigned i = 0; i < 3; i++)
|
||||
SuperCellMultiplier(i) = node["SuperCellMultiplier"][i].as<int>();
|
||||
|
||||
for (unsigned i = 0; i < 3; i++)
|
||||
for (unsigned j = 0; j < 3; j++)
|
||||
SuperCellDeformation(i, j) = node["SuperCellDeformation"][i][j].as<double>();
|
||||
|
||||
for (unsigned i = 0; i < 3; i++)
|
||||
PrimativeCellBasisNumber(i) = node["PrimativeCellBasisNumber"][i].as<int>();
|
||||
|
||||
if (auto value = node["Filter"])
|
||||
Filter = 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>();
|
||||
AtomPosition = atom_position_to_super_cell
|
||||
* (SuperCellDeformation * SuperCellMultiplier.cast<double>().asDiagonal() * PrimativeCell);
|
||||
|
||||
if (hdf5_file)
|
||||
{
|
||||
HighFive::File file(*hdf5_file, HighFive::File::ReadOnly);
|
||||
auto size = file.getDataSet("/frequency").getDimensions();
|
||||
auto frequency = file.getDataSet("/frequency")
|
||||
.read<std::vector<std::vector<std::vector<double>>>>();
|
||||
auto eigenvector_vector = file.getDataSet("/eigenvector")
|
||||
.read<std::vector<std::vector<std::vector<std::vector<PhonopyComplex>>>>>();
|
||||
auto path = file.getDataSet("/path")
|
||||
.read<std::vector<std::vector<std::vector<double>>>>();
|
||||
QPointData.resize(size[0] * size[1]);
|
||||
for (unsigned i = 0; i < size[0]; i++)
|
||||
for (unsigned j = 0; j < size[1]; j++)
|
||||
{
|
||||
QPointData[i * size[1] + j].QPoint = Eigen::Vector3d(path[i][j].data());
|
||||
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][l * 3 + m][k].r + eigenvector_vector[i][j][l * 3 + m][k].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();
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
179
src/ufo.cpp
Normal file
179
src/ufo.cpp
Normal file
@ -0,0 +1,179 @@
|
||||
# include <ufo/ufo.impl.hpp>
|
||||
|
||||
int main(int argc, const char** argv)
|
||||
{
|
||||
if (argc != 2)
|
||||
throw std::runtime_error(fmt::format("Usage: {} config.yaml", argv[0]));
|
||||
|
||||
std::cerr << "Reading input file..." << std::flush;
|
||||
Input input(argv[1]);
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
// 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
|
||||
// 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。
|
||||
// 这里 xyz_of_diff_of_sub_qpoint 即表示这个相对位置。
|
||||
// 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。
|
||||
// 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
|
||||
// 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）
|
||||
std::cerr << "Calculating basis..." << std::flush;
|
||||
std::vector<std::vector<Eigen::VectorXcd>> basis(input.SuperCellMultiplier.prod());
|
||||
// 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。
|
||||
// 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
|
||||
for (auto [xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell, i_of_sub_qpoint]
|
||||
: triplet_sequence(input.SuperCellMultiplier))
|
||||
{
|
||||
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 diff_of_sub_qpoint_by_reciprocal_primative_cell = xyz_of_basis.cast<double>()
|
||||
+ input.SuperCellMultiplier.cast<double>().cwiseInverse().asDiagonal()
|
||||
* xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell.cast<double>();
|
||||
// 将 q 点坐标转换为埃^-1
|
||||
auto qpoint = (diff_of_sub_qpoint_by_reciprocal_primative_cell.transpose()
|
||||
* (input.PrimativeCell.transpose().inverse())).transpose();
|
||||
// 计算基矢
|
||||
basis[i_of_sub_qpoint][i_of_basis]
|
||||
= (2i * std::numbers::pi_v<double> * (input.AtomPosition * qpoint)).array().exp();
|
||||
}
|
||||
}
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
// 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(sub qpoint)
|
||||
std::vector<std::vector<std::vector<double>>> projection_coefficient(input.QPointData.size());
|
||||
std::atomic<unsigned> finished_qpoint(0);
|
||||
// 对每个 q 点并行
|
||||
std::transform
|
||||
(
|
||||
std::execution::par, input.QPointData.begin(), input.QPointData.end(),
|
||||
projection_coefficient.begin(), [&](const auto& qpoint_data)
|
||||
{
|
||||
std::osyncstream(std::cerr) << fmt::format("\rCalculating projection coefficient...({}/{})",
|
||||
finished_qpoint, input.QPointData.size()) << std::flush;
|
||||
std::vector<std::vector<double>> projection_coefficient(qpoint_data.ModeData.size());
|
||||
// 这里, qpoint_data 和 projection_coefficient 均指对应于一个 q 点的数据
|
||||
for (unsigned i_of_mode = 0; i_of_mode < qpoint_data.ModeData.size(); i_of_mode++)
|
||||
{
|
||||
auto& _ = projection_coefficient[i_of_mode];
|
||||
_.resize(input.SuperCellMultiplier.prod());
|
||||
for (unsigned i_of_sub_qpoint = 0; i_of_sub_qpoint < input.SuperCellMultiplier.prod(); 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, 然后求模方和
|
||||
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().conjugate() * qpoint_data.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;
|
||||
}
|
||||
finished_qpoint++;
|
||||
std::osyncstream(std::cerr) << fmt::format("\rCalculating projection coefficient...({}/{})",
|
||||
finished_qpoint, input.QPointData.size()) << std::flush;
|
||||
return projection_coefficient;
|
||||
});
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
// 填充输出对象
|
||||
std::cerr << "Filling output object..." << std::flush;
|
||||
Output output;
|
||||
for (unsigned i_of_qpoint = 0; i_of_qpoint < input.QPointData.size(); i_of_qpoint++)
|
||||
{
|
||||
// 当 SuperCellDeformation 不是单位矩阵时, input.QPointData[i_of_qpoint].QPoint 不一定在 reciprocal_primative_cell 中
|
||||
// 需要首先将 q 点平移数个周期, 进入不包含 SuperCellDeformation 的超胞的倒格子中
|
||||
auto qpoint_by_reciprocal_super_cell_in_modified_reciprocal_super_cell
|
||||
= !input.SuperCellDeformation ? input.QPointData[i_of_qpoint].QPoint : [&]
|
||||
{
|
||||
auto current_qpoint = input.QPointData[i_of_qpoint].QPoint;
|
||||
// 给一个 q 点打分
|
||||
// 计算这个 q 点以 modified_reciprocal_supre_cell 为单位的坐标, 依次考虑每个维度, 总分为每个维度之和.
|
||||
// 如果这个坐标大于 0 小于 1, 则打 0 分.
|
||||
// 如果这个坐标小于 0, 则打这个坐标的相反数分.
|
||||
// 如果这个坐标大于 1, 则打这个坐标减去 1 的分.
|
||||
auto score = [&](Eigen::Vector3d qpoint_by_reciprocal_super_cell)
|
||||
{
|
||||
// SuperCell = SuperCellDeformation * SuperCellMultiplier.asDiagonal() * PrimativeCell
|
||||
// ModifiedSuperCell = SuperCellMultiplier.asDiagonal() * PrimativeCell
|
||||
// ReciprocalSuperCell = SuperCell.inverse().transpose()
|
||||
// ReciprocalModifiedSuperCell = ModifiedSuperCell.inverse().transpose()
|
||||
// qpoint.transpose() = qpoint_by_reciprocal_super_cell.transpose() * ReciprocalSuperCell
|
||||
// qpoint.transpose() = qpoint_by_reciprocal_modified_super_cell.transpose() * ReciprocalModifiedSuperCell
|
||||
auto qpoint_by_reciprocal_modified_super_cell =
|
||||
(input.SuperCellDeformation->inverse() * qpoint_by_reciprocal_super_cell).eval();
|
||||
double score = 0;
|
||||
for (unsigned i = 0; i < 3; i++)
|
||||
{
|
||||
auto coordinate = qpoint_by_reciprocal_modified_super_cell[i];
|
||||
if (coordinate < 0)
|
||||
score -= coordinate;
|
||||
else if (coordinate > 1)
|
||||
score += coordinate - 1;
|
||||
}
|
||||
return score;
|
||||
};
|
||||
while (score(current_qpoint) > 0)
|
||||
{
|
||||
double min_score = std::numeric_limits<double>::max();
|
||||
Eigen::Vector3d min_score_qpoint;
|
||||
for (int x = -1; x <= 1; x++)
|
||||
for (int y = -1; y <= 1; y++)
|
||||
for (int z = -1; z <= 1; z++)
|
||||
{
|
||||
auto this_qpoint = (current_qpoint
|
||||
+ Eigen::Matrix<int, 3, 1>{{x}, {y}, {z}}.cast<double>()).eval();
|
||||
auto this_score = score(this_qpoint);
|
||||
if (this_score < min_score)
|
||||
{
|
||||
min_score = this_score;
|
||||
min_score_qpoint = this_qpoint;
|
||||
}
|
||||
}
|
||||
current_qpoint = min_score_qpoint;
|
||||
}
|
||||
return current_qpoint;
|
||||
}();
|
||||
for (auto [xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell, i_of_sub_qpoint]
|
||||
: triplet_sequence(input.SuperCellMultiplier))
|
||||
{
|
||||
auto& _ = output.QPointData.emplace_back();
|
||||
// 这一步推导过程在计算 score 的函数中
|
||||
auto qpoint_by_reciprocal_modified_super_cell_in_modified_reciprocal_super_cell =
|
||||
input.SuperCellDeformation.value_or(Eigen::Matrix3d::Identity()).inverse()
|
||||
* qpoint_by_reciprocal_super_cell_in_modified_reciprocal_super_cell;
|
||||
auto reciprocal_modified_super_cell =
|
||||
(input.SuperCellMultiplier.cast<double>().asDiagonal() * input.PrimativeCell).inverse().transpose();
|
||||
// sub qpoint 的坐标，单位为埃^-1
|
||||
auto sub_qpoint = ((xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell.cast<double>()
|
||||
+ qpoint_by_reciprocal_modified_super_cell_in_modified_reciprocal_super_cell)
|
||||
.transpose() * reciprocal_modified_super_cell).transpose();
|
||||
// 将坐标转换为相对于单胞的倒格矢的坐标并写入
|
||||
// 由 sub_qpoint.transpose() = sub_qpoint_by_reciprocal_primative_cell.transpose()
|
||||
// * PrimativeCell.transpose().inverse()
|
||||
// 得到 sub_qpoint_by_reciprocal_primative_cell = PrimativeCell * sub_qpoint
|
||||
_.QPoint = input.PrimativeCell * sub_qpoint;
|
||||
_.Source = input.QPointData[i_of_qpoint].QPoint;
|
||||
_.SourceIndex_ = i_of_qpoint;
|
||||
for (unsigned i_of_mode = 0; i_of_mode < input.QPointData[i_of_qpoint].ModeData.size(); i_of_mode++)
|
||||
{
|
||||
auto& __ = _.ModeData.emplace_back();
|
||||
__.Frequency = input.QPointData[i_of_qpoint].ModeData[i_of_mode].Frequency;
|
||||
__.Weight = projection_coefficient[i_of_qpoint][i_of_mode][i_of_sub_qpoint];
|
||||
}
|
||||
}
|
||||
}
|
||||
std::cerr << "Done." << std::endl;
|
||||
|
||||
std::cerr << "Writing output file..." << std::flush;
|
||||
for (auto& output_file : input.QPointDataOutputFile)
|
||||
output.write(output_file.FileName, output_file.Format);
|
||||
std::cerr << "Done." << std::endl;
|
||||
}
|
||||
13
xmake.lua
Normal file
13
xmake.lua
Normal file
@ -0,0 +1,13 @@
|
||||
add_rules("mode.debug", "mode.release")
|
||||
set_languages("cxx23")
|
||||
|
||||
add_requires("pkgconfig::tbb")
|
||||
add_requires("pkgconfig::yaml-cpp")
|
||||
|
||||
target("ufo")
|
||||
set_kind("binary")
|
||||
add_includedirs("include")
|
||||
add_files("src/ufo.cpp")
|
||||
add_packages("tbb")
|
||||
add_packages("yaml-cpp")
|
||||
|
||||
Loading…
Reference in New Issue
Block a user