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不再平移 Q 点

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This commit is contained in:
陈浩南 2023-10-07 15:52:49 +08:00
parent f74258e8fc
commit e078cea43c
7 changed files with 45 additions and 76 deletions
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2
include/ufo/unfold.hpp
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@ -162,7 +162,7 @@ namespace ufo
const decltype(InputType::SuperCellMultiplier)& super_cell_multiplier,
const decltype(InputType::SuperCellDeformation)& super_cell_deformation,
const std::vector<std::reference_wrapper<const decltype
(InputType::QpointDataType::Qpoint)>>& qpoint,
(InputType::QpointDataType::Qpoint)>>& meta_qpoint_by_reciprocal_super_cell,
const std::vector<std::vector<std::reference_wrapper<const decltype
(InputType::QpointDataType::ModeDataType::Frequency)>>>& frequency,
const ProjectionCoefficientType_& projection_coefficient

99
src/unfold.cpp
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@ -418,98 +418,67 @@ namespace ufo
const decltype(InputType::SuperCellMultiplier)& super_cell_multiplier,
const decltype(InputType::SuperCellDeformation)& super_cell_deformation,
const std::vector<std::reference_wrapper<const decltype
(InputType::QpointDataType::Qpoint)>>& qpoint,
(InputType::QpointDataType::Qpoint)>>& meta_qpoint_by_reciprocal_super_cell,
const std::vector<std::vector<std::reference_wrapper<const decltype
(InputType::QpointDataType::ModeDataType::Frequency)>>>& frequency,
const ProjectionCoefficientType_& projection_coefficient
)
{
OutputType output;
for (unsigned i_of_qpoint = 0, num_of_mode_manipulated = 0; i_of_qpoint < qpoint.size(); i_of_qpoint++)
for
(
unsigned i_of_meta_qpoint = 0, num_of_mode_manipulated = 0;
i_of_meta_qpoint < meta_qpoint_by_reciprocal_super_cell.size();
i_of_meta_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 (称为 ModifiedSupreCell) 的倒格子中
auto qpoint_by_reciprocal_modified_super_cell_in_reciprocal_modified_super_cell
= !super_cell_deformation ? qpoint[i_of_qpoint].get() : [&]
{
auto current_qpoint = qpoint[i_of_qpoint].get();
// 给一个 q 点打分
// 计算这个 q 点以 reciprocal_modified_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 =
(super_cell_deformation->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>();
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 super_cell_deformation->inverse() * current_qpoint;
}();
for (auto [xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell, i_of_sub_qpoint]
: triplet_sequence(super_cell_multiplier))
{
auto& _ = output.QpointData.emplace_back();
/*
SubQpointByReciprocalModifiedSuperCell = XyzOfDiffOfSubQpointByReciprocalModifiedSuperCell +
QpointInReciprocalModifiedSuperCellByReciprocalModifiedSuperCell;
MetaQpointByReciprocalModifiedSuperCell;
SubQpoint = SubQpointByReciprocalModifiedSuperCell.transpose() * ReciprocalModifiedSuperCell;
SubQpoint = SubQpointByReciprocalPrimativeCell.transpose() * ReciprocalPrimativeCell;
ReciprocalModifiedSuperCell = ModifiedSuperCell.inverse().transpose();
ReciprocalPrimativeCell = PrimativeCell.inverse().transpose();
ModifiedSuperCell = SuperCellMultiplier.asDiagonal() * PrimativeCell;
MetaQpoint = MetaQpointByReciprocalModifiedSuperCell.transpose() * ReciprocalModifiedSuperCell;
MetaQpoint = MetaQpointByReciprocalSuperCell.transpose() * ReciprocalSuperCell;
ReciprocalModifiedSuperCell = ModifiedSuperCell.inverse().transpose();
ReciprocalSuperCell = SuperCell.inverse().transpose();
ModifiedSuperCell = SuperCellDeformation * SuperCell;
SuperCell = SuperCellMultiplier.asDiagonal() * PrimativeCell;
整理可以得到:
SubQpointByReciprocalPrimativeCell = SuperCellMultiplier.asDiagonal().inverse() *
(XyzOfDiffOfSubQpointByReciprocalModifiedSuperCell +
QpointInReciprocalModifiedSuperCellByReciprocalModifiedSuperCell);
SuperCellDeformation * MetaQpointByReciprocalSuperCell);
但注意到, 这样得到的 SubQpoint 可能不在 ReciprocalPrimativeCell 中
(当 SuperCellDeformation 不是单位矩阵时, 边界附近的一两条 SubQpoint 会出现这种情况).
解决办法是, 在赋值时, 仅取 SubQpointByReciprocalPrimativeCell 的小数部分.
*/
_.Qpoint = super_cell_multiplier.cast<double>().cwiseInverse().asDiagonal()
* (xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell.cast<double>()
+ qpoint_by_reciprocal_modified_super_cell_in_reciprocal_modified_super_cell);
_.Source = qpoint[i_of_qpoint];
_.SourceIndex_ = i_of_qpoint;
for (unsigned i_of_mode = 0; i_of_mode < frequency[i_of_qpoint].size(); i_of_mode++)
auto sub_qpoint_by_reciprocal_primative_cell =
(
super_cell_multiplier.cast<double>().cwiseInverse().asDiagonal()
* (
xyz_of_diff_of_sub_qpoint_by_reciprocal_modified_super_cell.cast<double>()
+ super_cell_deformation.value_or(Eigen::Matrix3d::Identity())
* meta_qpoint_by_reciprocal_super_cell[i_of_meta_qpoint].get().cast<double>()
)
).eval();
_.Qpoint = sub_qpoint_by_reciprocal_primative_cell.array()
- sub_qpoint_by_reciprocal_primative_cell.array().floor();
_.Source = meta_qpoint_by_reciprocal_super_cell[i_of_meta_qpoint];
_.SourceIndex_ = i_of_meta_qpoint;
for (unsigned i_of_mode = 0; i_of_mode < frequency[i_of_meta_qpoint].size(); i_of_mode++)
{
auto& __ = _.ModeData.emplace_back();
__.Frequency = frequency[i_of_qpoint][i_of_mode];
__.Frequency = frequency[i_of_meta_qpoint][i_of_mode];
__.Weight = projection_coefficient[num_of_mode_manipulated + i_of_mode][i_of_sub_qpoint];
}
}
num_of_mode_manipulated += frequency[i_of_qpoint].size();
num_of_mode_manipulated += frequency[i_of_meta_qpoint].size();
}
return output;
}

4
test/14.2.2.4.unfold.yaml
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@ -5,8 +5,8 @@ PrimativeCell:
SuperCellMultiplier: [ 3, 1, 1 ]
PrimativeCellBasisNumber: [ 8, 8, 8 ]
AtomPositionInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.2/14.2.2.4/band.yaml", Format: "yaml" }
QPointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.2/14.2.2.4/band.yaml", Format: "yaml" }
QPointDataOutputFile:
QpointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.2/14.2.2.4/band.yaml", Format: "yaml" }
QpointDataOutputFile:
- { FileName: "test/14.2.2.4.result.yaml", Format: "yaml" }
- { FileName: "test/14.2.2.4.result.human-readable.yaml", Format: "yaml-human-readable" }
- { FileName: "test/14.2.2.4.result.zpp", Format: "zpp" }

4
test/14.2.2.5.unfold.yaml
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@ -5,8 +5,8 @@ PrimativeCell:
SuperCellMultiplier: [ 3, 1, 1 ]
PrimativeCellBasisNumber: [ 8, 8, 8 ]
AtomPositionInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.2/14.2.2.5/band.yaml", Format: "yaml" }
QPointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.2/14.2.2.5/band.yaml", Format: "yaml" }
QPointDataOutputFile:
QpointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.2/14.2.2.5/band.yaml", Format: "yaml" }
QpointDataOutputFile:
- { FileName: "test/14.2.2.5.result.yaml", Format: "yaml" }
- { FileName: "test/14.2.2.5.result.human-readable.yaml", Format: "yaml-human-readable" }
- { FileName: "test/14.2.2.5.result.zpp", Format: "zpp" }

4
test/14.2.4.4.unfold.yaml
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@ -7,8 +7,8 @@ PrimativeCellBasisNumber: [ 8, 8, 8 ]
AtomPositionInputFile:
FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.4/14.2.4.4/phonopy.yaml"
Format: "yaml"
QPointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.4/14.2.4.4/band.hdf5", Format: "hdf5" }
QPointDataOutputFile:
QpointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.4/14.2.4.4/band.hdf5", Format: "hdf5" }
QpointDataOutputFile:
- { FileName: "test/14.2.4.4.result.yaml", Format: "yaml" }
- { FileName: "test/14.2.4.4.result.human-readable.yaml", Format: "yaml-human-readable" }
- { FileName: "test/14.2.4.4.result.zpp", Format: "zpp" }

4
test/14.2.5.5.unfold.yaml
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@ -11,8 +11,8 @@ PrimativeCellBasisNumber: [ 8, 8, 8 ]
AtomPositionInputFile:
FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.5/14.2.5.5/phonopy.yaml"
Format: "yaml"
QPointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.5/14.2.5.5/band.hdf5", Format: "hdf5" }
QPointDataOutputFile:
QpointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.5/14.2.5.5/band.hdf5", Format: "hdf5" }
QpointDataOutputFile:
- { FileName: "test/14.2.5.5.result.yaml", Format: "yaml" }
- { FileName: "test/14.2.5.5.result.human-readable.yaml", Format: "yaml-human-readable" }
- { FileName: "test/14.2.5.5.result.zpp", Format: "zpp" }

4
test/14.2.6.4.unfold.yaml
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@ -11,8 +11,8 @@ PrimativeCellBasisNumber: [ 8, 8, 8 ]
AtomPositionInputFile:
FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.6/14.2.6.4/phonopy.yaml"
Format: "yaml"
QPointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.6/14.2.6.4/band.hdf5", Format: "hdf5" }
QPointDataOutputFile:
QpointDataInputFile: { FileName: "/home/chn/Documents/lammps-SiC/14/14.2/14.2.6/14.2.6.4/band.hdf5", Format: "hdf5" }
QpointDataOutputFile:
- { FileName: "test/14.2.6.4.result.yaml", Format: "yaml" }
- { FileName: "test/14.2.6.4.result.human-readable.yaml", Format: "yaml-human-readable" }
- { FileName: "test/14.2.6.4.result.zpp", Format: "zpp" }