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public static OfArray ( System.Numerics.Complex array ) : |
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| array | System.Numerics.Complex | |
| Résultat | ||
/// <summary>
/// 平行ビームの電子回折計算
/// </summary>
/// <param name="maxNumOfBloch"></param>
/// <param name="voltage"></param>
/// <param name="rotation"></param>
/// <param name="thickness"></param>
/// <returns></returns>
public Beam[] GetDifractedBeamAmpriltudes(int maxNumOfBloch, double voltage, Matrix3D rotation, double thickness)
{
var useEigen = !MathNet.Numerics.Control.TryUseNativeMKL();
if (AccVoltage != voltage)
{
uDictionary = new Dictionary <int, (Complex, Complex)>();
}
//波数を計算
var k_vac = UniversalConstants.Convert.EnergyToElectronWaveNumber(voltage);
//U0を計算
var u0 = getU(voltage, (0, 0, 0), 0).Real.Real;
var vecK0 = getVecK0(k_vac, u0);
if (MaxNumOfBloch != maxNumOfBloch || AccVoltage != voltage || EigenValues == null || EigenVectors == null || !rotation.Equals(BaseRotation))
{
MaxNumOfBloch = maxNumOfBloch;
AccVoltage = voltage;
BaseRotation = new Matrix3D(rotation);
Thickness = thickness;
//計算対象のg-Vectorsを決める。
Beams = Find_gVectors(BaseRotation, vecK0);
if (Beams == null || Beams.Length == 0)
{
return(new Beam[0]);
}
var potentialMatrix = getEigenProblemMatrix(Beams);
//A行列に関する固有値、固有ベクトルを取得
if (useEigen)
{
(EigenValues, EigenVectors) = NativeWrapper.EigenSolver(potentialMatrix);
}
else
{
var evd = DMat.OfArray(potentialMatrix).Evd(Symmetricity.Asymmetric);
EigenValues = evd.EigenValues.AsArray();
EigenVectors = (DMat)evd.EigenVectors;
}
//(EigenVectors, EigenValues) = RefineEigenProblem(DMat.OfArray(potentialMatrix), (DMat)evd.EigenVectors, evd.EigenValues.ToArray());
}
int len = EigenValues.Count();
var psi0 = DVec.OfArray(new Complex[len]);//入射面での波動関数を定義
psi0[0] = 1;
var alpha = EigenVectors.Inverse() * psi0;//アルファベクトルを求める
//ガンマの対称行列×アルファを作成
var gamma_alpha = new DVec(Enumerable.Range(0, len).Select(n => Exp(TwoPiI * EigenValues[n] * thickness) * alpha[n]).ToArray());
//出射面での境界条件を考慮した位相にするため、以下の1行を追加 (20190827)
var p = new DiagonalMatrix(len, len, Beams.Select(b => Exp(PiI * (b.P - 2 * k_vac * Surface.Z) * thickness)).ToArray());
//var p = new DiagonalMatrix(len, len, Beams.Select(b => new Complex(1, 0)).ToArray());
//深さZにおけるψを求める
var psi_atZ = p * EigenVectors * gamma_alpha;
for (int i = 0; i < Beams.Length && i < len; i++)
{
Beams[i].Psi = psi_atZ[i];
}
return(Beams);
}
private void cbed_DoWork(object sender, DoWorkEventArgs e)
{
//波数を計算
var kvac = UniversalConstants.Convert.EnergyToElectronWaveNumber(AccVoltage);
//U0を計算
var u0 = getU(AccVoltage, (0, 0, 0), 0).Real.Real;
//k0ベクトルを計算
var vecK0 = getVecK0(kvac, u0);
//計算対象のg-Vectorsを決める。indexが小さく、かつsg(励起誤差)の小さいg-vectorを抽出する
Beams = Find_gVectors(BaseRotation, vecK0);
//入射面での波動関数を定義
var psi0 = DVec.OfArray(Enumerable.Range(0, Beams.Length).ToList().Select(g => g == 0 ? One : 0).ToArray());
//ポテンシャルマトリックスを取得
uDictionary = new Dictionary <int, (Complex, Complex)>();
var factorMatrix = getPotentialMatrix(Beams);
//有効なRotationだけを選択
var beamRotationsValid = new List <Matrix3D>();
for (int i = 0; i < BeamRotations.Length; i++)
{
if (BeamRotations[i] != null)
{
beamRotationsValid.Add(BeamRotations[i]);
}
}
RotationArrayValidLength = beamRotationsValid.Count;
//rotationsValidに対応するdiskValidを定義
var diskValid = new List <Complex[][]>();
//進捗状況報告用の各種定数を初期化
int count = 0, total = beamRotationsValid.Count;
var sw = new Stopwatch();
var bLen = Beams.Length;
//ローカル関数. RotationsValid(の一部)を対象にdisks[t][g]を計算し、diskValidに追加し、最後にかかった時間を返す
long func(Solver solver, int thread, bool speedTest = true)
{
if (solver == Solver.MKL)
{
MathNet.Numerics.Control.TryUseNativeMKL();
}
else if (solver == Solver.Managed)
{
MathNet.Numerics.Control.UseManaged();
}
var reportString = (solver == Solver.MKL ? "MKL" : "EIG") + thread.ToString();
var beamRotationsP = beamRotationsValid.AsParallel().WithDegreeOfParallelism(thread);
if (speedTest)//スピードテストのとき
{
var n = Math.Min(bLen < 64 ? 512 : bLen < 128 ? 256 : bLen < 256 ? 128 : bLen < 512 ? 64 : 32, beamRotationsValid.Count);
if (n == 0)
{
return(0);
}
beamRotationsP = beamRotationsValid.Take(n).ToArray().AsParallel().WithDegreeOfParallelism(thread);
beamRotationsValid.RemoveRange(0, n);
}
sw.Restart();
//disks[t][g]を計算.
var disk = beamRotationsP.Select(beamRotation =>
{
if (bwCBED.CancellationPending)
{
return(null);
}
var rotZ = beamRotation * zNorm;
var coeff = 1.0 / rotZ.Z; // = 1/cosTau
var vecK0 = getVecK0(kvac, u0, beamRotation);
var beams = reset_gVectors(Beams, BaseRotation, vecK0); //BeamsのPやQをリセット
var potentialMatrix = getEigenProblemMatrix(beams, factorMatrix); //ポテンシャル行列をセット
Complex[][] result;
//ポテンシャル行列の固有値、固有ベクトルを取得し、resultに格納
if (solver == Solver.Eigen)
{
result = NativeWrapper.CBEDSolver(potentialMatrix, psi0.ToArray(), Thicknesses, coeff);
}
else
{
var evd = DMat.OfArray(potentialMatrix).Evd(Symmetricity.Unknown);
var alpha = evd.EigenVectors.Inverse() * psi0;
result = Thicknesses.Select(t =>
{
//ガンマの対称行列×アルファを作成
var gammmaAlpha = DVec.OfArray(evd.EigenValues.Select((ev, i) => Exp(TwoPiI * ev * t * coeff) * alpha[i]).ToArray());
//深さtにおけるψを求める
return((evd.EigenVectors * gammmaAlpha).ToArray());
}).ToArray();
}
bwCBED.ReportProgress(Interlocked.Increment(ref count), reportString); //進捗状況を報告
return(result);
}).ToArray();
diskValid.AddRange(disk); //diskをdiskValidに加える
return(sw.ElapsedTicks); //経過時間を返す
}
//ここからチューニング＆本番
if ((Solver)((object[])e.Argument)[0] == Solver.Auto)
{
if (EigenEnabled && bLen < 512 && func(Solver.Eigen, Environment.ProcessorCount) < func(Solver.MKL, 8))//eigenの方が早い場合
{
func(Solver.Eigen, Environment.ProcessorCount, false);
}
else if (Environment.ProcessorCount <= 4)//MKLでコア数が4以下の場合
{
func(Solver.MKL, Environment.ProcessorCount, false);
}
else//コア数4,6,8,10,12,14,16を試して最速のもので
{
var list = new SortedList <long, int>();
foreach (var t in new[] { 4, 6, 8, 10, 12, 14, 16 })
{
if (t <= Environment.ProcessorCount)
{
list.Add(func(Solver.MKL, t), t);
}
}
func(Solver.MKL, list.Values[0], false);
}
}
else
{
func((Solver)((object[])e.Argument)[0], (int)((object[])e.Argument)[1], false);
}
//無効なRotationも考慮してdisk[RotationIndex][Z_index][G_index]を構築
var disk = new List <Complex[][]>();
for (int i = 0, j = 0; i < BeamRotations.Length; i++)
{
disk.Add(BeamRotations[i] != null ? diskValid[j++] : null);
}
//diskをコンパイルする
Disks = new CBED_Disk[Thicknesses.Length][];
Parallel.For(0, Thicknesses.Length, t =>
{
Disks[t] = new CBED_Disk[Beams.Length];
for (int g = 0; g < Beams.Length; g++)
{
var intensity = new double[BeamRotations.Length];
for (int r = 0; r < BeamRotations.Length; r++)
{
if (disk[r] != null)
{
intensity[r] = disk[r][t][g].Magnitude2();
}
}
Disks[t][g] = new CBED_Disk(new[] { Beams[g].H, Beams[g].K, Beams[g].L }, Beams[g].Vec, Thicknesses[t], intensity);
}
});
if (bwCBED.CancellationPending)
{
e.Cancel = true;
}
}