/// <summary>
/// 固有モードをソートする(伝搬モードを先に)
/// </summary>
/// <param name="evals"></param>
/// <param name="evecs"></param>
public static void Sort1DEigenMode(double k0, Complex[] evals, Complex[,] evecs)
{
/*
* // 符号調整
* {
* // 正の固有値をカウント
* //int positive_cnt = 0;
* //foreach (Complex c in evals)
* //{
* // if (c.Real > 0.0 && Math.Abs(c.Imaginary) <Constants.PrecisionLowerLimit)
* // {
* // positive_cnt++;
* // }
* //}
* // 計算範囲では、正の固有値(伝搬定数の二乗が正)は高々1個のはず
* // 半分以上正の固有値であれば、固有値が逆転して計算されていると判断する
* // 誘電体導波路の場合、これでは破綻する？
* // 最大、最小値を求め、最大値 > 最小値の絶対値なら逆転している
* double minEval = double.MaxValue;
* double maxEval = double.MinValue;
* foreach (Complex c in evals)
* {
* if (minEval > c.Real) { minEval = c.Real; }
* if (maxEval < c.Real) { maxEval = c.Real; }
* }
* //if (positive_cnt >= evals.Length / 2) // 導波管の場合
* if (Math.Abs(maxEval) > Math.Abs(minEval))
* {
* for (int i = 0; i < evals.Length; i++)
* {
* evals[i] = -evals[i];
* }
* System.Diagnostics.Debug.WriteLine("eval sign changed");
* }
* }
*/
EigenModeItem[] items = new EigenModeItem[evals.Length];
for (int i = 0; i < evals.Length; i++)
{
Complex[] evec = MyMatrixUtil.matrix_GetRowVec(evecs, i);
items[i] = new EigenModeItem(i, evals[i], evec);
}
Array.Sort(items);
int imode = 0;
foreach (EigenModeItem item in items)
{
evals[imode] = item.eval;
MyMatrixUtil.matrix_setRowVec(evecs, (int)imode, item.evec);
//System.Diagnostics.Debug.WriteLine("[sorted]( " + imode + " ) = " + evals[imode].Real + " + " + evals[imode].Imaginary + " i ");
imode++;
}
}
/// <summary>
/// Lisys(Lapack)による固有値解析(一般化固有値問題)
/// </summary>
private static bool solveEigen(MyDoubleSymmetricBandMatrix stiffnessMat, MyDoubleSymmetricBandMatrix massMat, out Complex[] evals, out Complex[,] evecs)
{
// Lisys(Lapack)による固有値解析
double[] A = MyMatrixUtil.matrix_ToBuffer(stiffnessMat, false);
double[] B = MyMatrixUtil.matrix_ToBuffer(massMat, false);
double[] r_evals = null;
double[][] r_evecs = null;
int a_row = stiffnessMat.RowSize;
int a_col = stiffnessMat.ColumnSize;
int a_superdiaSize = stiffnessMat.SuperdiaSize;
int b_row = massMat.RowSize;
int b_col = massMat.ColumnSize;
int b_superdiaSize = massMat.SuperdiaSize;
KrdLab.clapack.FunctionExt.dsbgv(A, a_row, a_col, a_superdiaSize, B, b_row, b_col, b_superdiaSize, ref r_evals, ref r_evecs);
evals = new Complex[r_evals.Length];
for (int i = 0; i < evals.Length; i++)
{
//evals[i] = new Complex(r_evals[i], 0.0);
evals[i].Real = r_evals[i];
evals[i].Imaginary = 0.0;
//System.Diagnostics.Debug.WriteLine("( " + i + " ) = " + evals[i].Real + " + " + evals[i].Imaginary + " i ");
}
evecs = new Complex[r_evecs.Length, r_evecs[0].Length];
for (int i = 0; i < evecs.GetLength(0); i++)
{
for (int j = 0; j < evecs.GetLength(1); j++)
{
//evecs[i, j] = new Complex(r_evecs[i][j], 0.0);
evecs[i, j].Real = r_evecs[i][j];
evecs[i, j].Imaginary = 0.0;
//System.Diagnostics.Debug.WriteLine("( " + i + ", " + j + " ) = " + evecs[i, j].Real + " + " + evecs[i, j].Imaginary + " i ");
}
}
return(true);
}
/// <summary>
/// ポート固有値解析
/// </summary>
public static void SolvePortWaveguideEigen(
FemSolver.WaveModeDV WaveModeDv,
double waveLength,
int maxModeSpecified,
IList <FemNode> Nodes,
Dictionary <string, IList <int> > EdgeToElementNoH,
IList <FemElement> Elements,
MediaInfo[] Medias,
Dictionary <int, bool> ForceNodeNumberH,
IList <int> portNodes,
out int[] nodesBoundary,
out MyDoubleMatrix ryy_1d,
out Complex[] eigenValues,
out Complex[,] eigenVecs)
{
//System.Diagnostics.Debug.WriteLine("solvePortWaveguideEigen: {0},{1}", waveLength, portNo);
nodesBoundary = null;
ryy_1d = null;
eigenValues = null;
eigenVecs = null;
// 2D次元数
const int ndim2d = Constants.CoordDim2D; //2;
// 波数
double k0 = 2.0 * pi / waveLength;
// 角周波数
double omega = k0 * c0;
// 節点番号リスト(要素インデックス: 1D節点番号 - 1 要素:2D節点番号)
IList <int> nodes = portNodes;
// 2D→1D節点番号マップ
Dictionary <int, int> to1dNodes = new Dictionary <int, int>();
// 節点座標リスト
IList <double> coords = new List <double>();
// 要素リスト
IList <FemLineElement> elements = new List <FemLineElement>();
// 1D節点番号リスト（ソート済み）
IList <int> sortedNodes = new List <int>();
// 1D節点番号→ソート済みリストインデックスのマップ
Dictionary <int, int> toSorted = new Dictionary <int, int>();
// 2Dの要素から次数を取得する
Constants.FemElementShapeDV elemShapeDv2d;
int order;
int vertexCnt2d;
FemMeshLogic.GetElementShapeDvAndOrderByElemNodeCnt(Elements[0].NodeNumbers.Length, out elemShapeDv2d, out order, out vertexCnt2d);
// 2D→1D節点番号マップ作成
for (int i = 0; i < nodes.Count; i++)
{
int nodeNumber2d = nodes[i];
if (!to1dNodes.ContainsKey(nodeNumber2d))
{
to1dNodes.Add(nodeNumber2d, i + 1);
}
}
// 原点
int nodeNumber0 = nodes[0];
int nodeIndex0 = nodeNumber0 - 1;
FemNode node0 = Nodes[nodeIndex0];
double[] coord0 = new double[ndim2d];
coord0[0] = node0.Coord[0];
coord0[1] = node0.Coord[1];
// 座標リスト作成
double[] coord = new double[ndim2d];
foreach (int nodeNumber in nodes)
{
int nodeIndex = nodeNumber - 1;
FemNode node = Nodes[nodeIndex];
coord[0] = node.Coord[0];
coord[1] = node.Coord[1];
double x = FemMeshLogic.GetDistance(coord, coord0);
//System.Diagnostics.Debug.WriteLine("{0},{1},{2},{3}", nodeIndex, coord[0], coord[1], x);
coords.Add(x);
}
// 線要素を作成する
if (order == Constants.FirstOrder)
{
// １次線要素
FemMat_Line_First.MkElements(
nodes,
EdgeToElementNoH,
Elements,
ref elements);
}
else
{
// ２次線要素
FemMat_Line_Second.MkElements(
nodes,
EdgeToElementNoH,
Elements,
ref elements);
}
// 強制境界節点と内部領域節点を分離
foreach (int nodeNumber2d in nodes)
{
int nodeNumber = to1dNodes[nodeNumber2d];
if (ForceNodeNumberH.ContainsKey(nodeNumber2d))
{
System.Diagnostics.Debug.WriteLine("{0}: {1} {2}", nodeNumber, Nodes[nodeNumber2d - 1].Coord[0], Nodes[nodeNumber2d - 1].Coord[1]);
}
else
{
sortedNodes.Add(nodeNumber);
toSorted.Add(nodeNumber, sortedNodes.Count - 1);
}
}
// 対称バンド行列のパラメータを取得する
int rowcolSize = 0;
int subdiaSize = 0;
int superdiaSize = 0;
{
bool[,] matPattern = null;
GetMatNonzeroPatternForEigen(elements, toSorted, out matPattern);
GetBandMatrixSubDiaSizeAndSuperDiaSizeForEigen(matPattern, out rowcolSize, out subdiaSize, out superdiaSize);
}
// ソート済み1D節点インデックス→2D節点番号マップ
nodesBoundary = new int[sortedNodes.Count];
for (int i = 0; i < sortedNodes.Count; i++)
{
int nodeNumber = sortedNodes[i];
int nodeIndex = nodeNumber - 1;
int nodeNumber2d = nodes[nodeIndex];
nodesBoundary[i] = nodeNumber2d;
}
// 節点数
int nodeCnt = sortedNodes.Count;
// 固有値、固有ベクトル
int maxMode = maxModeSpecified;
if (maxMode > nodeCnt)
{
maxMode = nodeCnt;
}
eigenValues = new Complex[maxMode];
eigenVecs = new Complex[maxMode, nodeCnt];
// 固有モード解析でのみ使用するuzz_1d, txx_1d
MyDoubleMatrix txx_1d = new MyDoubleSymmetricBandMatrix(nodeCnt, subdiaSize, superdiaSize);
MyDoubleMatrix uzz_1d = new MyDoubleSymmetricBandMatrix(nodeCnt, subdiaSize, superdiaSize);
// ryy_1dマトリクス (線要素)
ryy_1d = new MyDoubleSymmetricBandMatrix(nodeCnt, subdiaSize, superdiaSize);
for (int elemIndex = 0; elemIndex < elements.Count; elemIndex++)
{
// 線要素
FemLineElement element = elements[elemIndex];
// 1Dヘルムホルツ方程式固有値問題の要素行列を加算する
if (order == Constants.FirstOrder)
{
// １次線要素
FemMat_Line_First.AddElementMatOf1dEigenValueProblem(
waveLength, // E面の場合のみ使用
element,
coords,
toSorted,
Medias,
WaveModeDv,
ref txx_1d, ref ryy_1d, ref uzz_1d);
}
else
{
// ２次線要素
FemMat_Line_Second.AddElementMatOf1dEigenValueProblem(
waveLength, // E面の場合のみ使用
element,
coords,
toSorted,
Medias,
WaveModeDv,
ref txx_1d, ref ryy_1d, ref uzz_1d);
}
}
// [A] = [Txx] - k0 * k0 *[Uzz]
//メモリ節約
//MyDoubleMatrix matA = new MyDoubleMatrix(nodeCnt, nodeCnt);
MyDoubleSymmetricBandMatrix matA = new MyDoubleSymmetricBandMatrix(nodeCnt, subdiaSize, superdiaSize);
for (int ino = 0; ino < nodeCnt; ino++)
{
for (int jno = 0; jno < nodeCnt; jno++)
{
// 対称バンド行列対応
if (matA is MyDoubleSymmetricBandMatrix && ino > jno)
{
continue;
}
// 剛性行列
//matA[ino, jno] = txx_1d[ino, jno] - (k0 * k0) * uzz_1d[ino, jno];
// 質量行列matBが正定値行列となるように剛性行列matAの方の符号を反転する
matA[ino, jno] = -(txx_1d[ino, jno] - (k0 * k0) * uzz_1d[ino, jno]);
}
}
// ( [txx] - k0^2[uzz] + β^2[ryy]){Ez} = {0}より
// [A]{x} = λ[B]{x}としたとき、λ = β^2 とすると[B] = -[ryy]
//MyDoubleMatrix matB = MyMatrixUtil.product(-1.0, ryy_1d);
// 質量行列が正定値となるようにするため、上記符号反転を剛性行列の方に反映し、質量行列はryy_1dをそのまま使用する
//MyDoubleMatrix matB = new MyDoubleMatrix(ryy_1d);
MyDoubleSymmetricBandMatrix matB = new MyDoubleSymmetricBandMatrix((MyDoubleSymmetricBandMatrix)ryy_1d);
// 一般化固有値問題を解く
Complex[] evals = null;
Complex[,] evecs = null;
try
{
// 固有値、固有ベクトルを求める
solveEigen(matA, matB, out evals, out evecs);
// 固有値のソート
Sort1DEigenMode(k0, evals, evecs);
}
catch (Exception exception)
{
System.Diagnostics.Debug.WriteLine(exception.Message + " " + exception.StackTrace);
System.Diagnostics.Debug.Assert(false);
}
for (int imode = 0; imode < evecs.GetLength(0); imode++)
{
KrdLab.clapack.Complex phaseShift = 1.0;
double maxAbs = double.MinValue;
KrdLab.clapack.Complex fValueAtMaxAbs = 0.0;
{
// 境界上で位相調整する
for (int ino = 0; ino < evecs.GetLength(1); ino++)
{
KrdLab.clapack.Complex cvalue = evecs[imode, ino];
double abs = KrdLab.clapack.Complex.Abs(cvalue);
if (abs > maxAbs)
{
maxAbs = abs;
fValueAtMaxAbs = cvalue;
}
}
}
if (maxAbs >= MyUtilLib.Matrix.Constants.PrecisionLowerLimit)
{
phaseShift = fValueAtMaxAbs / maxAbs;
}
//System.Diagnostics.Debug.WriteLine("phaseShift: {0} (°)", Math.Atan2(phaseShift.Imaginary, phaseShift.Real) * 180.0 / pi);
for (int ino = 0; ino < evecs.GetLength(1); ino++)
{
evecs[imode, ino] /= phaseShift;
}
}
for (int imode = 0; imode < maxMode; imode++)
{
eigenValues[imode] = 0;
}
for (int tagtModeIdx = evals.Length - 1, imode = 0; tagtModeIdx >= 0 && imode < maxMode; tagtModeIdx--)
{
// 伝搬定数は固有値のsqrt
Complex betam = Complex.Sqrt(evals[tagtModeIdx]);
// 定式化BUGFIX
// 減衰定数は符号がマイナス(β = -jα)
bool isConjugateMode = false;
if (betam.Imaginary >= 0.0)
{
betam = new Complex(betam.Real, -betam.Imaginary);
isConjugateMode = true;
}
// 固有ベクトル
Complex[] evec = MyMatrixUtil.matrix_GetRowVec(evecs, tagtModeIdx);
if (isConjugateMode)
{
evec = MyMatrixUtil.vector_Conjugate(evec);
}
// 規格化定数を求める
// 実数の場合 [ryy]*t = [ryy]t ryyは対称行列より[ryy]t = [ryy]
Complex[] workVec = MyMatrixUtil.product(ryy_1d, evec);
Complex dm = MyMatrixUtil.vector_Dot(MyMatrixUtil.vector_Conjugate(evec), workVec);
{
// H面、平行平板
if (WaveModeDv == FemSolver.WaveModeDV.TM)
{
dm = Complex.Sqrt(omega * eps0 / Complex.Abs(betam) / dm);
}
else
{
dm = Complex.Sqrt(omega * mu0 / Complex.Abs(betam) / dm);
}
}
//System.Diagnostics.Debug.WriteLine("dm = " + dm);
// 伝搬定数の格納
eigenValues[imode] = betam;
// check
if (imode < 5)
{
//System.Diagnostics.Debug.WriteLine("eigenValues [ " + imode + "] = " + betam.Real + " + " + betam.Imaginary + " i " + " tagtModeIdx :" + tagtModeIdx + " " );
System.Diagnostics.Debug.WriteLine("β/k0 [ " + imode + "] = " + betam.Real / k0 + " + " + betam.Imaginary / k0 + " i " + " tagtModeIdx :" + tagtModeIdx + " ");
}
// 固有ベクトルの格納(規格化定数を掛ける)
for (int inoSorted = 0; inoSorted < nodeCnt; inoSorted++)
{
Complex fm = dm * evec[inoSorted];
eigenVecs[imode, inoSorted] = fm;
//System.Diagnostics.Debug.WriteLine("eigenVecs [ " + imode + ", " + inoSorted + "] = " + fm.Real + " + " + fm.Imaginary + " i Abs:" + Complex.Abs(fm));
}
imode++;
}
}
/// <summary>
/// 入出力ポート境界条件の追加
/// </summary>
/// <param name="waveLength"></param>
/// <param name="isInputPort"></param>
/// <param name="nodesBoundary"></param>
/// <param name="ryy_1d"></param>
/// <param name="eigenValues"></param>
/// <param name="eigenVecs"></param>
/// <param name="nodesRegion"></param>
/// <param name="mat"></param>
/// <param name="resVec"></param>
public static void AddPortBC(
FemSolver.WaveModeDV WaveModeDv,
double waveLength,
bool isInputPort,
int IncidentModeIndex,
int[] nodesBoundary,
MyDoubleMatrix ryy_1d,
Complex[] eigenValues,
Complex[,] eigenVecs,
int[] nodesRegion,
IList <FemElement> Elements,
MediaInfo[] Medias,
Dictionary <int, bool> ForceNodeNumberH,
MyComplexMatrix mat,
Complex[] resVec)
{
double k0 = 2.0 * pi / waveLength;
double omega = k0 / Math.Sqrt(mu0 * eps0);
// 境界上の節点数(1次線要素を想定)
int nodeCnt = nodesBoundary.Length;
// 考慮するモード数
int maxMode = eigenValues.Length;
// 全体剛性行列の作成
MyComplexMatrix matB = new MyComplexMatrix(nodeCnt, nodeCnt);
for (int imode = 0; imode < maxMode; imode++)
{
Complex betam = eigenValues[imode];
Complex[] fmVec = MyMatrixUtil.matrix_GetRowVec(eigenVecs, (int)imode);
// 2Dの境界積分
Complex[] veci = MyMatrixUtil.product(ryy_1d, fmVec);
// モード電力規格化の積分(1Dの積分)
// [ryy]が実数の場合
Complex[] vecj = MyMatrixUtil.product(ryy_1d, MyMatrixUtil.vector_Conjugate(fmVec));
for (int inoB = 0; inoB < nodeCnt; inoB++)
{
for (int jnoB = 0; jnoB < nodeCnt; jnoB++)
{
//Complex cvalue = (Complex.ImaginaryOne / (omega * myu0)) * betam * Complex.Abs(betam) * veci[inoB] * vecj[jnoB];
Complex cvalue;
{
// H面、平行平板
if (WaveModeDv == FemSolver.WaveModeDV.TM)
{
cvalue = (Complex.ImaginaryOne / (omega * eps0)) * betam * Complex.Abs(betam) * veci[inoB] * vecj[jnoB];
}
else
{
cvalue = (Complex.ImaginaryOne / (omega * mu0)) * betam * Complex.Abs(betam) * veci[inoB] * vecj[jnoB];
}
}
matB._body[inoB + jnoB * matB.RowSize] += cvalue;
}
}
}
// check 対称行列
for (int inoB = 0; inoB < matB.RowSize; inoB++)
{
for (int jnoB = inoB; jnoB < matB.ColumnSize; jnoB++)
{
if (Math.Abs(matB[inoB, jnoB].Real - matB[jnoB, inoB].Real) >= Constants.PrecisionLowerLimit)
{
System.Diagnostics.Debug.Assert(false);
}
if (Math.Abs(matB[inoB, jnoB].Imaginary - matB[jnoB, inoB].Imaginary) >= Constants.PrecisionLowerLimit)
{
System.Diagnostics.Debug.Assert(false);
}
}
}
//MyMatrixUtil.printMatrix("matB", matB);
// 残差ベクトルの作成
Complex[] resVecB = new Complex[nodeCnt];
if (isInputPort)
{
int imode = IncidentModeIndex;
Complex betam = eigenValues[imode];
Complex[] fmVec = MyMatrixUtil.matrix_GetRowVec(eigenVecs, (int)imode);
// 2Dの境界積分
Complex[] veci = MyMatrixUtil.product(ryy_1d, fmVec);
for (int inoB = 0; inoB < nodeCnt; inoB++)
{
// H面、平行平板、E面
Complex cvalue = 2.0 * Complex.ImaginaryOne * betam * veci[inoB];
resVecB[inoB].Real = cvalue.Real;
resVecB[inoB].Imaginary = cvalue.Imaginary;
}
}
//printVec("resVecB", resVecB);
// 2D節点番号→ソート済みリストインデックスのマップ
Dictionary <int, int> toSorted = new Dictionary <int, int>();
// 2D節点番号→ソート済みリストインデックスのマップ作成
for (int i = 0; i < nodesRegion.Length; i++)
{
int nodeNumber = nodesRegion[i];
if (!toSorted.ContainsKey(nodeNumber))
{
toSorted.Add(nodeNumber, i);
}
}
// 要素剛性行列にマージ
// この定式化では行列のスパース性は失われている(隣接していない要素の節点間にも関連がある)
// 要素剛性行列にマージする
for (int inoB = 0; inoB < nodeCnt; inoB++)
{
int iNodeNumber = nodesBoundary[inoB];
if (ForceNodeNumberH.ContainsKey(iNodeNumber))
{
continue;
}
int inoGlobal = toSorted[iNodeNumber];
for (int jnoB = 0; jnoB < nodeCnt; jnoB++)
{
int jNodeNumber = nodesBoundary[jnoB];
if (ForceNodeNumberH.ContainsKey(jNodeNumber))
{
continue;
}
int jnoGlobal = toSorted[jNodeNumber];
// Note: matBは一般行列 matはバンド行列
mat._body[mat.GetBufferIndex(inoGlobal, jnoGlobal)] += matB._body[inoB + jnoB * matB.RowSize];
}
}
// 残差ベクトルにマージ
for (int inoB = 0; inoB < nodeCnt; inoB++)
{
int iNodeNumber = nodesBoundary[inoB];
if (ForceNodeNumberH.ContainsKey(iNodeNumber))
{
continue;
}
int inoGlobal = toSorted[iNodeNumber];
resVec[inoGlobal] += resVecB[inoB];
}
}
/// <summary>
/// 散乱行列の計算
/// </summary>
/// <param name="waveLength"></param>
/// <param name="iMode"></param>
/// <param name="isIncidentMode"></param>
/// <param name="nodesBoundary"></param>
/// <param name="ryy_1d"></param>
/// <param name="eigenValues"></param>
/// <param name="eigenVecs"></param>
/// <param name="nodesRegion"></param>
/// <param name="valuesAll"></param>
/// <returns></returns>
public static Complex GetWaveguidePortReflectionCoef(
FemSolver.WaveModeDV WaveModeDv,
double waveLength,
int iMode,
bool isIncidentMode,
int[] nodesBoundary,
MyDoubleMatrix ryy_1d,
Complex[] eigenValues,
Complex[,] eigenVecs,
int[] nodesRegion,
IList <FemElement> Elements,
MediaInfo[] Medias,
Complex[] valuesAll)
{
// 2D節点番号→ソート済みリストインデックスのマップ
Dictionary <int, int> toSorted = new Dictionary <int, int>();
// 2D節点番号→ソート済みリストインデックスのマップ作成
for (int i = 0; i < nodesRegion.Length; i++)
{
int nodeNumber = nodesRegion[i];
if (!toSorted.ContainsKey(nodeNumber))
{
toSorted.Add(nodeNumber, i);
}
}
// ポート上の界を取得する
int nodeCnt = nodesBoundary.Length;
Complex[] valuesB = new Complex[nodeCnt];
for (int ino = 0; ino < nodeCnt; ino++)
{
int nodeNumber = nodesBoundary[ino];
int inoGlobal = toSorted[nodeNumber];
valuesB[ino] = valuesAll[inoGlobal];
}
double k0 = 2.0 * pi / waveLength;
double omega = k0 * c0;
Complex s11 = new Complex(0.0, 0.0);
int maxMode = eigenValues.Length;
// {tmp_vec}*t = {fm}*t[ryy]*t
// {tmp_vec}* = [ryy]* {fm}*
// ([ryy]*)t = [ryy]*
// [ryy]が実数のときは、[ryy]* -->[ryy]
Complex[] fmVec = MyMatrixUtil.matrix_GetRowVec(eigenVecs, iMode);
// ryyが実数のとき
Complex[] tmp_vec = MyMatrixUtil.product(ryy_1d, MyMatrixUtil.vector_Conjugate(fmVec));
// s11 = {tmp_vec}t {value_all}
s11 = MyMatrixUtil.vector_Dot(tmp_vec, valuesB);
Complex betam = eigenValues[iMode];
{
// H面、平行平板
if (WaveModeDv == FemSolver.WaveModeDV.TM)
{
s11 *= (Complex.Abs(betam) / (omega * eps0));
if (isIncidentMode)
{
s11 += -1.0;
}
}
else
{
s11 *= (Complex.Abs(betam) / (omega * mu0));
if (isIncidentMode)
{
s11 += -1.0;
}
}
}
return(s11);
}
