/// <summary>
/// 接続行列AとA^T*CAを表示。
/// </summary>
private void CalcConnectionMat()
{
var pList = mDGEditor.PointList();
var eList = mDGEditor.EdgeList();
if (pList.Count == 0 || eList.Count == 0)
{
return;
}
var A = CalcA();
AddLog(string.Format("A: {0}", A.ToString()));
var C = CalcC();
AddLog(string.Format("C: {0}", C.ToString()));
var CA = WWMatrix.Mul(C, A);
var AT = A.Transpose();
var AT_CA = WWMatrix.Mul(AT, CA);
AddLog(string.Format("A^T*CA: {0}", AT_CA.ToString()));
}
public void MatrixLU()
{
int N = 2;
var A = new WWMatrix(N, N, new double[]
{ 4, 3,
6, 3 });
WWMatrix L;
WWMatrix U;
var result = WWMatrix.LUdecompose(A, out L, out U);
Assert.IsTrue(result == WWMatrix.ResultEnum.Success);
// Lは下三角行列。
var Ltype = L.DetermineMatType();
Assert.IsTrue(0 != (Ltype & (ulong)WWMatrix.MatType.LowerTriangular));
// Uは上三角行列。
var Utype = U.DetermineMatType();
Assert.IsTrue(0 != (Utype & (ulong)WWMatrix.MatType.UpperTriangular));
// L * U = A
WWMatrix Arecovered = WWMatrix.Mul(L, U);
Assert.IsTrue(WWMatrix.IsSame(A, Arecovered));
}
public void MatrixLPU_4x4()
{
int N = 4;
var r = new Random();
for (int i = 0; i < 1000; ++i)
{
var A = new WWMatrix(N, N, new double[]
{ r.Next(10), r.Next(10), r.Next(10), r.Next(10),
r.Next(10), r.Next(10), r.Next(10), r.Next(10),
r.Next(10), r.Next(10), r.Next(10), r.Next(10),
r.Next(10), r.Next(10), r.Next(10), r.Next(10) });
WWMatrix P;
WWMatrix L;
WWMatrix U;
var result = WWMatrix.LUdecompose2(A, out L, out P, out U);
if (result == WWMatrix.ResultEnum.FailedToChoosePivot)
{
continue;
}
Assert.IsTrue(result == WWMatrix.ResultEnum.Success);
// Lは下三角行列。
var Ltype = L.DetermineMatType();
Assert.IsTrue(0 != (Ltype & (ulong)WWMatrix.MatType.LowerTriangular));
// Uは上三角行列。
var Utype = U.DetermineMatType();
Assert.IsTrue(0 != (Utype & (ulong)WWMatrix.MatType.UpperTriangular));
A.Print("A");
L.Print("L");
U.Print("U");
P.Print("P");
// P * A = L * U
var LU = WWMatrix.Mul(L, U);
var PA = WWMatrix.Mul(P, A);
Assert.IsTrue(WWMatrix.IsSame(PA, LU));
}
}
public void MatrixLPU_3x3a()
{
int N = 3;
var A = new WWMatrix(N, N, new double[]
{ 6, 4, 1,
3, 3, 2,
7, 7, 3 });
WWMatrix P;
WWMatrix L;
WWMatrix U;
var result = WWMatrix.LUdecompose2(A, out L, out P, out U);
Assert.IsTrue(result == WWMatrix.ResultEnum.Success);
// Lは下三角行列。
var Ltype = L.DetermineMatType();
Assert.IsTrue(0 != (Ltype & (ulong)WWMatrix.MatType.LowerTriangular));
// Uは上三角行列。
var Utype = U.DetermineMatType();
Assert.IsTrue(0 != (Utype & (ulong)WWMatrix.MatType.UpperTriangular));
A.Print("A");
L.Print("L");
U.Print("U");
P.Print("P");
// P * A = L * U
var LU = WWMatrix.Mul(L, U);
var PA = WWMatrix.Mul(P, A);
Assert.IsTrue(WWMatrix.IsSame(PA, LU));
}
/// <summary>
/// KKT行列を作って解く。
/// </summary>
private void SolveKKT()
{
var pList = mDGEditor.PointList();
var eList = mDGEditor.EdgeList();
var earthP = mDGEditor.EarthedPoint();
if (pList.Count == 0 || eList.Count == 0)
{
return;
}
var A = CalcA();
AddLog(string.Format("A: {0}", A.ToString()));
var C = CalcC();
// A^T
var AT = A.Transpose();
// K = A^T C Aを作る。
var K = new WWMatrix(pList.Count - 1, pList.Count - 1);
{
var CA = WWMatrix.Mul(C, A);
K = WWMatrix.Mul(AT, CA);
}
AddLog(string.Format("K: {0}", K.ToString()));
var b = new WWMatrix(eList.Count, 1);
{ // 電圧源b
for (int i = 0; i < eList.Count; ++i)
{
var e = eList[i];
b.Set(i, 0, e.B);
}
}
AddLog(string.Format("b: {0}", b.ToString()));
var f = new WWMatrix(pList.Count - 1, 1);
{ // fを作る。
int nP = 0;
for (int i = 0; i < pList.Count; ++i)
{
var point = pList[i];
if (point == earthP)
{
// アースされている点は除外。
continue;
}
f.Set(nP, 0, point.F);
++nP;
}
}
AddLog(string.Format("f: {0}", f.ToString()));
WWMatrix KKT;
{ // KKT行列
var Cinv = CalcCinv();
var Cinv_A = WWMatrix.JoinH(Cinv, A);
var AT_zero = WWMatrix.JoinH(AT, new WWMatrix(A.Column, A.Column));
KKT = WWMatrix.JoinV(Cinv_A, AT_zero);
}
AddLog(string.Format("KKT: {0}", KKT.ToString()));
WWMatrix bf;
{ // bとfを縦に連結した縦ベクトル。
bf = WWMatrix.JoinV(b, f);
}
AddLog(string.Format("bf: {0}", bf.ToString()));
var bfA = bf.ToArray();
// KKT u = bfを解いて uを求める。
var uA = WWLinearEquation.SolveKu_eq_f(KKT, bfA);
var u = new WWMatrix(uA.Length, 1, uA);
AddLog(string.Format("u: {0}", u.ToString()));
}
