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));
}
/// <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()));
}
/// <summary>
/// 接続行列Aを戻す。
/// </summary>
private WWMatrix CalcA()
{
var pList = mDGEditor.PointList();
var eList = mDGEditor.EdgeList();
var earthP = mDGEditor.EarthedPoint();
int aRow = eList.Count;
int aCol = pList.Count;
if (earthP != null)
{
// アースによって1列除去。これによりATAが可逆になる。
aCol = pList.Count - 1;
}
var A = new WWMatrix(aRow, aCol);
{ // 行列A(接続行列)を作成する。
// ストラング, 計算理工学 p143
for (int e = 0; e < eList.Count; ++e)
{
var edge = eList[e];
int nP = 0;
for (int p = 0; p < pList.Count; ++p)
{
var point = pList[p];
if (point == earthP)
{
// アースされている点は除外。
continue;
}
double v = 0;
// エッジのfromがpのとき、-1
// エッジのto がpのとき、+1
if (edge.fromPointIdx == point.Idx)
{
v = -1;
}
if (edge.toPointIdx == point.Idx)
{
v = +1;
}
A.Set(e, nP, v);
++nP;
}
}
}
return(A);
}
public void SolveTestK3_1()
{
int N = 3;
var K = new WWMatrix(N, N, new double[] {
2, -1, 0,
-1, 2, -1,
0, -1, 2
});
var f = new double[] { 4, 0, 0 };
double[] u = WWLinearEquation.SolveKu_eq_f(K, f);
Assert.IsTrue(IsApproxSame(u, new double[] { 3, 2, 1 }));
}
/// <summary>
/// 重み行列Cの逆行列。
/// </summary>
private WWMatrix CalcCinv()
{
var eList = mDGEditor.EdgeList();
var Cinv = new WWMatrix(eList.Count, eList.Count);
{ // 行列C 重み行列。
for (int x = 0; x < eList.Count; ++x)
{
var edge = eList[x];
Cinv.Set(x, x, 1.0 / edge.C);
}
}
return(Cinv);
}
public void SolveTestK4_1()
{
int N = 4;
var K = new WWMatrix(N, N, new double[] {
2, -1, 0, 0,
-1, 2, -1, 0,
0, -1, 2, -1,
0, 0, -1, 2
});
var f = new double[] { 1, 0, 0, 0 };
double[] u = WWLinearEquation.SolveKu_eq_f(K, f);
Assert.IsTrue(IsApproxSame(u, new double[] { 4.0 / 5, 3.0 / 5, 2.0 / 5, 1.0 / 5 }));
}
public void MatrixJoinH()
{
int N = 2;
var A = new WWMatrix(N, N, new double[]
{ 1, 2,
3, 4 });
var B = new WWMatrix(N, N, new double[]
{ 5, 6,
7, 8 });
var AB = WWMatrix.JoinH(A, B);
var ABref = new WWMatrix(N, N * 2, new double[]
{ 1, 2, 5, 6,
3, 4, 7, 8 });
Assert.IsTrue(WWMatrix.IsSame(AB, ABref));
}
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));
}
public void Test(double[] recorded)
{
// 動作テスト
int N = mOrder;
int P = (1 << N) - 1;
var from = new double[P + 1];
{
int copySize = recorded.Length;
if (from.Length < copySize)
{
copySize = from.Length;
}
Array.Copy(recorded, from, copySize);
}
byte[] mlsSeq;
{
var mls = new MaximumLengthSequence(N);
mlsSeq = mls.Sequence();
for (int i = 0; i < mlsSeq.Length; ++i)
{
Console.Write("{0} ", mlsSeq[i]);
}
Console.WriteLine("");
}
{
var mlsD = new double[mlsSeq.Length];
for (int i = 0; i < mlsD.Length; ++i)
{
mlsD[i] = mlsSeq[i] * 2.0 - 1.0;
}
var ccc = CrossCorrelation.CalcCircularCrossCorrelation(mlsD, mlsD);
for (int i = 0; i < ccc.Length; ++i)
{
Console.Write("{0:g2} ", ccc[i]);
}
Console.WriteLine("");
}
var mlsMat = new MatrixGF2(P, P);
{
for (int y = 0; y < P; ++y)
{
for (int x = 0; x < P; ++x)
{
mlsMat.Set(y, x, (0 != mlsSeq[(x + y) % P]) ? GF2.One : GF2.Zero);
}
}
}
mlsMat.Print("MLS matrix");
// σ: mlsMatの左上N*N要素
var σ = mlsMat.Subset(0, 0, N, N);
σ.Print("σ");
var σInv = σ.Inverse();
σInv.Print("σ^-1");
// S: MLS行列の上N行。
var S = mlsMat.Subset(0, 0, N, P);
S.Print("S");
// Sの転置S^T
S.Transpose().Print("S^T");
// L: Sの転置 x σInv
var L = S.Transpose().Mul(σInv);
L.Print("L");
// L x S == MLS行列
var LS = L.Mul(S);
LS.Print("L x S");
int diff = LS.CompareTo(mlsMat);
System.Diagnostics.Debug.Assert(diff == 0);
// 2進で0～P-1までの値が入っている行列
var B = new MatrixGF2(P + 1, N);
var Bt = new MatrixGF2(N, P + 1);
for (int r = 0; r < P + 1; ++r)
{
for (int c = 0; c < N; ++c)
{
int v = r & (1 << (N - 1 - c));
var b = (v == 0) ? GF2.Zero : GF2.One;
B.Set(r, c, b);
Bt.Set(c, r, b);
}
}
B.Print("B");
Bt.Print("Bt");
// アダマール行列H8
var H8 = MatrixGF2.Mul(B, Bt);
H8.Print("H8");
var vTest = new double[P + 1];
for (int i = 0; i < P + 1; ++i)
{
vTest[i] = i;
}
var r1 = H8.ToMatrix().Mul(vTest);
Print(r1, "R1");
var r2 = FastWalshHadamardTransform.Transform(vTest);
Print(r2, "R2");
// Ps: S行列の列の値を2進数として、順番入れ替え行列を作る
var Ps = new MatrixGF2(P + 1, P + 1);
var PsReorder = new List <int>();
PsReorder.Add(0);
for (int c = 0; c < P; ++c)
{
int sum = 0;
for (int r = 0; r < N; ++r)
{
sum += (1 << (N - 1 - r)) * S.At(r, c).Val;
}
Console.WriteLine("Ps: c={0} sum={1}", c, sum);
Ps.Set(sum, c + 1, GF2.One);
PsReorder.Add(sum);
}
Ps.Print("Ps");
{
var testMat = new WWMatrix(P + 1, 1);
for (int r = 0; r < P + 1; ++r)
{
testMat.Set(r, 0, PsReorder[r]);
}
var PsTest = Ps.ToMatrix().Mul(testMat);
PsTest.Print("Ps x n");
}
// Pl: L行列の列の値を2進数として、順番入れ替え行列を作る
var Pl = new MatrixGF2(P + 1, P + 1);
var PlReorder = new List <int>();
PlReorder.Add(0);
for (int r = 0; r < P; ++r)
{
int sum = 0;
for (int c = 0; c < N; ++c)
{
sum += (1 << (N - 1 - c)) * L.At(r, c).Val;
}
Console.WriteLine("Pl: r={0} sum={1}", r, sum);
Pl.Set(r + 1, sum, GF2.One);
PlReorder.Add(sum);
}
Pl.Print("Pl");
S.Print("S");
var BtPs = Bt.Mul(Ps);
BtPs.Print("BtPs");
L.Print("L");
var PlB = Pl.Mul(B);
PlB.Print("PlB");
{
var test2Mat = new WWMatrix(P + 1, 1);
for (int r = 0; r < P + 1; ++r)
{
test2Mat.Set(r, 0, r);
}
var PlTest = Pl.ToMatrix().Mul(test2Mat);
PlTest.Print("Pl x n");
}
mlsMat.Print("MLS mat");
var Mhat = Pl.Mul(H8).Mul(Ps);
Mhat.Print("Mhat");
// MLS deconvolution
var decon = Mhat.ToMatrix().Mul(from);
Print(decon, "decon");
// 同じ処理をWalsh-Hadamard変換を使って行う。
var reorderedFrom = new double[P + 1];
for (int i = 0; i < P + 1; ++i)
{
reorderedFrom[PsReorder[i]] = from[i];
}
#if true
var hR = FastWalshHadamardTransform.Transform(reorderedFrom);
#else
var hR = H8.ToMatrix().Mul(reorderedFrom);
#endif
var hTo = new double[P + 1];
for (int i = 0; i < P + 1; ++i)
{
hTo[i] = hR[PlReorder[i]];
}
Print(hTo, "hTo");
}
/// <summary>
/// Polynomial function fitting.
/// </summary>
/// <param name="knownYs">known y values.</param>
/// <param name="knownXs">known x values.</param>
/// <param name="nthOrder">Order of fitting polynomial function.</param>
/// <returns>List of nth order polynomial function coefficients.</returns>
public static Result Calc(double[] knownYs, double[] knownXs, int nthOrder)
{
System.Diagnostics.Debug.Assert(knownYs.Length == knownXs.Length);
System.Diagnostics.Debug.Assert(0 < nthOrder);
System.Diagnostics.Debug.Assert(nthOrder < knownXs.Length);
// 2d coordinate data sample count
int count = knownXs.Length;
int maxOrderXn = 2 * nthOrder;
var sumXn = new double[maxOrderXn + 1];
for (int i = 0; i < count; ++i)
{
double x = knownXs[i];
for (int h = 0; h <= maxOrderXn; ++h)
{
sumXn[h] += System.Math.Pow(x, h);
}
}
// Create Vandermonde matrix vm
var vm = new WWMatrix(nthOrder + 1, nthOrder + 1);
for (int y = 0; y <= nthOrder; ++y)
{
for (int x = 0; x <= nthOrder; ++x)
{
int order = (nthOrder - x) + (nthOrder - y);
vm.Set(y, x, sumXn[order]);
}
}
var sumXnY = new double[nthOrder + 1];
for (int i = 0; i < count; ++i)
{
double x = knownXs[i];
double y = knownYs[i];
for (int h = 0; h <= nthOrder; ++h)
{
sumXnY[h] += System.Math.Pow(x, h) * y;
}
}
// 若干わかり難いが、
// f[0] = sumXnY[nthOrder]
// f[nthOrder] = sumXnY[0] なので、
// fはnthOrder+1要素必要。
var f = new double[nthOrder + 1];
for (int i = 0; i <= nthOrder; ++i)
{
f[i] = sumXnY[nthOrder - i];
}
// Solve vm u = f to get u
var u = WWLinearEquation.SolveKu_eq_f(vm, f);
var r = new Result();
r.c = new double[nthOrder + 1];
for (int i = 0; i <= nthOrder; ++i)
{
r.c[i] = u[nthOrder - i];
}
return(r);
}
/// <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()));
}
private void Calc()
{
int N = 0;
if (!int.TryParse(textBoxNumElems.Text, out N) || N <= 0)
{
MessageBox.Show("Error: Num of Elems should be integer larger than 0");
return;
}
// 試験関数Vkとf(x)との積分Fk=∫f(x)Vk dxを求める。
var f = new double[N];
for (int i = 0; i < N; ++i)
{
double x = (double)(i + 1) / N;
double y = mGraphFx.Sample(x);
// 最後の区間は半区間。
double Vk = (i == N - 1) ? (1.0 / N / 2) : (1.0 / N);
f[i] = y * Vk;
}
// 合成行列K
// Kij = ∫c(x)dVi/dx dVj/dx dx
// i=j=0のとき、dVi/dxは、
// 0≦x＜1/N の区間でVi'=Vj'= +N → Vi'*Vj' = N^2
// 1/N≦x＜2/Nの区間でVi'=Vj'= -N → Vi'*Vj' = N^2
// 区間 値
// ∫c(x)dVi/dx dVj/dx dx = (2/N) * N^2
// i=0,j=1のとき
// 0≦x＜1/N の区間でVi'=+N, Vj'= 0 → Vi'Vj' = 0
// 1/N≦x＜2/Nの区間でVi'=-N, Vj'= N → Vi'Vj' = -N^2
// 2/N≦x＜3/Nの区間でVi'= 0, Vj'=-N → Vi'Vj' = 0
// 区間 値
// ∫c(x)dVi/dx dVj/dx dx = (1/N) * (-N^2)
// i=N-1, j=N-1のとき
// N-1/N≦x＜1の区間でVi'=Vj'=N → Vi'Vj' = N^2
// 区間 値
// ∫c(x)dVi/dx dVj/dx dx = (1/N) * (N^2)
var Kij = new double[N * N];
for (int i = 0; i < N; ++i)
{
for (int j = 0; j < N; ++j)
{
int pos = i * N + j;
double x = (double)(i + 1) / N;
double c = mGraphCx.Sample(x);
if (i == N - 1 && j == N - 1)
{
Kij[pos] = c * (double)(1.0 / N) * N * N;
}
else if (i == j)
{
Kij[pos] = c * (double)(2.0 / N) * N * N;
}
else if (Math.Abs(i - j) == 1)
{
Kij[pos] = c * (double)(1.0 / N) * (-N * N);
}
else
{
Kij[pos] = 0;
}
}
}
var K = new WWMatrix(N, N, Kij);
// Ku=fを解いてUを求める。
var u = WWLinearEquation.SolveKu_eq_f(K, f);
{ // 求まったUをグラフにする。
mGraphUx.SetArbitraryFunctionStart();
// U(0) = 0 : 境界条件。
mGraphUx.SetArbitraryFunctionPoint(0, 0);
for (int i = 0; i < u.Length; ++i)
{
double x = (double)(i + 1) / N;
double y = u[i];
mGraphUx.SetArbitraryFunctionPoint(x, y);
}
mGraphUx.SetArbitraryFunctionEnd();
}
}