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 }));
}
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 }));
}
/// <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();
}
}