/// <summary>
/// Maximum Length Sequenceを録再したものを入力し、
/// MLSとのCircular Cross Correlationを計算し出力する。
/// </summary>
/// <param name="recorded">Maximum Length Sequenceを録再したもの。長さは(1 << order)サンプル。</param>
/// <returns></returns>
public double[] Deconvolution(double[] from)
{
int N = mOrder;
int P = (1 << N) - 1;
if (from.Length != P + 1)
{
throw new ArgumentException("from.Length should be (1 << order)");
}
// Walsh-Hadamard変換を使ってMLS deconvolutionを行う。
var reorderedFrom = new double[P + 1];
for (int i = 0; i < P + 1; ++i)
{
reorderedFrom[mFromReorder[i]] = from[i];
}
var hR = FastWalshHadamardTransform.Transform(reorderedFrom);
var hTo = new double[P + 1];
for (int i = 0; i < P + 1; ++i)
{
hTo[i] = -(hR[mToReorder[i]] - 1.0) / (P + 1);
}
//Print(hTo, "hTo");
return(hTo);
}
public void TransformTest()
{
var dwht = new DiscreteWalshHadamardTransform();
var fwht = new FastWalshHadamardTransform();
var points = new List <double>(new double[] { 1, 2, 1, 2, 1, 3, 1, 5, 1, 1, 1, 8, 2, 1, 3, 4 });
var r1 = dwht.Transform(points.Select(d => new Point(0, d)).ToArray()).ToArray();
var r2 = fwht.Transform(points.Select(d => new Point(0, d)).ToArray()).ToArray();
for (var i = 0; i < 16; i++)
{
Assert.AreEqual(r1[i], r2[i]);
}
}
public void TransformTest()
{
var r = new Random();
var transformD = new DiscreteWalshHadamardTransform();
var transformF = new FastWalshHadamardTransform();
var points = new List <Point>();
for (int i = 0; i < 256; i++)
{
points.Add(new Point(i, r.Next()));
}
var first = transformD.Transform(points.ToArray()).ToList();
var second = transformF.Transform(points.ToArray()).ToList();
for (int i = 0; i < first.Count; i++)
{
Assert.AreEqual(first[i], second[i]);
}
}
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");
}
