public static NVector operator *(double a, NVector B)
{
NVector C = new NVector(B);
for (int i = 0; i < B._n; i++)
C._vector[i] *= a;
return C;
}
public NVector(NVector A)
{
_vector = new double[A._n];
_n = A._n;
for (int i = 0; i < A._n; i++)
_vector[i] = A._vector[i];
}
public static NVector operator *(NVector A, NVector B)
{
if (A._n != B._n) throw new Exception("NVector operator *: incompatable vector size");
NVector C = new NVector(A);
for (int i = 0; i < A._n; i++)
C._vector[i] *= B._vector[i];
return C;
}
public LevenbergMarquardt(Function func, JFunc Jfunc, NVector p_min, NVector p_max, NVector dp, double[] eps, UpdateType updateType)
{
this.func = func;
this.Jfunc = Jfunc;
n = p_min.N;
this.p_min = p_min;
if (p_max.N != n) throw new Exception("LevenbergMarquardt: size mismatch p_max");
this.p_max = p_max;
if (Jfunc == null)
{
if (dp.N != n) throw new Exception("LevenbergMarquardt: size mismatch dp");
this.dp = dp;
}
MaxIter = 50 * n;
this.eps = eps;
this.updateType = updateType;
}
private static bool fitSignal(double[] d, int start, int dataLength,
ref double A, ref double B, ref double C, ref double a, ref double b, ref double tOffset)
{
NVector t = new NVector(dataLength);
for (int t0 = 0; t0 < dataLength; t0++) t[t0] = (double)t0 / SR;
NVector y = new NVector(dataLength);
for (int i = 0; i < dataLength; i++)
y[i] = d[start + i];
NVector p = LM.Calculate(new NVector(new double[] { A, B, C, a, b, tOffset }), t, y);
A = p[0];
B = p[1];
C = p[2];
a = p[3];
b = p[4];
tOffset = p[5];
return LM.Result > 0;
}
public NVector Abs()
{
NVector A = new NVector(this);
for (int i = 0; i < _n; i++)
A._vector[i] = Math.Abs(_vector[i]);
return A;
}
public static NVector Uniform(double c, int dim)
{
NVector A = new NVector(dim);
for (int i = 0; i < dim; i++)
A._vector[i] = c;
return A;
}
public static NVector operator /(NVector A, double b)
{
NVector C = new NVector(A);
for (int i = 0; i < A._n; i++)
C._vector[i] /= b;
return C;
}
static NMMatrix Jfunc(NVector t, NVector p)
{
double eat;
double ebt;
NMMatrix J = new NMMatrix(t.N, p.N);
for (int i = 0; i < t.N; i++)
{
double t0 = t[i] - p[5];
if (t0 < 0D)
J[i, 2] = 1D;
else
{
eat = Math.Exp(-p[3] * t0);
ebt = Math.Exp(-p[4] * t0);
J[i, 0] = ebt * (1D - eat);
J[i, 1] = 1D - ebt;
J[i, 2] = ebt;
J[i, 3] = p[0] * t0 * eat * ebt;
J[i, 4] = -ebt * t0 * (p[0] * (1D - eat) + p[2] - p[1]);
J[i, 5] = ebt * (p[0] * (p[4] * (1D - eat) - p[3] * eat) + (p[2] - p[1]) * p[4]);
}
}
return J;
}
public double Dot(NVector A)
{
if (A._n != _n) throw new Exception("NVector.Dot: incompatable sizes");
double c = 0D;
for (int i = 0; i < A._n; i++)
c += A._vector[i] * _vector[i];
return c;
}
private NMMatrix Jacobian(NVector p, NVector y)
{
NVector ps = new NVector(p); //save a copy
NMMatrix J = new NMMatrix(m, n); //creating a new J from scratch
double del_p;
for (int j = 0; j < n; j++)
{
del_p = Math.Max(dp[j] * Math.Abs(p[j]), dp[j]);
p[j] = ps[j] + del_p;
NVector y1 = func(t, p);
if (dp[j] != 0D) //forward or backward difference
J.ReplaceColumn(j, (y1 - y) / del_p);
else //central difference
{
p[j] = ps[j] - del_p;
J.ReplaceColumn(j, (y1 - func(t, p)) / (2D * del_p));
}
p[j] = ps[j]; //restore this value
}
return J;
}
private NMMatrix Broyden(NVector p_old, NVector y_old, NMMatrix J, NVector p, NVector y)
{
NVector h = p - p_old;
J = J + (y - y_old - J * h).Cross(h) / h.Dot(h);
return J;
}
public NVector Calculate(NVector par_initial, NVector t, NVector y_dat)
{
_result = 0;
m = t.N;
if (par_initial.N != n) throw new Exception("LevenbergMarquardt.Calculate: size mismatch parms");
this.p = par_initial;
this.t = t;
if (y_dat.N != m) throw new Exception("LevenbergMarquardt.Calculate: size mismatch t-y");
this.y_dat = y_dat;
// weight_sq = (m - n + 1) / y_dat.Dot(y_dat);
DOF = (double)(m - n + 1);
//initalize Jacobian and related matrices
y_hat = func(t, p);
y_old = y_hat;
if (Jfunc == null)
J = Jacobian(p, y_hat);
else
J = Jfunc(t, p);
NVector delta_y = y_dat - y_hat;
X2 = delta_y.Dot(delta_y);
JtJ = J.Transpose() * J;
Jtdy = J.Transpose() * delta_y;
iteration = 0;
if (Jtdy.Abs().Max() < eps[0])
{
_result = 1;
return p; //Good guess!!!
}
if (updateType == UpdateType.Marquardt)
lambda = 0.01D;
else
lambda = 0.01D * JtJ.Diag().Max();
bool stop = false;
/************************** Begin Main loop ***********************/
// y_hat = vector of y estimates for current value of parameters
// y_try = vector of y estimates for current trial value of parameters
// y_dat = given dependent values (fixed)
// y_old = vector of y estimates for previous value of parameters (used in Broyden estimate of J)
// t = given independent values (fixed)
// p = current accepted estimate of parameters
// h = last calculated (trial) increment for the parameters
// p_try = current trial value for the parameters
// p_old = previous accepted value of parameters (used in Broyden estimate of J)
// X2 = chi^2 of last accepted estimate
// X2_try = chi^2 of current trial estimate
// J = current estimate of Jacobian at p
while (!stop)
{
iteration++;
NVector h;
if (updateType == UpdateType.Marquardt)
h = Jtdy / (JtJ + lambda * JtJ.Diag().Diag());
else
h = Jtdy / (JtJ + lambda * NMMatrix.I(n));
NVector p_try = (p + h).Max(p_min).Min(p_max);
NVector y_try = func(t, p_try);
delta_y = y_dat - y_try;
double X2_try = delta_y.Dot(delta_y);
if (updateType == UpdateType.Quadratic)
{
alpha = Jtdy.Dot(h) / ((X2_try - X2) / 2D + 2D * Jtdy.Dot(h));
h = h * alpha;
p_try = (p_try + h).Max(p_min).Min(p_max);
delta_y = y_dat - func(t, p_try);
X2_try = delta_y .Dot(delta_y);
}
dX2 = X2_try - X2;
double rho = -dX2 / (2D * (lambda * h + Jtdy).Dot(h));
if (dX2 < 0D) //found a better estimate
{
X2 = X2_try;
p_old = p;
p = p_try;
y_old = y_hat;
y_hat = y_try;
if (iteration % (2 * n) == 0) //|| dX2 > 0 or is it rho > ep[3] ?
if (Jfunc == null)
J = Jacobian(p, y_hat);
else
J = Jfunc(t, p);
else
J = J + (y_hat - y_old - J * h).Cross(h) / h.Dot(h); //Broyden rank-1 update of J
JtJ = J.Transpose() * J;
Jtdy = J.Transpose() * delta_y;
switch (updateType)
{
case UpdateType.Marquardt:
lambda = Math.Max(lambda / lambda_DN_fac, 1E-7);
break;
case UpdateType.Quadratic:
lambda = Math.Max(lambda / (1 + alpha), 1E-7);
break;
case UpdateType.Nielsen:
lambda = lambda * Math.Max(1D / 3D, 1D - Math.Pow(2D * rho - 1D, 3));
nu = 2D;
break;
}
if (Jtdy.Abs().Max() < eps[0] && iteration > 2)
{
_result = 1;
stop = true;
}
else if ((h / p).Abs().Max() < eps[1] && iteration > 2)
{
_result = 2;
stop = true;
}
else if (X2 / (m - n + 1) < eps[2] && iteration > 2)
{
_result = 3;
stop = true;
}
}
else //Not a better estimate
{
if (iteration % (2 * n) == 0) //update J every 2n th no matter what
{
if (Jfunc == null)
J = Jacobian(p, y_hat);
else
J = Jfunc(t, p);
JtJ = J.Transpose() * J;
Jtdy = J.Transpose() * (y_dat - y_hat);
}
switch (updateType)
{
case UpdateType.Marquardt:
lambda = Math.Min(lambda * lambda_UP_fac, 1E7);
break;
case UpdateType.Quadratic:
lambda = lambda + Math.Abs(dX2 / (2D * alpha));
break;
case UpdateType.Nielsen:
lambda = lambda * nu;
nu *= 2D;
break;
}
}
if (iteration > MaxIter && !stop)
{
_result = -1;
return p;
}
}
/************************** End Main loop ************************/
return p;
}
static void Main3(string[] args)
{
NVector t = new NVector(16000);
for (int t0 = 0; t0 < 16000; t0++) t[t0] = (double)t0 / 512D;
NVector p_true = new NVector(new double[] { -5000D, 5000D, 3000D, 4D, 0.01D, 0.12 });
NVector y = new NVector(func(t, p_true));
Random rand = new Random();
for (int i = 0; i < 16000; i++)
y[i] += (2D * rand.NextDouble() - 1D) * 90D;
NVector p = LM.Calculate(new NVector(new double[] { -4000D, 0D, 2900D, 10D, 0.025, 0.25D }), t, y);
Console.WriteLine("Result = " + LM.Result.ToString());
Console.WriteLine("Iterations = " + LM.Iterations.ToString("0"));
Console.WriteLine("Chi square = " + LM.ChiSquare);
Console.WriteLine("SE of fit = " + LM.normalizedStandardErrorOfFit);
Console.WriteLine("Estimates");
Console.WriteLine(p.ToString("0.00000"));
Console.WriteLine(LM.parameterStandardError.ToString("0.0000"));
Console.ReadKey();
}
static void Main2(string[] args)
{
NVector A = new NVector(new double[] { 1, 3, 5, -2, 0 });
NVector B = new NVector(new double[] { -1, -2, 3, 1, 2 });
NVector C = A + B;
Console.WriteLine("A =" + A.ToString("0.000"));
Console.WriteLine("B =" + B.ToString("0.000"));
Console.WriteLine("A+B =" + C.ToString("0.000"));
double p = A.Dot(B);
NMMatrix E = A.Cross(B);
Console.WriteLine("A x B =" + E.ToString("0.000"));
E[4, 0] = -2;
E[4, 1] = 3;
E[4, 2] = 5;
E[4, 3] = -5;
E[4, 4] = 7;
E[0, 0] = -7;
E[1, 3] = -3;
E[3, 4] = -3.5;
E[2, 4] = -2;
NMMatrix H = new NMMatrix(new double[,] { { 5, 3, -2 ,1}, { 0, 3, 2,-3 }, { 4, 2, 3,2 }, { -6, 2, 8,-5 } });
Console.WriteLine("H =" + H.ToString("0.000"));
NVector V = new NVector(new double[] { 1, -1, 3, -2 });
Console.WriteLine("V =" + V.ToString("0.000"));
Console.WriteLine(" V / H =" + (V / H).ToString("0.0000"));
NMMatrix HI = H.Inverse();
Console.WriteLine("Inverse H =" + HI.ToString("0.000"));
Console.WriteLine("H * HI " + (H * HI).ToString("0.00000"));
Console.ReadKey();
NVector F = C / E;
NMMatrix G = E.Inverse();
NMMatrix N = (G * E - NMMatrix.I(5)).Apply((LinearAlgebra.F)Math.Abs);
double e = N.Max();
Console.WriteLine((e*1E15).ToString("0.00"));
Console.ReadKey();
}
public NVector Apply(F func)
{
NVector A = new NVector(_n);
for (int i = 0; i < _n; i++)
A._vector[i] = func(_vector[i]);
return A;
}
public NMMatrix Cross(NVector A)
{
NMMatrix C = new NMMatrix(_n, A._n);
for (int i = 0; i < _n; i++)
for (int j = 0; j < A._n; j++)
C[i,j] += _vector[i] * A._vector[j];
return C;
}
public NMMatrix Augment(NVector V)
{
if (N != V.N) throw new Exception("NMMatrix.Concatenate: incompatable sizes");
NMMatrix B = new NMMatrix(N, M + 1);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
B[i, j] = this[i, j];
B[i, M] = V[i];
}
return B;
}
public NVector Min(NVector A)
{
NVector B = new NVector(this);
for (int i = 0; i < _n; i++)
if (A._vector[i] < _vector[i]) B._vector[i] = A._vector[i];
return B;
}
public NVector Diag()
{
if (_n != _m) throw new Exception("NMMatrix.Diag: non-square matrix");
NVector A = new NVector(_n);
for (int i = 0; i < _n; i++)
A[i] = _matrix[i, i];
return A;
}
public NVector ExtractColumn(int col)
{
if (col < 0 || col >= this.M) throw new Exception("NMMatrix.ReplaceColumn: invalid column number");
NVector V = new NVector(N);
for (int j = 0; j < _n; j++)
V[j] = this[j, col];
return V;
}
public void ReplaceColumn(int col, NVector V)
{
if (col < 0 || col >= this.M) throw new Exception("NMMatrix.ReplaceColumn: invalid column number");
for (int j = 0; j < _n; j++)
this[j, col] = V[j];
}
public static NVector operator *(NMMatrix A, NVector B)
{
if (A.M != B._n) throw new Exception("NVector.Mul: incompatable sizes");
NVector C = new NVector(A.N);
for (int i = 0; i < A.N; i++)
{
double c = 0D;
for (int j = 0; j < A.M; j++)
c += A[i, j] * B._vector[j];
C._vector[i] = c;
}
return C;
}
/* Five parameter fitting functions
static NVector func(NVector t, NVector p)
{
NVector y = new NVector(t.N);
for (int i = 0; i < t.N; i++)
{
double t0 = t[i] - p[3];
if (t0 > 0)
y[i] = p[4] + p[0] * (1D - Math.Exp(-p[1] * t0)) * Math.Exp(-p[2] * t0);
else
y[i] = p[4];
}
return y;
}
static NMMatrix Jfunc(NVector t, NVector p)
{
NMMatrix J = new NMMatrix(t.N, p.N);
for (int i = 0; i < t.N; i++)
{
J[i, 4] = 1D;
double t0 = t[i] - p[3];
if (t0 < 0D) continue;
J[i, 0] = (1D - Math.Exp(-p[1] * t0)) * Math.Exp(-p[2] * t0);
J[i, 1] = p[0] * t0 * Math.Exp(-(p[1] + p[2]) * t0);
J[i, 2] = -p[0] * t0 * (1D - Math.Exp(-p[1] * t0)) * Math.Exp(-p[2] * t0);
J[i, 3] = p[0] * (p[2] * (1D - Math.Exp(-p[1] * t0)) * Math.Exp(-p[2] * t0) - p[1] * Math.Exp(-(p[1] + p[2]) * t0));
}
return J;
}
*/
/* Six parameter fitting functions */
static NVector func(NVector t, NVector p)
{
//parameters: A, B, C, a, b, t0
NVector y = new NVector(t.N);
for (int i = 0; i < t.N; i++)
{
double t0 = t[i] - p[5];
if (t0 > 0)
{
double ebt = Math.Exp(-p[4] * t0);
y[i] = p[2] + p[0] * ebt * (1D - Math.Exp(-p[3] * t0)) + (p[1] - p[2]) * (1D - ebt);
}
else
y[i] = p[2];
}
return y;
}