/// <summary>
/// Uses the signal in vector x to build a model with <c>numberOfCoefficients</c> parameter.
/// </summary>
/// <param name="x">Signal for building the model.</param>
/// <param name="coefficients">Vector to be filled with the coefficients of the model.</param>
/// <param name="errors">Vector to be filled with the sum of forward and backward prediction error for every stage of the model.</param>
/// <param name="reflectionCoefficients">Vector to be filled with the reflection coefficients.</param>
/// <param name="tempStorage">Instance of this class used to hold the temporary arrays.</param>
/// <returns>The mean square error of backward and forward prediction.</returns>
private static double Execution(IROVector x, IVector coefficients, IVector errors, IVector reflectionCoefficients, BurgAlgorithm tempStorage)
{
int N = x.Length - 1;
int m = coefficients.Length;
double[] Ak; // Prediction coefficients, Ak[0] is always 1
double[] b; // backward prediction errors
double[] f; // forward prediction errors
if (null != tempStorage)
{
tempStorage.EnsureAllocation(x.Length, coefficients.Length);
Ak = tempStorage._Ak;
b = tempStorage._b;
f = tempStorage._f;
for (int i = 1; i <= coefficients.Length; i++)
Ak[i] = 0;
}
else
{
Ak = new double[coefficients.Length + 1];
b = new double[x.Length];
f = new double[x.Length];
}
Ak[0] = 1;
// Initialize forward and backward prediction errors with x
for (int i = 0; i <= N; i++)
f[i] = b[i] = x[i];
double Dk = 0;
for (int i = 0; i <= N; i++)
Dk += 2 * f[i] * f[i];
Dk -= f[0] * f[0] + b[N] * b[N];
// Burg recursion
int k;
double sumE = 0; // error sum
for (k = 0; (k < m) && (Dk > 0); k++)
{
// Compute mu
double mu = 0;
for (int n = 0; n < N - k; n++)
mu += f[n + k + 1] * b[n];
mu *= -2 / Dk;
// Update Ak
for (int n = 0; n <= (k + 1) / 2; n++)
{
double t1 = Ak[n] + mu * Ak[k + 1 - n];
double t2 = Ak[k + 1 - n] + mu * Ak[n];
Ak[n] = t1;
Ak[k + 1 - n] = t2;
}
if (null != reflectionCoefficients)
reflectionCoefficients[k] = Ak[k + 1];
// update forward and backward predition error with simultaneous total error calculation
sumE = 0;
for (int n = 0; n < N - k; n++)
{
double t1 = f[n + k + 1] + mu * b[n];
double t2 = b[n] + mu * f[n + k + 1];
f[n + k + 1] = t1;
b[n] = t2;
sumE += t1 * t1 + t2 * t2;
}
if (null != errors)
errors[k] = sumE / (2 * (N - k));
// Update Dk
// Note that it is possible to update Dk without total error calculation because sumE = Dk*(1-mu.GetModulusSquared())
// but this will render the algorithm numerically unstable especially for higher orders and low noise
Dk = sumE - (f[k + 1] * f[k + 1] + b[N - k - 1] * b[N - k - 1]);
}
// Assign coefficients
for (int i = 0; i < m; i++)
coefficients[i] = Ak[i + 1];
// Assign the rest of reflection coefficients and errors with zero
// if not all stages could be calculated because Dk was zero or because of rounding effects smaller than zero
for (int i = k + 1; i < m; i++)
{
if (null != reflectionCoefficients)
reflectionCoefficients[i] = 0;
if (null != errors)
errors[i] = 0;
}
return sumE / (2 * (N - k));
}
/// <summary>
/// Uses the signal in vector x to build a model with <c>numberOfCoefficients</c> parameter.
/// </summary>
/// <param name="x">Signal for building the model.</param>
/// <param name="coefficients">Vector to be filled with the coefficients of the model.</param>
/// <param name="errors">Vector to be filled with the sum of forward and backward prediction error for every stage of the model.</param>
/// <param name="reflectionCoefficients">Vector to be filled with the reflection coefficients.</param>
/// <param name="tempStorage">Instance of this class used to hold the temporary arrays.</param>
/// <returns>The mean square error of backward and forward prediction.</returns>
private static double Execution(IReadOnlyList <double> x, IVector <double> coefficients, IVector <double> errors, IVector <double> reflectionCoefficients, BurgAlgorithm tempStorage)
{
int N = x.Count - 1;
int m = coefficients.Length;
double[] Ak; // Prediction coefficients, Ak[0] is always 1
double[] b; // backward prediction errors
double[] f; // forward prediction errors
if (null != tempStorage)
{
tempStorage.EnsureAllocation(x.Count, coefficients.Length);
Ak = tempStorage._Ak;
b = tempStorage._b;
f = tempStorage._f;
for (int i = 1; i <= coefficients.Length; i++)
{
Ak[i] = 0;
}
}
else
{
Ak = new double[coefficients.Length + 1];
b = new double[x.Count];
f = new double[x.Count];
}
Ak[0] = 1;
// Initialize forward and backward prediction errors with x
for (int i = 0; i <= N; i++)
{
f[i] = b[i] = x[i];
}
double Dk = 0;
for (int i = 0; i <= N; i++)
{
Dk += 2 * f[i] * f[i];
}
Dk -= f[0] * f[0] + b[N] * b[N];
// Burg recursion
int k;
double sumE = 0; // error sum
for (k = 0; (k < m) && (Dk > 0); k++)
{
// Compute mu
double mu = 0;
for (int n = 0; n < N - k; n++)
{
mu += f[n + k + 1] * b[n];
}
mu *= -2 / Dk;
// Update Ak
for (int n = 0; n <= (k + 1) / 2; n++)
{
double t1 = Ak[n] + mu * Ak[k + 1 - n];
double t2 = Ak[k + 1 - n] + mu * Ak[n];
Ak[n] = t1;
Ak[k + 1 - n] = t2;
}
if (null != reflectionCoefficients)
{
reflectionCoefficients[k] = Ak[k + 1];
}
// update forward and backward predition error with simultaneous total error calculation
sumE = 0;
for (int n = 0; n < N - k; n++)
{
double t1 = f[n + k + 1] + mu * b[n];
double t2 = b[n] + mu * f[n + k + 1];
f[n + k + 1] = t1;
b[n] = t2;
sumE += t1 * t1 + t2 * t2;
}
if (null != errors)
{
errors[k] = sumE / (2 * (N - k));
}
// Update Dk
// Note that it is possible to update Dk without total error calculation because sumE = Dk*(1-mu.GetModulusSquared())
// but this will render the algorithm numerically unstable especially for higher orders and low noise
Dk = sumE - (f[k + 1] * f[k + 1] + b[N - k - 1] * b[N - k - 1]);
}
// Assign coefficients
for (int i = 0; i < m; i++)
{
coefficients[i] = Ak[i + 1];
}
// Assign the rest of reflection coefficients and errors with zero
// if not all stages could be calculated because Dk was zero or because of rounding effects smaller than zero
for (int i = k + 1; i < m; i++)
{
if (null != reflectionCoefficients)
{
reflectionCoefficients[i] = 0;
}
if (null != errors)
{
errors[i] = 0;
}
}
return(sumE / (2 * (N - k)));
}