/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="power"></param>
/// <param name="cf"></param>
/// <param name="error"></param>
/// <param name="equation"></param>
/// <returns></returns>
private static float[] expn(float[] x, float[] y, int power, out float[] cf, out float error, out string equation)
{
// Options:
int m = (power < 1) ? 2 : power + 1;
int n = x.Length, i;
float[] ya = new float[n];
// log-scale:
for (i = 0; i < n; i++)
{
ya[i] = Maths.Log(y[i], Maths.E);
}
// approximation:
cf = LeastSquaresOptions.Coefficients(x, ya, m);
float[] p = LeastSquaresOptions.Polynomial(x, cf);
// exponential-scale:
for (i = 0; i < n; i++)
{
ya[i] = Maths.Pow(Maths.E, p[i]);
}
error = LeastSquaresOptions.Error(ya, y);
equation = "EXP" + '(' + LeastSquaresOptions.Equation(cf) + ')';
return(ya);
}
/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="power"></param>
/// <param name="cf"></param>
/// <param name="error"></param>
/// <param name="equation"></param>
/// <returns></returns>
private static Complex32[] powr(Complex32[] x, Complex32[] y, int power, out Complex32[] cf, out Complex32 error, out string equation)
{
// Options:
int m = (power < 1) ? 2 : power + 1;
int n = x.Length, i;
Complex32[] xa = new Complex32[n];
Complex32[] ya = new Complex32[n];
// log-scale:
for (i = 0; i < n; i++)
{
xa[i] = Maths.Log(x[i]);
ya[i] = Maths.Log(y[i]);
}
// approximation:
cf = LeastSquaresOptions.Coefficients(xa, ya, m);
Complex32[] p = LeastSquaresOptions.Polynomial(xa, cf);
// exponential-scale:
for (i = 0; i < n; i++)
{
ya[i] = Maths.Exp(p[i]);
}
error = LeastSquaresOptions.Error(ya, y);
equation = "EXP" + '(' + LeastSquaresOptions.Equation(cf, " * LN(X)^") + ')';
return(ya);
}
/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="power"></param>
/// <param name="cf"></param>
/// <param name="error"></param>
/// <param name="equation"></param>
/// <returns></returns>
private static Complex32[] poly(Complex32[] x, Complex32[] y, int power, out Complex32[] cf, out Complex32 error, out string equation)
{
// Options:
int m = (power < 1) ? 2 : power + 1;
cf = LeastSquaresOptions.Coefficients(x, y, m);
Complex32[] ya = LeastSquaresOptions.Polynomial(x, cf);
error = LeastSquaresOptions.Error(ya, y);
equation = LeastSquaresOptions.Equation(cf);
return(ya);
}
/// <summary>
/// Returns an array of polynomial values.
/// </summary>
/// <param name="x">Argument</param>
/// <param name="c">Approximation coefficients</param>
/// <returns>Array</returns>
public static float[] Polynomial(float[] x, float[] c)
{
int n = x.Length, i;
float[] y = new float[n];
for (i = 0; i < n; i++)
{
y[i] = LeastSquaresOptions.Polynomial(x[i], c);
}
return(y);
}
/// <summary>
/// Returns an array of polynomial values.
/// </summary>
/// <param name="x">Argument</param>
/// <param name="c">Approximation coefficients</param>
/// <returns>Array</returns>
public static Complex32[] Polynomial(Complex32[] x, Complex32[] c)
{
int n = x.Length, i;
Complex32[] y = new Complex32[n];
for (i = 0; i < n; i++)
{
y[i] = LeastSquaresOptions.Polynomial(x[i], c);
}
return(y);
}
/// <summary>
/// Returns an array of polynomial values.
/// </summary>
/// <param name="x">Argument</param>
/// <param name="y">Function</param>
/// <param name="iterations">Number of iterations</param>
/// <returns>Array</returns>
public static float[] Coefficients(float[] x, float[] y, int iterations)
{
int i, j;
int n = x.Length;
int m = iterations < 1 ? 1 : iterations;
float[,] matrix = new float[m, m + 1];
for (i = 0; i < m; i++)
{
for (j = 0; j < m; j++)
{
matrix[i, j] = LeastSquaresOptions.SummaryPow(x, j + i);
}
matrix[i, m] = LeastSquaresOptions.SummaryPow(y, x, 1, i);
}
return(Matrice.Solve(matrix));
}
/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="power"></param>
/// <param name="cf"></param>
/// <param name="error"></param>
/// <param name="equation"></param>
/// <returns></returns>
private static Complex32[] logc(Complex32[] x, Complex32[] y, int power, out Complex32[] cf, out Complex32 error, out string equation)
{
// Options:
int n = x.Length, i;
int m = (power < 1) ? 2 : power + 1;
Complex32[] xa = new Complex32[n];
Complex32[] ya = new Complex32[n];
// log-scale:
for (i = 0; i < n; i++)
{
xa[i] = Maths.Log(x[i]);
}
// approximation:
cf = LeastSquaresOptions.Coefficients(xa, y, m);
ya = LeastSquaresOptions.Polynomial(xa, cf);
error = LeastSquaresOptions.Error(ya, y);
equation = LeastSquaresOptions.Equation(cf, " * LN(X)^");
return(ya);
}
