/// <summary>
/// Removes the third order of a matrix by calculating the parameters a, b, .. i, j of the regression of the matrix in the form: z = a + b*x + c*y + d*x*x + e*x*y + f*y*y + g*x*x*x + h*x*x*y + i*x*y*y + j*y*y*y (x and y are the rows and columns of the matrix, z the matrix elements ),
/// and then subtracting the regression function from each matrix element, thus effectively removing the third order.
/// Here, only matrix elements that have a finite value are included in the calculation of the regression.
/// </summary>
/// <param name="m">The matrix to change.</param>
public static void RemoveThirdOrderFromMatrixIgnoringInvalidElements(IMatrix <double> m)
{
int rows = m.RowCount;
int cols = m.ColumnCount;
int rowsBy2 = rows / 2;
int colsBy2 = cols / 2;
var independent = new List <double> [9];
for (int i = 0; i < independent.Length; ++i)
{
independent[i] = new List <double>();
}
var dependent = new List <double>();
for (int r = 0; r < rows; ++r)
{
for (int c = 0; c < cols; ++c)
{
var z = m[r, c];
if (RMath.IsFinite(z))
{
long x = c - colsBy2;
long y = r - rowsBy2;
independent[0].Add(x);
independent[1].Add(y);
independent[2].Add(x * x);
independent[3].Add(x * y);
independent[4].Add(y * y);
independent[5].Add(x * x * x);
independent[6].Add(x * x * y);
independent[7].Add(x * y * y);
independent[8].Add(y * y * y);
dependent.Add(z);
}
}
}
var regress = new Altaxo.Calc.Regression.LinearFitBySvd(new MyPriv2ndOrderIndependentMatrix(independent), dependent.ToArray(), null, dependent.Count, 1 + independent.Length, 1e-6);
var coef = regress.Parameter;
for (int r = 0; r < rows; ++r)
{
for (int c = 0; c < cols; ++c)
{
var z = m[r, c];
if (RMath.IsFinite(z))
{
long x = c - colsBy2;
long y = r - rowsBy2;
double offs = coef[0] + coef[1] * x + coef[2] * y + coef[3] * x * x + coef[4] * x * y + coef[5] * y * y + coef[6] * x * x * x + coef[7] * x * x * y + coef[8] * x * y * y + coef[9] * y * y * y;
m[r, c] -= offs;
}
}
}
}
/// <summary>
/// Removes the third order of a matrix by calculating the parameters a, b, .. i, j of the regression of the matrix in the form: z = a + b*x + c*y + d*x*x + e*x*y + f*y*y + g*x*x*x + h*x*x*y + i*x*y*y + j*y*y*y (x and y are the rows and columns of the matrix, z the matrix elements ),
/// and then subtracting the regression function from each matrix element, thus effectively removing the third order.
/// Here, only matrix elements that have a finite value are included in the calculation of the regression.
/// </summary>
/// <param name="m">The matrix to change.</param>
public static void RemoveThirdOrderFromMatrixIgnoringInvalidElements(IMatrix m)
{
int rows = m.Rows;
int cols = m.Columns;
int rowsBy2 = rows / 2;
int colsBy2 = cols / 2;
var independent = new List<double>[9];
for (int i = 0; i < independent.Length; ++i)
independent[i] = new List<double>();
var dependent = new List<double>();
for (int r = 0; r < rows; ++r)
{
for (int c = 0; c < cols; ++c)
{
var z = m[r, c];
if (RMath.IsFinite(z))
{
long x = c - colsBy2;
long y = r - rowsBy2;
independent[0].Add(x);
independent[1].Add(y);
independent[2].Add(x * x);
independent[3].Add(x * y);
independent[4].Add(y * y);
independent[5].Add(x * x * x);
independent[6].Add(x * x * y);
independent[7].Add(x * y * y);
independent[8].Add(y * y * y);
dependent.Add(z);
}
}
}
var regress = new Altaxo.Calc.Regression.LinearFitBySvd(new MyPriv2ndOrderIndependentMatrix(independent), dependent.ToArray(), null, dependent.Count, 1 + independent.Length, 1e-6);
var coef = regress.Parameter;
for (int r = 0; r < rows; ++r)
{
for (int c = 0; c < cols; ++c)
{
var z = m[r, c];
if (RMath.IsFinite(z))
{
long x = c - colsBy2;
long y = r - rowsBy2;
double offs = coef[0] + coef[1] * x + coef[2] * y + coef[3] * x * x + coef[4] * x * y + coef[5] * y * y + coef[6] * x * x * x + coef[7] * x * x * y + coef[8] * x * y * y + coef[9] * y * y * y;
m[r, c] -= offs;
}
}
}
}
