/// <summary>
/// Ctor
/// </summary>
/// <param name="columnCardinality">matrix size</param>
/// <param name="SubMatrix">the SubMatrix</param>
/// <param name="Det">determinant</param>
public SmallerDet(int columnCardinality, LinearAlgebra.RealMatrix SubMatrix, double Det)
{
this.SubMatrixSize = columnCardinality;// it's a square subMat.
this.SubMatrix = SubMatrix;
this.Det = Det;
} // end Ctor
}// end gestioneQuadrata
/// <summary>
/// metodo ricorsivo che, partendo da una nxn, trova tutte le sottomatrici kxk, con k in [1, n-1].
/// </summary>
/// <param name="quadrataAnalizzanda"></param>
/// <returns></returns>
private int sottomatriciTelescopiche(LinearAlgebra.RealMatrix quadrataAnalizzanda)
{
//
int Rank = 0;// init
#if debug
rangoQuadrata_recursion_ordinal++; //----dbg----
System.Console.WriteLine(" rangoQuadrata_recursion_ordinal= {0}", rangoQuadrata_recursion_ordinal); //----dbg----
#endif
//
for (int curRow = 0; curRow < quadrataAnalizzanda.Get_rows; curRow++)
{
for (int curCol = 0; curCol < quadrataAnalizzanda.Get_cols; curCol++)
{
LinearAlgebra.RealMatrix subMatrix = quadrataAnalizzanda.reductor(curRow, curCol); // current SubMatrix
#if debug
System.Console.WriteLine(" dimensione sottomatrice= {0}", subMatrix.Get_rows);
System.Console.WriteLine(" linee eliminate row, col = {0},{1}", curRow, curCol);
subMatrix.show();
#endif
//
if (0 == subMatrix.Get_rows) // size one matrix is a scalar;
{ // zero size matrix is no-number.
return(-1); //-1 means 0x0 matrix dimension reached.
}// avoid an exception, due to zero-sized matrix.
//
//---------##########################################
double subMatrix_det = subMatrix.det();//############
//---------##########################################
//
//-----scrivere estrattore di linee coinvolte nella firma
//
// codifica:
// -2 means by now determinant is null.
// -1 means 0x0 matrix dimension reached.
// 0 means null scalar submatrix reached.
// n_in_N means a positive Rank was found.
//
if (System.Math.Abs(subMatrix_det) < +1.0E-12) //-------- by now(i.e. in this dimension) determinant is null.--------------
{ // don't log anything, since determinant is null.
Rank = -2; // -2 means by now determinant is null.
}
else if (System.Math.Abs(subMatrix_det) < +1.0E-12 && subMatrix.Get_rows == 1) // 0 means null scalar submatrix reached.
{ // don't log anything, since determinant is null.
Rank = 0; // 0 means null scalar submatrix reached.
}
else if (System.Math.Abs(subMatrix_det) >= +1.0E-12) //-------#########----positive Rank found---#############--------------
{ //----- log dimension and signature----------###########################-----------------------------------------
Rank = subMatrix.Get_rows; // Rank = subMatrix.Get_rows==n_in_N means a positive Rank was found.
#if debug
System.Console.WriteLine(" first stop at Rank={0}", Rank);
#endif
//---#########################################################------data structure insertion here !-at position[dimension]----##################
((System.Collections.ArrayList)(involvedDimensions[subMatrix.Get_rows])).Add(new SmallerDet(
subMatrix.Get_rows,
subMatrix,
subMatrix_det)
);
#if LogSinkFs
LogSinkFs.Wrappers.LogWrappers.SectionContent("size = " + subMatrix.Get_rows, 0);
subMatrix.show_LogSinkFs();
LogSinkFs.Wrappers.LogWrappers.SectionContent("det = " + subMatrix_det, 0);
#endif
}
else
{
throw new System.Exception("exception in Rank if_instructions found");
}
//
#if debug
System.Console.WriteLine(" Rank= {0}", Rank);
System.Console.WriteLine(" det sottomatrice= {0}", subMatrix_det);
#endif
//
//---------------------------#########################___start recursion__#########################-------------------
Rank = sottomatriciTelescopiche(subMatrix); //-----#########################___start recursion__################-----
//
}// end for Get_cols
}// end for Get_rows
// ready
return(Rank);
}// end sottomatriciTelescopiche()
