private static ZpMatrix getWelchBerlekampMatrix(IList <Zp> XVlaues, IList <Zp> YVlaues, int n, int e, int prime)
{
var NVanderMonde = ZpMatrix.GetVandermondeMatrix(n - e, XVlaues, prime).Transpose;
var EVanderMonde = ZpMatrix.GetVandermondeMatrix(e, XVlaues, prime).Transpose;
int[] scalarVector = new int[YVlaues.Count];
int i = 0;
foreach (Zp zp in YVlaues)
{
scalarVector[i++] = -zp.Value;
}
EVanderMonde = EVanderMonde.MulMatrixByScalarsVector(scalarVector);
return(ZpMatrix.GetConcatenationMatrix(NVanderMonde, EVanderMonde));
}
/*
* Finds a solution to a system of linear equations represtented by an
* n-by-n+1 matrix A: namely, denoting by B the left n-by-n submatrix of A
* and by C the last column of A, finds a column vector x such that Bx=C.
* If more than one solution exists, chooses one arbitrarily by setting some
* values to 0. If no solutions exists, returns false. Otherwise, places
* a solution into the first argument and returns true.
*
* Note : matrix A changes (gets converted to row echelon form).
*/
private static Zp[] linearSolve(ZpMatrix A, ZpMatrix B, int prime)
{
var invArray = NumTheoryUtils.GetFieldInverse(prime);
var C = ZpMatrix.GetConcatenationMatrix(A, B); // augmented matrix
int n = C.RowCount;
int[] solution = new int[n];
int temp;
int firstDeterminedValue = n;
// we will be determining values of the solution
// from n-1 down to 0. At any given time,
// values from firstDeterminedValue to n-1 have been
// found. Initializing to n means
// no values have been found yet.
// To put it another way, the variabe firstDeterminedValue
// stores the position of first nonzero entry in the row just examined
// (except at initialization)
int rank = C.Gauss();
int[][] cContent = C.Data;
// can start at rank-1, because below that are all zeroes
for (int row = rank - 1; row >= 0; row--)
{
// remove all the known variables from the equation
temp = cContent[row][n];
int col;
for (col = n - 1; col >= firstDeterminedValue; col--)
{
temp = Zp.Modulo(temp - (cContent[row][col] * solution[col]), prime);
}
// now we need to find the first nonzero coefficient in this row
// if it exists before firstDeterminedValue
// because the matrix is in row echelon form, the first nonzero
// coefficient cannot be before the diagonal
for (col = row; col < firstDeterminedValue; col++)
{
if (cContent[row][col] != 0)
{
break;
}
}
if (col < firstDeterminedValue) // this means we found a nonzero coefficient
{
// we can determine the variables in position from col to firstDeterminedValue
// if this loop executes even once, then the system is undertermined
// we arbitrarily set the undetermined variables to 0, because it make math easier
for (int j = col + 1; j < firstDeterminedValue; j++)
{
solution[j] = 0;
}
// Now determine the variable at the nonzero coefficient
//div(solution[col], temp, A.getContent()[row][col]);
solution[col] = temp * invArray[Zp.Modulo(cContent[row][col], prime)];
firstDeterminedValue = col;
}
else
{
// this means there are no nonzero coefficients before firstDeterminedValue.
// Because we skip all the zero rows at the bottom, the matrix is in
// row echelon form, and firstDeterminedValue is equal to the
// position of first nonzero entry in row+1 (unless it is equal to n),
// this means we are at a row with all zeroes except in column n
// The system has no solution.
return(null);
}
}
// set the remaining undetermined values, if any, to 0
for (int col = 0; col < firstDeterminedValue; col++)
{
solution[col] = 0;
}
var ResultVec = new Zp[n];
for (int i = 0; i < n; i++)
{
ResultVec[i] = new Zp(prime, solution[i]);
}
return(ResultVec);
}