public int Gauss()
{
int[] invArr = NumTheoryUtils.GetFieldInverse(Prime);
// Gaussian elimination with partial pivoting
int i, j;
i = j = 0;
while ((i < RowCount) && (j < ColCount - 1))
{
// find pivot row and swap
int max = i;
for (int k = i + 1; k < RowCount; k++)
{
if (data[k][j] > data[max][j])
{
max = k;
}
}
if (data[max][j] != 0)
{
SwapRows(i, max);
int toMul = invArr[data[i][j]];
for (int k = 0; k < ColCount; k++)
{
data[i][k] = Modulo(data[i][k] * toMul);
}
for (int u = i + 1; u < RowCount; u++)
{
int m = Modulo(data[u][j]);
for (int v = 0; v < ColCount; v++)
{
data[u][v] = Modulo(data[u][v] - data[i][v] * m);
}
data[u][j] = 0;
}
i++;
}
j++;
}
// Get number of lines differrent from zero
int num = 0;
for (int k = 0; k < RowCount; k++)
{
for (int v = 0; v < ColCount; v++)
{
if (data[k][v] != 0)
{
num++;
break;
}
}
}
return(num);
}
public static Zp EvalutePolynomialAtPoint(IList <Zp> polynomial, Zp point)
{
int evaluation = 0;
for (int i = 0; i < polynomial.Count; i++)
{
evaluation += polynomial[i].Value * NumTheoryUtils.ModPow(point.Value, i, point.Prime);
}
return(new Zp(point.Prime, evaluation));
}
private BigZpMatrix SolveInv(BigZpMatrix B, int[] piv)
{
if (B.RowCount != RowCount)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!Nonsingular)
{
throw new ArgumentException("Matrix is singular.");
}
// Copy right hand side with pivoting
int nx = B.ColCount;
var Xmat = B.GetSubMatrix(piv, 0, nx - 1);
var X = Xmat.data;
// Solve L*Y = B(piv,:)
for (int k = 0; k < RowCount; k++)
{
for (int i = k + 1; i < RowCount; i++)
{
for (int j = 0; j < nx; j++)
{
X[i][j] = Modulo(X[i][j] - X[k][j] * data[i][k]);
}
}
}
// Solve U*X = Y;
for (int k = RowCount - 1; k >= 0; k--)
{
for (int j = 0; j < nx; j++)
{
X[k][j] = Modulo(X[k][j] * NumTheoryUtils.CalcInverse(data[k][k], Prime));
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < nx; j++)
{
X[i][j] = Modulo(X[i][j] - X[k][j] * data[i][k]);
}
}
}
return(Xmat);
}
public static ZpMatrix GetPrimitiveVandermondeMatrix(int rowNum, int colNum, int prime)
{
int primitive = NumTheoryUtils.GetFieldMinimumPrimitive(prime);
if (primitive == 0)
{
throw new ArgumentException("Cannot create a primitive Vandermonde matrix from a non-prime number. ");
}
var A = new ZpMatrix(rowNum, colNum, prime);
for (int j = 0; j < colNum; j++)
{
A.data[0][j] = 1;
}
if (rowNum == 1)
{
return(A);
}
/* This variable represents primitive^j for the j-th player*/
int primitive_j = 1;
for (int j = 0; j < colNum; j++)
{
A.data[1][j] = primitive_j;
primitive_j = Zp.Modulo(primitive_j * primitive, prime);
}
for (int j = 0; j < colNum; j++)
{
for (int i = 2; i < rowNum; i++)
{
A.data[i][j] = Zp.Modulo(A.data[i - 1][j] * A.data[1][j], prime);
}
}
return(A);
}
/// <param name="SamplePoint"> - the desired sampling point. </param>
/// <returns> the result of the polynom when replacing variable ("x") with the sampling point </returns>
public virtual Zp Sample(Zp SamplePoint)
{
if (Coefficients.Count == 0)
{
return(null);
}
/* The initialized sum is 0 */
var Sum = new Zp(CoefficinesFieldSize, 0);
for (int i = 0; i < Coefficients.Count; i++)
{
/* replace each "Ai*x^i" with "Ai*SamplePoint^i" */
var Xi = new Zp(CoefficinesFieldSize,
NumTheoryUtils.ModPow(SamplePoint.Value, i, CoefficinesFieldSize));
var Ai = new Zp(CoefficinesFieldSize, Coefficients[i].Value);
var AiXi = Xi.Mul(Ai);
/* Sum all these values(A0+A1X^1+...AnX^n) */
Sum = Sum.Add(AiXi);
}
return(Sum);
}
private ZpMatrix GetLUDecomposition(int[] pivot, int[] fieldInv)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
var LU = new ZpMatrix(this);
int[][] LUArr = LU.data;
int[] piv = pivot;
for (int i = 0; i < RowCount; i++)
{
piv[i] = i;
}
int pivsign = 1;
int[] LUrowi;
var LUcolj = new int[RowCount];
// Outer loop.
for (int j = 0; j < RowCount; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < RowCount; i++)
{
LUcolj[i] = LUArr[i][j];
}
// Apply previous transformations.
for (int i = 0; i < RowCount; i++)
{
LUrowi = LUArr[i];
// Most of the time is spent in the following dot product.
int kmax = Math.Min(i, j);
int s = 0;
for (int k = 0; k < kmax; k++)
{
s = Modulo(s + LUrowi[k] * LUcolj[k]);
}
LUrowi[j] = LUcolj[i] = Modulo(LUcolj[i] - s);
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < RowCount; i++)
{
if ((LUcolj[i]) > (LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < RowCount; k++)
{
int t = LUArr[p][k];
LUArr[p][k] = LUArr[j][k];
LUArr[j][k] = t;
}
int r = piv[p];
piv[p] = piv[j];
piv[j] = r;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < RowCount & LUArr[j][j] != 0)
{
for (int i = j + 1; i < RowCount; i++)
{
//LUArr[i][j] = Modulo(LUArr[i][j] * fieldInv[Modulo(LUArr[j][j])]);
LUArr[i][j] = Modulo(LUArr[i][j] * NumTheoryUtils.MultiplicativeInverse(Modulo(LUArr[j][j]), Prime));
}
}
}
return(LU);
}
