/// <summary>
/// Returns a Vandermonde matrix in the field (each element is modulu prime).
/// </summary>
public static ZpMatrix GetShamirRecombineMatrix(int matrixSize, int prime)
{
var A = new ZpMatrix(matrixSize, matrixSize, prime);
if (matrixSize == 1)
{
A.data[0][0] = 1;
return(A);
}
for (int i = 0; i < matrixSize; i++)
{
A.data[i][0] = 1;
}
for (int i = 0; i < matrixSize; i++)
{
A.data[i][1] = i + 1;
}
for (int i = 0; i < matrixSize; i++)
{
for (int j = 2; j < matrixSize; j++)
{
A.data[i][j] = Zp.Modulo(A.data[i][j - 1] * A.data[i][1], prime);
}
}
return(A);
}
public static ZpMatrix GetVandermondeMatrix(int rowNum, int colNum, long prime)
{
var A = new ZpMatrix(rowNum, colNum, prime);
for (int j = 0; j < colNum; j++)
{
A.data[0][j] = 1;
}
if (rowNum == 1)
{
return(A);
}
for (int j = 0; j < colNum; j++)
{
A.data[1][j] = j + 1;
}
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);
}
/// <summary>
/// Creates and return a random rowNum-by-colNum matrix with values between '0' and 'prime-1'.
/// </summary>
public static ZpMatrix GetRandomMatrix(int rowNum, int colNum, long prime)
{
var A = new ZpMatrix(rowNum, colNum, prime);
for (int i = 0; i < rowNum; i++)
{
for (int j = 0; j < colNum; j++)
{
A.data[i][j] = Zp.Modulo((long)(StaticRandom.NextDouble() * (prime)), prime);
}
}
return(A);
}
public static ZpMatrix GetPrimitiveVandermondeMatrix(int rowNum, int colNum, long 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*/
long 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);
}
public static ZpMatrix GetVandermondeMatrix(int rowNum, IList <Zp> values, int prime)
{
int colNum = values.Count;
var A = new ZpMatrix(rowNum, colNum, prime);
for (int j = 0; j < colNum; j++)
{
A.data[0][j] = 1;
}
if (rowNum == 1)
{
return(A);
}
for (int j = 0; j < colNum; j++)
{
for (int i = 1; i < rowNum; i++)
{
A.data[i][j] = Zp.Modulo(A.data[i - 1][j] * values[j].Value, prime);
}
}
return(A);
}
/* calculate i mod prime */
private long Modulo(long i)
{
return(Zp.Modulo(i, Prime));
}