/// <summary>
/// Strip leading zero coefficients from the given polynomial
/// </summary>
///
/// <param name="A">The polynomial</param>
///
/// <returns>The reduced polynomial</returns>
private static int[] NormalForm(int[] A)
{
int d = ComputeDegree(A);
// if a is the zero polynomial
if (d == -1)
{
return(new int[1]);
}
// if a already is in normal form
if (A.Length == d + 1)
{
return(IntUtils.DeepCopy(A));
}
// else, reduce a
int[] result = new int[d + 1];
Array.Copy(A, 0, result, 0, d + 1);
return(result);
}
/// <summary>
/// Adds another GF2Vector to this vector
/// </summary>
///
/// <param name="V">The GF2Vector to add</param>
///
/// <returns>Returns <c>this + V</c></returns>
public override Vector Add(Vector V)
{
if (!(V is GF2Vector))
{
throw new ArithmeticException("GF2Vector: Vector is not defined over GF(2)!");
}
GF2Vector otherVec = (GF2Vector)V;
if (Length != otherVec.Length)
{
throw new ArithmeticException("GF2Vector: Length mismatch!");
}
int[] vec = IntUtils.DeepCopy(((GF2Vector)V).m_elements);
for (int i = vec.Length - 1; i >= 0; i--)
{
vec[i] ^= m_elements[i];
}
return(new GF2Vector(Length, vec));
}
/// <summary>
/// Compute the inverse of this matrix
/// </summary>
///
/// <returns>Returns the inverse of this matrix</returns>
public override Matrix ComputeInverse()
{
if (RowCount != ColumnCount)
{
throw new ArithmeticException("GF2Matrix: Matrix is not invertible!");
}
// clone this matrix
int[][] tmpMatrix = ArrayUtils.CreateJagged <int[][]>(RowCount, _length);
for (int i = RowCount - 1; i >= 0; i--)
{
tmpMatrix[i] = IntUtils.DeepCopy(_matrix[i]);
}
// initialize inverse matrix as unit matrix
int[][] invMatrix = ArrayUtils.CreateJagged <int[][]>(RowCount, _length);
for (int i = RowCount - 1; i >= 0; i--)
{
int q = i >> 5;
int r = i & 0x1f;
invMatrix[i][q] = 1 << r;
}
// simultaneously compute Gaussian reduction of tmpMatrix and unit matrix
for (int i = 0; i < RowCount; i++)
{
int q = i >> 5;
int bitMask = 1 << (i & 0x1f);
// if diagonal element is zero
if ((tmpMatrix[i][q] & bitMask) == 0)
{
bool foundNonZero = false;
// find a non-zero element in the same column
for (int j = i + 1; j < RowCount; j++)
{
if ((tmpMatrix[j][q] & bitMask) != 0)
{
// found it, swap rows ...
foundNonZero = true;
SwapRows(tmpMatrix, i, j);
SwapRows(invMatrix, i, j);
// ... and quit searching
j = RowCount;
continue;
}
}
// if no non-zero element was found the matrix is not invertible
if (!foundNonZero)
{
throw new ArithmeticException("GF2Matrix: Matrix is not invertible!");
}
}
// normalize all but i-th row
for (int j = RowCount - 1; j >= 0; j--)
{
if ((j != i) && ((tmpMatrix[j][q] & bitMask) != 0))
{
AddToRow(tmpMatrix[i], tmpMatrix[j], q);
AddToRow(invMatrix[i], invMatrix[j], 0);
}
}
}
return(new GF2Matrix(ColumnCount, invMatrix));
}
/// <summary>
/// Copy constructor
/// </summary>
///
/// <param name="G">The GF2Vector to copy</param>
public GF2Vector(GF2Vector G)
{
this.Length = G.Length;
this.m_elements = IntUtils.DeepCopy(G.m_elements);
}
/// <summary>
/// Compute the inverse of this matrix
/// </summary>
///
/// <returns>Returns the inverse of this matrix (newly created)</returns>
public override Matrix ComputeInverse()
{
if (RowCount != ColumnCount)
{
throw new ArithmeticException("GF2mMatrix: Matrix is not invertible!");
}
// clone this matrix
int[][] tmpMatrix = ArrayUtils.CreateJagged <int[][]>(RowCount, RowCount);
for (int i = RowCount - 1; i >= 0; i--)
{
tmpMatrix[i] = IntUtils.DeepCopy(MatrixN[i]);
}
// initialize inverse matrix as unit matrix
int[][] invMatrix = ArrayUtils.CreateJagged <int[][]>(RowCount, RowCount);
for (int i = RowCount - 1; i >= 0; i--)
{
invMatrix[i][i] = 1;
}
// simultaneously compute Gaussian reduction of tmpMatrix and unit
// matrix
for (int i = 0; i < RowCount; i++)
{
// if diagonal element is zero
if (tmpMatrix[i][i] == 0)
{
bool foundNonZero = false;
// find a non-zero element in the same column
for (int j = i + 1; j < RowCount; j++)
{
if (tmpMatrix[j][i] != 0)
{
// found it, swap rows ...
foundNonZero = true;
SwapColumns(tmpMatrix, i, j);
SwapColumns(invMatrix, i, j);
// ... and quit searching
j = RowCount;
continue;
}
}
// if no non-zero element was found the matrix is not invertible
if (!foundNonZero)
{
throw new ArithmeticException("GF2mMatrix: Matrix is not invertible!");
}
}
// normalize i-th row
int coef = tmpMatrix[i][i];
int invCoef = FieldG.Inverse(coef);
MultRowWithElementThis(tmpMatrix[i], invCoef);
MultRowWithElementThis(invMatrix[i], invCoef);
// normalize all other rows
for (int j = 0; j < RowCount; j++)
{
if (j != i)
{
coef = tmpMatrix[j][i];
if (coef != 0)
{
int[] tmpRow = MultRowWithElement(tmpMatrix[i], coef);
int[] tmpInvRow = MultRowWithElement(invMatrix[i], coef);
AddToRow(tmpRow, tmpMatrix[j]);
AddToRow(tmpInvRow, invMatrix[j]);
}
}
}
}
return(new GF2mMatrix(FieldG, invMatrix));
}
/// <summary>
/// The copy constructor
/// </summary>
///
/// <param name="GF">The GF2mVector to copy</param>
public GF2mVector(GF2mVector GF)
{
m_field = new GF2mField(GF.m_field);
Length = GF.Length;
m_vector = IntUtils.DeepCopy(GF.m_vector);
}
/// <summary>
/// The permutation vector <c>(perm(0),perm(1),...,perm(n-1))</c>
/// </summary>
///
/// <returns>The permutation vector</returns>
public int[] GetVector()
{
return(IntUtils.DeepCopy(_perm));
}