/// <summary>
/// Compute the product of this matrix and a permutation matrix which is generated from an n-permutation
/// </summary>
///
/// <param name="P">The permutation</param>
///
/// <returns>Returns GF2Matrix <c>this*P</c></returns>
public override Matrix RightMultiply(Permutation P)//3
{
int[] pVec = P.GetVector();
if (pVec.Length != ColumnCount)
{
throw new ArithmeticException("GF2Matrix: Length mismatch!");
}
GF2Matrix result = new GF2Matrix(RowCount, ColumnCount);
for (int i = ColumnCount - 1; i >= 0; i--)
{
int q = IntUtils.URShift(i, 5);
int r = i & 0x1f;
int pq = IntUtils.URShift(pVec[i], 5);
int pr = pVec[i] & 0x1f;
for (int j = RowCount - 1; j >= 0; j--)
{
result._matrix[j][q] |= ((IntUtils.URShift(_matrix[j][pq], pr)) & 1) << r;
}
}
return(result);
}
/// <summary>
/// Multiply this vector with a permutation
/// </summary>
///
/// <param name="P">he permutation</param>
///
/// <returns>Returns <c>this*p = p*this</c></returns>
public override Vector Multiply(Permutation P)
{
int[] pVec = P.GetVector();
if (Length != pVec.Length)
{
throw new ArithmeticException("permutation size and vector size mismatch");
}
int[] result = new int[Length];
for (int i = 0; i < pVec.Length; i++)
{
result[i] = _vector[pVec[i]];
}
return(new GF2mVector(_field, result));
}
/// <summary>
/// Compute the product of a permutation matrix (which is generated from an n-permutation) and this matrix.
/// </summary>
///
/// <param name="P">The permutation</param>
///
/// <returns>Returns GF2Matrix <c>P*this</c></returns>
public Matrix LeftMultiply(Permutation P)
{
int[] pVec = P.GetVector();
if (pVec.Length != RowCount)
{
throw new ArithmeticException("GF2Matrix: length mismatch!");
}
int[][] result = new int[RowCount][];
for (int i = RowCount - 1; i >= 0; i--)
{
result[i] = IntUtils.DeepCopy(_matrix[pVec[i]]);
}
return(new GF2Matrix(RowCount, result));
}
/// <summary>
/// Create an nxn random regular matrix
/// </summary>
///
/// <param name="N">Number of rows (and columns)</param>
/// <param name="SecRnd">Source of randomness</param>
private void AssignRandomRegularMatrix(int N, IRandom SecRnd)
{
RowCount = N;
ColumnCount = N;
_length = IntUtils.URShift((N + 31), 5);
_matrix = ArrayUtils.CreateJagged <int[][]>(RowCount, _length);
GF2Matrix lm = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_LT, SecRnd);
GF2Matrix um = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_UT, SecRnd);
GF2Matrix rm = (GF2Matrix)lm.RightMultiply(um);
Permutation perm = new Permutation(N, SecRnd);
int[] p = perm.GetVector();
for (int i = 0; i < N; i++)
{
Array.Copy(rm._matrix[i], 0, _matrix[p[i]], 0, _length);
}
}
/// <summary>
/// Multiply this vector with a permutation
/// </summary>
///
/// <param name="P">The permutation</param>
///
/// <returns>Returns <c>this*p = p*this</c></returns>
public override Vector Multiply(Permutation P)
{
int[] pVec = P.GetVector();
if (Length != pVec.Length)
{
throw new ArithmeticException("GF2Vector: Length mismatch!");
}
GF2Vector result = new GF2Vector(Length);
for (int i = 0; i < pVec.Length; i++)
{
int e = _elements[pVec[i] >> 5] & (1 << (pVec[i] & 0x1f));
if (e != 0)
{
result._elements[i >> 5] |= 1 << (i & 0x1f);
}
}
return(result);
}
/// <summary>
/// Multiply this vector with a permutation
/// </summary>
///
/// <param name="P">he permutation</param>
///
/// <returns>Returns <c>this*p = p*this</c></returns>
public override Vector Multiply(Permutation P)
{
int[] pVec = P.GetVector();
if (Length != pVec.Length)
throw new ArithmeticException("permutation size and vector size mismatch");
int[] result = new int[Length];
for (int i = 0; i < pVec.Length; i++)
result[i] = _vector[pVec[i]];
return new GF2mVector(_field, result);
}
/// <summary>
/// Create a nxn random regular matrix and its inverse
/// </summary>
///
/// <param name="N">Number of rows (and columns)</param>
/// <param name="SecRnd">Source of randomness</param>
/// <returns>The created random regular matrix and its inverse</returns>
public static GF2Matrix[] CreateRandomRegularMatrixAndItsInverse(int N, IRandom SecRnd)
{
GF2Matrix[] result = new GF2Matrix[2];
// First part: create regular matrix
int length = (N + 31) >> 5;
GF2Matrix lm = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_LT, SecRnd);
GF2Matrix um = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_UT, SecRnd);
GF2Matrix rm = (GF2Matrix)lm.RightMultiply(um);
Permutation p = new Permutation(N, SecRnd);
int[] pVec = p.GetVector();
int[][] matrix = ArrayUtils.CreateJagged <int[][]>(N, length);
for (int i = 0; i < N; i++)
{
Array.Copy(rm._matrix[pVec[i]], 0, matrix[i], 0, length);
}
result[0] = new GF2Matrix(N, matrix);
// Second part: create inverse matrix
// inverse to lm
GF2Matrix invLm = new GF2Matrix(N, Matrix.MATRIX_TYPE_UNIT);
for (int i = 0; i < N; i++)
{
int rest = i & 0x1f;
int q = IntUtils.URShift(i, 5);
int r = 1 << rest;
for (int j = i + 1; j < N; j++)
{
int b = (lm._matrix[j][q]) & r;
if (b != 0)
{
for (int k = 0; k <= q; k++)
{
invLm._matrix[j][k] ^= invLm._matrix[i][k];
}
}
}
}
// inverse to um
GF2Matrix invUm = new GF2Matrix(N, Matrix.MATRIX_TYPE_UNIT);
for (int i = N - 1; i >= 0; i--)
{
int rest = i & 0x1f;
int q = IntUtils.URShift(i, 5);
int r = 1 << rest;
for (int j = i - 1; j >= 0; j--)
{
int b = (um._matrix[j][q]) & r;
if (b != 0)
{
for (int k = q; k < length; k++)
{
invUm._matrix[j][k] ^= invUm._matrix[i][k];
}
}
}
}
// inverse matrix
result[1] = (GF2Matrix)invUm.RightMultiply(invLm.RightMultiply(p));
return(result);
}
//3
/// <summary>
/// Compute the product of this matrix and a permutation matrix which is generated from an n-permutation
/// </summary>
///
/// <param name="P">The permutation</param>
///
/// <returns>Returns GF2Matrix <c>this*P</c></returns>
public override Matrix RightMultiply(Permutation P)
{
int[] pVec = P.GetVector();
if (pVec.Length != ColumnCount)
throw new ArithmeticException("GF2Matrix: Length mismatch!");
GF2Matrix result = new GF2Matrix(RowCount, ColumnCount);
for (int i = ColumnCount - 1; i >= 0; i--)
{
int q = IntUtils.URShift(i, 5);
int r = i & 0x1f;
int pq = IntUtils.URShift(pVec[i], 5);
int pr = pVec[i] & 0x1f;
for (int j = RowCount - 1; j >= 0; j--)
result._matrix[j][q] |= ((IntUtils.URShift(_matrix[j][pq], pr)) & 1) << r;
}
return result;
}
/// <summary>
/// Compute the product of a permutation matrix (which is generated from an n-permutation) and this matrix.
/// </summary>
///
/// <param name="P">The permutation</param>
///
/// <returns>Returns GF2Matrix <c>P*this</c></returns>
public Matrix LeftMultiply(Permutation P)
{
int[] pVec = P.GetVector();
if (pVec.Length != RowCount)
throw new ArithmeticException("GF2Matrix: length mismatch!");
int[][] result = new int[RowCount][];
for (int i = RowCount - 1; i >= 0; i--)
result[i] = IntUtils.DeepCopy(_matrix[pVec[i]]);
return new GF2Matrix(RowCount, result);
}
/// <summary>
/// Create a nxn random regular matrix and its inverse
/// </summary>
///
/// <param name="N">Number of rows (and columns)</param>
/// <param name="SecRnd">Source of randomness</param>
/// <returns>The created random regular matrix and its inverse</returns>
public static GF2Matrix[] CreateRandomRegularMatrixAndItsInverse(int N, IRandom SecRnd)
{
GF2Matrix[] result = new GF2Matrix[2];
// First part: create regular matrix
int length = (N + 31) >> 5;
GF2Matrix lm = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_LT, SecRnd);
GF2Matrix um = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_UT, SecRnd);
GF2Matrix rm = (GF2Matrix)lm.RightMultiply(um);
Permutation p = new Permutation(N, SecRnd);
int[] pVec = p.GetVector();
int[][] matrix = ArrayUtils.CreateJagged<int[][]>(N, length);
for (int i = 0; i < N; i++)
Array.Copy(rm._matrix[pVec[i]], 0, matrix[i], 0, length);
result[0] = new GF2Matrix(N, matrix);
// Second part: create inverse matrix
// inverse to lm
GF2Matrix invLm = new GF2Matrix(N, Matrix.MATRIX_TYPE_UNIT);
for (int i = 0; i < N; i++)
{
int rest = i & 0x1f;
int q = IntUtils.URShift(i, 5);
int r = 1 << rest;
for (int j = i + 1; j < N; j++)
{
int b = (lm._matrix[j][q]) & r;
if (b != 0)
{
for (int k = 0; k <= q; k++)
invLm._matrix[j][k] ^= invLm._matrix[i][k];
}
}
}
// inverse to um
GF2Matrix invUm = new GF2Matrix(N, Matrix.MATRIX_TYPE_UNIT);
for (int i = N - 1; i >= 0; i--)
{
int rest = i & 0x1f;
int q = IntUtils.URShift(i, 5);
int r = 1 << rest;
for (int j = i - 1; j >= 0; j--)
{
int b = (um._matrix[j][q]) & r;
if (b != 0)
{
for (int k = q; k < length; k++)
invUm._matrix[j][k] ^= invUm._matrix[i][k];
}
}
}
// inverse matrix
result[1] = (GF2Matrix)invUm.RightMultiply(invLm.RightMultiply(p));
return result;
}
/// <summary>
/// Create an nxn random regular matrix
/// </summary>
///
/// <param name="N">Number of rows (and columns)</param>
/// <param name="SecRnd">Source of randomness</param>
private void AssignRandomRegularMatrix(int N, IRandom SecRnd)
{
RowCount = N;
ColumnCount = N;
_length = IntUtils.URShift((N + 31), 5);
_matrix = ArrayUtils.CreateJagged<int[][]>(RowCount, _length);
GF2Matrix lm = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_LT, SecRnd);
GF2Matrix um = new GF2Matrix(N, Matrix.MATRIX_TYPE_RANDOM_UT, SecRnd);
GF2Matrix rm = (GF2Matrix)lm.RightMultiply(um);
Permutation perm = new Permutation(N, SecRnd);
int[] p = perm.GetVector();
for (int i = 0; i < N; i++)
Array.Copy(rm._matrix[i], 0, _matrix[p[i]], 0, _length);
}
/// <summary>
/// Multiply this vector with a permutation
/// </summary>
///
/// <param name="P">The permutation</param>
///
/// <returns>Returns <c>this*p = p*this</c></returns>
public override Vector Multiply(Permutation P)
{
int[] pVec = P.GetVector();
if (Length != pVec.Length)
throw new ArithmeticException("GF2Vector: Length mismatch!");
GF2Vector result = new GF2Vector(Length);
for (int i = 0; i < pVec.Length; i++)
{
int e = _elements[pVec[i] >> 5] & (1 << (pVec[i] & 0x1f));
if (e != 0)
result._elements[i >> 5] |= 1 << (i & 0x1f);
}
return result;
}
