C++ mat_GF2::NumCols方法代码示例

vec_GF2 GF2MatrixUtils::solve(mat_GF2 A, vec_GF2 b) {

    uint32_t nextRow = 0;
    for (uint32_t j =0; j < A.NumCols(); j++) {
        uint32_t i;
        for (i=nextRow; i < A.NumRows(); i++) {
            if (A[i][j] == 1) {
                break;
            }
        }
        if (i==A.NumRows()) {
            continue;
        }
        if (A[i][j] == 1) {
            if (nextRow !=i) {
                swap(A[nextRow],A[i]);
                swap(b[nextRow],b[i]);
            }
            for (uint32_t k=nextRow+1; k < A.NumRows(); k++) {
                if (A[k][j] == 1) {
                    A[k] = A[k] + A[nextRow];
                    b[k] = b[k] + b[nextRow];
                }
            }
            nextRow++;
        }
    }

    vec_GF2 sol;
    sol.SetLength(A.NumCols(), GF2(0));

    int32_t lastRow=A.NumRows()-1;

    while (A[lastRow][A.NumCols()-1]==0) {
        if ((A[lastRow]*sol) != b[lastRow]) {
            throw(system_error());
        }
        lastRow--;
        if (lastRow == -1) {
            throw(system_error());
        }
    }

    for (int32_t j=A.NumCols()-1; j >= 0; j--) {
        if (lastRow == -1) {
            throw(system_error());
        }

        if (A[lastRow][j]==0) {
            continue;
        }

        if ((A[lastRow]*sol) != b[lastRow]) {
            sol[j]=1;
        }
        lastRow--;
    }

    return sol;
}

void power(mat_GF2& X, const mat_GF2& A, const ZZ& e)
{
   if (A.NumRows() != A.NumCols()) Error("power: non-square matrix");

   if (e == 0) {
      ident(X, A.NumRows());
      return;
   }

   mat_GF2 T1, T2;
   long i, k;

   k = NumBits(e);
   T1 = A;

   for (i = k-2; i >= 0; i--) {
      sqr(T2, T1);
      if (bit(e, i))
         mul(T1, T2, A);
      else
         T1 = T2;
   }

   if (e < 0)
      inv(X, T1);
   else
      X = T1;
}

void AddToCol(mat_GF2& x, long j, const vec_GF2& a)
// add a to column j of x
// ALIAS RESTRICTION: a should not alias any row of x
{
   long n = x.NumRows();
   long m = x.NumCols();

   if (a.length() != n || j < 0 || j >= m)
      Error("AddToCol: bad args");

   long wj = j/NTL_BITS_PER_LONG;
   long bj = j - wj*NTL_BITS_PER_LONG;
   _ntl_ulong j_mask = 1UL << bj;

   const _ntl_ulong *ap = a.rep.elts();
   _ntl_ulong a_mask = 1;

   long i;
   for (i = 0; i < n; i++) {
      if (*ap & a_mask)
         x[i].rep.elts()[wj] ^= j_mask;

      a_mask <<= 1;
      if (!a_mask) {
         a_mask = 1;
         ap++;
      }
   }
}

static
void mul_aux(vec_GF2& x, const vec_GF2& a, const mat_GF2& B)
{
   long n = B.NumRows();
   long l = B.NumCols();

   if (n != a.length())
      Error("matrix mul: dimension mismatch");

   x.SetLength(l);
   clear(x);

   const _ntl_ulong *ap = a.rep.elts();
   _ntl_ulong a_mask = 1;

   _ntl_ulong *xp = x.rep.elts();

   long lw = (l + NTL_BITS_PER_LONG - 1)/NTL_BITS_PER_LONG;

   long i;
   for (i = 0; i < n; i++) {
      if (*ap & a_mask) {
         const _ntl_ulong *bp = B[i].rep.elts();
         long j;
         for (j = 0; j < lw; j++)
            xp[j] ^= bp[j];
      }

      a_mask <<= 1;
      if (!a_mask) {
         a_mask = 1;
         ap++;
      }
   }
}

long operator==(const mat_GF2& a, const mat_GF2& b)  
{  
   if (a.NumCols() != b.NumCols())  
      return 0;  
  
   if (a.NumRows() != b.NumRows())  
      return 0;  
  
   long n = a.NumRows();  
   long i;  
  
   for (i = 0; i < n; i++)  
      if (a[i] != b[i])  
         return 0;  
  
   return 1;  
}  

NTL_START_IMPL


mat_GF2::mat_GF2(const mat_GF2& a)  
{  
   _mat_GF2__numcols = 0;  
   SetDims(a.NumRows(), a.NumCols());  
   _mat_GF2__rep = a._mat_GF2__rep;  
}  

long IsDiag(const mat_GF2& A, long n, GF2 d)
{
   if (A.NumRows() != n || A.NumCols() != n)
      return 0;

   if (d == 1)
      return IsIdent(A, n);
   else
      return IsZero(A);
}

/**
 * Initializes matrix from specified array.
 * Data must be at least dimension of given matrix.
 */
int initMatrix(mat_GF2& M, long *data){
	long i,j,n,m;
	for(i=0, n=M.NumRows(); i<n; i++){
		for(j=0, m=M.NumCols(); j<m; j++){
			M.put(i,j,data[n*i+j]);
		}
	}

	return 0;
}

void transpose_aux(mat_GF2& X, const mat_GF2& A)
{
   long n = A.NumRows();
   long m = A.NumCols();

   X.SetDims(m, n);
   clear(X);

   long i;
   for (i = 0; i < n; i++)
      AddToCol(X, i, A[i]);
}

long gauss(mat_GF2& M, long w)
{
   long k, l;
   long i, j;
   long pos;

   long n = M.NumRows();
   long m = M.NumCols();

   if (w < 0 || w > m)
      Error("gauss: bad args");

   long wm = (m + NTL_BITS_PER_LONG - 1)/NTL_BITS_PER_LONG;

   l = 0;
   for (k = 0; k < w && l < n; k++) {
      long wk = k/NTL_BITS_PER_LONG;
      long bk = k - wk*NTL_BITS_PER_LONG;
      _ntl_ulong k_mask = 1UL << bk;


      pos = -1;
      for (i = l; i < n; i++) {
         if (M[i].rep.elts()[wk] & k_mask) {
            pos = i;
            break;
         }
      }

      if (pos != -1) {
         if (l != pos)
            swap(M[pos], M[l]);

         _ntl_ulong *y = M[l].rep.elts();

         for (i = l+1; i < n; i++) {
            // M[i] = M[i] + M[l]*M[i,k]

            if (M[i].rep.elts()[wk] & k_mask) {
               _ntl_ulong *x = M[i].rep.elts();

               for (j = wk; j < wm; j++)
                  x[j] ^= y[j];
            }
         }

         l++;
      }
   }

   return l;
}

void add(mat_GF2& X, const mat_GF2& A, const mat_GF2& B)
{
   long n = A.NumRows();
   long m = A.NumCols();

   if (B.NumRows() != n || B.NumCols() != m)
      Error("matrix add: dimension mismatch");

   X.SetDims(n, m);

   long mw = (m + NTL_BITS_PER_LONG - 1)/NTL_BITS_PER_LONG;

   long i;
   for (i = 0; i < n; i++) {
      _ntl_ulong *xp = X[i].rep.elts();
      const _ntl_ulong *ap = A[i].rep.elts();
      const _ntl_ulong *bp = B[i].rep.elts();
      long j;
      for (j = 0; j < mw; j++)
         xp[j] = ap[j] ^ bp[j];
   }
}

long IsIdent(const mat_GF2& A, long n)
{
   if (A.NumRows() != n || A.NumCols() != n)
      return 0;

   if (n == 0) return 1;

   long i;

   for (i = 0; i < n; i++)
      if (!IsUnitVector(A[i], i))
         return 0;

   return 1;
}

void kernel(mat_GF2& X, const mat_GF2& A)
{
   long m = A.NumRows();
   long n = A.NumCols();

   mat_GF2 M;
   long r;

   transpose(M, A);
   r = gauss(M);

   X.SetDims(m-r, m);
   clear(X);

   long i, j, k;

   vec_long D;
   D.SetLength(m);
   for (j = 0; j < m; j++) D[j] = -1;

   j = -1;
   for (i = 0; i < r; i++) {
      do {
         j++;
      } while (M.get(i, j) == 0);

      D[j] = i;
   }

   for (k = 0; k < m-r; k++) {
      vec_GF2& v = X[k];
      long pos = 0;
      for (j = m-1; j >= 0; j--) {
         if (D[j] == -1) {
            if (pos == k) {
               v[j] = 1;
               // v.put(j, to_GF2(1));
            }
            pos++;
         }
         else {
            v[j] = v*M[D[j]];
            // v.put(j, v*M[D[j]]);
         }
      }
   }
}

void inv(GF2& d, mat_GF2& X, const mat_GF2& A)
{
   long n = A.NumRows();
   if (A.NumCols() != n)
      Error("solve: nonsquare matrix");

   if (n == 0) {
      X.SetDims(0, 0);
      set(d);
   }

   long i, j, k, pos;

   mat_GF2 M;
   M.SetDims(n, 2*n);

   vec_GF2 aa;
   aa.SetLength(2*n);


   for (i = 0; i < n; i++) {
      aa = A[i];
      aa.SetLength(2*n);
      aa.put(n+i, 1);
      M[i] = aa;
   }

   long wn = ((2*n) + NTL_BITS_PER_LONG - 1)/NTL_BITS_PER_LONG;

   for (k = 0; k < n; k++) {
      long wk = k/NTL_BITS_PER_LONG;
      long bk = k - wk*NTL_BITS_PER_LONG;
      _ntl_ulong k_mask = 1UL << bk;

      pos = -1;
      for (i = k; i < n; i++) {
         if (M[i].rep.elts()[wk] & k_mask) {
            pos = i;
            break;
         }
      }

      if (pos != -1) {
         if (k != pos) {
            swap(M[pos], M[k]);
         }

         _ntl_ulong *y = M[k].rep.elts();

         for (i = k+1; i < n; i++) {
            // M[i] = M[i] + M[k]*M[i,k]

            if (M[i].rep.elts()[wk] & k_mask) {
               _ntl_ulong *x = M[i].rep.elts();

               for (j = wk; j < wn; j++)
                  x[j] ^= y[j];
            }


         }
      }
      else {
         clear(d);
         return;
      }
   }

   vec_GF2 XX;
   XX.SetLength(2*n);

   X.SetDims(n, n);
   clear(X);

   for (j = 0; j < n; j++) {
      XX.SetLength(n+j+1);
      clear(XX);
      XX.put(n+j, to_GF2(1));

      for (i = n-1; i >= 0; i--) {
         XX.put(i, XX*M[i]);
      }

      XX.SetLength(n);
      AddToCol(X, j, XX);
   }

   set(d);
   return;
}

void determinant(GF2& d, const mat_GF2& M_in)
{
   long k, n;
   long i, j;
   long pos;

   n = M_in.NumRows();

   if (M_in.NumCols() != n)
      Error("determinant: nonsquare matrix");

   if (n == 0) {
      set(d);
      return;
   }

   mat_GF2 M;

   M = M_in;

   long wn = (n + NTL_BITS_PER_LONG - 1)/NTL_BITS_PER_LONG;

   for (k = 0; k < n; k++) {
      long wk = k/NTL_BITS_PER_LONG;
      long bk = k - wk*NTL_BITS_PER_LONG;
      _ntl_ulong k_mask = 1UL << bk;

      pos = -1;
      for (i = k; i < n; i++) {
         if (M[i].rep.elts()[wk] & k_mask) {
            pos = i;
            break;
         }
      }

      if (pos != -1) {
         if (k != pos) {
            swap(M[pos], M[k]);
         }


         _ntl_ulong *y = M[k].rep.elts();

         for (i = k+1; i < n; i++) {
            // M[i] = M[i] + M[k]*M[i,k]

            if (M[i].rep.elts()[wk] & k_mask) {
               _ntl_ulong *x = M[i].rep.elts();

               for (j = wk; j < wn; j++)
                  x[j] ^= y[j];
            }

         }
      }
      else {
         clear(d);
         return;
      }
   }

   set(d);
   return;
}