initializeLLL()

bool LLLoperations::initializeLLL ( const MutableMatrix * A, gmp_QQ threshold, MutableMatrix *& LLLstate )

staticprivate

Definition at line 28 of file LLL.cpp.

{
  // First check m: should be a matrix over globalZZ.
  if (A == nullptr || A->get_ring() != globalZZ)
    {
      ERROR("LLL only defined for matrices over ZZ");
      return false;
    }
 
  ring_elem num = globalZZ->from_int(mpq_numref(threshold));
  ring_elem den = globalZZ->from_int(mpq_denref(threshold));
  // Check that 'threshold' is in range, and set the numerator, denom
  if (!checkThreshold(num, den))
    {
      ERROR("LLL threshold should be in the range (1/4, 1]");
      globalZZ->remove(num);
      globalZZ->remove(den);
      return false;
    }
 
  // LLLstate has n+4 columns, and n rows.
  // First n columns: LLLstate(i,i) = D#i
  //                  LLLstate(i,j) = lambda#(j,i) for
  // Last four columns just have entries in row 0:
  // The entries are: k, kmax, alphaTop, alphaBottom: all are ZZ values.
 
  size_t n = A->n_cols();
  LLLstate = MutableMatrix::zero_matrix(globalZZ, n, n + 4, A->is_dense());
  if (n > 0)
    {
      LLLstate->set_entry(0, n, globalZZ->from_long(1));  // k := 2
      // LLLstate->set_entry(0,n+1,globalZZ->from_long(0)); // kmax := 1
      LLLstate->set_entry(
          0, n + 2, num);  // Set threshold numerator, denominator
      LLLstate->set_entry(0, n + 3, den);
      ring_elem dot;
      A->dot_product(0, 0, dot);
      LLLstate->set_entry(0, 0, dot);  // D#1 := dot(A,0,0)
    }
  return true;
}

References checkThreshold(), MutableMatrix::dot_product(), ERROR, MutableMatrix::get_ring(), globalZZ, MutableMatrix::is_dense(), MutableMatrix::n_cols(), MutableMatrix::set_entry(), and MutableMatrix::zero_matrix().

Referenced by LLL().