solveInvertible()

template<class RingType>

bool DMatLinAlg< RingType >::solveInvertible	(	const Mat &	B,
		Mat &	X )

Input: B, a matrix, the right hand side of AX=B A, a square matrix (presumed to be invertible) Output: X, a matrix, solution to the above, if A is invertible returns false iff A is not invertible

Definition at line 535 of file dmat-lu.hpp.

{
  // printf("in dmat-lu solveInvertible\n");
  // possible TODO: incorporate a faster method if we know matrix is
  // invertible...
  assert(mLUObject.numRows() == mLUObject.numColumns());
  assert(mLUObject.numRows() == B.numRows());
 
  X.resize(mLUObject.numColumns(), B.numColumns());
  mLUObject.LUinPlace();
  if (rank() < mLUObject.numRows()) return false;
  solve(B, X);
  return true;
#if 0
  // The following code doesn't really seem to be any faster than the naive code we have
  // at least for sizes less than a few thousand rows/columns.
  Mat B1(ring(), LU.numRows(), LU.numRows()); // square matrix
  printf("in dmat-lu solveInvertible step 3\n");
  permuteRows<Mat>(B, mLUObject.permutation(), B1);
  printf("in dmat-lu solveInvertible step 4\n");
  solveLowerTriangular(LU, B, X);
  printf("in dmat-lu solveInvertible step 5\n");
  solveUpperTriangular(LU, X, X);
  printf("in dmat-lu solveInvertible step 6\n");
  return true;
#endif
}

References mLUObject, DMat< ACoeffRing >::numColumns(), DMat< ACoeffRing >::numRows(), permuteRows(), rank(), DMat< ACoeffRing >::resize(), ring(), solve(), solveLowerTriangular(), and solveUpperTriangular().

Referenced by MatrixOps::solveInvertible().