code: public static double[] solveLinearEquationSymmetric(double[][] matrix, double[] vector) {
  		if(isSolverUseApacheCommonsMath) {
  			DecompositionSolver solver = new LUDecomposition(new Array2DRowRealMatrix(matrix)).getSolver();
  			return solver.solve(new Array2DRowRealMatrix(vector)).getColumn(0);
  		}
  		else {
  			return org.jblas.Solve.solveSymmetric(new org.jblas.DoubleMatrix(matrix), new org.jblas.DoubleMatrix(vector)).data;
  			/* To use the linear algebra package colt from cern.
  			cern.colt.matrix.linalg.Algebra linearAlgebra = new cern.colt.matrix.linalg.Algebra();
  			double[] x = linearAlgebra.solve(new DenseDoubleMatrix2D(A), linearAlgebra.transpose(new DenseDoubleMatrix2D(new double[][] { b }))).viewColumn(0).toArray();
  
  			return x;
  			 */
  		}
  	}
docs: Find a solution of the linear equation A x = b where
  <ul>
  <li>A is an symmetric n x n - matrix given as double[n][n]</li>
  <li>b is an n - vector given as double[n],</li>
  <li>x is an n - vector given as double[n],</li>
  </ul>
  
  @param matrix The matrix A (left hand side of the linear equation).
  @param vector The vector b (right hand of the linear equation).
  @return A solution x to A x = b.