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Source: LuSolve
`# ifndef CPPAD_LU_SOLVE_HPP `
` # define CPPAD_LU_SOLVE_HPP

    # include <complex>
    # include <vector>

    // link exp for float and double cases
    # include <cppad/base_require.hpp>

    # include <cppad/core/cppad_assert.hpp>
    # include <cppad/utility/check_simple_vector.hpp>
    # include <cppad/utility/check_numeric_type.hpp>
    # include <cppad/utility/lu_factor.hpp>
    # include <cppad/utility/lu_invert.hpp>

    namespace CppAD { // BEGIN CppAD namespace

    // LeqZero
    template <typename Float>
    inline bool LeqZero(const Float &x)
    {     return x <= Float(0); }
    inline bool LeqZero( const std::complex<double> &x )
    {     return x == std::complex<double>(0); }
    inline bool LeqZero( const std::complex<float> &x )
    {     return x == std::complex<float>(0); }

    // LuSolve
    template <typename Float, typename FloatVector>
    int LuSolve(
         size_t             n      ,
         size_t             m      ,
         const FloatVector &A      ,
         const FloatVector &B      ,
         FloatVector       &X      ,
         Float        &logdet      )
    {
         // check numeric type specifications
         CheckNumericType<Float>();

         // check simple vector class specifications
         CheckSimpleVector<Float, FloatVector>();

         size_t        p;       // index of pivot element (diagonal of L)
         int     signdet;       // sign of the determinant
         Float     pivot;       // pivot element

         // the value zero
         const Float zero(0);

         // pivot row and column order in the matrix
         std::vector<size_t> ip(n);
         std::vector<size_t> jp(n);

         // -------------------------------------------------------
         CPPAD_ASSERT_KNOWN(
              size_t(A.size()) == n * n,
              "Error in LuSolve: A must have size equal to n * n"
         );
         CPPAD_ASSERT_KNOWN(
              size_t(B.size()) == n * m,
              "Error in LuSolve: B must have size equal to n * m"
         );
         CPPAD_ASSERT_KNOWN(
              size_t(X.size()) == n * m,
              "Error in LuSolve: X must have size equal to n * m"
         );
         // -------------------------------------------------------

         // copy A so that it does not change
         FloatVector Lu(A);

         // copy B so that it does not change
         X = B;

         // Lu factor the matrix A
         signdet = LuFactor(ip, jp, Lu);

         // compute the log of the determinant
         logdet  = Float(0);
         for(p = 0; p < n; p++)
         {     // pivot using the max absolute element
              pivot   = Lu[ ip[p] * n + jp[p] ];

              // check for determinant equal to zero
              if( pivot == zero )
              {     // abort the mission
                   logdet = Float(0);
                   return   0;
              }

              // update the determinant
              if( LeqZero ( pivot ) )
              {     logdet += log( - pivot );
                   signdet = - signdet;
              }
              else     logdet += log( pivot );

         }

         // solve the linear equations
         LuInvert(ip, jp, Lu, X);

         // return the sign factor for the determinant
         return signdet;
    }
    } // END CppAD namespace

# endif`

Input File: omh/lu_solve_hpp.omh