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@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@
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