First bits of code for PR training

git-svn-id: https://ws10smt.googlecode.com/svn/trunk@44 ec762483-ff6d-05da-a07a-a48fb63a330f

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+// The following code inverts the matrix input using LU-decomposition with
+// backsubstitution of unit vectors. Reference: Numerical Recipies in C, 2nd
+// ed., by Press, Teukolsky, Vetterling & Flannery. 
+// Code written by Fredrik Orderud.
+// http://www.crystalclearsoftware.com/cgi-bin/boost_wiki/wiki.pl?LU_Matrix_Inversion
+
+#ifndef INVERT_MATRIX_HPP
+#define INVERT_MATRIX_HPP
+
+// REMEMBER to update "lu.hpp" header includes from boost-CVS
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/vector_proxy.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+#include <boost/numeric/ublas/triangular.hpp>
+#include <boost/numeric/ublas/lu.hpp>
+#include <boost/numeric/ublas/io.hpp>
+
+namespace ublas = boost::numeric::ublas;
+
+/* Matrix inversion routine.
+   Uses lu_factorize and lu_substitute in uBLAS to invert a matrix */
+template<class T>
+bool invert_matrix(const ublas::matrix<T>& input, ublas::matrix<T>& inverse) 
+{
+    using namespace boost::numeric::ublas;
+    typedef permutation_matrix<std::size_t> pmatrix;
+    // create a working copy of the input
+    matrix<T> A(input);
+    // create a permutation matrix for the LU-factorization
+    pmatrix pm(A.size1());
+
+    // perform LU-factorization
+    int res = lu_factorize(A,pm);
+    if( res != 0 ) return false;
+
+    // create identity matrix of "inverse"
+    inverse.assign(ublas::identity_matrix<T>(A.size1()));
+
+    // backsubstitute to get the inverse
+    lu_substitute(A, pm, inverse);
+    
+    return true;
+}
+
+#endif //INVERT_MATRIX_HPP