dft_tools/triqs/arrays/linalg/inverse.hpp

/*******************************************************************************
 *
 * TRIQS: a Toolbox for Research in Interacting Quantum Systems
 *
 * Copyright (C) 2011 by O. Parcollet
 *
 * TRIQS is free software: you can redistribute it and/or modify it under the
 * terms of the GNU General Public License as published by the Free Software
 * Foundation, either version 3 of the License, or (at your option) any later
 * version.
 *
 * TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
 * details.
 *
 * You should have received a copy of the GNU General Public License along with
 * TRIQS. If not, see <http://www.gnu.org/licenses/>.
 *
 ******************************************************************************/
#ifndef TRIQS_ARRAYS_LINALG_DET_INV_H
#define TRIQS_ARRAYS_LINALG_DET_INV_H

#include <boost/type_traits/is_same.hpp>
#include <boost/typeof/typeof.hpp>
#include <boost/utility/enable_if.hpp>
#include "../impl/common.hpp"
#include "../matrix.hpp"
#include "../blas_lapack/getrf.hpp"
#include "../blas_lapack/getri.hpp"

namespace triqs { namespace arrays { 

 /// Error which occurs during the matrix inversion 
 class matrix_inverse_exception : public triqs::runtime_error {};

 /**
  * Lazy result of inverse(M) where M can be : 
  *  * a matrix, a matrix_view
  *  * any matrix expression
  * The object is lazy, it does not do any computation.
  * It can be copied at no cost
  * It keeps view of the object A if it a matrix, a copy if it is a formal expression.
  */ 
 template<typename A, class Enable = void> struct inverse_lazy;
 
 ///
 template<typename A> struct determinant_lazy;
 
 /// Lazy inversion 
 template<class A> inverse_lazy<A> inverse (A const & a) { return inverse_lazy<A>(a); }
 
 /// Lazy computation of det
 template<typename A> determinant_lazy<A> determinant (A const & a) { return determinant_lazy<A>(a); }

 // ----------------- implementation -----------------------------------------

 //worker takes a contiguous view and compute the det and inverse in two steps.
 //it is separated in case of multiple use (no reallocation of ipvi, etc...)
 //NB a view does not resize, only its elements can be changed
 template<typename ViewType> class det_and_inverse_worker { 
  static_assert ( (is_matrix_view<ViewType>::value),"class must have be a view");
  typedef typename ViewType::value_type VT;
  typedef matrix_view<VT> V_type;
  ViewType V;
  const size_t dim; 
  triqs::arrays::vector <int> ipiv;
  short step; 

  public:
  det_and_inverse_worker (ViewType const & a): V(a), dim(a.dim0()), ipiv(dim), step(0) { 
   if (a.dim0()!=a.dim1()) 
    TRIQS_RUNTIME_ERROR<<"Inverse/Det error : non-square matrix. Dimensions are : ("<<a.dim0()<<","<<a.dim1()<<")"<<"\n  ";
   if (!(has_contiguous_data(a))) TRIQS_RUNTIME_ERROR<<"det_and_inverse_worker only takes a contiguous view";
  }
  VT det() { V_type W = fortran_view(V); _step1(W); _compute_det(W); return _det;}
  ViewType const & inverse() { if (step<2) { V_type W = fortran_view(V); _step1(W); _step2(W);} return V;}

  private:
  int info; VT _det;

  // no need of special traversal
  template<typename MT> V_type fortran_view (MT const &x) { return (x.indexmap().memory_layout_is_c() ? x.transpose() : x);}

  void _step1(V_type & W) { 
   if (step >0) return;
   step=1; 
   info = lapack::getrf(W, ipiv);
   if (info<0) throw matrix_inverse_exception() << "Inverse/Det error : failure of getrf lapack routine ";
  }

  void _compute_det(V_type const & W) { 
   if (step>1) return;
   _det =1;
   for (size_t i =0; i<dim; i++) _det *= W(i,i);
   bool flip=false;// compute the sign of the permutation
   for (size_t i=0; i<dim; i++) {if (ipiv(i)!=int(i)+1) flip = !(flip);}
   _det= (flip ? - _det : _det) ;
  }

  void _step2(V_type & W) { 
   assert(step==1); //if (step==1) return;
   step=2;
   _compute_det(W); 
   info = lapack::getri(W, ipiv);
   if (info!=0) throw matrix_inverse_exception() << "Inverse/Det error : matrix is not invertible";
  }
 };

 //-----------------------------------------------------------

 // an implementation class to gather the common part to matrix and expression....
 template<typename A> struct inverse_lazy_impl : TRIQS_MODEL_CONCEPT(ImmutableMatrix) {
  typedef typename boost::remove_const<typename A::value_type>::type value_type;
  typedef typename A::domain_type domain_type;
  typedef typename domain_type::index_value_type index_value_type;
  typedef typename const_view_type_if_exists_else_type<A>::type A_type;
  const A_type a;
  inverse_lazy_impl(A const & a_):a (a_)  {
   if (a.dim0() != a.dim1()) TRIQS_RUNTIME_ERROR<< "Inverse : matrix is not square but of size "<< a.dim0()<<" x "<< a.dim1(); 
  }
  domain_type domain() const { return a.domain(); } 
  size_t dim0() const { return a.dim0();} 
  size_t dim1() const { return a.dim1();} 
  template<typename K0, typename K1> value_type operator() (K0 const & k0, K1 const & k1) const { activate();  return _id->M(k0,k1); }
  friend std::ostream & operator<<(std::ostream & out,inverse_lazy_impl const&x){return out<<"inverse("<<x.a<<")";}
  protected: 
  struct internal_data { // implementing the pattern LazyPreCompute
   //typedef typename A_type::non_view_type M_type;
   typedef matrix<value_type> M_type;
   typedef matrix_view<value_type> M_view_type;
   M_type M;
   internal_data(inverse_lazy_impl const & P):M(P.a){det_and_inverse_worker<M_view_type> worker(M); worker.inverse();}
  };
  friend struct internal_data;
  mutable boost::shared_ptr<internal_data> _id;
  void activate() const { if (!_id) _id= boost::make_shared<internal_data>(*this);}
 };

 // The general case
 template<typename A>
  struct inverse_lazy<A,typename boost::disable_if< is_matrix_or_view<A> >::type > : inverse_lazy_impl<A> { 
   inverse_lazy(A const & a):inverse_lazy_impl<A>(a) { }
  };

 // for matrix and matrix_views, we have more optimisation possible ....
 template<typename A>
  struct inverse_lazy<A,typename boost::enable_if< is_matrix_or_view<A> >::type >:inverse_lazy_impl<A>{
   inverse_lazy(A const & a):inverse_lazy_impl<A>(a) { }

   template<typename MT> // Optimized implementation of =
    friend void triqs_arrays_assign_delegation (MT & lhs, inverse_lazy const & rhs)  {
     static_assert(is_matrix_or_view<MT>::value, "Internal error");
     if ((lhs.indexmap().memory_indices_layout()  !=rhs.a.indexmap().memory_indices_layout())|| 
       (lhs.data_start() != rhs.a.data_start()) || !(has_contiguous_data(lhs))) { rhs.activate(); lhs = rhs._id->M;} 
     else {// if M = inverse(M) with the SAME object, then we do not need to copy the data
      blas_lapack_tools::reflexive_qcache<MT> C(lhs);// a reflexive cache will use a temporary "regrouping" copy if and only if needed
      det_and_inverse_worker<typename MT::view_type> W(C());// the worker to make the inversion of the lhs... 
      W.inverse(); // worker is working ...
     }
    }
   friend std::ostream & operator<<(std::ostream & out,inverse_lazy const&x){return out<<"inverse("<<x.a<<")";}
  };

 //------------------- det   ----------------------------------------

 template<typename A> struct determinant_lazy  { // : { Tag::expression_terminal, Tag::scalar_expression_terminal {
  typedef typename A::value_type value_type;
  typedef typename const_view_type_if_exists_else_type<A>::type A_type;
  A_type a;
  determinant_lazy(A const & a_):a(a_){}
  operator value_type()  { activate(); return _id->det; }
  value_type const & operator()() { activate(); return _id->det; }
  friend std::ostream & operator<<(std::ostream & out, determinant_lazy const & x){ return out<<"determinant("<<x.a<<")";}
  protected:
  struct internal_data {
   typedef typename A_type::non_view_type M_type;
   M_type M; typename A::value_type det;
   internal_data(determinant_lazy const & P):M(P.a){det_and_inverse_worker<A_type> worker(M); det = worker.det();}
  };
  friend struct internal_data;
  mutable boost::shared_ptr<internal_data> _id;
  void activate() const { if (!_id) _id= boost::make_shared<internal_data>(*this);}
 };

 }} // namespace triqs::arrays
#endif