EVOLUTION-MANAGER

Edit File: mat_operations.hpp

//Distributed under the Boost Software License, Version 1.0. (See accompanying
//file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifndef UUID_4F915D9ED30A11DF962186E3DFD72085
#define UUID_4F915D9ED30A11DF962186E3DFD72085

#include <boost/qvm/detail/mat_assign.hpp>
#include <boost/qvm/mat_operations2.hpp>
#include <boost/qvm/mat_operations3.hpp>
#include <boost/qvm/mat_operations4.hpp>
#include <boost/qvm/math.hpp>
#include <boost/qvm/detail/determinant_impl.hpp>
#include <boost/qvm/detail/cofactor_impl.hpp>
#include <boost/qvm/detail/transp_impl.hpp>
#include <boost/qvm/scalar_traits.hpp>
#include <string>

namespace
boost
    {
    namespace
    qvm
        {
        namespace
        qvm_detail
            {
            BOOST_QVM_INLINE_CRITICAL
            void const *
            get_valid_ptr_mat_operations()
                {
                static int const obj=0;
                return &obj;
                }
            }

////////////////////////////////////////////////

namespace
 qvm_to_string_detail
 {
 template <class T>
 std::string to_string( T const & x );
 }

namespace
 qvm_detail
 {
 template <int R,int C>
 struct
 to_string_m_defined
 {
 static bool const value=false;
 };

template <int I,int SizeMinusOne>
 struct
 to_string_matrix_elements
 {
 template <class A>
 static
 std::string
 f( A const & a )
 {
 using namespace qvm_to_string_detail;
 return
 ( (I%mat_traits<A>::cols)==0 ? '(' : ',' ) +
 to_string(mat_traits<A>::template read_element<I/mat_traits<A>::cols,I%mat_traits<A>::cols>(a)) +
 ( (I%mat_traits<A>::cols)==mat_traits<A>::cols-1 ? ")" : "" ) +
 to_string_matrix_elements<I+1,SizeMinusOne>::f(a);
 }
 };

template <int SizeMinusOne>
 struct
 to_string_matrix_elements<SizeMinusOne,SizeMinusOne>
 {
 template <class A>
 static
 std::string
 f( A const & a )
 {
 using namespace qvm_to_string_detail;
 return
 ( (SizeMinusOne%mat_traits<A>::cols)==0 ? '(' : ',' ) +
 to_string(mat_traits<A>::template read_element<SizeMinusOne/mat_traits<A>::cols,SizeMinusOne%mat_traits<A>::cols>(a)) +
 ')';
 }
 };
 }

template <class A>
 inline
 typename boost::enable_if_c<
 is_mat<A>::value &&
 !qvm_detail::to_string_m_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 std::string>::type
 to_string( A const & a )
 {
 return "("+qvm_detail::to_string_matrix_elements<0,mat_traits<A>::rows*mat_traits<A>::cols-1>::f(a)+')';
 }

////////////////////////////////////////////////

template <class A,class B,class Cmp>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols,
 bool>::type
 cmp( A const & a, B const & b, Cmp f )
 {
 typedef typename deduce_scalar<
 typename mat_traits<A>::scalar_type,
 typename mat_traits::scalar_type>::type T;
 int const rows=mat_traits<A>::rows;
 int const cols=mat_traits<A>::cols;
 T m1[rows][cols]; assign(m1,a);
 T m2[rows][cols]; assign(m2,b);
 for( int i=0; i!=rows; ++i )
 for( int j=0; j!=cols; ++j )
 if( !f(m1[i][j],m2[i][j]) )
 return false;
 return true;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 convert_to_m_defined
 {
 static bool const value=false;
 };
 }

template <class R,class A>
 BOOST_QVM_INLINE_TRIVIAL
 typename enable_if_c<
 is_mat<R>::value && is_mat<A>::value &&
 mat_traits<R>::rows==mat_traits<A>::rows &&
 mat_traits<R>::cols==mat_traits<A>::cols &&
 !qvm_detail::convert_to_m_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 R>::type
 convert_to( A const & a )
 {
 R r; assign(r,a);
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int D>
 struct
 determinant_defined
 {
 static bool const value=false;
 };
 }

template <class A>
 BOOST_QVM_INLINE_TRIVIAL
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 !qvm_detail::determinant_defined<mat_traits<A>::rows>::value,
 typename mat_traits<A>::scalar_type>::type
 determinant( A const & a )
 {
 return qvm_detail::determinant_impl(a);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <class T,int Dim>
 class
 identity_mat_
 {
 identity_mat_( identity_mat_ const & );
 identity_mat_ & operator=( identity_mat_ const & );
 ~identity_mat_();

public:

template <class R>
 BOOST_QVM_INLINE_TRIVIAL
 operator R() const
 {
 R r;
 assign(r,*this);
 return r;
 }
 };
 }

template <class T,int Dim>
 struct
 mat_traits< qvm_detail::identity_mat_<T,Dim> >
 {
 typedef qvm_detail::identity_mat_<T,Dim> this_matrix;
 typedef T scalar_type;
 static int const rows=Dim;
 static int const cols=Dim;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & /*x*/ )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Row<Dim);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Col<Dim);
 return scalar_traits<scalar_type>::value(Row==Col);
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & /*x*/ )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(row<Dim);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(col<Dim);
 return scalar_traits<scalar_type>::value(row==col);
 }
 };

template <class T,int Dim>
 BOOST_QVM_INLINE_TRIVIAL
 qvm_detail::identity_mat_<T,Dim> const &
 identity_mat()
 {
 return *(qvm_detail::identity_mat_<T,Dim> const *)qvm_detail::get_valid_ptr_mat_operations();
 }

template <class A>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols,
 void>::type
 set_identity( A & a )
 {
 assign(a,identity_mat<typename mat_traits<A>::scalar_type,mat_traits<A>::rows>());
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <class T>
 struct
 projection_
 {
 T const _00;
 T const _11;
 T const _22;
 T const _23;
 T const _32;

BOOST_QVM_INLINE_TRIVIAL
                projection_( T _00, T _11, T _22, T _23, T _32 ):
                    _00(_00),
                    _11(_11),
                    _22(_22),
                    _23(_23),
                    _32(_32)
                    {
                    }

template <class R>
 BOOST_QVM_INLINE_TRIVIAL
 operator R() const
 {
 R r;
 assign(r,*this);
 return r;
 }
 };

template <int Row,int Col>
 struct
 projection_get
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( projection_<T> const & )
 {
 return scalar_traits<T>::value(0);
 }
 };

template <> struct projection_get<0,0> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( projection_<T> const & m ) { return m._00; } };
 template <> struct projection_get<1,1> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( projection_<T> const & m ) { return m._11; } };
 template <> struct projection_get<2,2> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( projection_<T> const & m ) { return m._22; } };
 template <> struct projection_get<2,3> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( projection_<T> const & m ) { return m._23; } };
 template <> struct projection_get<3,2> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( projection_<T> const & m ) { return m._32; } };
 }

template <class T>
 struct
 mat_traits< qvm_detail::projection_<T> >
 {
 typedef qvm_detail::projection_<T> this_matrix;
 typedef T scalar_type;
 static int const rows=4;
 static int const cols=4;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Row<rows);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Col<cols);
 return qvm_detail::projection_get<Row,Col>::get(x);
 }
 };

template <class T>
 qvm_detail::projection_<T>
 BOOST_QVM_INLINE_OPERATIONS
 perspective_lh( T fov_y, T aspect_ratio, T z_near, T z_far )
 {
 T const one = scalar_traits<T>::value(1);
 T const ys = one/tan<T>(fov_y/scalar_traits<T>::value(2));
 T const xs = ys/aspect_ratio;
 T const zd = z_far-z_near;
 T const z1 = z_far/zd;
 T const z2 = -z_near*z1;
 return qvm_detail::projection_<T>(xs,ys,z1,z2,one);
 }

template <class T>
 qvm_detail::projection_<T>
 BOOST_QVM_INLINE_OPERATIONS
 perspective_rh( T fov_y, T aspect_ratio, T z_near, T z_far )
 {
 T const one = scalar_traits<T>::value(1);
 T const ys = one/tan<T>(fov_y/scalar_traits<T>::value(2));
 T const xs = ys/aspect_ratio;
 T const zd = z_near-z_far;
 T const z1 = z_far/zd;
 T const z2 = z_near*z1;
 return qvm_detail::projection_<T>(xs,ys,z1,z2,-one);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <class OriginalType,class Scalar>
 class
 matrix_scalar_cast_
 {
 matrix_scalar_cast_( matrix_scalar_cast_ const & );
 matrix_scalar_cast_ & operator=( matrix_scalar_cast_ const & );
 ~matrix_scalar_cast_();

public:

template <class T>
 BOOST_QVM_INLINE_TRIVIAL
 matrix_scalar_cast_ &
 operator=( T const & x )
 {
 assign(*this,x);
 return *this;
 }

template <bool> struct scalar_cast_matrix_filter { };
 template <> struct scalar_cast_matrix_filter<true> { typedef int type; };
 }

template <class OriginalType,class Scalar>
 struct
 mat_traits< qvm_detail::matrix_scalar_cast_<OriginalType,Scalar> >
 {
 typedef Scalar scalar_type;
 typedef qvm_detail::matrix_scalar_cast_<OriginalType,Scalar> this_matrix;
 static int const rows=mat_traits<OriginalType>::rows;
 static int const cols=mat_traits<OriginalType>::cols;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Row<rows);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Col<cols);
 return scalar_type(mat_traits<OriginalType>::template read_element<Row,Col>(reinterpret_cast<OriginalType const &>(x)));
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & x )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(row<rows);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(col<cols);
 return scalar_type(mat_traits<OriginalType>::read_element_idx(col,row,reinterpret_cast<OriginalType const &>(x)));
 }
 };

template <class OriginalType,class Scalar,int R,int C>
 struct
 deduce_mat<qvm_detail::matrix_scalar_cast_<OriginalType,Scalar>,R,C>
 {
 typedef mat<Scalar,R,C> type;
 };

template <class Scalar,class T>
 BOOST_QVM_INLINE_TRIVIAL
 qvm_detail::matrix_scalar_cast_<T,Scalar> const &
 scalar_cast( T const & x, typename qvm_detail::scalar_cast_matrix_filter<is_mat<T>::value>::type=0 )
 {
 return reinterpret_cast<qvm_detail::matrix_scalar_cast_<T,Scalar> const &>(x);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 div_eq_ms_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value && is_scalar::value &&
 !qvm_detail::div_eq_ms_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 A &>::type
 operator/=( A & a, B b )
 {
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<A>::write_element_idx(i,j,a)/=b;
 return a;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 div_ms_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename lazy_enable_if_c<
 is_mat<A>::value && is_scalar::value &&
 !qvm_detail::div_ms_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 deduce_mat<A> >::type
 operator/( A const & a, B b )
 {
 typedef typename deduce_mat<A>::type R;
 R r;
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<R>::write_element_idx(i,j,r)=mat_traits<A>::read_element_idx(i,j,a)/b;
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 eq_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols &&
 !qvm_detail::eq_mm_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 bool>::type
 operator==( A const & a, B const & b )
 {
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 if( mat_traits<A>::read_element_idx(i,j,a)!=mat_traits::read_element_idx(i,j,b) )
 return false;
 return true;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 minus_eq_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols &&
 !qvm_detail::minus_eq_mm_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 A &>::type
 operator-=( A & a, B const & b )
 {
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<A>::write_element_idx(i,j,a)-=mat_traits::read_element_idx(i,j,b);
 return a;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 minus_m_defined
 {
 static bool const value=false;
 };
 }

template <class A>
 BOOST_QVM_INLINE_OPERATIONS
 typename lazy_enable_if_c<
 is_mat<A>::value &&
 !qvm_detail::minus_m_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 deduce_mat<A> >::type
 operator-( A const & a )
 {
 typedef typename deduce_mat<A>::type R;
 R r;
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<R>::write_element_idx(i,j,r)=-mat_traits<A>::read_element_idx(i,j,a);
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 minus_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename lazy_enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols &&
 !qvm_detail::minus_mm_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
 operator-( A const & a, B const & b )
 {
 typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
 R r;
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<R>::write_element_idx(i,j,r)=mat_traits<A>::read_element_idx(i,j,a)-mat_traits::read_element_idx(i,j,b);
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int D>
 struct
 mul_eq_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 is_mat::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols &&
 !qvm_detail::mul_eq_mm_defined<mat_traits<A>::rows>::value,
 A &>::type
 operator*=( A & r, B const & b )
 {
 typedef typename mat_traits<A>::scalar_type Ta;
 Ta a[mat_traits<A>::rows][mat_traits<A>::cols];
 for( int i=0; i<mat_traits<A>::rows; ++i )
 for( int j=0; j<mat_traits::cols; ++j )
 a[i][j]=mat_traits<A>::read_element_idx(i,j,r);
 for( int i=0; i<mat_traits<A>::rows; ++i )
 for( int j=0; j<mat_traits::cols; ++j )
 {
 Ta x(scalar_traits<Ta>::value(0));
 for( int k=0; k<mat_traits<A>::cols; ++k )
 x += a[i][k]*mat_traits::read_element_idx(k,j,b);
 mat_traits<A>::write_element_idx(i,j,r) = x;
 }
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 mul_eq_ms_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value && is_scalar::value &&
 !qvm_detail::mul_eq_ms_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 A &>::type
 operator*=( A & a, B b )
 {
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<A>::write_element_idx(i,j,a)*=b;
 return a;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int R,int CR,int C>
 struct
 mul_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename lazy_enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::cols==mat_traits::rows &&
 !qvm_detail::mul_mm_defined<mat_traits<A>::rows,mat_traits<A>::cols,mat_traits::cols>::value,
 deduce_mat2<A,B,mat_traits<A>::rows,mat_traits::cols> >::type
 operator*( A const & a, B const & b )
 {
 typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits::cols>::type R;
 R r;
 for( int i=0; i<mat_traits<A>::rows; ++i )
 for( int j=0; j<mat_traits::cols; ++j )
 {
 typedef typename mat_traits<A>::scalar_type Ta;
 Ta x(scalar_traits<Ta>::value(0));
 for( int k=0; k<mat_traits<A>::cols; ++k )
 x += mat_traits<A>::read_element_idx(i,k,a)*mat_traits::read_element_idx(k,j,b);
 mat_traits<R>::write_element_idx(i,j,r) = x;
 }
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 mul_ms_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename lazy_enable_if_c<
 is_mat<A>::value && is_scalar::value &&
 !qvm_detail::mul_ms_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 deduce_mat<A> >::type
 operator*( A const & a, B b )
 {
 typedef typename deduce_mat<A>::type R;
 R r;
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<R>::write_element_idx(i,j,r)=mat_traits<A>::read_element_idx(i,j,a)*b;
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 mul_sm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename lazy_enable_if_c<
 is_scalar<A>::value && is_mat::value &&
 !qvm_detail::mul_sm_defined<mat_traits::rows,mat_traits::cols>::value,
 deduce_mat >::type
 operator*( A a, B const & b )
 {
 typedef typename deduce_mat::type R;
 R r;
 for( int i=0; i!=mat_traits::rows; ++i )
 for( int j=0; j!=mat_traits::cols; ++j )
 mat_traits<R>::write_element_idx(i,j,r)=a*mat_traits::read_element_idx(i,j,b);
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 neq_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols &&
 !qvm_detail::neq_mm_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 bool>::type
 operator!=( A const & a, B const & b )
 {
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 if( mat_traits<A>::read_element_idx(i,j,a)!=mat_traits::read_element_idx(i,j,b) )
 return true;
 return false;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 plus_eq_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols &&
 !qvm_detail::plus_eq_mm_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 A &>::type
 operator+=( A & a, B const & b )
 {
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<A>::write_element_idx(i,j,a)+=mat_traits::read_element_idx(i,j,b);
 return a;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int M,int N>
 struct
 plus_mm_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_OPERATIONS
 typename lazy_enable_if_c<
 is_mat<A>::value && is_mat::value &&
 mat_traits<A>::rows==mat_traits::rows &&
 mat_traits<A>::cols==mat_traits::cols &&
 !qvm_detail::plus_mm_defined<mat_traits<A>::rows,mat_traits<A>::cols>::value,
 deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols> >::type
 operator+( A const & a, B const & b )
 {
 typedef typename deduce_mat2<A,B,mat_traits<A>::rows,mat_traits<A>::cols>::type R;
 R r;
 for( int i=0; i!=mat_traits<A>::rows; ++i )
 for( int j=0; j!=mat_traits<A>::cols; ++j )
 mat_traits<R>::write_element_idx(i,j,r)=mat_traits<A>::read_element_idx(i,j,a)+mat_traits::read_element_idx(i,j,b);
 return r;
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <class T>
 class
 mref_
 {
 mref_( mref_ const & );
 mref_ & operator=( mref_ const & );
 ~mref_();

public:

template <class R>
 BOOST_QVM_INLINE_TRIVIAL
 mref_ &
 operator=( R const & x )
 {
 assign(*this,x);
 return *this;
 }

template <class M>
 struct
 mat_traits< qvm_detail::mref_<M> >
 {
 typedef typename mat_traits<M>::scalar_type scalar_type;
 typedef qvm_detail::mref_<M> this_matrix;
 static int const rows=mat_traits<M>::rows;
 static int const cols=mat_traits<M>::cols;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Row<rows);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Col<cols);
 return mat_traits<M>::template read_element<Row,Col>(reinterpret_cast<M const &>(x));
 }

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type &
 write_element( this_matrix & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Row<rows);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Col<cols);
 return mat_traits<M>::template write_element<Row,Col>(reinterpret_cast<M &>(x));
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & x )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(row<rows);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(col<cols);
 return mat_traits<M>::read_element_idx(row,col,reinterpret_cast<M const &>(x));
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type &
 write_element_idx( int row, int col, this_matrix & x )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(row<rows);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(col<cols);
 return mat_traits<M>::write_element_idx(row,col,reinterpret_cast<M &>(x));
 }
 };

template <class M,int R,int C>
 struct
 deduce_mat<qvm_detail::mref_<M>,R,C>
 {
 typedef mat<typename mat_traits<M>::scalar_type,R,C> type;
 };

template <class M>
 BOOST_QVM_INLINE_TRIVIAL
 typename enable_if_c<
 is_mat<M>::value,
 qvm_detail::mref_<M> const &>::type
 mref( M const & a )
 {
 return reinterpret_cast<qvm_detail::mref_<M> const &>(a);
 }

template <class M>
 BOOST_QVM_INLINE_TRIVIAL
 typename enable_if_c<
 is_mat<M>::value,
 qvm_detail::mref_<M> &>::type
 mref( M & a )
 {
 return reinterpret_cast<qvm_detail::mref_<M> &>(a);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <class T,int Rows,int Cols>
 class
 zero_mat_
 {
 zero_mat_( zero_mat_ const & );
 zero_mat_ & operator=( zero_mat_ const & );
 ~zero_mat_();

public:

template <class T,int Rows,int Cols>
 struct
 mat_traits< qvm_detail::zero_mat_<T,Rows,Cols> >
 {
 typedef qvm_detail::zero_mat_<T,Rows,Cols> this_matrix;
 typedef T scalar_type;
 static int const rows=Rows;
 static int const cols=Cols;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Row<Rows);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Col<Cols);
 return scalar_traits<scalar_type>::value(0);
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(row<rows);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(col<cols);
 return scalar_traits<scalar_type>::value(0);
 }
 };

template <class T,int Rows,int Cols,int R,int C>
 struct
 deduce_mat<qvm_detail::zero_mat_<T,Rows,Cols>,R,C>
 {
 typedef mat<T,R,C> type;
 };

template <class T,int Rows,int Cols>
 BOOST_QVM_INLINE_TRIVIAL
 qvm_detail::zero_mat_<T,Rows,Cols> const &
 zero_mat()
 {
 return *(qvm_detail::zero_mat_<T,Rows,Cols> const *)qvm_detail::get_valid_ptr_mat_operations();
 }

template <class T,int Dim>
 BOOST_QVM_INLINE_TRIVIAL
 qvm_detail::zero_mat_<T,Dim,Dim> const &
 zero_mat()
 {
 return *(qvm_detail::zero_mat_<T,Dim,Dim> const *)qvm_detail::get_valid_ptr_mat_operations();
 }

template <class A>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value,
 void>::type
 set_zero( A & a )
 {
 assign(a,zero_mat<typename mat_traits<A>::scalar_type,mat_traits<A>::rows,mat_traits<A>::cols>());
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int D,class S>
 struct
 rot_mat_
 {
 typedef S scalar_type;
 scalar_type a[3][3];

BOOST_QVM_INLINE
                rot_mat_(
                        scalar_type a00, scalar_type a01, scalar_type a02,
                        scalar_type a10, scalar_type a11, scalar_type a12,
                        scalar_type a20, scalar_type a21, scalar_type a22 )
                    {
                    a[0][0] = a00;
                    a[0][1] = a01;
                    a[0][2] = a02;
                    a[1][0] = a10;
                    a[1][1] = a11;
                    a[1][2] = a12;
                    a[2][0] = a20;
                    a[2][1] = a21;
                    a[2][2] = a22;
                    }

template <int Row,int Col>
 struct
 rot_m_get
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const (&)[3][3] )
 {
 return scalar_traits<T>::value(Row==Col);
 }
 };

template <> struct rot_m_get<0,0> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[0][0]; } };
 template <> struct rot_m_get<0,1> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[0][1]; } };
 template <> struct rot_m_get<0,2> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[0][2]; } };
 template <> struct rot_m_get<1,0> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[1][0]; } };
 template <> struct rot_m_get<1,1> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[1][1]; } };
 template <> struct rot_m_get<1,2> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[1][2]; } };
 template <> struct rot_m_get<2,0> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[2][0]; } };
 template <> struct rot_m_get<2,1> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[2][1]; } };
 template <> struct rot_m_get<2,2> { template <class T> static BOOST_QVM_INLINE_CRITICAL T get( T const (&a)[3][3] ) { return a[2][2]; } };
 }

template <class M>
 struct mat_traits;

template <int D,class S>
 struct
 mat_traits< qvm_detail::rot_mat_<D,S> >
 {
 typedef qvm_detail::rot_mat_<D,S> this_matrix;
 typedef typename this_matrix::scalar_type scalar_type;
 static int const rows=D;
 static int const cols=D;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Row<D);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Col<D);
 return qvm_detail::rot_m_get<Row,Col>::get(x.a);
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & x )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(row<D);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(col<D);
 return row<3 && col<3?
 x.a[row][col] :
 scalar_traits<scalar_type>::value(row==col);
 }
 };

template <int Dim,class V,class Angle>
 BOOST_QVM_INLINE
 typename enable_if_c<
 is_vec<V>::value && vec_traits<V>::dim==3,
 qvm_detail::rot_mat_<Dim,Angle> >::type
 rot_mat( V const & axis, Angle angle )
 {
 typedef Angle scalar_type;
 scalar_type const x=vec_traits<V>::template read_element<0>(axis);
 scalar_type const y=vec_traits<V>::template read_element<1>(axis);
 scalar_type const z=vec_traits<V>::template read_element<2>(axis);
 scalar_type const m2=x*x+y*y+z*z;
 if( m2==scalar_traits<scalar_type>::value(0) )
 BOOST_QVM_THROW_EXCEPTION(zero_magnitude_error());
 scalar_type const s = sin<scalar_type>(angle);
 scalar_type const c = cos<scalar_type>(angle);
 scalar_type const x2 = x*x;
 scalar_type const y2 = y*y;
 scalar_type const z2 = z*z;
 scalar_type const xy = x*y;
 scalar_type const xz = x*z;
 scalar_type const yz = y*z;
 scalar_type const xs = x*s;
 scalar_type const ys = y*s;
 scalar_type const zs = z*s;
 scalar_type const one = scalar_traits<scalar_type>::value(1);
 scalar_type const c1 = one-c;
 return qvm_detail::rot_mat_<Dim,Angle>(
 x2+(one-x2)*c, xy*c1-zs, xz*(one-c)+ys,
 xy*c1+zs, y2+(one-y2)*c, yz*c1-xs,
 xz*c1-ys, yz*c1+xs, z2+(one-z2)*c );
 }

template <class A,class B,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3 &&
 is_vec::value && vec_traits::dim==3,
 void>::type
 set_rot( A & a, B const & axis, Angle angle )
 {
 assign(a,rot_mat<mat_traits<A>::rows>(axis,angle));
 }

template <class A,class B,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3 &&
 is_vec::value && vec_traits::dim==3,
 void>::type
 rotate( A & a, B const & axis, Angle angle )
 {
 a *= rot_mat<mat_traits<A>::rows>(axis,angle);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_xzy( Angle x1, Angle z2, Angle y3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(x1);
 scalar_type const s1 = sin<scalar_type>(x1);
 scalar_type const c2 = cos<scalar_type>(z2);
 scalar_type const s2 = sin<scalar_type>(z2);
 scalar_type const c3 = cos<scalar_type>(y3);
 scalar_type const s3 = sin<scalar_type>(y3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c2*c3, -s2, c2*s3,
 s1*s3 + c1*c3*s2, c1*c2, c1*s2*s3 - c3*s1,
 c3*s1*s2 - c1*s3, c2*s1, c1*c3 + s1*s2*s3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_xzy( A & a, Angle x1, Angle z2, Angle y3 )
 {
 assign(a,rot_mat_xzy<mat_traits<A>::rows>(x1,z2,y3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_xzy( A & a, Angle x1, Angle z2, Angle y3 )
 {
 a *= rot_mat_xzy<mat_traits<A>::rows>(x1,z2,y3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_xyz( Angle x1, Angle y2, Angle z3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(x1);
 scalar_type const s1 = sin<scalar_type>(x1);
 scalar_type const c2 = cos<scalar_type>(y2);
 scalar_type const s2 = sin<scalar_type>(y2);
 scalar_type const c3 = cos<scalar_type>(z3);
 scalar_type const s3 = sin<scalar_type>(z3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c2*c3, -c2*s3, s2,
 c1*s3 + c3*s1*s2, c1*c3 - s1*s2*s3, -c2*s1,
 s1*s3 - c1*c3*s2, c3*s1 + c1*s2*s3, c1*c2 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_xyz( A & a, Angle x1, Angle y2, Angle z3 )
 {
 assign(a,rot_mat_xyz<mat_traits<A>::rows>(x1,y2,z3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_xyz( A & a, Angle x1, Angle y2, Angle z3 )
 {
 a *= rot_mat_xyz<mat_traits<A>::rows>(x1,y2,z3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_yxz( Angle y1, Angle x2, Angle z3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(y1);
 scalar_type const s1 = sin<scalar_type>(y1);
 scalar_type const c2 = cos<scalar_type>(x2);
 scalar_type const s2 = sin<scalar_type>(x2);
 scalar_type const c3 = cos<scalar_type>(z3);
 scalar_type const s3 = sin<scalar_type>(z3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c3 + s1*s2*s3, c3*s1*s2 - c1*s3, c2*s1,
 c2*s3, c2*c3, -s2,
 c1*s2*s3 - c3*s1, c1*c3*s2 + s1*s3, c1*c2 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_yxz( A & a, Angle y1, Angle x2, Angle z3 )
 {
 assign(a,rot_mat_yxz<mat_traits<A>::rows>(y1,x2,z3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_yxz( A & a, Angle y1, Angle x2, Angle z3 )
 {
 a *= rot_mat_yxz<mat_traits<A>::rows>(y1,x2,z3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_yzx( Angle y1, Angle z2, Angle x3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(y1);
 scalar_type const s1 = sin<scalar_type>(y1);
 scalar_type const c2 = cos<scalar_type>(z2);
 scalar_type const s2 = sin<scalar_type>(z2);
 scalar_type const c3 = cos<scalar_type>(x3);
 scalar_type const s3 = sin<scalar_type>(x3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c2, s1*s3 - c1*c3*s2, c3*s1 + c1*s2*s3,
 s2, c2*c3, -c2*s3,
 -c2*s1, c1*s3 + c3*s1*s2, c1*c3 - s1*s2*s3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_yzx( A & a, Angle y1, Angle z2, Angle x3 )
 {
 assign(a,rot_mat_yzx<mat_traits<A>::rows>(y1,z2,x3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_yzx( A & a, Angle y1, Angle z2, Angle x3 )
 {
 a *= rot_mat_yzx<mat_traits<A>::rows>(y1,z2,x3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_zyx( Angle z1, Angle y2, Angle x3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(z1);
 scalar_type const s1 = sin<scalar_type>(z1);
 scalar_type const c2 = cos<scalar_type>(y2);
 scalar_type const s2 = sin<scalar_type>(y2);
 scalar_type const c3 = cos<scalar_type>(x3);
 scalar_type const s3 = sin<scalar_type>(x3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c2, c1*s2*s3 - c3*s1, s1*s3 + c1*c3*s2,
 c2*s1, c1*c3 + s1*s2*s3, c3*s1*s2 - c1*s3,
 -s2, c2*s3, c2*c3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_zyx( A & a, Angle z1, Angle y2, Angle x3 )
 {
 assign(a,rot_mat_zyx<mat_traits<A>::rows>(z1,y2,x3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_zyx( A & a, Angle z1, Angle y2, Angle x3 )
 {
 a *= rot_mat_zyx<mat_traits<A>::rows>(z1,y2,x3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_zxy( Angle z1, Angle x2, Angle y3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(z1);
 scalar_type const s1 = sin<scalar_type>(z1);
 scalar_type const c2 = cos<scalar_type>(x2);
 scalar_type const s2 = sin<scalar_type>(x2);
 scalar_type const c3 = cos<scalar_type>(y3);
 scalar_type const s3 = sin<scalar_type>(y3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c3 - s1*s2*s3, -c2*s1, c1*s3 + c3*s1*s2,
 c3*s1 + c1*s2*s3, c1*c2, s1*s3 - c1*c3*s2,
 -c2*s3, s2, c2*c3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_zxy( A & a, Angle z1, Angle x2, Angle y3 )
 {
 assign(a,rot_mat_zxy<mat_traits<A>::rows>(z1,x2,y3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_zxy( A & a, Angle z1, Angle x2, Angle y3 )
 {
 a *= rot_mat_zxy<mat_traits<A>::rows>(z1,x2,y3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_xzx( Angle x1, Angle z2, Angle x3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(x1);
 scalar_type const s1 = sin<scalar_type>(x1);
 scalar_type const c2 = cos<scalar_type>(z2);
 scalar_type const s2 = sin<scalar_type>(z2);
 scalar_type const c3 = cos<scalar_type>(x3);
 scalar_type const s3 = sin<scalar_type>(x3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c2, -c3*s2, s2*s3,
 c1*s2, c1*c2*c3 - s1*s3, -c3*s1 - c1*c2*s3,
 s1*s2, c1*s3 + c2*c3*s1, c1*c3 - c2*s1*s3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_xzx( A & a, Angle x1, Angle z2, Angle x3 )
 {
 assign(a,rot_mat_xzx<mat_traits<A>::rows>(x1,z2,x3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_xzx( A & a, Angle x1, Angle z2, Angle x3 )
 {
 a *= rot_mat_xzx<mat_traits<A>::rows>(x1,z2,x3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_xyx( Angle x1, Angle y2, Angle x3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(x1);
 scalar_type const s1 = sin<scalar_type>(x1);
 scalar_type const c2 = cos<scalar_type>(y2);
 scalar_type const s2 = sin<scalar_type>(y2);
 scalar_type const c3 = cos<scalar_type>(x3);
 scalar_type const s3 = sin<scalar_type>(x3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c2, s2*s3, c3*s2,
 s1*s2, c1*c3 - c2*s1*s3, -c1*s3 - c2*c3*s1,
 -c1*s2, c3*s1 + c1*c2*s3, c1*c2*c3 - s1*s3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_xyx( A & a, Angle x1, Angle y2, Angle x3 )
 {
 assign(a,rot_mat_xyx<mat_traits<A>::rows>(x1,y2,x3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_xyx( A & a, Angle x1, Angle y2, Angle x3 )
 {
 a *= rot_mat_xyx<mat_traits<A>::rows>(x1,y2,x3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_yxy( Angle y1, Angle x2, Angle y3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(y1);
 scalar_type const s1 = sin<scalar_type>(y1);
 scalar_type const c2 = cos<scalar_type>(x2);
 scalar_type const s2 = sin<scalar_type>(x2);
 scalar_type const c3 = cos<scalar_type>(y3);
 scalar_type const s3 = sin<scalar_type>(y3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c3 - c2*s1*s3, s1*s2, c1*s3 + c2*c3*s1,
 s2*s3, c2, -c3*s2,
 -c3*s1 - c1*c2*s3, c1*s2, c1*c2*c3 - s1*s3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_yxy( A & a, Angle y1, Angle x2, Angle y3 )
 {
 assign(a,rot_mat_yxy<mat_traits<A>::rows>(y1,x2,y3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_yxy( A & a, Angle y1, Angle x2, Angle y3 )
 {
 a *= rot_mat_yxy<mat_traits<A>::rows>(y1,x2,y3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_yzy( Angle y1, Angle z2, Angle y3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(y1);
 scalar_type const s1 = sin<scalar_type>(y1);
 scalar_type const c2 = cos<scalar_type>(z2);
 scalar_type const s2 = sin<scalar_type>(z2);
 scalar_type const c3 = cos<scalar_type>(y3);
 scalar_type const s3 = sin<scalar_type>(y3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c2*c3 - s1*s3, -c1*s2, c3*s1 + c1*c2*s3,
 c3*s2, c2, s2*s3,
 -c1*s3 - c2*c3*s1, s1*s2, c1*c3 - c2*s1*s3 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_yzy( A & a, Angle y1, Angle z2, Angle y3 )
 {
 assign(a,rot_mat_yzy<mat_traits<A>::rows>(y1,z2,y3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_yzy( A & a, Angle y1, Angle z2, Angle y3 )
 {
 a *= rot_mat_yzy<mat_traits<A>::rows>(y1,z2,y3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_zyz( Angle z1, Angle y2, Angle z3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(z1);
 scalar_type const s1 = sin<scalar_type>(z1);
 scalar_type const c2 = cos<scalar_type>(y2);
 scalar_type const s2 = sin<scalar_type>(y2);
 scalar_type const c3 = cos<scalar_type>(z3);
 scalar_type const s3 = sin<scalar_type>(z3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c2*c3 - s1*s3, -c3*s1 - c1*c2*s3, c1*s2,
 c1*s3 + c2*c3*s1, c1*c3 - c2*s1*s3, s1*s2,
 -c3*s2, s2*s3, c2 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_zyz( A & a, Angle z1, Angle y2, Angle z3 )
 {
 assign(a,rot_mat_zyz<mat_traits<A>::rows>(z1,y2,z3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_zyz( A & a, Angle z1, Angle y2, Angle z3 )
 {
 a *= rot_mat_zyz<mat_traits<A>::rows>(z1,y2,z3);
 }

////////////////////////////////////////////////

template <int Dim,class Angle>
 BOOST_QVM_INLINE
 qvm_detail::rot_mat_<Dim,Angle>
 rot_mat_zxz( Angle z1, Angle x2, Angle z3 )
 {
 typedef Angle scalar_type;
 scalar_type const c1 = cos<scalar_type>(z1);
 scalar_type const s1 = sin<scalar_type>(z1);
 scalar_type const c2 = cos<scalar_type>(x2);
 scalar_type const s2 = sin<scalar_type>(x2);
 scalar_type const c3 = cos<scalar_type>(z3);
 scalar_type const s3 = sin<scalar_type>(z3);
 return qvm_detail::rot_mat_<Dim,Angle>(
 c1*c3 - c2*s1*s3, -c1*s3 - c2*c3*s1, s1*s2,
 c3*s1 + c1*c2*s3, c1*c2*c3 - s1*s3, -c1*s2,
 s2*s3, c3*s2, c2 );
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 set_rot_zxz( A & a, Angle z1, Angle x2, Angle z3 )
 {
 assign(a,rot_mat_zxz<mat_traits<A>::rows>(z1,x2,z3));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 mat_traits<A>::rows>=3,
 void>::type
 rotate_zxz( A & a, Angle z1, Angle x2, Angle z3 )
 {
 a *= rot_mat_zxz<mat_traits<A>::rows>(z1,x2,z3);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int Dim,class Angle>
 struct
 rotx_mat_
 {
 BOOST_QVM_INLINE_TRIVIAL
 rotx_mat_()
 {
 }

template <class R>
 BOOST_QVM_INLINE_TRIVIAL
 operator R() const
 {
 R r;
 assign(r,*this);
 return r;
 }

private:

rotx_mat_( rotx_mat_ const & );
                rotx_mat_ & operator=( rotx_mat_ const & );
                ~rotx_mat_();
                };

template <int Row,int Col>
 struct
 rotx_m_get
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & )
 {
 return scalar_traits<T>::value(Row==Col);
 }
 };

template <>
 struct
 rotx_m_get<1,1>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return cos<T>(angle);
 }
 };

template <>
 struct
 rotx_m_get<1,2>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return -sin<T>(angle);
 }
 };

template <>
 struct
 rotx_m_get<2,1>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return sin<T>(angle);
 }
 };

template <>
 struct
 rotx_m_get<2,2>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return cos<T>(angle);
 }
 };
 }

template <int Dim,class Angle>
 struct
 mat_traits< qvm_detail::rotx_mat_<Dim,Angle> >
 {
 typedef qvm_detail::rotx_mat_<Dim,Angle> this_matrix;
 typedef Angle scalar_type;
 static int const rows=Dim;
 static int const cols=Dim;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Row<Dim);
 BOOST_QVM_STATIC_ASSERT(Col<Dim);
 return qvm_detail::rotx_m_get<Row,Col>::get(reinterpret_cast<Angle const &>(x));
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & x )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(row<Dim);
 BOOST_QVM_ASSERT(col<Dim);
 Angle const & a=reinterpret_cast<Angle const &>(x);
 if( row==1 )
 {
 if( col==1 )
 return cos<scalar_type>(a);
 if( col==2 )
 return -sin<scalar_type>(a);
 }
 if( row==2 )
 {
 if( col==1 )
 return sin<scalar_type>(a);
 if( col==2 )
 return cos<scalar_type>(a);
 }
 return scalar_traits<scalar_type>::value(row==col);
 }
 };

template <int Dim,class Angle>
 struct
 deduce_mat<qvm_detail::rotx_mat_<Dim,Angle>,Dim,Dim>
 {
 typedef mat<Angle,Dim,Dim> type;
 };

template <int Dim,class Angle>
 struct
 deduce_mat2<qvm_detail::rotx_mat_<Dim,Angle>,qvm_detail::rotx_mat_<Dim,Angle>,Dim,Dim>
 {
 typedef mat<Angle,Dim,Dim> type;
 };

template <int Dim,class Angle>
 BOOST_QVM_INLINE_TRIVIAL
 qvm_detail::rotx_mat_<Dim,Angle> const &
 rotx_mat( Angle const & angle )
 {
 BOOST_QVM_STATIC_ASSERT(Dim>=3);
 return reinterpret_cast<qvm_detail::rotx_mat_<Dim,Angle> const &>(angle);
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows>=3 &&
 mat_traits<A>::rows==mat_traits<A>::cols,
 void>::type
 set_rotx( A & a, Angle angle )
 {
 assign(a,rotx_mat<mat_traits<A>::rows>(angle));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows>=3 &&
 mat_traits<A>::rows==mat_traits<A>::cols,
 void>::type
 rotate_x( A & a, Angle angle )
 {
 a *= rotx_mat<mat_traits<A>::rows>(angle);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int Dim,class Angle>
 struct
 roty_mat_
 {
 BOOST_QVM_INLINE_TRIVIAL
 roty_mat_()
 {
 }

private:

roty_mat_( roty_mat_ const & );
                roty_mat_ & operator=( roty_mat_ const & );
                ~roty_mat_();
                };

template <int Row,int Col>
 struct
 roty_m_get
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & )
 {
 return scalar_traits<T>::value(Row==Col);
 }
 };

template <>
 struct
 roty_m_get<0,0>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return cos<T>(angle);
 }
 };

template <>
 struct
 roty_m_get<0,2>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return sin<T>(angle);
 }
 };

template <>
 struct
 roty_m_get<2,0>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return -sin<T>(angle);
 }
 };

template <>
 struct
 roty_m_get<2,2>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return cos<T>(angle);
 }
 };
 }

template <int Dim,class Angle>
 struct
 mat_traits< qvm_detail::roty_mat_<Dim,Angle> >
 {
 typedef qvm_detail::roty_mat_<Dim,Angle> this_matrix;
 typedef Angle scalar_type;
 static int const rows=Dim;
 static int const cols=Dim;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Row<Dim);
 BOOST_QVM_STATIC_ASSERT(Col<Dim);
 return qvm_detail::roty_m_get<Row,Col>::get(reinterpret_cast<Angle const &>(x));
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & x )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(row<Dim);
 BOOST_QVM_ASSERT(col<Dim);
 Angle const & a=reinterpret_cast<Angle const &>(x);
 if( row==0 )
 {
 if( col==0 )
 return cos<scalar_type>(a);
 if( col==2 )
 return sin<scalar_type>(a);
 }
 if( row==2 )
 {
 if( col==0 )
 return -sin<scalar_type>(a);
 if( col==2 )
 return cos<scalar_type>(a);
 }
 return scalar_traits<scalar_type>::value(row==col);
 }
 };

template <int Dim,class Angle>
 struct
 deduce_mat<qvm_detail::roty_mat_<Dim,Angle>,Dim,Dim>
 {
 typedef mat<Angle,Dim,Dim> type;
 };

template <int Dim,class Angle>
 struct
 deduce_mat2<qvm_detail::roty_mat_<Dim,Angle>,qvm_detail::roty_mat_<Dim,Angle>,Dim,Dim>
 {
 typedef mat<Angle,Dim,Dim> type;
 };

template <int Dim,class Angle>
 BOOST_QVM_INLINE_TRIVIAL
 qvm_detail::roty_mat_<Dim,Angle> const &
 roty_mat( Angle const & angle )
 {
 BOOST_QVM_STATIC_ASSERT(Dim>=3);
 return reinterpret_cast<qvm_detail::roty_mat_<Dim,Angle> const &>(angle);
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows>=2 &&
 mat_traits<A>::rows==mat_traits<A>::cols,
 void>::type
 set_roty( A & a, Angle angle )
 {
 assign(a,roty_mat<mat_traits<A>::rows>(angle));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows>=3 &&
 mat_traits<A>::rows==mat_traits<A>::cols,
 void>::type
 rotate_y( A & a, Angle angle )
 {
 a *= roty_mat<mat_traits<A>::rows>(angle);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int Dim,class Angle>
 struct
 rotz_mat_
 {
 BOOST_QVM_INLINE_TRIVIAL
 rotz_mat_()
 {
 }

private:

rotz_mat_( rotz_mat_ const & );
                rotz_mat_ & operator=( rotz_mat_ const & );
                ~rotz_mat_();
                };

template <int Row,int Col>
 struct
 rotz_m_get
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & )
 {
 return scalar_traits<T>::value(Row==Col);
 }
 };

template <>
 struct
 rotz_m_get<0,0>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return cos<T>(angle);
 }
 };

template <>
 struct
 rotz_m_get<0,1>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return -sin<T>(angle);
 }
 };

template <>
 struct
 rotz_m_get<1,0>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return sin<T>(angle);
 }
 };

template <>
 struct
 rotz_m_get<1,1>
 {
 template <class T>
 static
 BOOST_QVM_INLINE_CRITICAL
 T
 get( T const & angle )
 {
 return cos<T>(angle);
 }
 };
 }

template <int Dim,class Angle>
 struct
 mat_traits< qvm_detail::rotz_mat_<Dim,Angle> >
 {
 typedef qvm_detail::rotz_mat_<Dim,Angle> this_matrix;
 typedef Angle scalar_type;
 static int const rows=Dim;
 static int const cols=Dim;

template <int Row,int Col>
 static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element( this_matrix const & x )
 {
 BOOST_QVM_STATIC_ASSERT(Row>=0);
 BOOST_QVM_STATIC_ASSERT(Col>=0);
 BOOST_QVM_STATIC_ASSERT(Row<Dim);
 BOOST_QVM_STATIC_ASSERT(Col<Dim);
 return qvm_detail::rotz_m_get<Row,Col>::get(reinterpret_cast<Angle const &>(x));
 }

static
 BOOST_QVM_INLINE_CRITICAL
 scalar_type
 read_element_idx( int row, int col, this_matrix const & x )
 {
 BOOST_QVM_ASSERT(row>=0);
 BOOST_QVM_ASSERT(col>=0);
 BOOST_QVM_ASSERT(row<Dim);
 BOOST_QVM_ASSERT(col<Dim);
 Angle const & a=reinterpret_cast<Angle const &>(x);
 if( row==0 )
 {
 if( col==0 )
 return cos<scalar_type>(a);
 if( col==1 )
 return -sin<scalar_type>(a);
 }
 if( row==1 )
 {
 if( col==0 )
 return sin<scalar_type>(a);
 if( col==1 )
 return cos<scalar_type>(a);
 }
 return scalar_traits<scalar_type>::value(row==col);
 }
 };

template <int Dim,class Angle>
 struct
 deduce_mat<qvm_detail::rotz_mat_<Dim,Angle>,Dim,Dim>
 {
 typedef mat<Angle,Dim,Dim> type;
 };

template <int Dim,class Angle,int R,int C>
 struct
 deduce_mat2<qvm_detail::rotz_mat_<Dim,Angle>,qvm_detail::rotz_mat_<Dim,Angle>,R,C>
 {
 typedef mat<Angle,R,C> type;
 };

template <int Dim,class Angle>
 BOOST_QVM_INLINE_TRIVIAL
 qvm_detail::rotz_mat_<Dim,Angle> const &
 rotz_mat( Angle const & angle )
 {
 BOOST_QVM_STATIC_ASSERT(Dim>=2);
 return reinterpret_cast<qvm_detail::rotz_mat_<Dim,Angle> const &>(angle);
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows>=2 &&
 mat_traits<A>::rows==mat_traits<A>::cols,
 void>::type
 set_rotz( A & a, Angle angle )
 {
 assign(a,rotz_mat<mat_traits<A>::rows>(angle));
 }

template <class A,class Angle>
 BOOST_QVM_INLINE_OPERATIONS
 typename enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows>=2 &&
 mat_traits<A>::rows==mat_traits<A>::cols,
 void>::type
 rotate_z( A & a, Angle angle )
 {
 a *= rotz_mat<mat_traits<A>::rows>(angle);
 }

////////////////////////////////////////////////

namespace
 qvm_detail
 {
 template <int D>
 struct
 inverse_m_defined
 {
 static bool const value=false;
 };
 }

template <class A,class B>
 BOOST_QVM_INLINE_TRIVIAL
 typename lazy_enable_if_c<
 is_mat<A>::value && is_scalar::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 !qvm_detail::inverse_m_defined<mat_traits<A>::rows>::value,
 deduce_mat<A> >::type
 inverse( A const & a, B det )
 {
 typedef typename mat_traits<A>::scalar_type T;
 BOOST_QVM_ASSERT(det!=scalar_traits<T>::value(0));
 T f=scalar_traits<T>::value(1)/det;
 typedef typename deduce_mat<A>::type cofactor_return_type;
 cofactor_return_type c=qvm_detail::cofactor_impl(a);
 return reinterpret_cast<qvm_detail::transposed_<cofactor_return_type> const &>(c) * f;
 }

template <class A>
 BOOST_QVM_INLINE_TRIVIAL
 typename lazy_enable_if_c<
 is_mat<A>::value &&
 mat_traits<A>::rows==mat_traits<A>::cols &&
 !qvm_detail::inverse_m_defined<mat_traits<A>::rows>::value,
 deduce_mat<A> >::type
 inverse( A const & a )
 {
 typedef typename mat_traits<A>::scalar_type T;
 T det=determinant(a);
 if( det==scalar_traits<T>::value(0) )
 BOOST_QVM_THROW_EXCEPTION(zero_determinant_error());
 return inverse(a,det);
 }

////////////////////////////////////////////////

namespace
        sfinae
            {
            using ::boost::qvm::to_string;
            using ::boost::qvm::assign;
            using ::boost::qvm::determinant;
            using ::boost::qvm::cmp;
            using ::boost::qvm::convert_to;
            using ::boost::qvm::set_identity;
            using ::boost::qvm::set_zero;
            using ::boost::qvm::scalar_cast;
            using ::boost::qvm::operator/=;
            using ::boost::qvm::operator/;
            using ::boost::qvm::operator==;
            using ::boost::qvm::operator-=;
            using ::boost::qvm::operator-;
            using ::boost::qvm::operator*=;
            using ::boost::qvm::operator*;
            using ::boost::qvm::operator!=;
            using ::boost::qvm::operator+=;
            using ::boost::qvm::operator+;
            using ::boost::qvm::mref;
            using ::boost::qvm::rot_mat;
            using ::boost::qvm::set_rot;
            using ::boost::qvm::rotate;
            using ::boost::qvm::set_rotx;
            using ::boost::qvm::rotate_x;
            using ::boost::qvm::set_roty;
            using ::boost::qvm::rotate_y;
            using ::boost::qvm::set_rotz;
            using ::boost::qvm::rotate_z;
            using ::boost::qvm::inverse;
            }

////////////////////////////////////////////////
        }
    }

#endif