# mln::algebra Namespace Reference

Namespace of algebraic structure. More...

## Classes

struct  h_mat
N-Dimensional matrix with homogeneous coordinates. More...
struct  h_vec
N-Dimensional vector with homogeneous coordinates. More...

## Functions

template<unsigned N, typename T >
bool ldlt_decomp (mat< N, N, T > &A, vec< N, T > &rdiag)
Perform LDL^T decomposition of a symmetric positive definite matrix.
template<unsigned N, typename T >
void ldlt_solve (const mat< N, N, T > &A, const vec< N, T > &rdiag, const vec< N, T > &B, vec< N, T > &x)
Solve A x = B after mln::algebra::ldlt_decomp.
template<unsigned n, typename T , typename U >
mln::trait::value_< typename
mln::trait::op::times< T, U >
::ret >::sum
operator* (const vec< n, T > &lhs, const vec< n, U > &rhs)
Scalar product (dot product).
template<typename T , typename U >
vec< 3, typename
mln::trait::op::times< T, U >
::ret >
vprod (const vec< 3, T > &lhs, const vec< 3, U > &rhs)
Vectorial product (cross product).

## Detailed Description

Namespace of algebraic structure.

## Function Documentation

template<unsigned N, typename T >
 bool mln::algebra::ldlt_decomp ( mat< N, N, T > & A, vec< N, T > & rdiag ) ` [inline]`

Perform LDL^T decomposition of a symmetric positive definite matrix.

Like Cholesky, but no square roots. Overwrites lower triangle of matrix.

From Trimesh's ldltdc routine.

Referenced by mln::geom::mesh_curvature().

template<unsigned N, typename T >
 void mln::algebra::ldlt_solve ( const mat< N, N, T > & A, const vec< N, T > & rdiag, const vec< N, T > & B, vec< N, T > & x ) ` [inline]`

Solve A x = B after mln::algebra::ldlt_decomp.

Referenced by mln::geom::mesh_curvature().

template<unsigned n, typename T , typename U >
 mln::trait::value_< typename mln::trait::op::times< T, U >::ret >::sum mln::algebra::operator* ( const vec< n, T > & lhs, const vec< n, U > & rhs ) ` [inline]`

Scalar product (dot product).

References mln::literal::zero.

template<typename T , typename U >
 vec< 3, typename mln::trait::op::times< T, U >::ret > mln::algebra::vprod ( const vec< 3, T > & lhs, const vec< 3, U > & rhs ) ` [inline]`

Vectorial product (cross product).

References vprod().

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