/**
 * File: linearAlgebra_fwd.h
 *
 * Author: Andrew Stein (andrew)
 * Created: 5/2/2014
 *
 * Information on last revision to this file:
 *    $LastChangedDate$
 *    $LastChangedBy$
 *    $LastChangedRevision$
 *
 * Description: 
 *    Defines various linear algebra methods. Templated implementations are
 *    in a separate linearAlgebra.h file.
 *
 *  NOTE: This header "forward declares" templated definitions.
 *        To get the implementations, you must include linearAlgebra.h.
 *
 * Copyright: Anki, Inc. 2014
 *
 **/

#ifndef ANKI_COMMON_BASESTATION_MATH_LINEAR_ALGEBRA_H
#define ANKI_COMMON_BASESTATION_MATH_LINEAR_ALGEBRA_H

#include "coretech/common/shared/math/matrix_fwd.h"
#include "coretech/common/shared/math/point_fwd.h"

namespace Anki {
  
// Returns a projection operator for the given plane normal, n,
//
//   P = I - n*n^T
//
// such that
//
//   v' = P*v
//
// removes all variation of v along the normal. Note that the normal
// must be a unit vector!
//
// TODO: make normal a UnitVector type
template<size_t N, typename T>
SmallSquareMatrix<N,T> GetProjectionOperator(const Point<N,T>& normal);

enum class LeastSquaresMethod : u8 {
  LU,
  Cholesky,
  Eigenvalue,
  SVD,
  QR
};

// Returns x for the linear system Ax = b
// 1. b and x are columns stored as a SmallMatrix
template<MatDimType M, MatDimType N, typename T>
Result LeastSquares(const SmallMatrix<M, N, T>&   A,
                    const SmallMatrix<M, 1, T>&   b,
                    SmallMatrix<N,1,T>&           x,
                    LeastSquaresMethod            method = LeastSquaresMethod::LU);

// 2. b and x are stored as vectors (points)
template<MatDimType M, MatDimType N, typename T>
Result LeastSquares(const SmallMatrix<M, N, T>&   A,
                    const Point<M,T>&             b,
                    Point<N,T>&                   x,
                    LeastSquaresMethod            method = LeastSquaresMethod::LU);

  
} // namespace Anki

#endif // ANKI_COMMON_BASESTATION_MATH_LINEAR_ALGEBRA_H