orthonormal.h

// Description: Perpendicular vectors
// Detail: orthonormalize, perpendicular, etc.
// Documentation: common.txt

#ifndef PASTELMATH_ORTHONORMAL_H
#define PASTELMATH_ORTHONORMAL_H

#include "pastel/sys/vector.h"
#include "pastel/math/matrix/matrix.h"

#include <vector>

namespace Pastel
{

    //! Orthonormalizes the columns of a matrix.
    /*!
   This is stabilized Gram-Schmidt orthonormalization.
   It is numerically ok; if you need more stability, 
   use the QR-decomposition instead. 

   matrix:
   An mxn-matrix Q.

   returns:
   A matrix Q such that Q^T Q = I.

   throws:
   SingularMatrix_Exception if the matrix has 
   effectively linearly dependent columns.
   */
    template <typename Real>
    Matrix<Real> orthonormalize(Matrix<Real> matrix);

    //! Calculates a perpendicular to a set of vectors
    /*!
   Preconditions:
   Vectors in 'orthonormalSet' are orthonormal.

   If the set is bigger than the dimensionality, 
   a zero vector is returned. 
   This is because every set bigger than dimensionality 
   is linearly dependent. If the set is empty, a unit vector 
   of the form (1, 0, 0, ..., 0) is returned.

   See also:
   orthonormalize()
   */

    template <typename Real, integer N>
    Vector<Real, N> perpendicular(
        const std::vector<Vector<Real, N> >& orthonormalSet);

    template <typename Real, integer N>
    Vector<Real, N> perpendicular(
        integer dimension,
        const std::vector<Vector<Real, N> >& orthonormalSet);

}

#include "pastel/math/matrix/orthonormal.hpp"

#endif