matrix_norm.h

// Description: Matrix norm

#ifndef PASTELMATH_MATRIX_NORM_H
#define PASTELMATH_MATRIX_NORM_H

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

namespace Pastel
{

    //! Returns a pointwise matrix norm given by the norm bijection.
    /*!
   This function considers the matrix as a long vector, and
   computes a vector norm for it. In particular, a euclidean norm 
   bijection gives the Frobenius norm (without the square root).
   See 'pastel/math/normbijection/normbijections.h" for predefined norm bijections.
   */
    template <typename Real, 
        typename Expression, typename NormBijection>
    Real norm2(const MatrixExpression<Real, Expression>& matrix,
        const NormBijection& normBijection);

    //! Returns the induced manhattan matrix norm.
    /*!
   returns:
   max(sum(abs(matrix)))
   */
    template <typename Real, typename Expression>
    Real manhattanNorm(
        const MatrixExpression<Real, Expression>& matrix);

    //! Returns the squared Frobenius matrix norm.
    /*!
   returns:
   norm2(matrix, Euclidean_NormBijection())
   */
    template <typename Real, typename Expression>
    Real frobeniusNorm2(
        const MatrixExpression<Real, Expression>& matrix);

    //! Returns the Frobenius matrix norm.
    /*!
   returns:
   sqrt(frobeniusNorm2(matrix))
   */
    template <typename Real, typename Expression>
    Real frobeniusNorm(
        const MatrixExpression<Real, Expression>& matrix);

    //! Returns the induced infinity matrix norm.
    /*!
   returns:
   max(sum(abs(transpose(matrix))))
   */
    template <typename Real, typename Expression>
    Real maxNorm(
        const MatrixExpression<Real, Expression>& matrix);

}

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

#endif