MsqMatrix.hpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2006 Sandia National Laboratories.  Developed at the
    University of Wisconsin--Madison under SNL contract number
    624796.  The U.S. Government and the University of Wisconsin
    retain certain rights to this software.

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2006) [email protected]

  ***************************************************************** */

/** \file MsqMatrix.hpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#ifndef MSQ_MSQ_MATRIX_HPP
#define MSQ_MSQ_MATRIX_HPP

#include "Mesquite.hpp"

#include <string>
#include <istream>
#include <ostream>
#include <sstream>

namespace MBMesquite
{

/**\brief Fixed-size matrix class
 *
 * This class implements a fixed-size 2-dimensional matrix.
 * The actual size is specified with template parameters.
 */
template < unsigned R, unsigned C >
class MsqMatrix
{
  protected:
    double m[R * C];

  public:
    typedef MsqMatrix< R, C > my_type;

    enum
    {
        ROWS = R,
        COLS = C
    };

    /** Constructor for uninitialized matrix */
    MsqMatrix() {}
    /** Initialize diagonal values, zero others */
    MsqMatrix( double v )
    {
        diag( v );
    }
    /** Initialize to an array of values */
    MsqMatrix( const double* v )
    {
        set( v );
    }
    /** Initialize from 2D array */
    MsqMatrix( const double v[R][C] )
    {
        set( v );
    }
    /** Initialize with column vectors */
    MsqMatrix( const MsqMatrix< R, 1 >* c )
    {
        set_columns( c );
    }
    /** Initialize with row vectors */
    MsqMatrix( const MsqMatrix< 1, C >* r )
    {
        set_rows( r );
    }
    /** Parse initial values from string */
    MsqMatrix( const char* s )
    {
        set( s );
    }
    /** Parse initial values from string */
    MsqMatrix( const std::string& s )
    {
        set( s );
    }
    /** Initialize to the minor of a larger matrix
     *  This matrix is the passed matrix with the
     *  specified row and column removed.
     */
    MsqMatrix( const MsqMatrix< R + 1, C + 1 >& p_m, unsigned p_r, unsigned p_c )
    {
        make_minor( p_m, p_r, p_c );
    }

    MsqMatrix< R, C >& operator=( double v )
    {
        set( v );
        return *this;
    }
    MsqMatrix< R, C >& operator=( const double* v )
    {
        set( v );
        return *this;
    }
    MsqMatrix< R, C >& operator=( const char* s )
    {
        set( s );
        return *this;
    }
    MsqMatrix< R, C >& operator=( const std::string& s )
    {
        set( s );
        return *this;
    }

    double& operator()( unsigned r, unsigned c )
    {
        return m[r * C + c];
    }
    double operator()( unsigned r, unsigned c ) const
    {
        return m[r * C + c];
    }
    double* data()
    {
        return m;
    }
    const double* data() const
    {
        return m;
    }

    void zero()
    {
        set( 0.0 );
    }
    void identity()
    {
        diag( 1.0 );
    }
    void set( double v )
    {
        for( unsigned i = 0; i < R * C; ++i )
            m[i] = v;
    }
    void set( const double* v )
    {
        for( unsigned i = 0; i < R * C; ++i )
            m[i] = v[i];
    }
    void set( const double v[R][C] );
    void set( const char* s )
    {
        std::istringstream i( s );
        i >> *this;
    }
    void set( const std::string& s )
    {
        set( s.c_str() );
    }
    /** Set diagonal value to passed values, others to zero. */
    inline void diag( double v );
    /** Set diagonal values to passed values, others to zero. */
    inline void diag( const double* v );
    /** Set this matrix to the minor of a larger matrix */
    inline void make_minor( const MsqMatrix< R + 1, C + 1 >& m, unsigned r, unsigned c );

    /** *this += transpose(other) */
    inline MsqMatrix< R, C >& assign_add_transpose( const MsqMatrix< C, R >& other );
    /** *this = s*m */
    inline MsqMatrix< R, C >& assign_product( double s, const MsqMatrix< R, C >& m );
    /** *this += s*m */
    inline MsqMatrix< R, C >& assign_add_product( double s, const MsqMatrix< R, C >& m );
    /** multiply each element by the cooresponding element in m */
    inline MsqMatrix< R, C >& assign_multiply_elements( const MsqMatrix< R, C >& m );

    inline MsqMatrix< R, C >& operator+=( const MsqMatrix< R, C >& other );
    inline MsqMatrix< R, C >& operator-=( const MsqMatrix< R, C >& other );
    inline MsqMatrix< R, C >& operator+=( double scalar );
    inline MsqMatrix< R, C >& operator-=( double scalar );
    inline MsqMatrix< R, C >& operator*=( double scalar );
    inline MsqMatrix< R, C >& operator/=( double scalar );

    //      MsqMatrix<1,C>& row( unsigned r )       { return *(MsqMatrix<1,C>*)(m+C*r); }
    // const MsqMatrix<1,C>& row( unsigned r ) const { return *(MsqMatrix<1,C>*)(m+C*r); }
    MsqMatrix< 1, C > row( unsigned r ) const
    {
        return MsqMatrix< 1, C >( m + C * r );
    }
    MsqMatrix< R, 1 > column( unsigned c ) const;
    MsqMatrix< 1, R > column_transpose( unsigned c ) const;

    void set_row( unsigned r, const MsqMatrix< 1, C >& v );
    void add_row( unsigned r, const MsqMatrix< 1, C >& v );
    void set_row_transpose( unsigned r, const MsqMatrix< C, 1 >& v );
    void set_rows( const MsqMatrix< 1, C >* v );
    void set_column( unsigned c, const MsqMatrix< R, 1 >& v );
    void add_column( unsigned c, const MsqMatrix< R, 1 >& v );
    void set_column_transpose( unsigned c, const MsqMatrix< 1, R >& v );
    void set_columns( const MsqMatrix< R, 1 >* v );
};

template <>
class MsqMatrix< 1, 1 >
{
  protected:
    double m;

  public:
    typedef MsqMatrix< 1, 1 > my_type;

    enum
    {
        ROWS = 1,
        COLS = 1
    };

    /** Constructor for uninitialized matrix */
    MsqMatrix() {}
    /** Initialize diagonal values, zero others */
    MsqMatrix( double v ) : m( v ) {}
    /** Initialize to an array of values */
    MsqMatrix( const double* v ) : m( *v ) {}
    /** Parse initial values from string */
    MsqMatrix( const char* s )
    {
        set( s );
    }
    /** Parse initial values from string */
    MsqMatrix( const std::string& s )
    {
        set( s );
    }
    /** Initialize to the minor of a larger matrix
     *  This matrix is the passed matrix with the
     *  specified row and column removed.
     */
    MsqMatrix( const MsqMatrix< 2, 2 >& M, unsigned r, unsigned c ) : m( M( r, c ) ) {}

    MsqMatrix< 1, 1 >& operator=( double v )
    {
        m = v;
        return *this;
    }
    MsqMatrix< 1, 1 >& operator=( const double* v )
    {
        m = *v;
        return *this;
    }
    MsqMatrix< 1, 1 >& operator=( const char* s )
    {
        set( s );
        return *this;
    }
    MsqMatrix< 1, 1 >& operator=( const std::string& s )
    {
        set( s );
        return *this;
    }

    double& operator()( unsigned, unsigned )
    {
        return m;
    }
    double operator()( unsigned, unsigned ) const
    {
        return m;
    }
    double* data()
    {
        return &m;
    }
    const double* data() const
    {
        return &m;
    }

    void zero()
    {
        m = 0.0;
    }
    void identity()
    {
        m = 1.0;
    }
    void set( double v )
    {
        m = v;
    }
    void set( const double* v )
    {
        m = *v;
    }
    void set( const char* s )
    {
        std::istringstream i( s );
        i >> m;
    }
    void set( const std::string& s )
    {
        set( s.c_str() );
    }
    /** Set diagonal value to passed values, others to zero. */
    inline void diag( double v )
    {
        m = v;
    }
    /** Set diagonal values to passed values, others to zero. */
    inline void diag( const double* v )
    {
        m = *v;
    }
    /** Set this matrix to the minor of a larger matrix */
    inline void make_minor( const MsqMatrix< 2, 2 >& M, unsigned r, unsigned c )
    {
        m = M( r, c );
    }

    /** *this += transpose(other) */
    inline MsqMatrix< 1, 1 >& assign_add_transpose( const MsqMatrix< 1, 1 >& other )
    {
        m += other.m;
        return *this;
    }
    /** *this = s*m */
    inline MsqMatrix< 1, 1 >& assign_product( double s, const MsqMatrix< 1, 1 >& other )
    {
        m = s * other.m;
        return *this;
    }
    /** *this += s*m */
    inline MsqMatrix< 1, 1 >& assign_add_product( double s, const MsqMatrix< 1, 1 >& other )
    {
        m += s * other.m;
        return *this;
    }
    /** multiply each element by the cooresponding element in m */
    inline MsqMatrix< 1, 1 >& assign_multiply_elements( const MsqMatrix< 1, 1 >& other )
    {
        m *= other.m;
        return *this;
    }

    operator double() const
    {
        return m;
    }
};

/** \brief Vector is a 1xL Matrix
 *
 * Define a Vector as a 1xL Matrix
 * Add single-index access operators
 */
template < unsigned L >
class MsqVector : public MsqMatrix< L, 1 >
{
  public:
    MsqVector() {}
    MsqVector( double v )
    {
        MsqMatrix< L, 1 >::set( v );
    }
    MsqVector( const double* v )
    {
        MsqMatrix< L, 1 >::set( v );
    }
    MsqVector( const char* s )
    {
        MsqMatrix< L, 1 >::set( s );
    }
    MsqVector( const std::string& s )
    {
        MsqMatrix< L, 1 >::set( s );
    }
    MsqVector( const MsqMatrix< L, 1 >& pm ) : MsqMatrix< L, 1 >( pm ) {}

    double& operator[]( unsigned idx )
    {
        return MsqMatrix< L, 1 >::operator()( idx, 0 );
    }
    double operator[]( unsigned idx ) const
    {
        return MsqMatrix< L, 1 >::operator()( idx, 0 );
    }
    double& operator()( unsigned idx )
    {
        return MsqMatrix< L, 1 >::operator()( idx, 0 );
    }
    double operator()( unsigned idx ) const
    {
        return MsqMatrix< L, 1 >::operator()( idx, 0 );
    }

    MsqVector< L >& operator=( const MsqMatrix< L, 1 >& p_m )
    {
        MsqMatrix< L, 1 >::operator=( p_m );
        return *this;
    }
};

/**\brief A subclass of MsqMatrix that behaves more like the old Matrix3D class
 *
 * A MsqMartix that behaves more like the old Matrx3D class.
 * * Constructors are different--be careful.
 * * Adds operator[] for c-array style access.
 */
template < unsigned R, unsigned C >
class MsqMatrixA : public MsqMatrix< R, C >
{
  public:
    /** Initialize all elements to zero */
    MsqMatrixA()
    {
        MsqMatrix< R, C >::set( 0 );
    }
    /** Initialize all elements to passed value */
    MsqMatrixA( double v )
    {
        MsqMatrix< R, C >::set( v );
    }
    MsqMatrixA( const double* v )
    {
        MsqMatrix< R, C >::set( v );
    }
    MsqMatrixA( const char* s )
    {
        MsqMatrix< R, C >::set( s );
    }
    MsqMatrixA( const std::string& s )
    {
        MsqMatrix< R, C >::set( s );
    }
    MsqMatrixA( const MsqMatrix< R, C >& m ) : MsqMatrix< R, C >( m ) {}
    MsqMatrixA( const MsqMatrix< R + 1, C + 1 >& m, unsigned r, unsigned c )
    {
        MsqMatrix< R, C >::make_minor( m, r, c );
    }

    double* operator[]( unsigned idx )
    {
        return MsqMatrix< R, C >::m + C * idx;
    }
    const double* operator[]( unsigned idx ) const
    {
        return MsqMatrix< R, C >::m + C * idx;
    }

    MsqMatrixA< R, C >& operator=( const MsqMatrixA< R, C >& m )
    {
        MsqMatrixA< R, C >::operator=( m );
        return *this;
    }
};

template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::set( const double v[R][C] )
{
    for( unsigned r = 0; r < R; ++r )
        for( unsigned c = 0; c < C; ++c )
            operator()( r, c ) = v[r][c];
}

template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::diag( double v )
{
    // for (unsigned r = 0; r < R; ++r)
    //  for (unsigned c = 0; c < C; ++c)
    //    operator()(r,c) = (r == c) ? v : 0.0;

    switch( R )
    {
        default:
            for( unsigned r = 4; r < R; ++r )
                switch( C )
                {
                    default:
                        for( unsigned k = 4; k < C; ++k )
                            operator()( r, k ) = r == k ? v : 0.0;
                    case 4:
                        operator()( r, 3 ) = 0.0;
                    case 3:
                        operator()( r, 2 ) = 0.0;
                    case 2:
                        operator()( r, 1 ) = 0.0;
                    case 1:
                        operator()( r, 0 ) = 0.0;
                }
        case 4:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 3, k ) = 0.0;
                case 4:
                    operator()( 3, 3 ) = v;
                case 3:
                    operator()( 3, 2 ) = 0.0;
                case 2:
                    operator()( 3, 1 ) = 0.0;
                case 1:
                    operator()( 3, 0 ) = 0.0;
            }
        case 3:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 2, k ) = 0.0;
                case 4:
                    operator()( 2, 3 ) = 0.0;
                case 3:
                    operator()( 2, 2 ) = v;
                case 2:
                    operator()( 2, 1 ) = 0.0;
                case 1:
                    operator()( 2, 0 ) = 0.0;
            }
        case 2:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 1, k ) = 0.0;
                case 4:
                    operator()( 1, 3 ) = 0.0;
                case 3:
                    operator()( 1, 2 ) = 0.0;
                case 2:
                    operator()( 1, 1 ) = v;
                case 1:
                    operator()( 1, 0 ) = 0.0;
            }
        case 1:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 0, k ) = 0.0;
                case 4:
                    operator()( 0, 3 ) = 0.0;
                case 3:
                    operator()( 0, 2 ) = 0.0;
                case 2:
                    operator()( 0, 1 ) = 0.0;
                case 1:
                    operator()( 0, 0 ) = v;
            }
    }
}

template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::diag( const double* v )
{
    // for (unsigned r = 0; r < R; ++r)
    //  for (unsigned c = 0; c < C; ++c)
    //    operator()(r,c) = (r == c) ? v[r] : 0.0;

    switch( R )
    {
        default:
            for( unsigned r = 4; r < R; ++r )
                switch( C )
                {
                    default:
                        for( unsigned k = 4; k < C; ++k )
                            operator()( r, k ) = r == k ? v[r] : 0.0;
                    case 4:
                        operator()( r, 3 ) = 0.0;
                    case 3:
                        operator()( r, 2 ) = 0.0;
                    case 2:
                        operator()( r, 1 ) = 0.0;
                    case 1:
                        operator()( r, 0 ) = 0.0;
                }
        case 4:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 3, k ) = 0.0;
                case 4:
                    operator()( 3, 3 ) = v[3];
                case 3:
                    operator()( 3, 2 ) = 0.0;
                case 2:
                    operator()( 3, 1 ) = 0.0;
                case 1:
                    operator()( 3, 0 ) = 0.0;
            }
        case 3:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 2, k ) = 0.0;
                case 4:
                    operator()( 2, 3 ) = 0.0;
                case 3:
                    operator()( 2, 2 ) = v[2];
                case 2:
                    operator()( 2, 1 ) = 0.0;
                case 1:
                    operator()( 2, 0 ) = 0.0;
            }
        case 2:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 1, k ) = 0.0;
                case 4:
                    operator()( 1, 3 ) = 0.0;
                case 3:
                    operator()( 1, 2 ) = 0.0;
                case 2:
                    operator()( 1, 1 ) = v[1];
                case 1:
                    operator()( 1, 0 ) = 0.0;
            }
        case 1:
            switch( C )
            {
                default:
                    for( unsigned k = 4; k < C; ++k )
                        operator()( 0, k ) = 0.0;
                case 4:
                    operator()( 0, 3 ) = 0.0;
                case 3:
                    operator()( 0, 2 ) = 0.0;
                case 2:
                    operator()( 0, 1 ) = 0.0;
                case 1:
                    operator()( 0, 0 ) = v[0];
            }
    }
}

/**\brief Extract minor of a matrix and assign to *this
 *
 * Given a matrix m, a row r and an column c, set *this to
 * the matrix that is m with row r and column c deleted.
 */
template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::make_minor( const MsqMatrix< R + 1, C + 1 >& M, unsigned r, unsigned c )
{
    for( unsigned i = 0; i < r; ++i )
    {
        for( unsigned j = 0; j < c; ++j )
            operator()( i, j ) = M( i, j );
        for( unsigned j = c; j < C; ++j )
            operator()( i, j ) = M( i, j + 1 );
    }
    for( unsigned i = r; i < R; ++i )
    {
        for( unsigned j = 0; j < c; ++j )
            operator()( i, j ) = M( i + 1, j );
        for( unsigned j = c; j < C; ++j )
            operator()( i, j ) = M( i + 1, j + 1 );
    }
}

template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::set_row( unsigned r, const MsqMatrix< 1, C >& v )
{
    for( unsigned i = 0; i < C; ++i )
        operator()( r, i ) = v( 0, i );
}
template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::add_row( unsigned r, const MsqMatrix< 1, C >& v )
{
    for( unsigned i = 0; i < C; ++i )
        operator()( r, i ) += v( 0, i );
}
template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::set_row_transpose( unsigned r, const MsqMatrix< C, 1 >& v )
{
    for( unsigned i = 0; i < C; ++i )
        operator()( r, i ) = v( i, 0 );
}
template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::set_rows( const MsqMatrix< 1, C >* v )
{
    for( unsigned r = 0; r < R; ++r )
        set_row( r, v[r] );
}

template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::set_column( unsigned c, const MsqMatrix< R, 1 >& v )
{
    for( unsigned i = 0; i < R; ++i )
        operator()( i, c ) = v( i, 0 );
}
template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::add_column( unsigned c, const MsqMatrix< R, 1 >& v )
{
    for( unsigned i = 0; i < R; ++i )
        operator()( i, c ) += v( i, 0 );
}
template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::set_column_transpose( unsigned c, const MsqMatrix< 1, R >& v )
{
    for( unsigned i = 0; i < R; ++i )
        operator()( i, c ) = v( 0, i );
}
template < unsigned R, unsigned C >
inline void MsqMatrix< R, C >::set_columns( const MsqMatrix< R, 1 >* v )
{
    for( unsigned c = 0; c < C; ++c )
        set_column( c, v[c] );
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, 1 > MsqMatrix< R, C >::column( unsigned c ) const
{
    MsqMatrix< R, 1 > result;
    for( unsigned i = 0; i < R; ++i )
        result( i, 0 ) = operator()( i, c );
    return result;
}

template < unsigned R, unsigned C >
inline MsqMatrix< 1, R > MsqMatrix< R, C >::column_transpose( unsigned c ) const
{
    MsqMatrix< 1, R > result;
    for( unsigned i = 0; i < R; ++i )
        result( 0, i ) = operator()( i, c );
    return result;
}

/**\brief Set a subset of this matrix to some other matrix */
template < unsigned R1, unsigned C1, unsigned R2, unsigned C2 >
inline void set_region( MsqMatrix< R1, C1 >& d, unsigned r, unsigned c, MsqMatrix< R2, C2 >& s )
{
    const unsigned rmax = r + R2 > R1 ? R1 : r + R2;
    const unsigned cmax = c + C2 > C1 ? C1 : c + C2;
    for( unsigned i = r; i < rmax; ++i )
        for( unsigned j = c; j < cmax; ++j )
            d( i, j ) = s( i - r, j - c );
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::assign_add_transpose( const MsqMatrix< C, R >& other )
{
    for( unsigned r = 0; r < R; ++r )
        for( unsigned c = 0; c < C; ++c )
            operator()( r, c ) += other( c, r );
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::assign_multiply_elements( const MsqMatrix< R, C >& other )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] *= other.data()[i];
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::assign_product( double s, const MsqMatrix< R, C >& other )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] = s * other.data()[i];
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::assign_add_product( double s, const MsqMatrix< R, C >& other )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] += s * other.data()[i];
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::operator+=( const MsqMatrix< R, C >& other )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] += other.data()[i];
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::operator-=( const MsqMatrix< R, C >& other )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] -= other.data()[i];
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::operator+=( double s )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] += s;
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::operator-=( double s )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] -= s;
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::operator*=( double s )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] *= s;
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C >& MsqMatrix< R, C >::operator/=( double s )
{
    for( unsigned i = 0; i < R * C; ++i )
        m[i] /= s;
    return *this;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator-( const MsqMatrix< R, C >& m )
{
    MsqMatrix< R, C > result;
    for( unsigned i = 0; i < R * C; ++i )
        result.data()[i] = -m.data()[i];
    return result;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator+( const MsqMatrix< R, C >& m, double s )
{
    MsqMatrix< R, C > tmp( m );
    tmp += s;
    return tmp;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator+( double s, const MsqMatrix< R, C >& m )
{
    MsqMatrix< R, C > tmp( m );
    tmp += s;
    return tmp;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator+( const MsqMatrix< R, C >& A, const MsqMatrix< R, C >& B )
{
    MsqMatrix< R, C > tmp( A );
    tmp += B;
    return tmp;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator-( const MsqMatrix< R, C >& m, double s )
{
    MsqMatrix< R, C > tmp( m );
    tmp -= s;
    return tmp;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator-( double s, const MsqMatrix< R, C >& m )
{
    MsqMatrix< R, C > tmp( m );
    tmp -= s;
    return tmp;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator-( const MsqMatrix< R, C >& A, const MsqMatrix< R, C >& B )
{
    MsqMatrix< R, C > tmp( A );
    tmp -= B;
    return tmp;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator*( const MsqMatrix< R, C >& m, double s )
{
    MsqMatrix< R, C > tmp( m );
    tmp *= s;
    return tmp;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator*( double s, const MsqMatrix< R, C >& m )
{
    MsqMatrix< R, C > tmp( m );
    tmp *= s;
    return tmp;
}

template < unsigned R, unsigned RC, unsigned C >
inline double multiply_helper_result_val( unsigned r,
                                          unsigned c,
                                          const MsqMatrix< R, RC >& A,
                                          const MsqMatrix< RC, C >& B )
{
    double tmp = A( r, 0 ) * B( 0, c );
    switch( RC )
    {
        default:
            for( unsigned k = 6; k < RC; ++k )
                tmp += A( r, k ) * B( k, c );
        case 6:
            tmp += A( r, 5 ) * B( 5, c );
        case 5:
            tmp += A( r, 4 ) * B( 4, c );
        case 4:
            tmp += A( r, 3 ) * B( 3, c );
        case 3:
            tmp += A( r, 2 ) * B( 2, c );
        case 2:
            tmp += A( r, 1 ) * B( 1, c );
        case 1:;
    }
    return tmp;
}

template < unsigned R, unsigned RC, unsigned C >
inline MsqMatrix< R, C > operator*( const MsqMatrix< R, RC >& A, const MsqMatrix< RC, C >& B )
{
    // MsqMatrix<R,C> result(0.0);
    // for (unsigned i = 0; i < R; ++i)
    //  for (unsigned j = 0; j < C; ++j)
    //    for (unsigned k = 0; k < RC; ++k)
    //      result(i,j) += A(i,k) * B(k,j);

    MsqMatrix< R, C > result;
    for( unsigned r = 0; r < R; ++r )
        for( unsigned c = 0; c < C; ++c )
            result( r, c ) = multiply_helper_result_val( r, c, A, B );

    return result;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > operator/( const MsqMatrix< R, C >& m, double s )
{
    MsqMatrix< R, C > tmp( m );
    tmp /= s;
    return tmp;
}

template < unsigned RC >
inline double cofactor( const MsqMatrix< RC, RC >& m, unsigned r, unsigned c )
{
    const double sign[] = { 1.0, -1.0 };
    return sign[( r + c ) % 2] * det( MsqMatrix< RC - 1, RC - 1 >( m, r, c ) );
}

template < unsigned RC >
inline double det( const MsqMatrix< RC, RC >& m )
{
    double result = 0.0;
    for( unsigned i = 0; i < RC; ++i )
        result += m( 0, i ) * cofactor< RC >( m, 0, i );
    return result;
}

// inline
// double det( const MsqMatrix<1,1>& m )
//  { return m(0,0); }

inline double det( const MsqMatrix< 2, 2 >& m )
{
    return m( 0, 0 ) * m( 1, 1 ) - m( 0, 1 ) * m( 1, 0 );
}

inline double det( const MsqMatrix< 3, 3 >& m )
{
    return m( 0, 0 ) * ( m( 1, 1 ) * m( 2, 2 ) - m( 2, 1 ) * m( 1, 2 ) ) +
           m( 0, 1 ) * ( m( 2, 0 ) * m( 1, 2 ) - m( 1, 0 ) * m( 2, 2 ) ) +
           m( 0, 2 ) * ( m( 1, 0 ) * m( 2, 1 ) - m( 2, 0 ) * m( 1, 1 ) );
}

inline MsqMatrix< 2, 2 > adj( const MsqMatrix< 2, 2 >& m )
{
    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = m( 1, 1 );
    result( 0, 1 ) = -m( 0, 1 );
    result( 1, 0 ) = -m( 1, 0 );
    result( 1, 1 ) = m( 0, 0 );
    return result;
}

inline MsqMatrix< 2, 2 > transpose_adj( const MsqMatrix< 2, 2 >& m )
{
    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = m( 1, 1 );
    result( 1, 0 ) = -m( 0, 1 );
    result( 0, 1 ) = -m( 1, 0 );
    result( 1, 1 ) = m( 0, 0 );
    return result;
}

inline MsqMatrix< 3, 3 > adj( const MsqMatrix< 3, 3 >& m )
{
    MsqMatrix< 3, 3 > result;

    result( 0, 0 ) = m( 1, 1 ) * m( 2, 2 ) - m( 1, 2 ) * m( 2, 1 );
    result( 0, 1 ) = m( 0, 2 ) * m( 2, 1 ) - m( 0, 1 ) * m( 2, 2 );
    result( 0, 2 ) = m( 0, 1 ) * m( 1, 2 ) - m( 0, 2 ) * m( 1, 1 );

    result( 1, 0 ) = m( 1, 2 ) * m( 2, 0 ) - m( 1, 0 ) * m( 2, 2 );
    result( 1, 1 ) = m( 0, 0 ) * m( 2, 2 ) - m( 0, 2 ) * m( 2, 0 );
    result( 1, 2 ) = m( 0, 2 ) * m( 1, 0 ) - m( 0, 0 ) * m( 1, 2 );

    result( 2, 0 ) = m( 1, 0 ) * m( 2, 1 ) - m( 1, 1 ) * m( 2, 0 );
    result( 2, 1 ) = m( 0, 1 ) * m( 2, 0 ) - m( 0, 0 ) * m( 2, 1 );
    result( 2, 2 ) = m( 0, 0 ) * m( 1, 1 ) - m( 0, 1 ) * m( 1, 0 );

    return result;
}

inline MsqMatrix< 3, 3 > transpose_adj( const MsqMatrix< 3, 3 >& m )
{
    MsqMatrix< 3, 3 > result;

    result( 0, 0 ) = m( 1, 1 ) * m( 2, 2 ) - m( 1, 2 ) * m( 2, 1 );
    result( 0, 1 ) = m( 1, 2 ) * m( 2, 0 ) - m( 1, 0 ) * m( 2, 2 );
    result( 0, 2 ) = m( 1, 0 ) * m( 2, 1 ) - m( 1, 1 ) * m( 2, 0 );

    result( 1, 0 ) = m( 0, 2 ) * m( 2, 1 ) - m( 0, 1 ) * m( 2, 2 );
    result( 1, 1 ) = m( 0, 0 ) * m( 2, 2 ) - m( 0, 2 ) * m( 2, 0 );
    result( 1, 2 ) = m( 0, 1 ) * m( 2, 0 ) - m( 0, 0 ) * m( 2, 1 );

    result( 2, 0 ) = m( 0, 1 ) * m( 1, 2 ) - m( 0, 2 ) * m( 1, 1 );
    result( 2, 1 ) = m( 0, 2 ) * m( 1, 0 ) - m( 0, 0 ) * m( 1, 2 );
    result( 2, 2 ) = m( 0, 0 ) * m( 1, 1 ) - m( 0, 1 ) * m( 1, 0 );

    return result;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > inverse( const MsqMatrix< R, C >& m )
{
    return adj( m ) * ( 1.0 / det( m ) );
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > transpose( const MsqMatrix< C, R >& m )
{
    MsqMatrix< R, C > result;
    for( unsigned r = 0; r < R; ++r )
        for( unsigned c = 0; c < C; ++c )
            result( r, c ) = m( c, r );
    return result;
}
/*
template <unsigned R> inline
const MsqMatrix<R,1>& transpose( const MsqMatrix<1,R>& m )
  { return *reinterpret_cast<const MsqMatrix<R,1>*>(&m); }

template <unsigned C> inline
const MsqMatrix<1,C>& transpose( const MsqMatrix<C,1>& m )
  { return *reinterpret_cast<const MsqMatrix<1,C>*>(&m); }
*/
template < unsigned RC >
inline double trace( const MsqMatrix< RC, RC >& m )
{
    double result = m( 0, 0 );
    for( unsigned i = 1; i < RC; ++i )
        result += m( i, i );
    return result;
}

template < unsigned R, unsigned C >
inline double sqr_Frobenius( const MsqMatrix< R, C >& m )
{
    double result = *m.data() * *m.data();
    for( unsigned i = 1; i < R * C; ++i )
        result += m.data()[i] * m.data()[i];
    return result;
}

template < unsigned R, unsigned C >
inline double Frobenius( const MsqMatrix< R, C >& m )
{
    return std::sqrt( sqr_Frobenius< R, C >( m ) );
}

template < unsigned R, unsigned C >
inline bool operator==( const MsqMatrix< R, C >& A, const MsqMatrix< R, C >& B )
{
    for( unsigned i = 0; i < R * C; ++i )
        if( A.data()[i] != B.data()[i] ) return false;
    return true;
}

template < unsigned R, unsigned C >
inline bool operator!=( const MsqMatrix< R, C >& A, const MsqMatrix< R, C >& B )
{
    return !( A == B );
}

template < unsigned R, unsigned C >
inline std::ostream& operator<<( std::ostream& str, const MsqMatrix< R, C >& m )
{
    str << m.data()[0];
    for( unsigned i = 1; i < R * C; ++i )
        str << ' ' << m.data()[i];
    return str;
}

template < unsigned R, unsigned C >
inline std::istream& operator>>( std::istream& str, MsqMatrix< R, C >& m )
{
    for( unsigned i = 0; i < R * C; ++i )
        str >> m.data()[i];
    return str;
}

template < unsigned R >
inline double sqr_length( const MsqMatrix< R, 1 >& v )
{
    return sqr_Frobenius( v );
}

template < unsigned C >
inline double sqr_length( const MsqMatrix< 1, C >& v )
{
    return sqr_Frobenius( v );
}

template < unsigned R >
inline double length( const MsqMatrix< R, 1 >& v )
{
    return Frobenius( v );
}

template < unsigned C >
inline double length( const MsqMatrix< 1, C >& v )
{
    return Frobenius( v );
}

template < unsigned R, unsigned C >
inline double inner_product( const MsqMatrix< R, C >& m1, const MsqMatrix< R, C >& m2 )
{
    double result = 0.0;
    for( unsigned r = 0; r < R; ++r )
        for( unsigned c = 0; c < C; ++c )
            result += m1( r, c ) * m2( r, c );
    return result;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > outer( const MsqMatrix< R, 1 >& v1, const MsqMatrix< C, 1 >& v2 )
{
    MsqMatrix< R, C > result;
    for( unsigned r = 0; r < R; ++r )
        for( unsigned c = 0; c < C; ++c )
            result( r, c ) = v1( r, 0 ) * v2( c, 0 );
    return result;
}

template < unsigned R, unsigned C >
inline MsqMatrix< R, C > outer( const MsqMatrix< 1, R >& v1, const MsqMatrix< 1, C >& v2 )
{
    MsqMatrix< R, C > result;
    for( unsigned r = 0; r < R; ++r )
        for( unsigned c = 0; c < C; ++c )
            result( r, c ) = v1( 0, r ) * v2( 0, c );
    return result;
}

inline double vector_product( const MsqMatrix< 2, 1 >& v1, const MsqMatrix< 2, 1 >& v2 )
{
    return v1( 0, 0 ) * v2( 1, 0 ) - v1( 1, 0 ) * v2( 0, 0 );
}

inline double vector_product( const MsqMatrix< 1, 2 >& v1, const MsqMatrix< 1, 2 >& v2 )
{
    return v1( 0, 0 ) * v2( 0, 1 ) - v1( 0, 1 ) * v2( 0, 0 );
}

inline MsqMatrix< 3, 1 > vector_product( const MsqMatrix< 3, 1 >& a, const MsqMatrix< 3, 1 >& b )
{
    MsqMatrix< 3, 1 > result;
    result( 0, 0 ) = a( 1, 0 ) * b( 2, 0 ) - a( 2, 0 ) * b( 1, 0 );
    result( 1, 0 ) = a( 2, 0 ) * b( 0, 0 ) - a( 0, 0 ) * b( 2, 0 );
    result( 2, 0 ) = a( 0, 0 ) * b( 1, 0 ) - a( 1, 0 ) * b( 0, 0 );
    return result;
}

inline MsqMatrix< 1, 3 > vector_product( const MsqMatrix< 1, 3 >& a, const MsqMatrix< 1, 3 >& b )
{
    MsqMatrix< 1, 3 > result;
    result( 0, 0 ) = a( 0, 1 ) * b( 0, 2 ) - a( 0, 2 ) * b( 0, 1 );
    result( 0, 1 ) = a( 0, 2 ) * b( 0, 0 ) - a( 0, 0 ) * b( 0, 2 );
    result( 0, 2 ) = a( 0, 0 ) * b( 0, 1 ) - a( 0, 1 ) * b( 0, 0 );
    return result;
}

template < unsigned R, unsigned C >
inline double operator%( const MsqMatrix< R, C >& v1, const MsqMatrix< R, C >& v2 )
{
    return inner_product( v1, v2 );
}

inline double operator*( const MsqMatrix< 2, 1 >& v1, const MsqMatrix< 2, 1 >& v2 )
{
    return vector_product( v1, v2 );
}

inline double operator*( const MsqMatrix< 1, 2 >& v1, const MsqMatrix< 1, 2 >& v2 )
{
    return vector_product( v1, v2 );
}

inline MsqMatrix< 3, 1 > operator*( const MsqMatrix< 3, 1 >& v1, const MsqMatrix< 3, 1 >& v2 )
{
    return vector_product( v1, v2 );
}

inline MsqMatrix< 1, 3 > operator*( const MsqMatrix< 1, 3 >& v1, const MsqMatrix< 1, 3 >& v2 )
{
    return vector_product( v1, v2 );
}

/** Compute QR factorization of A */
inline void QR( const MsqMatrix< 3, 3 >& A, MsqMatrix< 3, 3 >& Q, MsqMatrix< 3, 3 >& R )
{
    Q = A;

    R( 0, 0 )       = sqrt( Q( 0, 0 ) * Q( 0, 0 ) + Q( 1, 0 ) * Q( 1, 0 ) + Q( 2, 0 ) * Q( 2, 0 ) );
    double temp_dbl = 1.0 / R( 0, 0 );
    R( 1, 0 )       = 0.0;
    R( 2, 0 )       = 0.0;
    Q( 0, 0 ) *= temp_dbl;
    Q( 1, 0 ) *= temp_dbl;
    Q( 2, 0 ) *= temp_dbl;

    R( 0, 1 ) = Q( 0, 0 ) * Q( 0, 1 ) + Q( 1, 0 ) * Q( 1, 1 ) + Q( 2, 0 ) * Q( 2, 1 );
    Q( 0, 1 ) -= Q( 0, 0 ) * R( 0, 1 );
    Q( 1, 1 ) -= Q( 1, 0 ) * R( 0, 1 );
    Q( 2, 1 ) -= Q( 2, 0 ) * R( 0, 1 );

    R( 0, 2 ) = Q( 0, 0 ) * Q( 0, 2 ) + Q( 1, 0 ) * Q( 1, 2 ) + Q( 2, 0 ) * Q( 2, 2 );
    Q( 0, 2 ) -= Q( 0, 0 ) * R( 0, 2 );
    Q( 1, 2 ) -= Q( 1, 0 ) * R( 0, 2 );
    Q( 2, 2 ) -= Q( 2, 0 ) * R( 0, 2 );

    R( 1, 1 ) = sqrt( Q( 0, 1 ) * Q( 0, 1 ) + Q( 1, 1 ) * Q( 1, 1 ) + Q( 2, 1 ) * Q( 2, 1 ) );
    temp_dbl  = 1.0 / R( 1, 1 );
    R( 2, 1 ) = 0.0;
    Q( 0, 1 ) *= temp_dbl;
    Q( 1, 1 ) *= temp_dbl;
    Q( 2, 1 ) *= temp_dbl;

    R( 1, 2 ) = Q( 0, 1 ) * Q( 0, 2 ) + Q( 1, 1 ) * Q( 1, 2 ) + Q( 2, 1 ) * Q( 2, 2 );
    Q( 0, 2 ) -= Q( 0, 1 ) * R( 1, 2 );
    Q( 1, 2 ) -= Q( 1, 1 ) * R( 1, 2 );
    Q( 2, 2 ) -= Q( 2, 1 ) * R( 1, 2 );

    R( 2, 2 ) = sqrt( Q( 0, 2 ) * Q( 0, 2 ) + Q( 1, 2 ) * Q( 1, 2 ) + Q( 2, 2 ) * Q( 2, 2 ) );
    temp_dbl  = 1.0 / R( 2, 2 );
    Q( 0, 2 ) *= temp_dbl;
    Q( 1, 2 ) *= temp_dbl;
    Q( 2, 2 ) *= temp_dbl;
}

/** Compute QR factorization of A */
inline void QR( const MsqMatrix< 2, 2 >& A, MsqMatrix< 2, 2 >& Q, MsqMatrix< 2, 2 >& R )
{
    R( 0, 0 )          = std::sqrt( A( 0, 0 ) * A( 0, 0 ) + A( 1, 0 ) * A( 1, 0 ) );
    const double r0inv = 1.0 / R( 0, 0 );
    Q( 0, 0 ) = Q( 1, 1 ) = A( 0, 0 ) * r0inv;
    Q( 1, 0 )             = A( 1, 0 ) * r0inv;
    Q( 0, 1 )             = -Q( 1, 0 );
    R( 0, 1 )             = r0inv * ( A( 0, 0 ) * A( 0, 1 ) + A( 1, 0 ) * A( 1, 1 ) );
    R( 1, 1 )             = r0inv * ( A( 0, 0 ) * A( 1, 1 ) - A( 0, 1 ) * A( 1, 0 ) );
    R( 1, 0 )             = 0.0;
}

}  // namespace MBMesquite

#endif