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matrix.h
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matrix.h
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//
// Elvis Chen
// chene@cs.queensu.ca
//
// Department of Computing and Information Science
// Queen's University, Kingston, Ontario, Canada
//
// Feb. 16, 2000
//
//
// Filename: matrix.h
//
// Initial implementation of a matrix class, based on TNT (Template
// Numerical Toolkit, http://math.nist.gov/tnt).
//
//
// C compatible matrix: row-oriented, 0-based[i][j] indexing
//
// Numerical Recipes compatible matrix: row-oriented, 1-based(i,j) indexing
//
// This is actually a subset/change of TNT, since we don't really
// care about Fortran-style (column-oriented, 1-based) indexing.
// However, we would like to have ROW-oriented, 1-based indexing
// so we can implement Numerical Recipes with ease.
#ifndef __MATRIX_H__
#define __MATRIX_H__
#include <cassert>
#include <iostream>
#include <strstream>
#include <cmath>
#include <cstdlib>
// Quote from the web page:
//
// A good deal of the segmentation faults produced by numerical
// codes are related to indexing a vector or matrix past its
// pre-allocated bounds. By default, TNT verifies that the index
// used to access vector elements is always within the vector's bounds.
// (Just like Java does.) This can be turned off by using the
// following compile flag
//
// -DNO_BOUNDS_CHECK
//
// which removes all performance penalties incurred for performing
// this check. (Typically done only after final debugging.)
#define BOUNDS_CHECK
#ifdef NO_BOUNDS_CHECK
#undef BOUNDS_CHECK
#endif
//---------------------------------------------------------------------
// Define the data type used for matrix and vector Subscripts.
// This will default to "int", but it can be overriden at compile time,
// e.g.
//
// g++ -DMATRIX_SUBSCRIPT_TYPE='unsinged long' ...
//
//---------------------------------------------------------------------
#ifndef MATRIX_SUBSCRIPT_TYPE
#define MATRIX_SUBSCRIPT_TYPE int
#endif
typedef MATRIX_SUBSCRIPT_TYPE Subscript;
template <class T> class Vec
{
public:
typedef Subscript size_type;
typedef T value_type;
typedef T element_type;
typedef T* pointer;
typedef T* iterator;
typedef T& reference;
typedef const T* const_iterator;
typedef const T& const_reference;
protected:
T *_v; // c-style indexing, 0-based
T *_v1; // row-major, 1-based
Subscript _size;
// internal helper function to create the array
// of row pointers
void initialize( Subscript N )
{
assert( _v == NULL );
_v = new T[N];
assert( _v != NULL );
_v1 = _v - 1;
_size = N;
}
void copy( const T *v )
{
for (Subscript i = 0; i < _size; i++) _v[i] = v[i];
}
void set( const T &val )
{
for (Subscript i = 0; i < _size; i++) _v[i] = val;
}
void destroy()
{
if ( _v == NULL) return;
delete [] ( _v );
_v = NULL;
_v1 = NULL;
}
public:
// access
iterator begin() { return _v; }
iterator end() { return (_v + _size); }
const iterator begin() const { return _v; }
const iterator end() const{ return ( _v + _size ); }
// destructor
~Vec() { destroy(); }
// constructors
Vec() : _v(0), _v1(0), _size(0) {};
Vec( const Vec<T> &A ) : _v(0), _v1(0), _size(0)
{
initialize( A._size );
copy( A._v );
};
Vec( Subscript N, const T &value = T(0) ) : _v(0), _v1(0), _size(0)
{
initialize( N );
set( value );
};
Vec( Subscript N, const T *v ): _v(0), _v1(0),_size(0)
{
initialize( N );
copy( v );
};
Vec( Subscript N, char *s ) : _v(0), _size(0)
{
initialize( N );
std::istrstream ins(s);
Subscript i;
for (i = 0; i < N; i++) ins >> _v[i];
};
//
// methods
//
Vec<T> &newsize( Subscript N )
{
if ( _size == N ) return *this;
destroy();
initialize( N );
return *this;
};
//
// assignments
//
Vec<T>& operator= (const Vec<T> &A)
{
if ( _v == A._v ) return *this;
if ( _size == A._size ) // no need to re-allocate
copy( A._v );
else {
destroy();
initialize( A._size );
copy( A._v );
}
return *this;
};
Vec<T>& operator= (const T &scalar)
{
set(scalar);
return *this;
};
Vec<T>& operator+=( const Vec<T> &A )
{
assert( _size == A._size );
for (Subscript i = 0; i < _size; i++) _v[i] += A[i];
return *this;
};
template<class S>
Vec<T>& operator+=( const S &val )
{
for (Subscript i = 0; i < _size; i++) _v[i] += (T)val;
return *this;
};
Vec<T>& operator-=( const Vec<T> &A )
{
assert( _size == A._size );
for (Subscript i = 0; i < _size; i++) _v[i] -= A[i];
return *this;
};
template<class S>
Vec<T>& operator-=( const S &val )
{
for (Subscript i = 0; i < _size; i++) _v[i] -= (T)val;
return *this;
};
Vec<T>& operator*=( const Vec<T> &A )
{
assert( _size == A._size );
for (Subscript i = 0; i < _size; i++) _v[i] *= A[i];
return *this;
};
template<class S>
Vec<T>& operator*=( const S &val )
{
for (Subscript i = 0; i < _size; i++) _v[i] *= (T)val;
return *this;
};
Vec<T>& operator/=( const Vec<T> &A )
{
assert( _size == A._size );
for (Subscript i = 0; i < _size; i++) _v[i] /= A[i];
return *this;
};
template<class S>
Vec<T>& operator/=( const S &val )
{
for (Subscript i = 0; i < _size; i++) _v[i] /= (T)val;
return *this;
};
inline Subscript dim() const
{
return _size;
};
inline Subscript size() const
{
return _size;
};
inline reference operator() ( Subscript i )
{
#ifdef BOUND_CHECK
assert( 1 <= i );
assert( i <= _size );
#endif
return _v1[ i ];
};
inline const_reference operator() ( Subscript i ) const
{
#ifdef BOUND_CHECK
assert( 1 <= i );
assert( i <= _size );
#endif
return _v1[ i ];
};
inline reference operator[] ( Subscript i )
{
#ifdef BOUNDS_CHECK
assert( 0 <= i );
assert( i < _size );
#endif
return _v[i];
};
inline const_reference operator[] ( Subscript i ) const
{
#ifdef BOUNDS_CHECK
assert( 0 <= i );
assert( i < _size );
#endif
return _v[i];
};
// min and max values of the given vector
inline T min()
{
T tmp = _v[0];
for (Subscript i = 1; i < _size; i++) if ( _v[i] < tmp ) tmp = _v[i];
return (tmp);
};
inline T max()
{
T tmp = _v[0];
for (Subscript i = 1; i < _size; i++) if ( _v[i] > tmp ) tmp = _v[i];
return (tmp) ;
};
};
template <class T> class Matrix
{
public:
typedef Subscript size_type;
typedef T value_type;
typedef T element_type;
typedef T* pointer;
typedef T* iterator;
typedef T& reference;
typedef const T* const_iterator;
typedef const T& const_reference;
protected:
Subscript size_x;
Subscript size_y;
Subscript totalSize; // total size
T *_v;
T **_row; // c-style, 0-based
T *_v1;
T **_row1; // row-major, 1-based
// internal helper function to create the array
// of row pointers
void initialize( Subscript X, Subscript Y )
{
totalSize = X * Y;
size_x = X;
size_y = Y;
_v = new T[ totalSize ];
_row = new T*[ X ];
_row1 = new T*[ X ];
assert( _v != NULL );
assert( _row != NULL );
assert( _row1 != NULL );
T *p = _v;
_v1 = _v - 1;
for (Subscript i = 0; i < X; i++) {
_row[i] = p;
_row1[i] = p - 1;
p += Y;
}
_row1 --; // compensate for 1-based offset
};
// copy two matrices
void copy( const T *v )
{
for (Subscript i = 0; i < (size_x * size_y); i++) _v[i] = v[i];
};
// Initial the matrix with a given value
void set( const T& val )
{
for (Subscript i = 0; i < (size_x * size_y); i++) _v[i] = val;
};
// helper function for destructor
void destroy()
{
// do nothing, if no memory has been previously allocated
if ( _v == NULL ) return;
// de-allocate the memory
if ( _v != NULL ) delete [] ( _v );
if ( _row != NULL ) delete [] ( _row );
// return _row1 back to the original value
_row1 ++;
if ( _row1 != NULL) delete [] ( _row1 );
_v = NULL;
_row = NULL;
_row1 = NULL;
};
public:
operator T**() { return _row; }
operator T**() const { return _row; }
Subscript size() const { return totalSize; }
// constructors
Matrix() : size_x(0), size_y(0), totalSize(0),
_v(0), _row(0), _v1(0), _row1(0) {};
Matrix( const Matrix<T> &A )
{
initialize( A.size_x, A.size_y );
copy( A._v );
};
Matrix( Subscript X, Subscript Y, const T& value = T(0) )
{
initialize( X, Y );
set( value );
};
Matrix( Subscript X, Subscript Y, const T *v )
{
initialize( X, Y );
copy( v );
};
Matrix(Subscript X, Subscript Y, char *s )
{
initialize( X, Y );
std::istrstream ins(s);
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
ins >> _row[i][j];
};
//
// descructor
//
~Matrix()
{
destroy();
};
// reallocating
Matrix<T>& newsize( Subscript X, Subscript Y )
{
if ( num_rows() == X && num_cols() == Y ) return *this;
destroy();
initialize( X, Y );
return *this;
};
Matrix<T>& newsize( Subscript X, Subscript Y, const T &value )
{
if ( num_rows() == X && num_cols() == Y ) {
set( value );
return *this;
}
destroy();
initialize( X, Y );
set( value );
return *this;
};
//
// assignments
//
Matrix<T>& operator= (const Matrix<T> &A)
{
if ( _v == A._v ) return *this;
if ( size_x == A.size_x && size_y == A.size_y ) // no need to re-allocate
copy( A._v );
else {
destroy();
initialize( A.size_x, A.size_y );
copy( A._v );
}
return *this;
};
Matrix<T>& operator= (const T& scalar)
{
set(scalar);
return *this;
};
Matrix<T>& operator+= (const Matrix<T> &A)
{
assert ( (size_x == A.size_x) && (size_y == A.size_y) );
for (Subscript i = 0; i < totalSize; i++) _v[i] += A._v[i];
return *this;
};
template<class S>
Matrix<T>& operator+= (const S &scalar)
{
T val = (T)scalar;
for (Subscript i = 0; i < totalSize; i++) _v[i] += val;
return *this;
};
Matrix<T>& operator-= (const Matrix<T> &A)
{
assert ( (size_x == A.size_x) && (size_y == A.size_y) );
for (Subscript i = 0; i < totalSize; i++) _v[i] -= A._v[i];
return *this;
};
template<class S>
Matrix<T>& operator-= (const S &scalar)
{
T val = (T)scalar;
for (Subscript i = 0; i < totalSize; i++) _v[i] -= val;
return *this;
};
template<class S>
Matrix<T>& operator*= (const S &scalar)
{
T val = (T)scalar;
for (Subscript i = 0; i < totalSize; i++) _v[i] *= val;
return *this;
};
template<class S>
Matrix<T>& operator/= (const S &scalar)
{
T val = (T)scalar;
for (Subscript i = 0; i < totalSize; i++) _v[i] /= val;
return *this;
};
Subscript dim(Subscript d) const
{
#ifdef BOUNDS_CHECK
assert( d >= 1 );
assert( d <= 2 );
#endif
return (d == 1) ? size_x : ((d==2) ? size_y : 0);
};
Subscript num_rows() const { return size_x; }
Subscript num_cols() const { return size_y; }
inline T* operator[] (Subscript i)
{
#ifdef BOUNDS_CHECK
assert( 0 <= i );
assert( i < size_x );
#endif
return _row[i];
};
inline const T* operator[] (Subscript i) const
{
#ifdef BOUNDS_CHECK
assert( 0 <= i );
assert( i < size_x );
#endif
return _row[i];
};
inline reference operator() (Subscript i)
{
#ifdef BOUNDS_CHECK
assert( 1 <= i );
assert( i <= totalSize );
#endif
return _v1[i];
};
inline const_reference operator() (Subscript i) const
{
#ifdef BOUNDS_CHECK
assert( 1 <= i );
assert( i <= totalSize );
#endif
return _v1[i-1];
};
inline reference operator() (Subscript i, Subscript j)
{
#ifdef BOUNDS_CHECK
assert( 1 <= i );
assert( i <= size_x );
assert( 1 <= j);
assert( j <= size_y );
#endif
return _row1[i][j];
};
inline const_reference operator() (Subscript i, Subscript j) const
{
#ifdef BOUNDS_CHECK
assert( 1 <= i );
assert( i <= size_x );
assert( 1 <= j );
assert( j <= size_y );
#endif
return _row1[i][j];
};
// min/max value of the given matrix
inline T min()
{
T tmp = _v[0];
for (Subscript i = 1; i < totalSize; i++) if ( _v[i] < tmp ) tmp = _v[i];
return (tmp);
};
inline T max()
{
T tmp = _v[0];
for (Subscript i = 1; i < totalSize; i++) if ( _v[i] > tmp ) tmp = _v[i];
return (tmp);
};
};
//
// I/O operation
//
//
// I/O for Vec
//
template <class T>
inline std::ostream& operator<< (std::ostream &s, const Vec<T> &A)
{
Subscript N = A.dim();
s << N << std::endl;
for (Subscript i = 0; i < N; i++) s << A[i] << " " << std::endl;
s << std::endl;
return s;
}
template <class T>
inline std::istream & operator>> (std::istream &s, Vec<T> &A)
{
Subscript N;
s >> N;
if ( !(N == A.size()) ){
A.destroy();
A.initialize(N);
}
for (Subscript i = 0; i < N; i++) s >> A[i];
return s;
}
//
// I/O for Matrix
//
template <class T>
inline std::ostream& operator<< ( std::ostream &s,
const Matrix<T> &A )
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
s << X << " " << Y << std::endl;
for (Subscript i = 0; i < X; i++) {
for (Subscript j = 0; j < Y; j++) {
s << A[i][j] << " ";
}
s << std::endl;
}
return s;
}
template <class T>
inline std::istream& operator>> (std::istream &s,
Matrix<T> &A )
{
Subscript X, Y;
s >> X >> Y;
if ( !(X == A.num_rows() && Y == A.num_cols()) ){
A.newsize( X, Y );
}
for (Subscript i = 0; i < X; i++)
for (Subscript j = 0; j < Y; j++)
s >> A[i][j];
return s;
}
//
// basic vector algorithms
//
template <class T>
inline Vec<T> operator+ (const Vec<T> &A, const Vec<T> &B)
{
Subscript N = A.dim();
assert( N == B.dim() );
Vec<T> tmp(N);
for (Subscript i = 0; i < N; i++) tmp[i] = A[i] + B[i];
return tmp;
}
template <class T>
inline Vec<T> operator- (const Vec<T> &A, const Vec<T> &B)
{
Subscript N = A.dim();
assert( N == B.dim() );
Vec<T> tmp(N);
for (Subscript i = 0; i < N; i++) tmp[i] = A[i] - B[i];
return tmp;
}
template <class T>
inline Vec<T> operator* (const T &val, const Vec<T> &A)
{
Subscript N = A.dim();
Vec<T> tmp( N );
for (Subscript i = 0; i < N; i++) tmp[i] = val * A[i];
return tmp;
}
template<class T>
inline Vec<T> operator* (const Vec<T> &A, const T &val)
{
Subscript N = A.dim();
Vec<T> tmp( N );
for (Subscript i = 0; i < N; i++) tmp[i] = val * A[i];
return tmp;
}
template<class T>
inline Vec<T> operator/ (const Vec<T> &A, const T &val)
{
Subscript N = A.dim();
Vec<T> tmp( N );
for (Subscript i = 0; i < N; i++) tmp[i] = A[i] / val;
return tmp;
}
template <class T>
inline Vec<T> operator* (const Vec<T> &A, const Vec<T> &B)
{
Subscript N = A.dim();
assert( N == B.dim() );
Vec<T> tmp(N);
for (Subscript i = 0; i < N; i++) tmp[i] = A[i] * B[i];
return tmp;
}
template <class T>
inline T dot_prod( const Vec<T> &A, const Vec<T> &B )
{
Subscript N = A.dim();
assert( N == B.dim() );
T sum = (T)0;
for (Subscript i = 0; i < N; i++) sum += A[i] * B[i];
return sum;
}
//
// basic matrix algorithms
//
template <class T>
inline Matrix<T> operator+ ( const Matrix<T> & A, const Matrix<T> &B )
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
assert( X == B.num_rows() );
assert( Y == B.num_cols() );
Matrix<T> tmp(X, Y);
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
tmp[i][j] = A[i][j] + B[i][j];
return tmp;
}
template <class T>
inline Matrix<T> operator- (const Matrix<T> &A, const Matrix<T> &B)
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
assert( X == B.num_rows() );
assert( Y == B.num_cols() );
Matrix<T> tmp( X, Y );
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
tmp[i][j] = A[i][j] - B[i][j];
return tmp;
}
template <class T>
inline Matrix<T> operator* (const Matrix<T> &A, const T &val)
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
Matrix<T> tmp( X, Y );
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
tmp[i][j] = A[i][j] * val;
return tmp;
}
template <class T>
inline Matrix<T> operator* (const T &val, const Matrix<T> &A)
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
Matrix<T> tmp( X, Y );
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
tmp[i][j] = A[i][j] * val;
return tmp;
}
template <class T>
inline Matrix<T> operator/ (const Matrix<T> &A, const T &val)
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
Matrix<T> tmp( X, Y );
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
tmp[i][j] = A[i][j] / val;
return tmp;
}
template <class T>
inline bool isEqual( const Matrix<T> &A, const Matrix<T> &B )
{
// return true if two matrices are equal in all elements
bool result = true;
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
if ( (X != B.num_rows()) || (Y != B.num_cols()) ) {
result = false;
return result;
}
Subscript i, j;
for (i = 0; i < X; i++) {
for (j = 0; j < Y; j++) {
if ( A[i][j] != B[i][j] ) {
result = false;
return result;
}
}
}
return result;
}
template <class T>
inline Matrix<T> mult_element( const Matrix<T> &A, const Matrix<T> &B )
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
assert( X == B.num_rows() );
assert( Y == B.num_cols() );
Matrix<T> tmp( X, Y );
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
tmp[i][j] = A[i][j] * B[i][j];
return tmp;
}
template <class T>
inline Matrix<T> div_element( const Matrix<T> &A, const Matrix<T> &B )
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();
assert( X == B.num_rows() );
assert( Y == B.num_cols() );
Matrix<T> tmp( X, Y );
Subscript i, j;
for (i = 0; i < X; i++)
for (j = 0; j < Y; j++)
tmp[i][j] = A[i][j] / B[i][j];
return tmp;
}
template <class T>
inline void mult_element( const Matrix<T> &A, const Matrix<T> &B, Matrix<T> out )
{
Subscript X = A.num_rows();
Subscript Y = A.num_cols();