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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program 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 General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/***************************************************************************
$Log: not supported by cvs2svn $
Revision 1.9 2006/09/11 16:11:39 marfr960
Added const to declarations of the overloaded (operators *).
Otherwise the * operator would always attempt to convert any type of data passed as an argument to Point3<TYPE>
Revision 1.8 2006/08/23 15:24:45 marfr960
Copy constructor : faster memcpy instead of slow 'for' cycle
empty constructor
Revision 1.7 2006/04/29 10:26:04 fiorin
Added some utility methods (swapping of columns and rows, matrix-vector multiplication)
Revision 1.6 2006/04/11 08:09:35 zifnab1974
changes necessary for gcc 3.4.5 on linux 64bit. Please take note of case-sensitivity of filenames
Revision 1.5 2005/12/12 11:25:00 ganovelli
added diagonal matrix, outer produce and namespace
***************************************************************************/
#ifndef MATRIX_VCGLIB
#define MATRIX_VCGLIB
#include <stdio.h>
#include <math.h>
#include <memory.h>
#include <assert.h>
#include <algorithm>
#include <vcg/space/point.h>
#include <vcg/math/lin_algebra.h>
namespace vcg{
namespace ndim{
/** \addtogroup math */
/* @{ */
/*!
* This class represent a diagonal <I>m</I><3E><I>m</I> matrix.
*/
class MatrixDiagBase{public:
virtual const int & Dimension()const =0;
virtual const float operator[](const int & i)const = 0;
};
template<int N, class S>
class MatrixDiag: public Point<N,S>, public MatrixDiagBase{
public:
const int & Dimension() const {return N;}
MatrixDiag(const Point<N,S>&p):Point<N,S>(p){}
};
/*!
* This class represent a generic <I>m</I><3E><I>n</I> matrix. The class is templated over the scalar type field.
* @param TYPE (Templete Parameter) Specifies the ScalarType field.
*/
template<class TYPE>
class Matrix
{
public:
typedef TYPE ScalarType;
/*!
* Default constructor
* All the elements are initialized to zero.
* \param m the number of matrix rows
* \param n the number of matrix columns
*/
Matrix(unsigned int m, unsigned int n)
{
_rows = m;
_columns = n;
_data = new ScalarType[m*n];
memset(_data, 0, m*n*sizeof(ScalarType));
};
/*!
* Constructor
* The matrix elements are initialized with the values of the elements in \i values.
* \param m the number of matrix rows
* \param n the number of matrix columns
* \param values the values of the matrix elements
*/
Matrix(unsigned int m, unsigned int n, TYPE *values)
{
_rows = m;
_columns = n;
unsigned int dim = m*n;
_data = new ScalarType[dim];
memcpy(_data, values, dim*sizeof(ScalarType));
//unsigned int i;
//for (i=0; i<_rows*_columns; i++)
// _data[i] = values[i];
};
/*!
* Empty constructor
* Just create the object
*/
Matrix()
{
_rows = 0;
_columns = 0;
_data = NULL;
};
/*!
* Copy constructor
* The matrix elements are initialized with the value of the corresponding element in \i m
* \param m the matrix to be copied
*/
Matrix(const Matrix<TYPE> &m)
{
_rows = m._rows;
_columns = m._columns;
_data = new ScalarType[_rows*_columns];
unsigned int dim = _rows * _columns;
memcpy(_data, m._data, dim * sizeof(ScalarType));
// for (unsigned int i=0; i<_rows*_columns; i++)
// _data[i] = m._data[i];
};
/*!
* Default destructor
*/
~Matrix()
{
delete []_data;
};
/*!
* Number of columns
*/
inline unsigned int ColumnsNumber() const
{
return _columns;
};
/*!
* Number of rows
*/
inline unsigned int RowsNumber() const
{
return _rows;
};
/*!
* Equality operator.
* \param m
* \return true iff the matrices have same size and its elements have same values.
*/
bool operator==(const Matrix<TYPE> &m) const
{
if (_rows==m._rows && _columns==m._columns)
{
bool result = true;
for (unsigned int i=0; i<_rows*_columns && result; i++)
result = (_data[i]==m._data[i]);
return result;
}
return false;
};
/*!
* Inequality operator
* \param m
* \return true iff the matrices have different size or if their elements have different values.
*/
bool operator!=(const Matrix<TYPE> &m) const
{
if (_rows==m._rows && _columns==m._columns)
{
bool result = false;
for (unsigned int i=0; i<_rows*_columns && !result; i++)
result = (_data[i]!=m._data[i]);
return result;
}
return true;
};
/*!
* Return the element stored in the <I>i</I>-th rows at the <I>j</I>-th column
* \param i the row index
* \param j the column index
* \return the element
*/
inline TYPE ElementAt(unsigned int i, unsigned int j)
{
assert(i>=0 && i<_rows);
assert(j>=0 && j<_columns);
return _data[i*_columns+j];
};
/*!
* Calculate and return the matrix determinant (Laplace)
* \return the matrix determinant
*/
TYPE Determinant() const
{
assert(_rows == _columns);
switch (_rows)
{
case 2:
{
return _data[0]*_data[3]-_data[1]*_data[2];
break;
};
case 3:
{
return _data[0]*(_data[4]*_data[8]-_data[5]*_data[7]) -
_data[1]*(_data[3]*_data[8]-_data[5]*_data[6]) +
_data[2]*(_data[3]*_data[7]-_data[4]*_data[6]) ;
break;
};
default:
{
// da migliorare: si puo' cercare la riga/colonna con maggior numero di zeri
ScalarType det = 0;
for (unsigned int j=0; j<_columns; j++)
if (_data[j]!=0)
det += _data[j]*this->Cofactor(0, j);
return det;
}
};
};
/*!
* Return the cofactor <I>A<SUB>i,j</SUB></I> of the <I>a<SUB>i,j</SUB></I> element
* \return ...
*/
TYPE Cofactor(unsigned int i, unsigned int j) const
{
assert(_rows == _columns);
assert(_rows>2);
TYPE *values = new TYPE[(_rows-1)*(_columns-1)];
unsigned int u, v, p, q, s, t;
for (u=0, p=0, s=0, t=0; u<_rows; u++, t+=_rows)
{
if (i==u)
continue;
for (v=0, q=0; v<_columns; v++)
{
if (j==v)
continue;
values[s+q] = _data[t+v];
q++;
}
p++;
s+=(_rows-1);
}
Matrix<TYPE> temp(_rows-1, _columns-1, values);
return (pow(-1, i+j)*temp.Determinant());
};
/*!
* Subscript operator:
* \param i the index of the row
* \return a reference to the <I>i</I>-th matrix row
*/
inline TYPE* operator[](const unsigned int i)
{
assert(i>=0 && i<_rows);
return _data + i*_columns;
};
/*!
* Const subscript operator
* \param i the index of the row
* \return a reference to the <I>i</I>-th matrix row
*/
inline const TYPE* operator[](const unsigned int i) const
{
assert(i>=0 && i<_rows);
return _data + i*_columns;
};
/*!
* Get the <I>j</I>-th column on the matrix.
* \param j the column index.
* \return the reference to the column elements. This pointer must be deallocated by the caller.
*/
TYPE* GetColumn(const unsigned int j)
{
assert(j>=0 && j<_columns);
ScalarType *v = new ScalarType[_columns];
unsigned int i, p;
for (i=0, p=j; i<_rows; i++, p+=_columns)
v[i] = _data[p];
return v;
};
/*!
* Get the <I>i</I>-th row on the matrix.
* \param i the column index.
* \return the reference to the row elements. This pointer must be deallocated by the caller.
*/
TYPE* GetRow(const unsigned int i)
{
assert(i>=0 && i<_rows);
ScalarType *v = new ScalarType[_rows];
unsigned int j, p;
for (j=0, p=i*_columns; j<_columns; j++, p++)
v[j] = _data[p];
return v;
};
/*!
* Swaps the values of the elements between the <I>i</I>-th and the <I>j</I>-th column.
* \param i the index of the first column
* \param j the index of the second column
*/
void SwapColumns(const unsigned int i, const unsigned int j)
{
assert(0<=i && i<_columns);
assert(0<=j && j<_columns);
if (i==j)
return;
unsigned int r, e0, e1;
for (r=0, e0=i, e1=j; r<_rows; r++, e0+=_columns, e1+=_columns)
std::swap(_data[e0], _data[e1]);
};
/*!
* Swaps the values of the elements between the <I>i</I>-th and the <I>j</I>-th row.
* \param i the index of the first row
* \param j the index of the second row
*/
void SwapRows(const unsigned int i, const unsigned int j)
{
assert(0<=i && i<_rows);
assert(0<=j && j<_rows);
if (i==j)
return;
unsigned int r, e0, e1;
for (r=0, e0=i*_columns, e1=j*_columns; r<_columns; r++, e0++, e1++)
std::swap(_data[e0], _data[e1]);
};
/*!
* Assignment operator
* \param m ...
*/
Matrix<TYPE>& operator=(const Matrix<TYPE> &m)
{
if (this != &m)
{
assert(_rows == m._rows);
assert(_columns == m._columns);
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] = m._data[i];
}
return *this;
};
/*!
* Adds a matrix <I>m</I> to this matrix.
* \param m reference to matrix to add to this
* \return the matrix sum.
*/
Matrix<TYPE>& operator+=(const Matrix<TYPE> &m)
{
assert(_rows == m._rows);
assert(_columns == m._columns);
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] += m._data[i];
return *this;
};
/*!
* Subtracts a matrix <I>m</I> to this matrix.
* \param m reference to matrix to subtract
* \return the matrix difference.
*/
Matrix<TYPE>& operator-=(const Matrix<TYPE> &m)
{
assert(_rows == m._rows);
assert(_columns == m._columns);
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] -= m._data[i];
return *this;
};
/*!
* (Modifier) Add to each element of this matrix the scalar constant <I>k</I>.
* \param k the scalar constant
* \return the modified matrix
*/
Matrix<TYPE>& operator+=(const TYPE k)
{
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] += k;
return *this;
};
/*!
* (Modifier) Subtract from each element of this matrix the scalar constant <I>k</I>.
* \param k the scalar constant
* \return the modified matrix
*/
Matrix<TYPE>& operator-=(const TYPE k)
{
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] -= k;
return *this;
};
/*!
* (Modifier) Multiplies each element of this matrix by the scalar constant <I>k</I>.
* \param k the scalar constant
* \return the modified matrix
*/
Matrix<TYPE>& operator*=(const TYPE k)
{
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] *= k;
return *this;
};
/*!
* (Modifier) Divides each element of this matrix by the scalar constant <I>k</I>.
* \param k the scalar constant
* \return the modified matrix
*/
Matrix<TYPE>& operator/=(const TYPE k)
{
assert(k!=0);
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] /= k;
return *this;
};
/*!
* Matrix multiplication: calculates the cross product.
* \param m reference to the matrix to multiply by
* \return the matrix product
*/
Matrix<TYPE> operator*(const Matrix<TYPE> &m) const
{
assert(_columns == m._rows);
Matrix<TYPE> result(_rows, m._columns);
unsigned int i, j, k, p, q, r;
for (i=0, p=0, r=0; i<result._rows; i++, p+=_columns, r+=result._columns)
for (j=0; j<result._columns; j++)
{
ScalarType temp = 0;
for (k=0, q=0; k<_columns; k++, q+=m._columns)
temp+=(_data[p+k]*m._data[q+j]);
result._data[r+j] = temp;
}
return result;
};
/*!
* Matrix-Vector product. Computes the product of the matrix by the vector v.
* \param v reference to the vector to multiply by
* \return the matrix-vector product. This pointer must be deallocated by the caller
*/
ScalarType* operator*(const ScalarType v[]) const
{
ScalarType *result = new ScalarType[_rows];
memset(result, 0, _rows*sizeof(ScalarType));
unsigned int r, c, i;
for (r=0, i=0; r<_rows; r++)
for (c=0; c<_columns; c++, i++)
result[r] += _data[i]*v[c];
return result;
};
/*!
* Matrix multiplication: calculates the cross product.
* \param reference to the matrix to multiply by
* \return the matrix product
*/
template <int N,int M>
void DotProduct(Point<N,TYPE> &m,Point<M,TYPE> &result)
{
unsigned int i, j, p, r;
for (i=0, p=0, r=0; i<M; i++)
{ result[i]=0;
for (j=0; j<N; j++)
result[i]+=(*this)[i][j]*m[j];
}
};
/*!
* Matrix multiplication by a diagonal matrix
*/
Matrix<TYPE> operator*(const MatrixDiagBase &m) const
{
assert(_columns == _rows);
assert(_columns == m.Dimension());
int i,j;
Matrix<TYPE> result(_rows, _columns);
for (i=0; i<result._rows; i++)
for (j=0; j<result._columns; j++)
result[i][j]*= m[j];
return result;
};
/*!
* Matrix from outer product.
*/
template <int N, int M>
void OuterProduct(const Point<N,TYPE> a, const Point< M,TYPE> b)
{
assert(N == _rows);
assert(M == _columns);
Matrix<TYPE> result(_rows,_columns);
unsigned int i, j;
for (i=0; i<result._rows; i++)
for (j=0; j<result._columns; j++)
(*this)[i][j] = a[i] * b[j];
};
/*!
* Matrix-vector multiplication.
* \param reference to the 3-dimensional vector to multiply by
* \return the resulting vector
*/
Point3<TYPE> operator*(Point3<TYPE> &p) const
{
assert(_columns==3 && _rows==3);
vcg::Point3<TYPE> result;
result[0] = _data[0]*p[0]+_data[1]*p[1]+_data[2]*p[2];
result[1] = _data[3]*p[0]+_data[4]*p[1]+_data[5]*p[2];
result[2] = _data[6]*p[0]+_data[7]*p[1]+_data[8]*p[2];
return result;
};
/*!
* Scalar sum.
* \param k
* \return the resultant matrix
*/
Matrix<TYPE> operator+(const TYPE k)
{
Matrix<TYPE> result(_rows, _columns);
for (unsigned int i=0; i<_rows*_columns; i++)
result._data[i] = _data[i]+k;
return result;
};
/*!
* Scalar difference.
* \param k
* \return the resultant matrix
*/
Matrix<TYPE> operator-(const TYPE k)
{
Matrix<TYPE> result(_rows, _columns);
for (unsigned int i=0; i<_rows*_columns; i++)
result._data[i] = _data[i]-k;
return result;
};
/*!
* Negate all matrix elements
* \return the modified matrix
*/
Matrix<TYPE> operator-() const
{
Matrix<TYPE> result(_rows, _columns, _data);
for (unsigned int i=0; i<_columns*_rows; i++)
result._data[i] = -1*_data[i];
return result;
};
/*!
* Scalar multiplication.
* \param k value to multiply every member by
* \return the resultant matrix
*/
Matrix<TYPE> operator*(const TYPE k) const
{
Matrix<TYPE> result(_rows, _columns);
for (unsigned int i=0; i<_rows*_columns; i++)
result._data[i] = _data[i]*k;
return result;
};
/*!
* Scalar division.
* \param k value to divide every member by
* \return the resultant matrix
*/
Matrix<TYPE> operator/(const TYPE k)
{
Matrix<TYPE> result(_rows, _columns);
for (unsigned int i=0; i<_rows*_columns; i++)
result._data[i] = _data[i]/k;
return result;
};
/*!
* Set all the matrix elements to zero.
*/
void SetZero()
{
for (unsigned int i=0; i<_rows*_columns; i++)
_data[i] = ScalarType(0.0);
};
/*!
* Set the matrix to identity.
*/
void SetIdentity()
{
assert(_rows==_columns);
for (unsigned int i=0; i<_rows; i++)
for (unsigned int j=0; j<_columns; j++)
_data[i] = (i==j) ? ScalarType(1.0) : ScalarType(0.0f);
};
/*!
* Set the values of <I>j</I>-th column to v[j]
* \param j the column index
* \param v ...
*/
void SetColumn(const unsigned int j, TYPE* v)
{
assert(j>=0 && j<_columns);
unsigned int i, p;
for (i=0, p=j; i<_rows; i++, p+=_columns)
_data[p] = v[i];
};
/*!
* Set the elements of the <I>i</I>-th row to v[j]
* \param i the row index
* \param v ...
*/
void SetRow(const unsigned int i, TYPE* v)
{
assert(i>=0 && i<_rows);
unsigned int j, p;
for (j=0, p=i*_rows; j<_columns; j++, p++)
_data[p] = v[j];
};
/*!
* Set the diagonal elements <I>v<SUB>i,i</SUB></I> to v[i]
* \param v
*/
void SetDiagonal(TYPE *v)
{
assert(_rows == _columns);
for (unsigned int i=0, p=0; i<_rows; i++, p+=_rows)
_data[p+i] = v[i];
};
/*!
* Resize the current matrix.
* \param m the number of matrix rows.
* \param n the number of matrix columns.
*/
void Resize(const unsigned int m, const unsigned int n)
{
assert(m>=2);
assert(n>=2);
_rows = m;
_columns = n;
delete []_data;
_data = new ScalarType[m*n];
for (unsigned int i=0; i<m*n; i++)
_data[i] = 0;
};
/*!
* Matrix transposition operation: set the current matrix to its transpose
*/
void Transpose()
{
ScalarType *temp = new ScalarType[_rows*_columns];
unsigned int i, j, p, q;
for (i=0, p=0; i<_rows; i++, p+=_columns)
for (j=0, q=0; j<_columns; j++, q+=_rows)
temp[q+i] = _data[p+j];
std::swap(_columns, _rows);
std::swap(_data, temp);
delete []temp;
};
/*!
* Print all matrix elements
*/
void Dump()
{
unsigned int i, j, p;
for (i=0, p=0; i<_rows; i++, p+=_columns)
{
printf("[\t");
for (j=0; j<_columns; j++)
printf("%f\t", _data[p+j]);
printf("]\n");
}
printf("\n");
};
protected:
/// the number of matrix rows
unsigned int _rows;
/// the number of matrix rows
unsigned int _columns;
/// the matrix elements
ScalarType *_data;
};
typedef vcg::ndim::Matrix<double> MatrixMNd;
typedef vcg::ndim::Matrix<float> MatrixMNf;
/*! @} */
template <class MatrixType>
void Invert(MatrixType & m){
typedef typename MatrixType::ScalarType X;
X *diag;
diag = new X [m.ColumnsNumber()];
MatrixType res(m.RowsNumber(),m.ColumnsNumber());
vcg::SingularValueDecomposition<MatrixType > (m,&diag[0],res,LeaveUnsorted,50 );
m.Transpose();
// prodotto per la diagonale
unsigned int i,j;
for (i=0; i<m.RowsNumber(); i++)
for (j=0; j<m.ColumnsNumber(); j++)
res[i][j]/= diag[j];
m = res *m;
}
}
}; // end of namespace
#endif
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