787 lines
20 KiB
C++
787 lines
20 KiB
C++
/****************************************************************************
|
||
* VCGLib o o *
|
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004-2016 \/)\/ *
|
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
|
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* *
|
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* This program is free software; you can redistribute it and/or modify *
|
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* it under the terms of the GNU General Public License as published by *
|
||
* the Free Software Foundation; either version 2 of the License, or *
|
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* (at your option) any later version. *
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* *
|
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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||
****************************************************************************/
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/***************************************************************************
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$Log: not supported by cvs2svn $
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Revision 1.9 2006/09/11 16:11:39 marfr960
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Added const to declarations of the overloaded (operators *).
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Otherwise the * operator would always attempt to convert any type of data passed as an argument to Point3<TYPE>
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Revision 1.8 2006/08/23 15:24:45 marfr960
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Copy constructor : faster memcpy instead of slow 'for' cycle
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empty constructor
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Revision 1.7 2006/04/29 10:26:04 fiorin
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Added some utility methods (swapping of columns and rows, matrix-vector multiplication)
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Revision 1.6 2006/04/11 08:09:35 zifnab1974
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changes necessary for gcc 3.4.5 on linux 64bit. Please take note of case-sensitivity of filenames
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Revision 1.5 2005/12/12 11:25:00 ganovelli
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added diagonal matrix, outer produce and namespace
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***************************************************************************/
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#ifndef MATRIX_VCGLIB
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#define MATRIX_VCGLIB
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#include <stdio.h>
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#include <math.h>
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#include <memory.h>
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#include <assert.h>
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#include <algorithm>
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#include <vcg/space/point.h>
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namespace vcg{
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namespace ndim{
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/** \addtogroup math */
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/* @{ */
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/*!
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* This class represent a diagonal <I>m</I><3E><I>m</I> matrix.
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*/
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class MatrixDiagBase{public:
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virtual const int & Dimension()const =0;
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virtual float operator[](const int & i)const = 0;
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};
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template<int N, class S>
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class MatrixDiag: public Point<N,S>, public MatrixDiagBase{
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public:
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const int & Dimension() const {return N;}
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MatrixDiag(const Point<N,S>&p):Point<N,S>(p){}
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};
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/*!
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* This class represent a generic <I>m</I><3E><I>n</I> matrix. The class is templated over the scalar type field.
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* @param TYPE (Templete Parameter) Specifies the ScalarType field.
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*/
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template<class TYPE>
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class Matrix
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{
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public:
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typedef TYPE ScalarType;
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/*!
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* Default constructor
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* All the elements are initialized to zero.
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* \param m the number of matrix rows
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* \param n the number of matrix columns
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*/
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Matrix(unsigned int m, unsigned int n)
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{
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_rows = m;
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_columns = n;
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_data = new ScalarType[m*n];
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memset(_data, 0, m*n*sizeof(ScalarType));
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};
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/*!
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* Constructor
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* The matrix elements are initialized with the values of the elements in \i values.
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* \param m the number of matrix rows
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* \param n the number of matrix columns
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* \param values the values of the matrix elements
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*/
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Matrix(unsigned int m, unsigned int n, TYPE *values)
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{
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_rows = m;
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_columns = n;
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unsigned int dim = m*n;
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_data = new ScalarType[dim];
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memcpy(_data, values, dim*sizeof(ScalarType));
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//unsigned int i;
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//for (i=0; i<_rows*_columns; i++)
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// _data[i] = values[i];
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};
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/*!
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* Empty constructor
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* Just create the object
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*/
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Matrix()
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{
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_rows = 0;
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_columns = 0;
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_data = NULL;
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};
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||
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/*!
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* Copy constructor
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* The matrix elements are initialized with the value of the corresponding element in \i m
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* \param m the matrix to be copied
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*/
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Matrix(const Matrix<TYPE> &m)
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{
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_rows = m._rows;
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_columns = m._columns;
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_data = new ScalarType[_rows*_columns];
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unsigned int dim = _rows * _columns;
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memcpy(_data, m._data, dim * sizeof(ScalarType));
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// for (unsigned int i=0; i<_rows*_columns; i++)
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// _data[i] = m._data[i];
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};
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||
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/*!
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* Default destructor
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||
*/
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~Matrix()
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{
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delete []_data;
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};
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||
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/*!
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* Number of columns
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*/
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inline unsigned int ColumnsNumber() const
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{
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return _columns;
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};
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/*!
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* Number of rows
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*/
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inline unsigned int RowsNumber() const
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{
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return _rows;
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};
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/*!
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* Equality operator.
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* \param m
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* \return true iff the matrices have same size and its elements have same values.
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*/
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bool operator==(const Matrix<TYPE> &m) const
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{
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if (_rows==m._rows && _columns==m._columns)
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{
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bool result = true;
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for (unsigned int i=0; i<_rows*_columns && result; i++)
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result = (_data[i]==m._data[i]);
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return result;
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}
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return false;
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};
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/*!
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* Inequality operator
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* \param m
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* \return true iff the matrices have different size or if their elements have different values.
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*/
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bool operator!=(const Matrix<TYPE> &m) const
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{
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if (_rows==m._rows && _columns==m._columns)
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{
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bool result = false;
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for (unsigned int i=0; i<_rows*_columns && !result; i++)
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result = (_data[i]!=m._data[i]);
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return result;
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}
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return true;
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};
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/*!
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* Return the element stored in the <I>i</I>-th rows at the <I>j</I>-th column
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* \param i the row index
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* \param j the column index
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* \return the element
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*/
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inline TYPE ElementAt(unsigned int i, unsigned int j)
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{
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assert(i>=0 && i<_rows);
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assert(j>=0 && j<_columns);
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return _data[i*_columns+j];
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};
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/*!
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* Calculate and return the matrix determinant (Laplace)
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* \return the matrix determinant
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*/
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TYPE Determinant() const
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{
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assert(_rows == _columns);
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switch (_rows)
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{
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case 2:
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{
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return _data[0]*_data[3]-_data[1]*_data[2];
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break;
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};
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case 3:
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{
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return _data[0]*(_data[4]*_data[8]-_data[5]*_data[7]) -
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_data[1]*(_data[3]*_data[8]-_data[5]*_data[6]) +
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_data[2]*(_data[3]*_data[7]-_data[4]*_data[6]) ;
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break;
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};
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default:
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{
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// da migliorare: si puo' cercare la riga/colonna con maggior numero di zeri
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ScalarType det = 0;
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for (unsigned int j=0; j<_columns; j++)
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if (_data[j]!=0)
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det += _data[j]*this->Cofactor(0, j);
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return det;
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||
}
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||
};
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};
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/*!
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* Return the cofactor <I>A<SUB>i,j</SUB></I> of the <I>a<SUB>i,j</SUB></I> element
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* \return ...
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*/
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TYPE Cofactor(unsigned int i, unsigned int j) const
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{
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assert(_rows == _columns);
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assert(_rows>2);
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TYPE *values = new TYPE[(_rows-1)*(_columns-1)];
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unsigned int u, v, p, q, s, t;
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for (u=0, p=0, s=0, t=0; u<_rows; u++, t+=_rows)
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{
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if (i==u)
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continue;
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for (v=0, q=0; v<_columns; v++)
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{
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if (j==v)
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continue;
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values[s+q] = _data[t+v];
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q++;
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}
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p++;
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s+=(_rows-1);
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}
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Matrix<TYPE> temp(_rows-1, _columns-1, values);
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return (pow(TYPE(-1.0), TYPE(i+j))*temp.Determinant());
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};
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||
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/*!
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* Subscript operator:
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* \param i the index of the row
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* \return a reference to the <I>i</I>-th matrix row
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*/
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inline TYPE* operator[](const unsigned int i)
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{
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assert(i<_rows);
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return _data + i*_columns;
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};
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/*!
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* Const subscript operator
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* \param i the index of the row
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* \return a reference to the <I>i</I>-th matrix row
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*/
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inline const TYPE* operator[](const unsigned int i) const
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{
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assert(i<_rows);
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return _data + i*_columns;
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};
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||
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/*!
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* Get the <I>j</I>-th column on the matrix.
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* \param j the column index.
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* \return the reference to the column elements. This pointer must be deallocated by the caller.
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*/
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TYPE* GetColumn(const unsigned int j)
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{
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assert(j>=0 && j<_columns);
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ScalarType *v = new ScalarType[_columns];
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unsigned int i, p;
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for (i=0, p=j; i<_rows; i++, p+=_columns)
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v[i] = _data[p];
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return v;
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};
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/*!
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* Get the <I>i</I>-th row on the matrix.
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* \param i the column index.
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* \return the reference to the row elements. This pointer must be deallocated by the caller.
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*/
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TYPE* GetRow(const unsigned int i)
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{
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assert(i>=0 && i<_rows);
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ScalarType *v = new ScalarType[_rows];
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unsigned int j, p;
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for (j=0, p=i*_columns; j<_columns; j++, p++)
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v[j] = _data[p];
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return v;
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};
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||
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/*!
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* Swaps the values of the elements between the <I>i</I>-th and the <I>j</I>-th column.
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* \param i the index of the first column
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* \param j the index of the second column
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||
*/
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void SwapColumns(const unsigned int i, const unsigned int j)
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{
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assert(0<=i && i<_columns);
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assert(0<=j && j<_columns);
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if (i==j)
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return;
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||
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||
unsigned int r, e0, e1;
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for (r=0, e0=i, e1=j; r<_rows; r++, e0+=_columns, e1+=_columns)
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std::swap(_data[e0], _data[e1]);
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||
};
|
||
|
||
/*!
|
||
* 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
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||
* \param j the index of the second row
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||
*/
|
||
void SwapRows(const unsigned int i, const unsigned int j)
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||
{
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assert(0<=i && i<_rows);
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assert(0<=j && j<_rows);
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if (i==j)
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return;
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||
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||
unsigned int r, e0, e1;
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for (r=0, e0=i*_columns, e1=j*_columns; r<_columns; r++, e0++, e1++)
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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++)
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_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);
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||
for (unsigned int i=0; i<_rows*_columns; i++)
|
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_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++)
|
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_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;
|
||
};
|
||
|
||
// for the transistion to eigen
|
||
Matrix transpose()
|
||
{
|
||
Matrix res = *this;
|
||
res.Transpose();
|
||
return res;
|
||
}
|
||
void transposeInPlace() { Transpose(); }
|
||
// for the transistion to eigen
|
||
|
||
/*!
|
||
* 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
|