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#include <vcg/math/matrix44.h>
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namespace vcg
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{
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/** \addtogroup math */
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/* @{ */
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/*!
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* Computes all eigenvalues and eigenvectors of a real symmetric matrix .
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* On output, elements of the input matrix above the diagonal are destroyed.
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* \param d returns the eigenvalues of a.
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* \param v is a matrix whose columns contain, the normalized eigenvectors
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* \param nrot returns the number of Jacobi rotations that were required.
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*/
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template <typename TYPE>
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static void Jacobi(Matrix44<TYPE> &w, Point4<TYPE> &d, Matrix44<TYPE> &v, int &nrot)
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{
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int j,iq,ip,i;
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//assert(w.IsSymmetric());
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TYPE tresh, theta, tau, t, sm, s, h, g, c;
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Point4<TYPE> b, z;
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v.SetIdentity();
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for (ip=0;ip<4;++ip) //Initialize b and d to the diagonal of a.
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{
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b[ip]=d[ip]=w[ip][ip];
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z[ip]=0.0; //This vector will accumulate terms of the form tapq as in equation (11.1.14).
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}
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nrot=0;
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for (i=0;i<50;i++)
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{
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sm=0.0;
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for (ip=0;ip<3;++ip) // Sum off diagonal elements
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{
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for (iq=ip+1;iq<4;++iq)
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sm += fabs(w[ip][iq]);
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}
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if (sm == 0.0) //The normal return, which relies on quadratic convergence to machine underflow.
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{
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return;
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}
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if (i < 4)
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tresh=0.2*sm/(4*4); //...on the first three sweeps.
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else
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tresh=0.0; //...thereafter.
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for (ip=0;ip<4-1;++ip)
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{
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for (iq=ip+1;iq<4;iq++)
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{
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g=100.0*fabs(w[ip][iq]);
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//After four sweeps, skip the rotation if the off-diagonal element is small.
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if(i>4 && (float)(fabs(d[ip])+g) == (float)fabs(d[ip]) && (float)(fabs(d[iq])+g) == (float)fabs(d[iq]))
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w[ip][iq]=0.0;
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else if (fabs(w[ip][iq]) > tresh)
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{
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h=d[iq]-d[ip];
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if ((float)(fabs(h)+g) == (float)fabs(h))
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t=(w[ip][iq])/h; //t =1/(2#)
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else
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{
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theta=0.5*h/(w[ip][iq]); //Equation (11.1.10).
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t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
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if (theta < 0.0) t = -t;
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}
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c=1.0/sqrt(1+t*t);
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s=t*c;
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tau=s/(1.0+c);
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h=t*w[ip][iq];
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z[ip] -= h;
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z[iq] += h;
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d[ip] -= h;
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d[iq] += h;
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w[ip][iq]=0.0;
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for (j=0;j<=ip-1;j++) { //Case of rotations 1 <= j < p.
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JacobiRotate<TYPE>(w,s,tau,j,ip,j,iq) ;
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}
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for (j=ip+1;j<=iq-1;j++) { //Case of rotations p < j < q.
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JacobiRotate<TYPE>(w,s,tau,ip,j,j,iq);
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}
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for (j=iq+1;j<4;j++) { //Case of rotations q< j <= n.
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JacobiRotate<TYPE>(w,s,tau,ip,j,iq,j);
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}
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for (j=0;j<4;j++) {
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JacobiRotate<TYPE>(w,s,tau,j,ip,j,iq);
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}
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++nrot;
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}
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}
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}
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for (ip=0;ip<4;ip++)
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{
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b[ip] += z[ip];
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d[ip]=b[ip]; //Update d with the sum of ta_pq ,
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z[ip]=0.0; //and reinitialize z.
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}
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}
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};
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/*!
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*
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*/
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template< typename TYPE >
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void JacobiRotate(Matrix44<TYPE> &A, TYPE s, TYPE tau, int i,int j,int k,int l)
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{
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TYPE g=A[i][j];
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TYPE h=A[k][l];
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A[i][j]=g-s*(h+g*tau);
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A[k][l]=h+s*(g-h*tau);
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};
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/*!
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* Given a matrix <I>A<SUB>m×n</SUB></I>, this routine computes its singular value decomposition,
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* i.e. <I>A=U·W·V<SUP>T</SUP></I>. The matrix <I>A</I> will be destroyed!
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* \param A ...
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* \param W the diagonal matrix of singular values <I>W</I>, stored as a vector <I>W[1...N]</I>
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* \param V the matrix <I>V</I> (not the transpose <I>V<SUP>T</SUP></I>)
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*/
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template <typename MATRIX_TYPE>
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static void SingularValueDecomposition(MATRIX_TYPE &A, typename MATRIX_TYPE::ScalarType *W, MATRIX_TYPE &V)
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{
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typedef typename MATRIX_TYPE::ScalarType ScalarType;
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};
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/*!
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* Solves A·X = B for a vector X, where A is specified by the matrices <I>U<SUB>m×n</SUB></I>,
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* <I>W<SUB>n×1</SUB></I> and <I>V<SUB>n×n</SUB></I> as returned by <CODE>SingularValueDecomposition</CODE>.
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* No input quantities are destroyed, so the routine may be called sequentially with different b’s.
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* \param x is the output solution vector (<I>x<SUB>n×1</SUB></I>)
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* \param b is the input right-hand side (<I>b<SUB>n×1</SUB></I>)
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*/
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template <typename MATRIX_TYPE>
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static void SingularValueBacksubstitution(const MATRIX_TYPE &U,
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const typename MATRIX_TYPE::ScalarType *W,
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const MATRIX_TYPE &V,
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typename MATRIX_TYPE::ScalarType *x,
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const typename MATRIX_TYPE::ScalarType *b)
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{
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unsigned int jj, j, i;
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ScalarType s;
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ScalarType tmp = new ScalarType[U._columns];
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for (j=0; j<U._columns; j++) //Calculate U^T * B.
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{
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s = 0;
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if (W[j]!=0) //Nonzero result only if wj is nonzero.
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{
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for (i=0; i<U._rows; i++)
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s += U[i][j]*b[i];
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s /= w[j]; //This is the divide by wj .
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}
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tmp[j]=s;
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}
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for (j=0;j<U._columns;j++) //Matrix multiply by V to get answer.
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{
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s = 0;
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for (jj=0; jj<U._columns; jj++)
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s += V[j][jj]*tmp[jj];
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x[j]=s;
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}
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delete []tmp;
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};
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// Computes (a^2 + b^2)^(1/2) without destructive underflow or overflow.
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template <typename TYPE>
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inline TYPE pythagora(TYPE a, TYPE b)
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{
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TYPE abs_a = fabs(a);
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TYPE abs_b = fabs(b);
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if (abs_a > abs_b)
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return abs_a*sqrt(1.0+sqr(abs_b/abs_a));
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else
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return (abs_b == 0.0 ? 0.0 : abs_b*sqrt(1.0+sqr(abs_a/abs_b)));
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};
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/*! @} */
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}; // end of namespace
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@ -0,0 +1,557 @@
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/****************************************************************************
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* 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 \/)\/ *
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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 *
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* 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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#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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namespace vcg
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{
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/** \addtogroup math */
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/* @{ */
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/*!
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* This class represent a generic <I>m</I>×<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, ScalarType(0.0), 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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_data = new ScalarType[m*n];
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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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* 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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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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* 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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* Number of columns
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*/
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inline unsigned int ColumnsNumber()
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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()
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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(-1, i+j)*temp.Determinant());
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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>=0 && i<_columns);
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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>=0 && i<_columns);
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return _data + i*_columns;
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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.
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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.
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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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* Assignment operator
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* \param m ...
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*/
|
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Matrix<TYPE>& operator=(const Matrix<TYPE> &m)
|
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{
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if (this != &m)
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||||
{
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assert(_rows == m._rows);
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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];
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}
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return *this;
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};
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/*!
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* Adds a matrix <I>m</I> to this matrix.
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* \param m reference to matrix to add to this
|
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* \return the matrix sum.
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*/
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Matrix<TYPE>& operator+=(const Matrix<TYPE> &m)
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{
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assert(_rows == m._rows);
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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];
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return *this;
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};
|
||||
|
||||
/*!
|
||||
* 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 reference to the matrix to multiply by
|
||||
* \result the matrix product
|
||||
*/
|
||||
Matrix<TYPE> operator*(const Matrix<TYPE> &m)
|
||||
{
|
||||
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;
|
||||
};
|
||||
|
||||
/*!
|
||||
* 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++)
|
||||
results._data[i] = _data[i]-k;
|
||||
return result;
|
||||
};
|
||||
|
||||
/*!
|
||||
* Negate all matrix elements
|
||||
* \return ...
|
||||
*/
|
||||
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)
|
||||
{
|
||||
Matrix<TYPE> result(_rows, _columns);
|
||||
for (unsigned int i=0; i<_rows*_columns; i++)
|
||||
results._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++)
|
||||
results._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 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=0; 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];
|
||||
};
|
||||
|
||||
/*!
|
||||
* 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("%g\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;
|
||||
};
|
||||
|
||||
/*! @} */
|
||||
}; // end of namespace
|
||||
Loading…
Reference in New Issue