121 lines
2.7 KiB
C++
121 lines
2.7 KiB
C++
#pragma once
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#include <cgv/math/mat.h>
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#include <cgv/math/perm_mat.h>
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#include <cgv/math/diag_mat.h>
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#include <cgv/math/low_tri_mat.h>
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#include <cgv/math/up_tri_mat.h>
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#include <cgv/math/lu.h>
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namespace cgv {
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namespace math {
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//compute determinant of a diagonal matrix
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template <typename T>
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T det(const diag_mat<T>& m)
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{
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T v = (T)1.0;
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for(unsigned i =0; i< m.nrows(); i++)
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v *= m(i);
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return v;
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}
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//compute determinant of an lower triangular matrix
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template <typename T>
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T det(const low_tri_mat<T>& m)
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{
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T v = (T)1.0;
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for(unsigned i =0; i< m.nrows(); i++)
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v *= m(i,i);
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return v;
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}
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//compute determinant of an upper triangular matrix
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template <typename T>
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T det(const up_tri_mat<T>& m)
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{
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T v = (T)1.0;
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for(unsigned i =0; i< m.nrows(); i++)
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v *= m(i,i);
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return v;
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}
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//compute determinant of a permutation matrix
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inline int det(const perm_mat& m)
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{
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//count number of transpositions needed to get the identity permutation
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perm_mat temp = m;
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unsigned num_transpositions = 0;
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for(unsigned i = 0; i < m.size();i++)
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{
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while(temp(i) != i)
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{
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std::swap(temp(i),temp(temp(i)));
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num_transpositions++;
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}
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}
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//if number of transpositions is even return 1 else -1
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if(num_transpositions % 2 == 0)
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return 1;
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else
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return -1;
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}
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//compute determinant of a square matrix m
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template <typename T>
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T det(const mat<T>& m)
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{
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assert(m.is_square());
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perm_mat p;
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low_tri_mat<T> l;
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up_tri_mat<T> u;
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lu(m,p,l,u);
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return det(p)*det(l)*det(u);
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}
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//compute determinant of 2x2 matrix
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template<typename T>
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T det_22(const T a11,const T a12,
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const T a21,const T a22)
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{
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return a11*a22-a21*a12;
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}
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//compute determinant of 3x3 matrix
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template<typename T>
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T det_33(const T a11,const T a12,const T a13,
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const T a21,const T a22,const T a23,
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const T a31,const T a32,const T a33)
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{
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return a11 * (a22 * a33 - a32 * a23) -
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a21 * (a12 * a33 - a32 * a13) +
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a31 * (a12 * a23 - a22 * a13);
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}
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//compute determinant of 4x4 matrix
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template<typename T>
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T det_44(const T a11,const T a12,const T a13,const T a14,
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const T a21,const T a22,const T a23,const T a24,
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const T a31,const T a32,const T a33,const T a34,
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const T a41,const T a42,const T a43,const T a44)
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{
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T a3344 = a33 * a44 - a43 * a34;
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T a2344 = a23 * a44 - a43 * a24;
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T a2334 = a23 * a34 - a33 * a24;
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T a1344 = a13 * a44 - a43 * a14;
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T a1334 = a13 * a34 - a33 * a14;
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T a1324 = a13 * a24 - a23 * a14;
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return a11 * (a22 * a3344 - a32 * a2344 + a42 * a2334) -
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a21 * (a12 * a3344 - a32 * a1344 + a42 * a1334) +
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a31 * (a12 * a2344 - a22 * a1344 + a42 * a1324) -
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a41 * (a12 * a2334 - a22 * a1334 + a32 * a1324);
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}
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}
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}
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