增强中的矩阵求逆

Question

我正在尝试使用boost进行简单的矩阵求逆操作.但是我收到了一个错误.基本上我想找到的是inversted_matrix = inverse(trans(matrix)*matrix)但是我收到一个错误

Check failed in file boost_1_53_0/boost/numeric/ublas/lu.hpp at line 299: 
detail::expression_type_check (prod (triangular_adaptor<const_matrix_type, 
upper> (m), e), cm2) 
terminate called after throwing an instance of 
'boost::numeric::ublas::internal_logic' 
  what(): internal logic 
Aborted (core dumped) 

我的尝试:

#include <boost/numeric/ublas/matrix.hpp> 
#include <boost/numeric/ublas/vector.hpp> 
#include <boost/numeric/ublas/io.hpp> 
#include <boost/numeric/ublas/vector_proxy.hpp> 
#include <boost/numeric/ublas/matrix.hpp> 
#include <boost/numeric/ublas/triangular.hpp> 
#include <boost/numeric/ublas/lu.hpp> 

namespace ublas = boost::numeric::ublas; 
template<class T> 
bool InvertMatrix (const ublas::matrix<T>& input, ublas::matrix<T>& inverse) { 
    using namespace boost::numeric::ublas; 
    typedef permutation_matrix<std::size_t> pmatrix; 
    // create a working copy of the input 
    matrix<T> A(input); 
    // create a permutation matrix for the LU-factorization 
    pmatrix pm(A.size1()); 
    // perform LU-factorization 
    int res = lu_factorize(A,pm); 
    if( res != 0 )
        return false; 
    // create identity matrix of "inverse" 
    inverse.assign(ublas::identity_matrix<T>(A.size1())); 
    // backsubstitute to get the inverse 
    lu_substitute(A, pm, inverse); 
    return true; 
}

int main(){ 
    using namespace boost::numeric::ublas; 
    matrix<double> m(4,5); 
    vector<double> v(4); 
    vector<double> thetas; 
    m(0,0) = 1; m(0,1) = 2104; m(0,2) = 5; m(0,3) = 1;m(0,4) = 45; 
    m(1,0) = 1; m(1,1) = 1416; m(1,2) = 3; m(1,3) = 2;m(1,4) = 40; 
    m(2,0) = 1; m(2,1) = 1534; m(2,2) = 3; m(2,3) = 2;m(2,4) = 30; 
    m(3,0) = 1; m(3,1) = 852; m(3,2) = 2; m(3,3) = 1;m(3,4) = 36; 
    std::cout<<m<<std::endl; 
    matrix<double> product = prod(trans(m), m); 
    std::cout<<product<<std::endl; 
    matrix<double> inversion(5,5); 
    bool inverted; 
    inverted = InvertMatrix(product, inversion); 
    std::cout << inversion << std::endl; 
} 

Answer 1

Boost Ublas具有运行时检查功能,以确保数值稳定性.如果你看一下错误的来源,你可以看到它试图确保 U*X = B, X = U^-1*B, U*X = B(或类似的那样)在某个epsilon中是coorect.如果你在数字上有太多的偏差,这可能不会成立.

您可以通过-DBOOST_UBLAS_NDEBUG或旋转来禁用检查BOOST_UBLAS_TYPE_CHECK_EPSILON, BOOST_UBLAS_TYPE_CHECK_MIN.

Answer 2

由于m只有 4 行，prod(trans(m), m)秩不能高于 4，并且由于乘积是 5x5 矩阵，因此它必须是奇异矩阵（即行列式为 0），并且计算奇异矩阵的逆矩阵就像除以 0 一样。添加独立矩阵行来m解决这个奇点问题。