MatDoub SVD::nullspace(Doub thresh = -1.){
Int j,jj,nn=0;
MatDoub nullsp(n,nullity(thresh));
for (j=0;j<n;j++) {
if (w[j] <= tsh) {
for (jj=0;jj<n;jj++) nullsp[jj][nn] = v[jj][j];
nn++;
}
}
return nullsp;
}
DoubleVector* hansen_gaussian_elimination_v2(DoubleMatrix A, DoubleVector b)
{
unsigned int rows = mtl::mat::num_rows(A);
unsigned int cols = mtl::mat::num_cols(A);
if(rows == cols)
{
std::cout << "det(A) = " << det(A) << std::endl << std::endl;
if(boost::numeric::zero_in(det(A)) == true)
throw std::string("Cannot approximate bounding box as solution set is unbounded");
}
if(rows == cols)
{
DoubleMatrix mid;
mid = m(A);
if(boost::numeric::zero_in(det(mid)) == false)
{
DoubleMatrix M(rows, cols);
DoubleVector r(mtl::num_rows(b), (DoubleInterval)0);
DoubleMatrix B(rows, cols);
B = mtl::mat::inv(mid);
M = B * A;
r = B * b;
std::cout << "M: " << std::endl;
std::cout << M << std::endl;
std::cout << "r: " << std::endl;
std::cout << r << std::endl << std::endl;
A = M;
b = r;
}
}
DoubleMatrix New_A(rows, cols);
DoubleVector New_b(mtl::num_rows(b), (DoubleInterval)0);
New_A = A;
New_b = b;
for(unsigned int k = 1; k <= rows; k++)
{
for(unsigned int i = 1; i <= rows; i++)
{
for(unsigned int j = 1; j <= cols; j++)
{
if(i <= k && j <= cols)
{}
else if(i > k && j > k && boost::numeric::interval_lib::posne(A(k-1,k-1), (DoubleInterval)0) == true)
New_A(i-1,j-1) = A(i-1,j-1) - ((A(i-1,k-1) * A(k-1,j-1))/A(k-1,k-1));
else
New_A(i-1,j-1) = 0;
if(i <= k)
New_b[i-1] = b[i-1];
else if(i > k && boost::numeric::interval_lib::posne(A(k-1,k-1), (DoubleInterval)0) == true)
New_b[i-1] = b[i-1] - ((A(i-1,k-1)/A(k-1,k-1))*b[k-1]);
}
}
A = New_A;
b = New_b;
}
std::cout << "A_reduced: " << std::endl;
std::cout << A << std::endl;
unsigned int rk = rank(A);
unsigned int nul = nullity(A);
std::cout << "rk(A) = " << rk << " nul(A) = " << nul << std::endl << std::endl;
std::cout << "b_reduced: " << std::endl;
std::cout << b << std::endl << std::endl;
if(cols == rk && rows > rk)
{
DoubleMatrix A_smaller(rk,rk);
DoubleVector b_smaller(rk, (DoubleInterval)0);
for(unsigned int i = 0; i < rk; i++)
{
b_smaller[i] = b[i];
for(unsigned int j = 0; j < rk; j++)
A_smaller(i,j) = A(i,j);
}
std::cout << "New A = " << std::endl;
std::cout << A_smaller << std::endl;
std::cout << "New b = " << std::endl;
std::cout << b_smaller << std::endl << std::endl;
return hansen_gaussian_elimination_v2(A_smaller, b_smaller);
}
else if(cols > rk)
{
std::cout << "The system of equations has no exact solutions" << std::endl << std::endl;
return NULL;
}
DoubleVector *x = new DoubleVector(cols, (DoubleInterval)0);
*x = mtl::mat::upper_trisolve(A,b);
return x;
}
