int main(int argc, char *argv[]) {
int info;
int n = 6;
if (argc > 1) n = boost::lexical_cast<int>(argv[1]);
std::cout << "n = " << n << std::endl;
// generate symmmetric random martix
matrix_t mat = matrix_t::Random(n, n);
mat += mat.transpose().eval(); // eval() is required to avoid aliasing issue
std::cout << "Input random matrix A:\n" << mat << std::endl;
// diagonalization
vector_t w(n);
matrix_t v = mat; // v will be overwritten by eigenvectors
info = LAPACKE_dsyev(LAPACK_COL_MAJOR, 'V', 'U', n, &v(0, 0), n, &w(0));
std::cout << "Eigenvalues:\n" << w << std::endl;
std::cout << "Eigenvectors:\n" << v << std::endl;
// check correctness of diagonalization
matrix_t wmat = matrix_t::Zero(n, n);
for (int i = 0; i < n; ++i) wmat(i, i) = w(i);
matrix_t check = v.transpose() * mat * v;
std::cout << "Vt * A * V:\n" << check << std::endl;
std::cout << "| W - Vt * A * V | = " << (wmat - check).norm() << std::endl;
}
double
Simplex::getVolume() const {
// See http://www.math.niu.edu/~rusin/known-math/97/volumes.polyh
double res = 0.0;
if (mndims == 0) return res;
if (mnpdims == 0) return res;
// all vertices have been set
std::vector< std::vector<double> > wmat(mndims, std::vector<double>(mnpdims));
for (size_t jcol = 0; jcol < mnpdims; ++jcol) {
for (size_t irow = 0; irow < mndims; ++irow) {
wmat[irow][jcol] = mvertices[jcol + 1][irow] - mvertices[0][irow];
}
}
// transpose(wmat) * wmat
std::vector<double> wmatTDotWmat(mnpdims * mnpdims, 0.0);
for (size_t jcol = 0; jcol < mnpdims; ++jcol) {
for (size_t irow = 0; irow < mnpdims; ++irow) {
size_t k = irow + mnpdims*jcol;
for (size_t el = 0; el < mndims; ++el) {
wmatTDotWmat[k] += wmat[el][irow] * wmat[el][jcol];
}
}
}
double det = this->getDeterminant(wmatTDotWmat);
res = det / factorial(mnpdims);
return res;
}
