lapacke repro

#define EIGEN_USE_LAPACKE

#include <cblas.h>
#include <lapacke.h>

#include <Eigen/Core>
#include <Eigen/Dense>

#include <iostream>
#include <memory>

template<typename T>
using Matrix = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor>;

template<typename T>
using Vector = Eigen::Matrix<T, Eigen::Dynamic, 1, Eigen::ColMajor>;

int main(int argc, char** argv) {
    Matrix<double> a(3,3);
    a << 12, -51,   4,
          6, 167, -68,
         -4,  24, -41;

    std::cout << "A =\n" << a << "\n";
    Vector<double> b = Vector<double>::Random(5);
    std::cout << "b =\n" << b << "\n";

    std::cout << "LAPACKE:\n";
    Matrix<double> m = a;
    Vector<int> jpvt(m.rows());
    jpvt.fill(0);

    Vector<double> tau(m.rows());
    tau.fill(0);

    auto status = LAPACKE_dgeqp3(CblasColMajor, m.rows(), m.cols(), m.data(), m.rows(), jpvt.data(), tau.data());
    std::cout << "status = " << status << "\n";

    decltype(m) m1 = m.triangularView<Eigen::Upper>();
    std::cout << "m:\n" << m1 << "\n";
    std::cout << "jpvt:\n" << jpvt << "\n";
    std::cout << "tau:\n" << tau << "\n";

    std::cout << "\n\nEIGEN:\n";
    Eigen::ColPivHouseholderQR<decltype(a)> qr = a.colPivHouseholderQr();
    std::cout << "hcoeff:\n" << qr.hCoeffs() << "\n";

    Matrix<double> q = qr.householderQ();
    Matrix<double> r = qr.matrixR().template triangularView<Eigen::Upper>();
    decltype(qr)::PermutationType p = qr.colsPermutation();
    std::cout << "Q:\n" << q << "\n";
    std::cout << "P:\n" << p.toDenseMatrix() << "\n";
    std::cout << "R:\n" << r << "\n";

    Matrix<double> aa = q * r;
    std::cout << "Q * R:\n" << aa << "\n";

    Matrix<double> ap = aa * p.transpose();
    std::cout << "A * P:\n" << ap << "\n";

    return 0;
}