Basic usage

[ykozw]

Hi.
Thanks for great library.

I start to use this library, but have trouble.
I want to solve least square Ax=b under constraint Ex ≦ (1,1,1....), all variables are under 1.

Code is following.

void test()
{
    // construct Ax = b
    const int32_t numSample = 128;
    Eigen::SparseMatrix<double> A;
    Eigen::VectorXd b;
    A.resize(numSample,3);
    b.resize(numSample);
    for(int32_t sn=0;sn<numSample;++sn)
    {
        // something funtion
        const float x = float(sn)/float(numSample);
        const float y = 2.5f * x * x + 2.4f * x + 2.3f;
        //
        A.insert(sn,0) = x * x;
        A.insert(sn,1) = x;
        A.insert(sn,2) = 1.0f;
        b(sn) = y;
    }
    A.makeCompressed();
    
    // Make constraint. All coeffs are under 1. (Ex<I)
    // https://scicomp.stackexchange.com/a/11588
    Eigen::MatrixXd Q = A.transpose() * A;
    Eigen::VectorXd c = -A.transpose() * b;
    Eigen::MatrixXd A2;
    Eigen::VectorXd b2;
    A2.resize(3,3);
    b2.resize(3);
    A2.setIdentity();
    b2.setOnes();
    //
    Eigen::VectorXd x;
    x.resize(3);
    EigenQP::quadprog(Q, c, A2, b2, x);
    std::cout << x << std::endl;
}

I get x as (2.5,2.4,2.3). But this is not constraint.
And "b2.setOnes();" rewrite to "b2 << 10.0,10.0,10.0;", I got x as (0.106648, 0.355828, 0.216527).
Totally bad results, I might did bad operation, bud I can't figure out it.

Thanks.