TMatrix left-handside multiplication

[meyerma]

Hello,

I am playing with complex matrices and vectors and I couldn’t find that much documentation about matrices-vector operations. I would like to make the operation: B = (V*)A(V), where A,B are TMatrix type and V is TVectorT vector.

I first define TMatrix/TVector conjugate as following

TVectorC Conjugate(const TVectorC &v)
{
    TVectorC v_c(v.GetNoElements());

    for(int i = 0, N = v.GetNoElements(); i < N; i++) {
        v_c(i) = TComplex::Conjugate(v(i));
    }

    return v_c;
}

TMatrixC Conjugate(const TMatrixC &m)
{
    TMatrixC m_c(m.GetNrows(), m.GetNcols());

    for(int i = 0, I = m.GetNrows(); i < I; i++) {
        for(int j = 0, J = m.GetNcols(); j < J; j++) {

            m_c(i,j) = TComplex::Conjugate(m(i,j));
        }
    }

    return m_c;
}

And then after that I was hoping to make the simple operation:

{
      using TMatrixC = TMatrixT<TComplex>;
      using TVectorC = TVectorT<TComplex>;
      TMatrixC A = /*[...]*/;
      TVectorC V = /*[...]*/;

      TMatrixC B = Conjugate(V)*A*V;
}

This throw me an error because of the left handside multiplication.

error: invalid operands to binary expression ('TVectorC' (aka 'TVectorT<TComplex>') and 'TMatrixC' (aka 'TMatrixT<TComplex>'))
    return TMath::Sqrt(Conjugate(this->Z) * this->P * this->Z);
                       ~~~~~~~~~~~~~~~~~~ ^ ~~~~~~~

This seems obvious… How should I modify my code here ?

[meyerma]

This is not what I want to do, because my vectors are differents.
But for the records… this might be useful for someone else. Naming doesn’t sound obvious.

TMatrixT<Element>
[...]
Element 	Similarity (const TVectorT< Element > &v) const
 	Calculate scalar v * (*this) * v^T.
[..]

NB: It seems complex algebra might not be supported yet. Fail to compile TMatrixT<TComplex> @moneta Were there some progress in this regards ?

[moneta]

Hi,

We are not supporting TMatrix or TMatruxstd::complex. You probably need to use another matrix package for performing operations on complex matrices

Lorenzo

[meyerma]

Any plan for implementing that ? Or some arguments against it maybe ?

[Eddy_Offermann]

If you search for “matrix complex” you will see that there has been some interest for complex matrix algebra over the last 2 decades, but … implementing this feature in all elements of the linear package is a big task:

installing it

• in all the decomposition classes
• in the eigen value classes
• sparse methods
• ROOT dictionary etc.

[Eddy_Offermann]

your algebra syntax is not correct ! An expression is always interpreted from left to right unless parentheses are placed. V * A * V will result first in calculating V * A.

We could have implemented to interpret this as V^T * A . Just to keep the syntax
clean and simple that is left out and the preferred way is, V * (A * V) which
will result in a dot product of two vectors.

As far as the naming of “Similarity” goes. The code contains also the well-known matrix similarity operations and this one is with a vector.

[meyerma]

Pretty sure it doesn’t takes two decades to implement complex matrices… but I definitely need a robust/mature solution.

I definitely didn’t found any vector transpose function, so I assumed that multiplying a vector-matrix from the left was implicit. Additionally, I only know matrix similarities not vector-matrix.
Many thanks for the clarifications !