Matrix multiplication is very slow in Eigen

Question

I implemented the Gauss-Newton optimization process, which includes the calculation of the increment by solving a linearized system Hx = b. The matrix is Hcalculated using H = J.transpose() * W * J, and bcalculated from b = J.transpose() * (W * e), where eis the error vector. The Jacobian here is an n-by-6 matrix, where n is in thousands and remains unchanged in iterations, and Wis an n-in-n diagonal matrix matrix that will change in iterations (some diagonal elements will be set to zero). However, I ran into a speed issue.

When I do not add weight matrix W, namely, H = J.transpose()*Jand b = J.transpose()*emy Gauss-Newton process can work very quickly at 0.02 seconds for 30 iterations. However, when I add a matrix Wthat is defined outside the iteration loop, it becomes so slow (0.3 ~ 0.7 s for 30 iterations), and I don’t understand if this is my encoding problem, or usually it takes a lot of time.

Everything here is eigenmatrices and vectors.

I defined my matrix Wusing the function .asDiagonal()in the Eigen library from the inverse dispersion vector. then just used it to calculate Had b. Then it becomes very slow. I want to talk about the potential causes of this huge decline.

EDIT:

. . vec.asDiagonal(), , , .

, , - . :

for (int iter=0; iter<max_iter; ++iter) {
    // obtain error vector
    error = ...  
    // calculate H and b - the fast one
    Eigen::MatrixXf H = J.transpose() * J;
    Eigen::VectorXf b = J.transpose() * error;
    // calculate H and b - the slow one
    Eigen::MatrixXf H = J.transpose() * weight_ * J;
    Eigen::VectorXf b = J.transpose() * (weight_ * error);
    // obtain delta and update state
    del = H.ldlt().solve(b);
    T <- T(del)   // this is pseudo code, meaning update T with del
}

, , , .

Answer 1

, , :

MatrixXd m;
VectorXd w;
w.setLinSpaced(5, 2, 6);

m.setOnes(5,5);

std::cout << (m.array().rowwise() * w.array().transpose()).matrix() << "\n";

, :

(w.array() * error.array()).matrix()

. MCVE , , YMMV...

Answer 2

, weight_ MatrixXf? , w.asDiagonal() , weight_, asDiagonal:

auto weight = w.asDiagonal();

, Eigen , weight , , .