Eigen Value of Gradient of a vector
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How does the gradient of a vector(delta V) become a 3x3 matrix? And how do you compute it's eigen value efficiently? Is there c++ library that can do this (can the c++ library Eigen do this
"Gradient" is not quite the right word here. If you have a differentiable mapping from R^3 to R^3, you can compute how the vector changes as you move infinitesimally in each of the axes, and this indeed is a 3x3 matrix, but it's called the Jacobian.
There are lots of libraries that compute eigenvalues efficiently, but for a 3x3 matrix you can probably use just about any method.
What are you trying to do exactly?
Author
I'm trying to calculate a scalar field for marching cubes based on an equation in this paper https://www.researchgate.net/publication/220357083_A_unified_particle_model_for_fluid-solid_interactions. I need to find the biggest Eigen value efficiently. It says the gradient of a vector.
Because of curvature, some grid points in the field maybe moving faster than the point being sampled. So need to need Eigen values to correct this.
Because of curvature, some grid points in the field maybe moving faster than the point being sampled. So need to need Eigen values to correct this.
I would probably try Armadillo first. It's generally easy to work with and it has served me well in the past. I don't have direct experience with the Armadillo functions that compute eigenvalue and eigenvectors, though.
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