jhtu
commented
4 years ago - There are certain requirements for a function to be an inner product. However, for any numerical data that you think of as a vector (a list of numbers), you can use the standard inner product: <x, y> = x^H y, where ^H denotes the Hermitian transpose. That is, if you have vectors [x_0, x_1, x_2, ..., x_n] and [y_0, y_1, y_2, ..., y_n], then you can compute the inner product as <x, y> = conj(x_0) y_0 + conj(x_1) y_1 + conj(x_2) y_2 + ... + conj(x_n) y_n.
For certain problems, you may wish to use a modified inner product. For instance, sometimes data from finite element simulations are meant to approximate continuous functions, which means the inner product sum approximates an integral. In that case, you might want to weight each element of the sum by a differential volume dV, so that large elements in the simulation mesh get more weight. You might also have different weights if different elements of your data have different physical units (e.g. meters vs kilometers). If you have questions on this, let us know.
- put_mat is just a function to save data, with certain requirements on the interface. If you don't have a function to save data, you can likely use a standard one, like numpy.save. I believe that you would have to wrap that function though, since I believe that put_mat requires the data argument followed by the filename, while the numpy save function has the opposite order of arguments.
SebiK91
Hi everybody,
after installing the modred package I'd like to use it for a model order reduction. For this want to apply the Proper Orthogonal Decomposition (POD) and Eigensystem Realization Algorithm (ERA) on my dataset. This consists of an input (m x n) and an output matrix (n x p). Unfortunately I have a problem with the function variables:
1) According to the modred.pod-documentation I need a inner_product as an input for the calculation: https://modred.readthedocs.io/en/stable/pod.html. How do I get the inner_product from my dataset?
2) According to the modred.era-documentation I need a put_mat as an input for the calculation: https://modred.readthedocs.io/en/stable/era.html. How do I get the put_mat from my dataset? Where do I get the Markov parameters in the next step? As I understand the documentation the function expects it as an input but I don't know how to calculate it.
Thanks and regards Markus