frobenius_error()

frobenius_error(Qtrue, Qapprox)

Compute the absolute and relative Frobenius-norm errors between the snapshot sets Qtrue and Qapprox, where Qapprox approximates Qtrue:

absolute_error = ||Qtrue - Qapprox||_F, relative_error = ||Qtrue - Qapprox||_F / ||Qtrue||_F.

Parameters:

Qtrue(n, k)

“True” data. Each column is one snapshot, i.e., Qtrue[:, j] is the data at some time t[j].

Qapprox(n, k)

An approximation to Qtrue, i.e., Qapprox[:, j] approximates Qtrue[:, j] and corresponds to some time t[j].

Returns:

abs_errfloat

Absolute error ||Qtrue - Qapprox||_F.

rel_errfloat

Relative error ||Qtrue - Qapprox||_F / ||Qtrue||_F.