This is a PyTorch implementation of the joint matrix diagonalization algorithm proposed in the paper
Vollgraf, Roland, and Klaus Obermayer. "Quadratic optimization for simultaneous matrix diagonalization." IEEE Transactions on Signal Processing 54.9 (2006): 3270-3278. (https://ieeexplore.ieee.org/abstract/document/1677895)
Run a simple test script with
python -m qdiagfrom qdiag import qdiag, errW = qdiag( C0, C) finds a matrix W so that W.T @ C0 @ W has diagonal elements
equal to 1 and W.T @ C[i] @ W has smallest possible off-diagonal
elements. C0 is a positive definite NxN matrix, and C is a KxNxN array
of K correlation matrices.
W = qdiag( C0, C, p)where p is a vector with K positive elements, weights the matrices in C according to them. An empty vector has the effect that all matrices are weighted equally.
qdiag( C0, C, p, **kwargs)allows to pass optional arguments. These can be the following (default values are taken for missing fields):
| key | value |
|---|---|
verbose |
print informational messages in every iteration (default: false) |
approach |
implementation of QDIAG, O(KN^3) or O(N^5), see [1]. Possible values 'OKN3', 'ON5' (default: 'OKN3') |
Nit |
maximum number of iteration (default 100) |
tol_w |
Stopping criterion. Changes of w smaller than this value terminate the iterations (default: 1e-4) |
W |
used as the inital W (default: random NxN matrix) |
M |
number components, columns of W (default: M=N matrix) opt.W has priority over opt.M |
return_errlog |
return also a (Nit) tensor of diagonalization error history (default: False) |
return_Wlog |
return a (Nit,N,M) tensor of diagonalization matrix history (default: False) |
E = err(W, C0, C, p)computes the joint-diagonalization error achieved with the columns of W
The code is derived from https://www.ni.tu-berlin.de/menue/software_and_data/approximate_simultaneous_matrix_diagonalization_qdiag