This code implements a matrix completion and decomposition algorithm, based on this paper.

The main method you will want to use is matrix_decomposition() which decomposes an optionally incomplete matrix, into two components, one low rank, and one sparse. It takes the following arguments:

• Y: the matrix to decompose. Y is assumed to be equal to TH + GA + W, where TH is an approximately low rank matrix, GA is a sparse "spiky" matrix, and W is noise. A full matrix needs to be given, but some parts can be ignored, as specified by the mask.
• Mask: a mask can be given to treat the matrix as incomplete. It must be of the same dimentions as Y. It must have 0 or False in the positions where Y is incomplete, 1 or True elsewhere. Defaults to None.
• lambda_d: regularization paramater for the low rank TH matrix.
• mu_d: regularization parameter for the sparse GA matrix. Use higher values if no spikes are expected.
• alpha: parameter that limits the maximum element of the low rank TH matrix. Bigger matrices will need bigger alpha` values.

The method will return TH and GA.

Additionally the code contains some methods and classes to generate synthetic matrices and to test the decomposition in various ways.