@@ -39,10 +39,6 @@ Define a vector signs that contains the expected sign of each pivot:
3939- -1 for pivots expected to be negative
4040- 0 for pivots without an expected sign.
4141This is used to determine the sign of the regularisation to apply.
42- Only pivots in the (1,1)-block are allowed to have unknown sign, so that pivots
43- with unknown sign receive a static regularisation contribution equal to -reg_p.
44- Dynamic regularisation uses the computed sign of the pivot, if the sign is
45- unknown.
4642
4743Then, the factorization is performed as follows.
4844
@@ -62,6 +58,19 @@ To add static regularisation when the pivots are selected, use
6258setRegularisation(reg_p,reg_d) to choose values of primal and dual
6359regularisation. If regularisation is already added to the matrix, ignore.
6460
61+ The expected sign of a pivot is used to determine which static regularisation to
62+ apply. Pivots with negative expected sign are regularised with -reg_p, pivots
63+ with positive expected sign are regularised with +reg_d. If the sign is unknown,
64+ the computed sign of the pivot is used to determine which regularisation to
65+ apply.
66+
67+ Notice that this sign convention corresponds to a saddle point system with
68+ negative (1,1) block and positive (2,2) block.
69+
70+ Dynamic regularisation may perturb a pivot if it is too small, and it
71+ does so based on the expected sign of the pivot. This procedure uses the
72+ computed sign of the pivot, if the sign is unknown.
73+
6574Notice that the fill-reducing ordering can be modified during the call to
6675analyse. The inverse permutation used during the factorisation can be accessed
6776via the Symbolic object, S.iperm().
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