Comments (1)
Commit ab317d5 solves the issue.
Now all transition matrices have row probabilities which add up to 1, within 1e-6 tolerance level:
[P[i].sum(axis=1) for i in range(len(P))]
[array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 1., 1., 1.]),
array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 1., 1., 1.]),
array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 1., 1., 1.]),
array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 1., 1., 1.]),
array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 1., 1., 1.]),
array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
1., 1., 1., 1., 1., 1., 1.])]
An additional benefit is that the discrepancy between q @ P[0] @ ... @ P[-1]
and q
is now greatly reduced:
q @ np.linalg.multi_dot([P[i] for i in range(len(P))]) - q
array([ 1.79717352e-15, 7.58421104e-15, 2.13717932e-15,
-1.37390099e-15, 1.23026589e-14, -1.08940634e-15,
-3.25434124e-15, -1.02071129e-14, -5.82867088e-15,
-4.99600361e-15, -9.61730695e-15, 6.07847106e-15,
-3.76088050e-15, -2.08166817e-17, 1.60982339e-15,
8.16707812e-15, 9.64506253e-16, 7.46624984e-15,
-1.37875822e-14, -2.15417961e-14])
Finally, the tree is much more regular now:
from willowtree.
Related Issues (9)
- Enhancement: Replace wrongly specified transition matrices. HOT 2
- Enhancement: Scrap last matrices in the chain if bad. HOT 1
- Bug: Last replaceable matrix in the chain not replaced; vector t always shortened. HOT 3
- Bug: LP algorithm occasionally returns probabilities outside range. HOT 3
- Enhancement: Scrap first matrices in the chain if bad. HOT 1
- Enhancement: Use Python's multiprocessing to speed up the algorithm.
- Bug: IndexError when P[0] is bad and only one matrix in the chain is well-behaved. HOT 1
- Enhancement: Plot willow tree even if no transition matrix is well-defined. Case: k > 1. HOT 1
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from willowtree.