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from .pysheaf import * | ||
""" | ||
# Python 3.6 Sheaf theoretic toolbox | ||
This library provides tools for manipulating sheaves of pseudometric spaces on partially ordered sets. The primarly class is a `Sheaf`, which subclasses `NetworkX.DiGraph`; the idea is that the `DiGraph` specifies the Hasse diagram for the partially ordered set. | ||
Most of the details you need to get started are in the `pysheaf` module. Start there first. For specific sheaves that havew linear maps as restrictions, you might consider looking at `dataTools`. Finally, there are several detailed examples to explore. | ||
## General usage instructions | ||
1. First (usually on paper!) lay out the cell complex that will serve as the base for your sheaf. *Give each cell a unique label.* | ||
2. Determine all of the stalks over each cell, and the restriction maps. Restriction maps can be a mixture of `numpy` matrices or arbitrary single-input Python function objects. | ||
3. Construct a `Sheaf` instance and add each of your cells as `Cell` instances with the `Sheaf.AddCell` method. Make sure to use your unique label for each `Cell`, because that is how PySheaf identifies them! Once you've done that, create each restriction as a `Coface` instance and add it to the sheaf using the `Sheaf.AddCoface` method. The `Sheaf.AddCoface` method will connect the listed `Cell`s based on their labels. `Cell`s and `Coface`s can be added later if you want, and they can be added in any order provided any `Coface` refers to `Cell`s that already exist. | ||
4. Install some data into the sheaf by way of an `Assignment` to some of the `Cell`s. | ||
5. Analyze the sheaf and its data: | ||
a. You can compute consistency radius with `Sheaf.ComputeConsistencyRadius()` | ||
b. You can improve the consistency radius by extending or altering the values of the assignment with `Sheaf.FuseAssignment()`. This will only alter Cells whose `Cell.mOptimizationCell` attribute is `True`. You can also change the optimization algorithm if you want. | ||
c. You can find all star open sets whose local consistency is less than a desired bound using `Sheaf.CellIndexesLessThanConsistencyThreshold()`. | ||
""" |
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