petls.PersistentSheafLaplacian.spectra

PersistentSheafLaplacian.spectra(dim=None, a=None, b=None, request_list=None, allpairs=False)

Compute the eigenvalues of L_{dim}^{a,b} or for every tuple (dim, a, b) in request_list.

Parameters:

dimint, optional

Dimension.

afloat, optional

Start filtration value.

bfloat, optional

End filtration value

request_listList[List[int, float, float]], optional

List of (dim, a, b) to compute the spectra of

Returns:

List[float]

If passed dim, a, and b, returns eigenvalues of L_{dim}^{a,b}

List[Tuple[int, float, float, List[float]]]

If passed request_list, returns a tuple (dim, a, b, eigenvalues) for each request in request_list If passed no arguments, returns as if request_list is of all combinations (dim, a, b) where b is the next filtration after a, and (dim, a, a) when a is the largest filtration value

Examples

>>> d1 = np.array([[-1,0,-1],
        [1,-1,0],
        [0,1,1]])
>>> d2 = np.array([[1],[1],[-1]]) 
>>> boundaries = [d1,d2]
>>> filtrations = [[0,1,2],[3,4,5],[5]]
>>> pl = Complex(boundaries, filtrations)
>>> pl.spectra(0, 1.2, 4.5)
[0.0,  1.9999998807907104]
>>> pl.spectra(request_list = [[0, 1.2, 4.5]])
[(0, 1.2, 4.5, [0.0, 1.9999998807907104])]
>>> pl.spectra()
[(0, 0.0, 3.0, [0.0]), (1, 0.0, 3.0, []), (2, 0.0, 3.0, []), (0, 3.0, 4.0, [0.0, 0.9999998807907104, 3.0]), (1, 3.0, 4.0, [2.0]), (2, 3.0, 4.0, []), (0, 4.0, 5.0, [0.0, 2.999999761581421, 3.0]), (1, 4.0, 5.0, [0.9999999403953552, 2.999999761581421]), (2, 4.0, 5.0, []), (0, 5.0, 5.0, [0.0, 2.999999761581421, 3.0]), (1, 5.0, 5.0, [3.0, 3.0, 3.0]), (2, 5.0, 5.0, [3.0])]