from ctypes import *
from depth.multivariate.Depth_approximation import depth_approximation
import sys, os, glob
import platform
from depth.multivariate.import_CDLL import libApprox
[docs]def cexpchullstar(x, data,
solver = "neldermead",
NRandom = 1000,
option = 1,
n_refinements = 10,
sphcap_shrink = 0.5,
alpha_Dirichlet = 1.25,
cooling_factor = 0.95,
cap_size = 1,
start = "mean",
space = "sphere",
line_solver = "goldensection",
bound_gc = True):
return depth_approximation(x, data, "cexpchullstar", solver, NRandom, option, n_refinements,
sphcap_shrink, alpha_Dirichlet, cooling_factor, cap_size, start, space, line_solver, bound_gc)
cexpchullstar.__doc__="""
Description
Calculates approximately the continuous modified explected convex hull depth of points w.r.t. a multivariate data set.
Arguments
x
Matrix of objects (numerical vector as one object) whose depth is to be calculated;
each row contains a d-variate point. Should have the same dimension as data.
data
Matrix of data where each row contains a d-variate point, w.r.t. which the depth
is to be calculated.
solver
The type of solver used to approximate the depth.
{``'simplegrid'``, ``'refinedgrid'``, ``'simplerandom'``, ``'refinedrandom'``, ``'coordinatedescent'``, ``'randomsimplices'``, ``'neldermead'``, ``'simulatedannealing'``}
NRandom
The total number of iterations to compute the depth. Some solvers are converging
faster so they are run several time to achieve ``NRandom`` iterations.
option
| If ``option=1``, only approximated depths are returned.
| If ``option=2``, best directions to approximate depths are also returned.
| If ``option=3``, depths calculated at every iteration are also returned.
| If ``option=4``, random directions used to project depths are also returned with indices of converging for the solver selected.
n_refinements
Set the maximum of iteration for computing the depth of one point.
For ``solver='refinedrandom'`` or ``'refinedgrid'``.
sphcap_shrink
It's the shrinking of the spherical cap. For ``solver='refinedrandom'`` or ``'refinedgrid'``.
alpha_Dirichlet
It's the parameter of the Dirichlet distribution. For ``solver='randomsimplices'``.
cooling_factor
It's the cooling factor. For ``solver='simulatedannealing'``.
cap_size
It's the size of the spherical cap. For ``solver='simulatedannealing'`` or ``'neldermead'``.
start
{'mean', 'random'}.
For ``solver='simulatedannealing'`` or ``'neldermead'``, it's the method used to compute the first depth.
space
{``'sphere'``, ``'euclidean'``}.
For ``solver='coordinatedescent'`` or ``'neldermead'``, it's the type of spacecin which the solver is running.
line_solver
{``'uniform'``, ``'goldensection'``}.
For ``solver='coordinatedescent'``, it's the line searh strategy used by this solver.
bound_gc
For ``solver='neldermead'``, it's ``True`` if the search is limited to the closed hemisphere.
References
* Dyckerhoff, R. and Mosler, K. (2011). Weighted-mean trimming of multivariate data. *Journal of Multivariate Analysis*, 102, 405–421.
* Dyckerhoff, R., Mozharovskyi, P., and Nagy, S. (2021). Approximate computation of projection depths. *Computational Statistics and Data Analysis*, 157, 107166.
Examples
>>> import numpy as np
>>> from depth.multivariate import *
>>> np.random.seed(0)
>>> mat1=[[1, 0, 0, 0, 0],[0, 2, 0, 0, 0],[0, 0, 3, 0, 0],[0, 0, 0, 2, 0],[0, 0, 0, 0, 1]]
>>> mat2=[[1, 0, 0, 0, 0],[0, 1, 0, 0, 0],[0, 0, 1, 0, 0],[0, 0, 0, 1, 0],[0, 0, 0, 0, 1]]
>>> x = np.random.multivariate_normal([1,1,1,1,1], mat2, 10)
>>> data = np.random.multivariate_normal([0,0,0,0,0], mat1, 100)
>>> cexpchull(x, data, NRandom=1000)
[0.090223 0.19577999 0.15769263 0.20123535 0.10375507 0.14635662
0.20611053 0.17846703 0.19801984 0.23230606]
"""