def _uniform_weights(samples): """generate a nested list of N x 1D weights from a nested list of N x 1D discrete measure positions, where the weights have norm 1.0 and are uniform. >>> c.pos [[1, 2, 3], [4, 5], [6]] >>> _uniform_weights(c.pos) [[0.333333333333333, 0.333333333333333, 0.333333333333333], [0.5, 0.5], [1.0]] """ from mystic.math.measures import normalize return [normalize([1.]*len(xi)) for xi in samples]
def _uniform_weights(samples): """generate a nested list of N x 1D weights from a nested list of N x 1D discrete measure positions, where the weights have norm 1.0 and are uniform. >>> c.pos [[1, 2, 3], [4, 5], [6]] >>> _uniform_weights(c.pos) [[0.333333333333333, 0.333333333333333, 0.333333333333333], [0.5, 0.5], [1.0]] """ from mystic.math.measures import normalize return [normalize([1.]*len(xi), 1.0) for xi in samples]
def norm(x):
return normalize(x, mass=1.0)
def constraint(x): # impose exactly
return normalize(x, 1.0)
# # Author: Mike McKerns (mmckerns @caltech and @uqfoundation) # Copyright (c) 1997-2016 California Institute of Technology. # Copyright (c) 2016-2021 The Uncertainty Quantification Foundation. # License: 3-clause BSD. The full license text is available at: # - https://github.com/uqfoundation/mystic/blob/master/LICENSE import numpy as np import mystic.math.measures as mm x = np.arange(1., 5) y = np.array([-1., -2, 0, 3]) z = np.array([-1., -2, 0, 7]) # L1 and L2 norms q = mm.normalize(x, mass='l1', zsum=True) p = [0.10000000000000001, 0.20000000000000001, 0.29999999999999999, 0.40000000000000002] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(x, mass='l2', zsum=True) p = [0.18257418583505536, 0.36514837167011072, 0.54772255750516607, 0.73029674334022143] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(y, mass='l2', zsum=True) p = [-0.2672612419124244, -0.53452248382484879, 0.0, 0.80178372573727319] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(y, mass='l1', zsum=True) p = [-0.16666666666666666, -0.33333333333333331, 0.0, 0.5] assert np.sum(np.array(q) - p) <= 1e-15
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation) # Copyright (c) 1997-2016 California Institute of Technology. # Copyright (c) 2016-2017 The Uncertainty Quantification Foundation. # License: 3-clause BSD. The full license text is available at: # - http://trac.mystic.cacr.caltech.edu/project/mystic/browser/mystic/LICENSE import numpy as np import mystic.math.measures as mm x = np.arange(1.0, 5) y = np.array([-1.0, -2, 0, 3]) z = np.array([-1.0, -2, 0, 7]) # L1 and L2 norms q = mm.normalize(x, mass="l1", zsum=True) p = [0.10000000000000001, 0.20000000000000001, 0.29999999999999999, 0.40000000000000002] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(x, mass="l2", zsum=True) p = [0.18257418583505536, 0.36514837167011072, 0.54772255750516607, 0.73029674334022143] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(y, mass="l2", zsum=True) p = [-0.2672612419124244, -0.53452248382484879, 0.0, 0.80178372573727319] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(y, mass="l1", zsum=True) p = [-0.16666666666666666, -0.33333333333333331, 0.0, 0.5] assert np.sum(np.array(q) - p) <= 1e-15
def constraint(x): # impose exactly
return normalize(x, 1.0)
# # Author: Mike McKerns (mmckerns @caltech and @uqfoundation) # Copyright (c) 1997-2016 California Institute of Technology. # Copyright (c) 2016-2019 The Uncertainty Quantification Foundation. # License: 3-clause BSD. The full license text is available at: # - https://github.com/uqfoundation/mystic/blob/master/LICENSE import numpy as np import mystic.math.measures as mm x = np.arange(1., 5) y = np.array([-1., -2, 0, 3]) z = np.array([-1., -2, 0, 7]) # L1 and L2 norms q = mm.normalize(x, mass='l1', zsum=True) p = [0.10000000000000001, 0.20000000000000001, 0.29999999999999999, 0.40000000000000002] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(x, mass='l2', zsum=True) p = [0.18257418583505536, 0.36514837167011072, 0.54772255750516607, 0.73029674334022143] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(y, mass='l2', zsum=True) p = [-0.2672612419124244, -0.53452248382484879, 0.0, 0.80178372573727319] assert np.sum(np.array(q) - p) <= 1e-15 q = mm.normalize(y, mass='l1', zsum=True) p = [-0.16666666666666666, -0.33333333333333331, 0.0, 0.5] assert np.sum(np.array(q) - p) <= 1e-15
def norm(x):
return normalize(x, mass=1.0)