How to use the getdist.gaussian_mixtures.Mixture2D function in getdist
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cmbant / getdist / getdist_tests / test_distributions.py View on Github 
def __init__(self):
self.gauss = Gaussian2D([0, 0], (0.7, 1, 0.3), label='Gaussian')
self.bending = Mixture2D([[0, 0], [2, 1.8]], [(np.sqrt(0.5), 1, 0.9), (1, 1, 0.8)], [0.6, 0.4], xmin=-1, label='bending')
self.hammer = Mixture2D([[0, 0], [1, 1.8]], [(np.sqrt(0.5), 1, 0.9), (0.3, 1, -0.7)], [0.5, 0.5], label='hammer')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.skew = Mixture2D([[0, 0], [0, 1.2]], [cov, cov / 4], [0.5, 0.5], label='skew')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.broadtail = Mixture2D([[0, 0], [0, 0.2]], [cov, cov * 8], [0.9, 0.1], label='broad tail')
self.tensorlike = Mixture2D([[0, 0.03], [0, 0.03]], [(0.03, 0.03, 0.1), (0.03, 0.06, 0.1)], [0.85, 0.15], ymin=0, label='tensor like')
self.rotating = Mixture2D([[0, 0], [0, 0.2]], [(1, 1, 0.5), (2, 2, -0.5)], [0.6, 0.4], label='rotating')
self.tight = Mixture2D([[0, 0], [2.5, 3.5]], [(1, 1, 0.99), (1, 1.5, 0.98)], [0.6, 0.4], label='tight')
self.cut_correlated = Gaussian2D([0, 0], (0.7, 1, 0.95), ymin=0.3, xmax=1.2, label='cut correlated')
self.shape_set = [self.gauss, self.bending, self.hammer, self.skew, self.broadtail, self.rotating, self.tight,def __init__(self):
self.gauss = Gaussian2D([0, 0], (0.7, 1, 0.3), label='Gaussian')
self.bending = Mixture2D([[0, 0], [2, 1.8]], [(np.sqrt(0.5), 1, 0.9), (1, 1, 0.8)], [0.6, 0.4], xmin=-1, label='bending')
self.hammer = Mixture2D([[0, 0], [1, 1.8]], [(np.sqrt(0.5), 1, 0.9), (0.3, 1, -0.7)], [0.5, 0.5], label='hammer')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.skew = Mixture2D([[0, 0], [0, 1.2]], [cov, cov / 4], [0.5, 0.5], label='skew')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.broadtail = Mixture2D([[0, 0], [0, 0.2]], [cov, cov * 8], [0.9, 0.1], label='broad tail')
self.tensorlike = Mixture2D([[0, 0.03], [0, 0.03]], [(0.03, 0.03, 0.1), (0.03, 0.06, 0.1)], [0.85, 0.15], ymin=0, label='tensor like')
self.rotating = Mixture2D([[0, 0], [0, 0.2]], [(1, 1, 0.5), (2, 2, -0.5)], [0.6, 0.4], label='rotating')
self.tight = Mixture2D([[0, 0], [2.5, 3.5]], [(1, 1, 0.99), (1, 1.5, 0.98)], [0.6, 0.4], label='tight')
self.cut_correlated = Gaussian2D([0, 0], (0.7, 1, 0.95), ymin=0.3, xmax=1.2, label='cut correlated')
self.shape_set = [self.gauss, self.bending, self.hammer, self.skew, self.broadtail, self.rotating, self.tight,
self.cut_correlated, self.tensorlike]
self.cut_gaussians = self.cutGaussians((0.7, 1, 0.3))
# these examples are from Wand and Jones 93
self.bimodal = []
self.bimodal.append(Mixture2D([[-1, 0], [1, 0]], [(2. / 3, 2. / 3, 0), (2. / 3, 2. / 3, 0)], label='bimodal WJ1'))
self.bimodal.append(Mixture2D([[-3. / 2, 0], [3. / 2, 0]], [(1. / 4, 1, 0), (1. / 4, 1, 0)], label='bimodal WJ2'))# these examples are from Wand and Jones 93
self.bimodal = []
self.bimodal.append(
Mixture2D([[-1, 0], [1, 0]], [(2. / 3, 2. / 3, 0), (2. / 3, 2. / 3, 0)], label='bimodal WJ1'))
self.bimodal.append(
Mixture2D([[-3. / 2, 0], [3. / 2, 0]], [(1. / 4, 1, 0), (1. / 4, 1, 0)], label='bimodal WJ2'))
self.bimodal.append(
Mixture2D([[-1, 1], [1, -1]], [(2. / 3, 2. / 3, 3. / 5), (2. / 3, 2. / 3, 3. / 5)], label='bimodal WJ3'))
self.bimodal.append(
Mixture2D([[1, -1], [-1, 1]], [(2. / 3, 2. / 3, 7. / 10), (2. / 3, 2. / 3, 0)], label='bimodal WJ4'))
self.trimodal = []
self.trimodal.append(Mixture2D([[-6. / 5, 6. / 5], [6. / 5, -6. / 5], [0, 0]],
[(3. / 5, 3. / 5, 3. / 10), (3. / 5, 3. / 5, -3. / 5), (0.25, 0.25, 0.2)],
weights=[9, 9, 2], label='trimodal WJ1'))
self.trimodal.append(Mixture2D([[-6. / 5, 0], [6. / 5, 0], [0, 0]],
[(3. / 5, 3. / 5, 0.7), (3. / 5, 3. / 5, 0.7), (0.25, 0.25, -0.7)],
label='trimodal WJ2'))
self.trimodal.append(Mixture2D([[-1, 0], [1, 2 * np.sqrt(3) / 3], [1, -2 * np.sqrt(3) / 3]],
[(0.6, 0.7, 0.6), (0.6, 0.7, 0), (0.4, 0.7, 0)], weights=[3, 3, 1],
label='trimodal WJ3'))
self.quadrimodal = []
self.quadrimodal.append(Mixture2D([[-1, 1], [-1, -1], [1, -1], [1, 1]],
[(2. / 3, 2. / 3, 2. / 5), (2. / 3, 2. / 3, 3. / 5), (2. / 3, 2. / 3, -0.7),
(2. / 3, 2. / 3, -0.5)],
weights=[1, 3, 1, 3], label='quadrimodal'))
self.all = self.shape_set + self.bimodal + self.trimodal + self.quadrimodal + self.cut_gaussiansself.bending = Mixture2D([[0, 0], [2, 1.8]], [(np.sqrt(0.5), 1, 0.9), (1, 1, 0.8)], [0.6, 0.4], xmin=-1, label='bending')
self.hammer = Mixture2D([[0, 0], [1, 1.8]], [(np.sqrt(0.5), 1, 0.9), (0.3, 1, -0.7)], [0.5, 0.5], label='hammer')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.skew = Mixture2D([[0, 0], [0, 1.2]], [cov, cov / 4], [0.5, 0.5], label='skew')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.broadtail = Mixture2D([[0, 0], [0, 0.2]], [cov, cov * 8], [0.9, 0.1], label='broad tail')
self.tensorlike = Mixture2D([[0, 0.03], [0, 0.03]], [(0.03, 0.03, 0.1), (0.03, 0.06, 0.1)], [0.85, 0.15], ymin=0, label='tensor like')
self.rotating = Mixture2D([[0, 0], [0, 0.2]], [(1, 1, 0.5), (2, 2, -0.5)], [0.6, 0.4], label='rotating')
self.tight = Mixture2D([[0, 0], [2.5, 3.5]], [(1, 1, 0.99), (1, 1.5, 0.98)], [0.6, 0.4], label='tight')
self.cut_correlated = Gaussian2D([0, 0], (0.7, 1, 0.95), ymin=0.3, xmax=1.2, label='cut correlated')
self.shape_set = [self.gauss, self.bending, self.hammer, self.skew, self.broadtail, self.rotating, self.tight,
self.cut_correlated, self.tensorlike]
self.cut_gaussians = self.cutGaussians((0.7, 1, 0.3))
# these examples are from Wand and Jones 93
self.bimodal = []
self.bimodal.append(Mixture2D([[-1, 0], [1, 0]], [(2. / 3, 2. / 3, 0), (2. / 3, 2. / 3, 0)], label='bimodal WJ1'))
self.bimodal.append(Mixture2D([[-3. / 2, 0], [3. / 2, 0]], [(1. / 4, 1, 0), (1. / 4, 1, 0)], label='bimodal WJ2'))
self.bimodal.append(Mixture2D([[-1, 1], [1, -1]], [(2. / 3, 2. / 3, 3. / 5), (2. / 3, 2. / 3, 3. / 5)], label='bimodal WJ3'))
self.bimodal.append(Mixture2D([[1, -1], [-1, 1]], [(2. / 3, 2. / 3, 7. / 10), (2. / 3, 2. / 3, 0)], label='bimodal WJ4'))
self.trimodal = []def __init__(self):
self.gauss = Gaussian2D([0, 0], (0.7, 1, 0.3), label='Gaussian')
self.bending = Mixture2D([[0, 0], [2, 1.8]], [(np.sqrt(0.5), 1, 0.9), (1, 1, 0.8)], [0.6, 0.4], xmin=-1, label='bending')
self.hammer = Mixture2D([[0, 0], [1, 1.8]], [(np.sqrt(0.5), 1, 0.9), (0.3, 1, -0.7)], [0.5, 0.5], label='hammer')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.skew = Mixture2D([[0, 0], [0, 1.2]], [cov, cov / 4], [0.5, 0.5], label='skew')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.broadtail = Mixture2D([[0, 0], [0, 0.2]], [cov, cov * 8], [0.9, 0.1], label='broad tail')
self.tensorlike = Mixture2D([[0, 0.03], [0, 0.03]], [(0.03, 0.03, 0.1), (0.03, 0.06, 0.1)], [0.85, 0.15], ymin=0, label='tensor like')
self.rotating = Mixture2D([[0, 0], [0, 0.2]], [(1, 1, 0.5), (2, 2, -0.5)], [0.6, 0.4], label='rotating')
self.tight = Mixture2D([[0, 0], [2.5, 3.5]], [(1, 1, 0.99), (1, 1.5, 0.98)], [0.6, 0.4], label='tight')
self.cut_correlated = Gaussian2D([0, 0], (0.7, 1, 0.95), ymin=0.3, xmax=1.2, label='cut correlated')
self.shape_set = [self.gauss, self.bending, self.hammer, self.skew, self.broadtail, self.rotating, self.tight,
self.cut_correlated, self.tensorlike]
self.cut_gaussians = self.cutGaussians((0.7, 1, 0.3))self.gauss = Gaussian2D([0, 0], (0.7, 1, 0.3), label='Gaussian')
self.bending = Mixture2D([[0, 0], [2, 1.8]], [(np.sqrt(0.5), 1, 0.9), (1, 1, 0.8)], [0.6, 0.4], xmin=-1, label='bending')
self.hammer = Mixture2D([[0, 0], [1, 1.8]], [(np.sqrt(0.5), 1, 0.9), (0.3, 1, -0.7)], [0.5, 0.5], label='hammer')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.skew = Mixture2D([[0, 0], [0, 1.2]], [cov, cov / 4], [0.5, 0.5], label='skew')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.broadtail = Mixture2D([[0, 0], [0, 0.2]], [cov, cov * 8], [0.9, 0.1], label='broad tail')
self.tensorlike = Mixture2D([[0, 0.03], [0, 0.03]], [(0.03, 0.03, 0.1), (0.03, 0.06, 0.1)], [0.85, 0.15], ymin=0, label='tensor like')
self.rotating = Mixture2D([[0, 0], [0, 0.2]], [(1, 1, 0.5), (2, 2, -0.5)], [0.6, 0.4], label='rotating')
self.tight = Mixture2D([[0, 0], [2.5, 3.5]], [(1, 1, 0.99), (1, 1.5, 0.98)], [0.6, 0.4], label='tight')
self.cut_correlated = Gaussian2D([0, 0], (0.7, 1, 0.95), ymin=0.3, xmax=1.2, label='cut correlated')
self.shape_set = [self.gauss, self.bending, self.hammer, self.skew, self.broadtail, self.rotating, self.tight,
self.cut_correlated, self.tensorlike]
self.cut_gaussians = self.cutGaussians((0.7, 1, 0.3))
# these examples are from Wand and Jones 93
self.bimodal = []
self.bimodal.append(Mixture2D([[-1, 0], [1, 0]], [(2. / 3, 2. / 3, 0), (2. / 3, 2. / 3, 0)], label='bimodal WJ1'))
self.bimodal.append(Mixture2D([[-3. / 2, 0], [3. / 2, 0]], [(1. / 4, 1, 0), (1. / 4, 1, 0)], label='bimodal WJ2'))
self.bimodal.append(Mixture2D([[-1, 1], [1, -1]], [(2. / 3, 2. / 3, 3. / 5), (2. / 3, 2. / 3, 3. / 5)], label='bimodal WJ3'))
self.bimodal.append(Mixture2D([[1, -1], [-1, 1]], [(2. / 3, 2. / 3, 7. / 10), (2. / 3, 2. / 3, 0)], label='bimodal WJ4'))def __init__(self):
self.gauss = Gaussian2D([0, 0], (0.7, 1, 0.3), label='Gaussian')
self.bending = Mixture2D([[0, 0], [2, 1.8]], [(np.sqrt(0.5), 1, 0.9), (1, 1, 0.8)], [0.6, 0.4], xmin=-1, label='bending')
self.hammer = Mixture2D([[0, 0], [1, 1.8]], [(np.sqrt(0.5), 1, 0.9), (0.3, 1, -0.7)], [0.5, 0.5], label='hammer')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.skew = Mixture2D([[0, 0], [0, 1.2]], [cov, cov / 4], [0.5, 0.5], label='skew')
cov = make_2D_Cov(np.sqrt(0.5), 1, 0.1)
self.broadtail = Mixture2D([[0, 0], [0, 0.2]], [cov, cov * 8], [0.9, 0.1], label='broad tail')
self.tensorlike = Mixture2D([[0, 0.03], [0, 0.03]], [(0.03, 0.03, 0.1), (0.03, 0.06, 0.1)], [0.85, 0.15], ymin=0, label='tensor like')
self.rotating = Mixture2D([[0, 0], [0, 0.2]], [(1, 1, 0.5), (2, 2, -0.5)], [0.6, 0.4], label='rotating')
self.tight = Mixture2D([[0, 0], [2.5, 3.5]], [(1, 1, 0.99), (1, 1.5, 0.98)], [0.6, 0.4], label='tight')
self.cut_correlated = Gaussian2D([0, 0], (0.7, 1, 0.95), ymin=0.3, xmax=1.2, label='cut correlated')def pdf(self, x, y=None):
"""
Calculate the PDF. Note this assumes x and y are within the boundaries (does not return zero outside)
Result is also only normalized if no boundaries
:param x: value of x to evaluate pdf
:param y: optional value of y to evaluate pdf. If not specified, returns 1D marginalized value for x.
:return: value of pdf at x or x,y
"""
if y is None:
return super(Mixture2D, self).pdf(x)
tot = None
for i, (mean, icov, weight, norm) in enumerate(zip(self.means, self.invcovs, self.weights, self.norms)):
dx = x - mean[0]
dy = y - mean[1]
res = np.exp(-(dx ** 2 * icov[0, 0] + 2 * dx * dy * icov[0, 1] + dy ** 2 * icov[1, 1]) / 2) / norm
if not i:
tot = res * weight
else:
tot += res * weight
return totnames = [self.names[i] for i in indices]
else:
names = None
if self.lims is not None:
lims = [self.lims[i] for i in indices]
else:
lims = None
if label is None:
label = self.label
covs = [cov[np.ix_(indices, indices)] for cov in self.covs]
means = [mean[indices] for mean in self.means]
if len(indices) == 2:
tp = Mixture2D
else:
tp = MixtureND
mixture = tp(means, covs, self.weights, lims=lims,
names=names, label=label)
mixture.paramNames.setLabelsAndDerivedFromParamNames(self.paramNames)
return mixture"""
if y is None:
return super(Mixture2D, self).pdf(x)
tot = None
for i, (mean, icov, weight, norm) in enumerate(zip(self.means, self.invcovs, self.weights, self.norms)):
dx = x - mean[0]
dy = y - mean[1]
res = np.exp(-(dx ** 2 * icov[0, 0] + 2 * dx * dy * icov[0, 1] + dy ** 2 * icov[1, 1]) / 2) / norm
if not i:
tot = res * weight
else:
tot += res * weight
return tot
class Gaussian2D(Mixture2D):
"""
Simple special case of a 2D Gaussian mixture model with only one Gaussian component
"""
def __init__(self, mean, cov, **kwargs):
"""
:param mean: 2 element array with mean
:param cov: 2x2 array of covariance, or list of [sigma_x, sigma_y, correlation] values
:param kwargs: arguments passed to :class:`Mixture2D`
"""
super(Gaussian2D, self).__init__([mean], [cov], **kwargs)
class GaussianND(MixtureND):
"""
Simple special case of a Gaussian mixture model with only one Gaussian componentgetdist
GetDist Monte Carlo sample analysis, plotting and GUI
Package Health Score
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