def _inliers_outliers(self, sample=None, inliers=True):
"""Inliers or outliers cloud drawing.
:param sample: Sample of size (n_samples, n_dims).
:type sample: :class:`openturns.Sample`
:param bool inliers: Whether to draw inliers or outliers.
:return: OpenTURNS Cloud or Pair object if :attr:`dim` > 2.
:rtype: :class:`openturns.Cloud` or :class:`openturns.Pairs`
"""
if inliers:
idx = self.computeOutlierIndices(False)
legend = "Inliers at alpha=%.4f" % (self.outlierAlpha)
marker_color = 'blue'
else:
idx = self.computeOutlierIndices()
legend = "Outliers at alpha=%.4f" % (self.outlierAlpha)
marker_color = 'red'
if sample is None:
sample = np.array(self.sample)
else:
sample = np.asarray(sample)
sample = sample[idx, :]
if sample.size == 0:
return
if sample.shape[1] == 2:
cloud = ot.Cloud(sample, marker_color, self.data_marker, legend)
else:
cloud = ot.Pairs(sample, '', self.sample.getDescription(),
marker_color, self.data_marker)
return cloud
def pairs(data, filename):
print(" Draw pairs")
print(" Distribution")
g = ot.Graph()
pairs_data = ot.Pairs(data)
pairs_data.setPointStyle('dot')
g.add(pairs_data)
view = otv.View(g, (800, 800), square_axes=True)
view.save(filename)
print("Saving figure in {}".format(filename))
view.close()
print(" Copula")
g = ot.Graph()
pairs_data = ot.Pairs((data.rank() + 0.5) / data.getSize())
pairs_data.setPointStyle('dot')
g.add(pairs_data)
view = otv.View(g, (800, 800), square_axes=True)
view.save(filename)
print("Saving figure in {}".format(filename))
view.close()
def drawDimensionReduction(self):
"""Pairdraw of the principal components.
:return: OpenTURNS Graph object.
:rtype: :class:`openturns.Graph`
"""
graph = ot.Graph('Reduced Space', '', '', True, 'topright')
cloud = ot.Pairs(self.principalComponents)
cloud.setLabels(self.principalComponents.getDescription())
graph.add(cloud)
return graph
def pairs(data, filename):
''' Allows to plot the data for each pair of component random variable'''
print(" Draw pairs")
print(" Distribution")
g = ot.Graph()
pairs_data = ot.Pairs(data)
pairs_data.setPointStyle('dot')
g.add(pairs_data)
view = otv.View(g, (800, 800), square_axes=True)
view.save(filename)
print("Saving figure in {}".format(filename))
view.close()
print(" Copula")
g = ot.Graph()
pairs_data = ot.Pairs((data.rank() + 0.5) / data.getSize())
pairs_data.setPointStyle('dot')
g.add(pairs_data)
view = otv.View(g, (800, 800), square_axes=True)
view.save(
filename.parent.joinpath(filename.stem + '_copula' + filename.suffix))
print("Saving figure in {}".format(
filename.parent.joinpath(filename.stem + '_copula' + filename.suffix)))
view.close()
import openturns as ot
from openturns.viewer import View
# Factorial
d = ot.Factorial([1.5, 2.5, 3.5], [1, 2, 3])
s = d.generate()
s.setDescription(["X1", "X2", "X3"])
g = ot.Graph()
g.setTitle("Factorial experiment")
g.setGridColor("black")
p = ot.Pairs(s)
g.add(p)
View(g)
# Create a Funky distribution
corr = ot.CorrelationMatrix(3)
corr[0, 1] = 0.2
corr[1, 2] = -0.3
copula = ot.NormalCopula(corr)
x1 = ot.Normal(-1., 1)
x2 = ot.Normal(2, 1)
x3 = ot.Normal(-2, 1)
x_funk = ot.ComposedDistribution([x1, x2, x3], copula)
# Create a Punk distribution
x1 = ot.Normal(1., 1)
x2 = ot.Normal(-2, 1)
x3 = ot.Normal(3, 1)
x_punk = ot.ComposedDistribution([x1, x2, x3], copula)
# Merge the distributions
distribution = ot.Mixture([x_funk, x_punk], [0.5, 1.])
# Sample from the mixture
n = 500
sample = distribution.getSample(n)
myGraph = ot.Graph('Sample n=%d' % (n), ' ', ' ', True, '')
myPairs = ot.Pairs(sample, 'Pairs', sample.getDescription(), 'blue', 'bullet')
myGraph.add(myPairs)
View(myGraph)
sample.exportToCSVFile("gauss-mixture-3D.csv")
# view.save('curve8.png')
view.show()
# Pairs
dim = 5
meanPoint = ot.NumericalPoint(dim, 0.0)
sigma = ot.NumericalPoint(dim, 1.0)
R = ot.CorrelationMatrix(dim)
for i in range(dim):
meanPoint[i] = (i + 1) * dim
distribution = ot.Normal(meanPoint, sigma, R)
size = 1000
sample = distribution.getSample(size)
graph = ot.Graph('Pairs', ' ', ' ', True, 'topright')
labels = list(['x' + str(i) for i in range(dim)])
myPairs = ot.Pairs(sample, 'Pairs example', labels, 'green', 'bullet')
graph.add(myPairs)
# graph.draw('curve9.png')
view = View(graph)
# view.save('curve9.png')
view.show(block=False)
# Convergence graph curve
aCollection = []
aCollection.append(ot.LogNormal(300., 30., 0., ot.LogNormal.MUSIGMA))
aCollection.append(ot.Normal(75e3, 5e3))
myDistribution = ot.ComposedDistribution(aCollection)
vect = ot.RandomVector(myDistribution)
LimitState = ot.NumericalMathFunction(('R', 'F'), ('G', ),
('R-F/(_pi*100.0)', ))
G = ot.RandomVector(LimitState, vect)
# Create a Funky distribution
corr = ot.CorrelationMatrix(3)
corr[0, 1] = 0.2
corr[1, 2] = -0.3
copula = ot.NormalCopula(corr)
x1 = ot.Normal(-1.0, 1)
x2 = ot.Normal(2, 1)
x3 = ot.Normal(-2, 1)
x_funk = ot.ComposedDistribution([x1, x2, x3], copula)
# Create a Punk distribution
x1 = ot.Normal(1.0, 1)
x2 = ot.Normal(-2, 1)
x3 = ot.Normal(3, 1)
x_punk = ot.ComposedDistribution([x1, x2, x3], copula)
# Merge the distributions
distribution = ot.Mixture([x_funk, x_punk], [0.5, 1.0])
# Sample from the mixture
n = 500
sample = distribution.getSample(n)
myGraph = ot.Graph("Sample n=%d" % (n), " ", " ", True, "")
myPairs = ot.Pairs(sample, "Pairs", sample.getDescription(), "blue", "bullet")
myGraph.add(myPairs)
View(myGraph)
sample.exportToCSVFile("gauss-mixture-3D.csv")
sampleLearn.exportToCSVFile("samplelearn.csv", ",")
sample.exportToCSVFile("sample.csv", ",")
print("cbn sample=", sample)
logL = 0.0
pdfSample = cbn.computePDF(sample)
pdfSample.exportToCSVFile("pdfSample.csv", ",")
for i in range(size):
logL += m.log(pdfSample(i, 0))
logL /= size
print("log-l=", logL)
copula = ot.NormalCopulaFactory().buildAsNormalCopula(sampleLearn)
print("copula=", copula)
print("log-l=", copula.computeLogPDF(sample).computeMean()[0])
gr = ot.Graph()
pairs = ot.Pairs(sample)
pairs.setPointStyle("dot")
gr.add(pairs)
import openturns.viewer as otv
view = otv.View(gr, (800, 820), square_axes=True)
view.save("pairs.png")
view.close()
gr = ot.Graph()
pairs = ot.Pairs(copula.getSample(size))
pairs.setPointStyle("dot")
gr.add(pairs)
view = otv.View(gr, (800, 820), square_axes=True)
view.save("pairsCopula.png")
view.close()
def functional_scatter_matrix(x,
y,
operator,
color="blue",
q_levels=None,
values=None,
colors=None):
def _highlight_plot(view, x_array, y_array, operator, y_values, colors):
# Find corresponding indices
if colors is None or len(colors) != len(y_values):
from matplotlib.colors import cnames
lcolors = list(cnames.keys())
i = ot.RandomGenerator.IntegerGenerate(len(y_values), len(lcolors))
colors = [lcolors[_] for _ in i]
dim = len(x_array[0])
for k, val in enumerate(y_values):
I = np.array([operator(_[0], val) for _ in y_array])
indices = np.where(I)[0]
if len(indices) > 0:
for i in range(dim):
x = x_array[:, i]
z = y_array[:, 0]
index_i_i = 1 + i * dim + i
view._ax[index_i_i].plot(x[indices],
z[indices],
'.',
color=colors[k])
for j in range(i + 1, dim):
y = x_array[:, j]
index_i_j = 1 + i * dim + j
index_j_i = 1 + j * dim + i
view._ax[index_i_j].plot(x[indices],
y[indices],
'.',
color=colors[k])
view._ax[index_j_i].plot(y[indices],
x[indices],
'.',
color=colors[k])
return view
# Functional scatter matrix
X = ot.NumericalSample(x)
dim = X.getDimension()
X.setDescription([""] * dim)
Y = ot.NumericalSample(y)
assert (len(X) == len(Y))
assert Y.getDimension() == 1
if q_levels is not None and values is not None:
raise ValueError("Expected q_Levels or values or no one")
# Start the graphs
p = ot.Pairs(X)
p.setColor(color)
g = ot.Graph()
g.add(p)
view = View(g)
for i in range(dim):
index_i_i = 1 + i * dim + i
view._ax[index_i_i] = view._fig.add_subplot(dim, dim, index_i_i)
view._ax[index_i_i].plot(X[:, i], Y, '.', color=color)
# Now we get the view
if q_levels is not None:
# check q_level type
if type(q_levels) is float:
values = list(Y.computeQuantile(q_levels))
else:
values = [Y.computeQuantile(q)[0] for q in q_levels]
return _highlight_plot(view, np.array(X), np.array(Y), operator,
values, colors)
elif values is not None:
# check values
if type(values) is float:
values = [values]
else:
values = list(values)
return _highlight_plot(view, np.array(X), np.array(Y), operator,
values, colors)
else:
return view
isStationary = False
graph = cov.draw(0, 0, tmin, tmax, 128, isStationary, asCorrelation)
View(graph)
# Sample of coefficients Xi
sampleKsi = KLResult.project(outputSample)
# Chaque marginale est reconstruite par noyau gaussien
# False, 0, False: pas de binning (non aggergation des donnees dnas des segments), nbre de bins, pas d'effet de bord
nbmodes = sampleKsi.getDimension()
xi_marges = [ot.KernelSmoothing(ot.Normal(), False, 0, False).build(sampleKsi.getMarginal(i)) for i in range(nbmodes)]
# graphes des pdf marginales
for i in range(len(xi_marges)):
monHisto = ot.HistogramFactory().build(sampleKsi.getMarginal(i)).drawPDF()
monHisto.setColors(["blue"])
graph.add(monHisto)
graph = xi_marges[i].drawPDF()
graph.setTitle(r"Distribution of $\xi$" + str(i))
graph.setXTitle(r"$\xi$" + str(i))
graph.setYTitle("PDF")
graph.add(monHisto)
graph.setLegends(["KS","Histogram"])
View(graph)
# graphe des pairs dans l'espace des rangs
pairs = ot.Pairs(sampleKsi.rank())
pairs.setPointStyle("bullet")
View(pairs)
