def plot_ICBounds(x_test, y_test, nTest, sigma) :
vUp = [[x_test[i][0], y_test[i][0] + sigma ] for i in range(nTest)]
vLow = [[x_test[i][0], y_test[i][0] - sigma ] for i in range(nTest)]
polyData = [[vLow[i], vLow[i+1], vUp[i+1], vUp[i]] for i in range(nTest-1)]
polygonList = [ot.Polygon(polyData[i], "grey", "grey") for i in range(nTest-1)]
boundsPoly = ot.PolygonArray(polygonList)
return boundsPoly
def CreatePolygonArray(polyData, color):
numberOfPolygons = len(polyData)
polygonList = [
ot.Polygon(polyData[i], color, color)
for i in range(numberOfPolygons)
]
polygonArray = ot.PolygonArray(polygonList)
return polygonArray
def drawInTheBounds(vLow,vUp,n_test):
"""
Draw the area within the bounds.
"""
palette = ot.Drawable.BuildDefaultPalette(2)
myPaletteColor = palette[0]
polyData = [[vLow[i], vLow[i+1], vUp[i+1], vUp[i]] for i in range(n_test-1)]
polygonList = [ot.Polygon(polyData[i], myPaletteColor, myPaletteColor) for i in range(n_test-1)]
boundsPoly = ot.PolygonArray(polygonList)
return boundsPoly
def fill_between(lower, upper, legend, color):
"""Draw a shaded area between two curves."""
disc = len(lower)
poly_data = [[lower[i], lower[i + 1], upper[i + 1], upper[i]]
for i in range(disc - 1)]
polygon = [
ot.Polygon(poly_data[i], color, color) for i in range(disc - 1)
]
bounds_poly = ot.PolygonArray(polygon)
bounds_poly.setLegend(legend)
return bounds_poly
def plot_kriging_bounds(vLow,vUp,n_test):
'''
From two lists containing the lower and upper bounds of the region,
create a PolygonArray.
'''
palette = ot.Drawable.BuildDefaultPalette(2)
myPaletteColor = palette[1]
polyData = [[vLow[i], vLow[i+1], vUp[i+1], vUp[i]] for i in range(n_test-1)]
polygonList = [ot.Polygon(polyData[i], myPaletteColor, myPaletteColor) for i in range(n_test-1)]
boundsPoly = ot.PolygonArray(polygonList)
boundsPoly.setLegend("95% bounds")
return boundsPoly
def fill_between_(lower, upper, legend):
"""Draw a shaded area between two curves."""
disc = len(lower)
palette = ot.Drawable.BuildDefaultPalette(2)[1]
poly_data = [[lower[i], lower[i + 1], upper[i + 1], upper[i]]
for i in range(disc - 1)]
polygon = [
ot.Polygon(poly_data[i], palette, palette)
for i in range(disc - 1)
]
bounds_poly = ot.PolygonArray(polygon)
bounds_poly.setLegend(legend)
return bounds_poly
def plot_kriging_bounds(dataLower, dataUpper, n_test, color=[120, 1.0, 1.0]):
"""
From two lists containing the lower and upper bounds of the region,
create a PolygonArray.
Default color is green given by HSV values in color list.
"""
vLow = [[x_test[i, 0], dataLower[i, 0]] for i in range(n_test)]
vUp = [[x_test[i, 0], dataUpper[i, 0]] for i in range(n_test)]
myHSVColor = ot.Polygon.ConvertFromHSV(color[0], color[1], color[2])
polyData = [[vLow[i], vLow[i+1], vUp[i+1], vUp[i]]
for i in range(n_test-1)]
polygonList = [ot.Polygon(polyData[i], myHSVColor, myHSVColor)
for i in range(n_test-1)]
boundsPoly = ot.PolygonArray(polygonList)
return boundsPoly
Y1 = ot.CompositeRandomVector(f1, X)
Y2 = ot.CompositeRandomVector(f2, X)
Y3 = ot.CompositeRandomVector(f3, X)
# %%
# We define three basic events :math:`E_1=\{(x_0,x_1)~:~x_0 < 0 \}`, :math:`E_2=\{(x_0,x_1)~:~x_1 > 0 \}` and :math:`E_3=\{(x_0,x_1)~:~x_0+x_1>0 \}`.
e1 = ot.ThresholdEvent(Y1, ot.Less(), 0.0)
e2 = ot.ThresholdEvent(Y2, ot.Greater(), 0.0)
e3 = ot.ThresholdEvent(Y3, ot.Greater(), 0.0)
# %%
# The restriction of the domain :math:`E_1` to :math:`[-4,4] \times [-4, 4]` is the grey area.
myGraph = ot.Graph(r'Representation of the event $E_1$', r'$x_1$', r'$x_2$',
True, '')
data = [[-4, -4], [0, -4], [0, 4], [-4, 4]]
myPolygon = ot.Polygon(data)
myPolygon.setColor('grey')
myPolygon.setEdgeColor('black')
myGraph.add(myPolygon)
view = otv.View(myGraph)
axes = view.getAxes()
_ = axes[0].set_xlim(-4.0, 4.0)
_ = axes[0].set_ylim(-4.0, 4.0)
# %%
# The restriction of the domain :math:`E_2` to :math:`[-4,4] \times [-4, 4]` is the grey area.
myGraph = ot.Graph(r'Representation of the event $E_2$', r'$x_1$', r'$x_2$',
True, '')
data = [[-4, 0], [4, 0], [4, 4], [-4, 4]]
myPolygon = ot.Polygon(data)
myPolygon.setColor('grey')
# Polygon
size = 50
cursor = [0.] * 2
data1 = ot.Sample(size, 2) # polygon y = 2x for x in [-25]
data2 = ot.Sample(size, 2) # polygon y = x*x for x in [-11]
for i in range(size):
tmp = 7. * i / size + 2
cursor[0] = tmp
cursor[1] = 2 * tmp
data1[i] = cursor
tmp = 9. * i / size + 1
cursor[0] = tmp
cursor[1] = tmp * tmp
data2[i] = cursor
graph = ot.Graph('Some polygons', 'x1', 'x2', True, 'topright', 1.0)
myPolygon1 = ot.Polygon(data1)
myPolygon1.setColor('blue')
myPolygon1.setLegend('polygon 1')
graph.add(myPolygon1)
myPolygon2 = ot.Polygon(data2)
myPolygon2.setColor('red')
myPolygon2.setLegend('polygon 2')
graph.add(myPolygon2)
# graph.draw('curve11.png')
view = View(graph)
# view.save('curve11.png')
view.ShowAll(block=True)
# PolygonArray
generator = ot.Normal(2)
size = 5
for i in range(size):
tmp = 7. * i / size + 2
cursor[0] = tmp
cursor[1] = 2 * tmp
data1[i] = cursor
tmp = 9. * i / size + 1
cursor[0] = tmp
cursor[1] = tmp * tmp
data2[i] = cursor
# Create an empty graph
graph = ot.Graph("Polygons example", "x1", "x2", True, "", 1.0)
# Create the first polygon
myPolygon1 = ot.Polygon(data1)
myPolygon1.setColor("blue")
# Then, draw it
graph.add(myPolygon1)
# Create the second polygon
myPolygon2 = ot.Polygon(data2)
myPolygon2.setColor("red")
# Add it to the graph and draw everything
graph.add(myPolygon2)
graph.setLogScale(1)
fig = plt.figure(figsize=(5, 5))
View(graph, figure=fig)
graph_meta = meta.draw(xMin, xMax)
data = graph_meta.getDrawable(0).getData()
xGrid = data.getMarginal(0)
covGrid = result.getConditionalCovariance(xGrid)
a = ot.DistFunc.qNormal(0.975)
c = ot.Cloud([data[2]])
c.setPointStyle("square")
c.setColor("green")
c.setLegend("95% confidence bound")
dataLower = [[data[i, 0], data[i, 1] - a * covGrid[i, i]]
for i in range(len(data))]
dataUpper = [[data[i, 0], data[i, 1] + a * covGrid[i, i]]
for i in range(len(data))]
bounds = ot.PolygonArray([
ot.Polygon(
[dataLower[i], dataLower[i + 1], dataUpper[i + 1], dataUpper[i]],
"green", "green") for i in range(len(dataLower) - 1)
])
graph = ot.Graph()
graph.setLegendPosition("bottomright")
graph.setAxes(True)
graph.setGrid(True)
graph.add(c)
graph.add(bounds)
d = f.draw(xMin, xMax).getDrawable(0)
d.setLineStyle("dashed")
d.setColor("magenta")
d.setLineWidth(2)
graph.add(d)
graph.add(graph_meta)
import openturns as ot
from openturns.viewer import View
ot.RandomGenerator.SetSeed(0)
generator = ot.Normal(2)
size = 5
array = []
palette = ot.Drawable.BuildDefaultPalette(size)
for i in range(size):
vertices = generator.getSample(3)
array.append(ot.Polygon(vertices, palette[i], palette[size - i - 1]))
graph = ot.Graph('PolygonArray example', 'x1', 'x2', True, '', 1.0)
graph.add(ot.PolygonArray(array))
View(graph, figure_kwargs={'figsize': (4, 4)})
