Uncecomp 2025 general presentation

README.rst

@@ -112,10 +112,6 @@ OpenTURNS Presentations
   - `OTICSCREAM: A Python module (and a cooking recipe) for the identification of penalizing configurations in computer experiments <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/JU_OT_2025_ChabridonMure.pdf>`_
   - `Uncertainty Propagation and Sensitivity Analysis in Additive Manufacturing Simulation <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/JU_OT_2025_Braydi.pdf>`_
 
-- Uncecomp 2023
-
-  - `Slides <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/uncecomp_2023_slides_OpenTURNS.pdf>`_
-
 - CHORUS
 
   - `Low rank tensor approximation <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/lowranktensor.pdf>`_
@@ -148,6 +144,8 @@ OpenTURNS Presentations
 
 - `SIAM-UQ 2022 <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/siamuq-2022-slides-OpenTURNS.pdf>`_
 
+- `Uncecomp 2023 <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/uncecomp_2023_slides_OpenTURNS.pdf>`_
+
 - `Applibugs 2023 <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/applibugs-2023-slides_OpenTURNS_MetropolisHastings.pdf>`_
 
 - `SIAM-UQ 2024 <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/siamuq-2024-slides-OpenTURNS.pdf>`_
@@ -156,3 +154,5 @@ OpenTURNS Presentations
 
   - `OpenTURNS and Persalys Overview <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/bepu-2024-slides-OpenTURNS.pdf>`_
   - `Bayesian inference using MCMC in OpenTURNS <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/bepu-2024-slides_OpenTURNS_MetropolisHastings.pdf>`_
+
+- `Uncecomp 2025 <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/uncecomp_2025_slides_OpenTURNS.pdf>`_

uncecomp2025/macros.tex

@@ -0,0 +1,30 @@
+% Copyright (C) 2012 - EDF R&D - Michael Baudin
+
+
+% To highlight source code
+\usepackage{listings}
+\definecolor{darkgreen}{rgb}{0,0.5,0}
+\definecolor{violet}{rgb}{0.5,0,1}
+
+\usepackage{lmodern}% http://ctan.org/pkg/lm
+
+
+
+\usetheme{Montpellier}
+\setbeamertemplate{navigation symbols}{} % Remove navigation
+\useoutertheme{infolines}
+
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+
+
+%\usepackage[french]{babel}
+%\uselanguage{French}
+%\languagepath{French}
+
+\def\bx{{\bf x}}
+\def\RR{\mathbb{R}}
+
+\newcommand{\pyvar}[1]{\texttt{#1}}
+
+\def \ot {OpenTURNS}

uncecomp2025/scripts/illustration.py

@@ -0,0 +1,185 @@
+# -*- coding: utf-8 -*-
+"""
+Spyder Editor
+
+This is a temporary script file.
+"""
+# %%
+import openturns as ot
+import numpy as np
+
+def free_fall(X):
+    g  = 9.81
+    z0,v0,m,c = X
+    tau=m/c
+    vinf=-m*g/c
+    t = np.array(mesh.getVertices().asPoint())
+    z=z0+vinf*t+tau*(v0-vinf)*(1-np.exp(-t/tau))
+    z=np.maximum(z,0.0)
+    return ot.Field(mesh, z.reshape(-1, 1))
+
+tmin=0. 
+tmax=12.
+gridsize=100 
+mesh = ot.IntervalMesher([gridsize-1]).build(
+ot.Interval(tmin, tmax))
+
+alti = ot.PythonPointToFieldFunction(4, mesh,  1, free_fall)
+
+distZ0 = ot.Uniform(50.0, 200.0)
+distV0 = ot.Normal(55.0, 10.0)
+distM = ot.Normal(80.0, 8.0)
+distC = ot.Uniform(0.0, 30.0)
+distX = ot.ComposedDistribution([distZ0, distV0,
+ distM, distC])
+
+size = 100
+inputSample = distX.getSample(size)
+outputField = alti(inputSample)
+
+
+
+# %%
+# Draw
+from openturns.viewer import View
+
+graph = outputField.draw().getGraph(0,0)
+graph.setTitle("Free fall in viscous fluid")
+graph.setXTitle("t")
+graph.setYTitle("z")
+v= View(graph)
+v.save("trajectories.pdf")
+v.save("trajectories.png")
+
+# %%
+
+meanField = outputField.computeMean()
+meanFunction = ot.P1LagrangeEvaluation(
+	meanField)
+trend = ot.TrendTransform(meanFunction, mesh)
+invTrend = trend.getInverse()
+outputFieldCentered = invTrend(outputField)
+
+truncThreshold = 1.0e-5
+algo = ot.KarhunenLoeveSVDAlgorithm( 
+	outputFieldCentered, truncThreshold)
+algo.run()
+KLResult = algo.getResult()
+
+eigenValues = KLResult.getEigenvalues()
+
+# %%
+# Graphical
+import matplotlib.pyplot as plt
+
+plt.plot(eigenValues)
+plt.semilogy()
+plt.xlabel("k")
+plt.ylabel("$\lambda_k$")
+plt.title("Fredholm problem eigenvalues")
+plt.grid("both")
+
+# %%
+
+scaledModes = KLResult.getScaledModesAsProcessSample()
+graph = scaledModes.drawMarginal(0)
+graph.setTitle('Modes de KL, chute visqueuse')
+graph.setXTitle(r'$t$')
+graph.setYTitle(r'$\varphi_k$')
+leg = ot.Description([ 'Mode '+str(i +1) for
+	 i in range(eigenValues.getDimension()) ])
+graph.setLegends(leg)
+graph.setLegendPosition('topleft')
+view=View(graph)
+
+# %%
+
+projectionFunction = ot.KarhunenLoeveProjection(KLResult)
+sampleKsi = projectionFunction(outputFieldCentered)
+sampleKsi = sampleKsi[:,:2]
+cloud = ot.Cloud(sampleKsi)
+graph = ot.Graph("Trajectories in the reduced space", "$\\xi_1$", "$\\xi_2$", True)
+graph.add(cloud)
+v= View(graph)
+v.save("Reduced_Space.pdf")
+
+# %%
+ot.ResourceMap.SetAsString("Contour-DefaultColorMap", "viridis")
+ot.ResourceMap.SetAsBool("Contour-DefaultIsFilled", True)
+ot.ResourceMap.SetAsUnsignedInteger("Contour-DefaultLevelsNumber", 15)
+
+
+cov = KLResult.getCovarianceModel()
+
+# As a covariance function
+isStationary = False
+asCorrelation = False
+graph = cov.draw(0, 0, tmin, tmax, 128, isStationary, asCorrelation)
+graph.setTitle("Viscous free fall covariance")
+v = View(graph)#, contour_kw={"levels": 50})
+v.save("Covariance.pdf")
+
+# %%
+
+# As a correlation function
+asCorrelation = True
+graph = cov.draw(0, 0, tmin, tmax, 128, isStationary, asCorrelation)
+graph.setTitle("Viscous free fall correlation")
+v = View(graph)#, contour_kw={"levels": 50})
+v.save("Correlation.pdf")
+
+# %%
+# Copulas
+
+
+R = ot.CorrelationMatrix(2)
+R[1, 0] = 0.2
+c = ot.NormalCopula(R).drawPDF()
+c.setTitle("Normal copula")
+v = View(c, contour_kw={"vmin": 0.4, "vmax": 1.4})
+v.save("Copula1.pdf")
+
+# %%
+
+c = ot.ClaytonCopula().drawPDF()
+c.setTitle("Clayton copula")
+v = View(c, contour_kw={"vmin": 0.0, "vmax": 2.6})
+v.save("Copula2.pdf")
+
+# %%
+
+
+c = ot.AliMikhailHaqCopula().drawPDF()
+c.setTitle("AliMikhailHaq copula")
+v = View(c, contour_kw={"vmin": 0.5, "vmax": 1.4})
+v.save("Copula3.pdf")
+
+# %%
+
+c = ot.GumbelCopula().drawPDF()
+c.setTitle("Gumbel copula")
+v = View(c, contour_kw={"vmin": 0.0, "vmax": 2.6})
+v.save("Copula4.pdf")
+
+# %%
+
+marg1 = ot.Gumbel(1.0, 0.0)
+marg2 = ot.TruncatedNormal(0.0, 1.0, -2.0, 2.0)
+joint = ot.JointDistribution([marg1, marg2])
+g = joint.drawPDF()
+v = View(g, contour_kw={"vmin": 0.0, "vmax": 0.13})
+v.save("Dist.pdf")
+
+# %%
+marg1 = ot.Gumbel(1.0, 0.0)
+marg2 = ot.TruncatedNormal(0.0, 1.0, -2.0, 2.0)
+copula = ot.GumbelCopula()
+joint = ot.JointDistribution([marg1, marg2], copula)
+graph = joint.drawPDF()
+title = "Joint distribution "
+title += "from marginals and copula"
+graph.setTitle(title)
+v = View(graph)
+v.save("ComposedGumbel.pdf")
+
+# %%