Fix maths

openturns · Oct 8, 2024 · 5b824c4 · 5b824c4
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diff --git a/doc/examples/plot_check_reliability_reference_probabilities.py b/doc/examples/plot_check_reliability_reference_probabilities.py
@@ -7,7 +7,7 @@
 # In this example, we check that the reference probabilities in the reliability problems
 # are consistent with confidence bounds from Monte-Carlo simulations.
 # These 95% confidence bounds are stored in 'reliability_compute_reference_proba.csv'
-# and required approximately than :math`10^9` function evaluations for each problem.
+# and required approximately than :math:`10^9` function evaluations for each problem.
 #
 # We consider two different metrics:
 #

diff --git a/doc/examples/reliability/README.txt b/doc/examples/reliability/README.txt
diff --git a/...methods/plot_compute_reference_rp55_pf.py → ...methods/plot_compute_reference_rp55_pf.py b/...methods/plot_compute_reference_rp55_pf.py → ...methods/plot_compute_reference_rp55_pf.py
diff --git a/...thods/plot_print_reliability_benchmark.py → ...thods/plot_print_reliability_benchmark.py b/...thods/plot_print_reliability_benchmark.py → ...thods/plot_print_reliability_benchmark.py
diff --git a/...ity/methods/plot_reliability_benchmark.py → ...ity_methods/plot_reliability_benchmark.py b/...ity/methods/plot_reliability_benchmark.py → ...ity_methods/plot_reliability_benchmark.py
diff --git a/...thods/plot_reliability_benchmark_table.py → ...thods/plot_reliability_benchmark_table.py b/...thods/plot_reliability_benchmark_table.py → ...thods/plot_reliability_benchmark_table.py
diff --git a/...ot_reliability_compute_reference_proba.py → ...ot_reliability_compute_reference_proba.py b/...ot_reliability_compute_reference_proba.py → ...ot_reliability_compute_reference_proba.py
diff --git a/...ples/reliability/problems/plot_case_rs.py → ...ples/reliability_problems/plot_case_rs.py b/...ples/reliability/problems/plot_case_rs.py → ...ples/reliability_problems/plot_case_rs.py
diff --git a/.../plot_four_branch_serial_system_waarts.py → .../plot_four_branch_serial_system_waarts.py b/.../plot_four_branch_serial_system_waarts.py → .../plot_four_branch_serial_system_waarts.py
diff --git a/...amples/reliability/problems/plot_rp110.py → ...amples/reliability_problems/plot_rp110.py b/...amples/reliability/problems/plot_rp110.py → ...amples/reliability_problems/plot_rp110.py
diff --git a/...amples/reliability/problems/plot_rp111.py → ...amples/reliability_problems/plot_rp111.py b/...amples/reliability/problems/plot_rp111.py → ...amples/reliability_problems/plot_rp111.py
diff --git a/...xamples/reliability/problems/plot_rp22.py → ...xamples/reliability_problems/plot_rp22.py b/...xamples/reliability/problems/plot_rp22.py → ...xamples/reliability_problems/plot_rp22.py
diff --git a/...xamples/reliability/problems/plot_rp24.py → ...xamples/reliability_problems/plot_rp24.py b/...xamples/reliability/problems/plot_rp24.py → ...xamples/reliability_problems/plot_rp24.py
diff --git a/...xamples/reliability/problems/plot_rp25.py → ...xamples/reliability_problems/plot_rp25.py b/...xamples/reliability/problems/plot_rp25.py → ...xamples/reliability_problems/plot_rp25.py
diff --git a/...xamples/reliability/problems/plot_rp28.py → ...xamples/reliability_problems/plot_rp28.py b/...xamples/reliability/problems/plot_rp28.py → ...xamples/reliability_problems/plot_rp28.py
diff --git a/...xamples/reliability/problems/plot_rp31.py → ...xamples/reliability_problems/plot_rp31.py b/...xamples/reliability/problems/plot_rp31.py → ...xamples/reliability_problems/plot_rp31.py
diff --git a/...xamples/reliability/problems/plot_rp33.py → ...xamples/reliability_problems/plot_rp33.py b/...xamples/reliability/problems/plot_rp33.py → ...xamples/reliability_problems/plot_rp33.py
diff --git a/...xamples/reliability/problems/plot_rp35.py → ...xamples/reliability_problems/plot_rp35.py b/...xamples/reliability/problems/plot_rp35.py → ...xamples/reliability_problems/plot_rp35.py
diff --git a/...xamples/reliability/problems/plot_rp53.py → ...xamples/reliability_problems/plot_rp53.py b/...xamples/reliability/problems/plot_rp53.py → ...xamples/reliability_problems/plot_rp53.py
diff --git a/...xamples/reliability/problems/plot_rp55.py → ...xamples/reliability_problems/plot_rp55.py b/...xamples/reliability/problems/plot_rp55.py → ...xamples/reliability_problems/plot_rp55.py
diff --git a/...xamples/reliability/problems/plot_rp57.py → ...xamples/reliability_problems/plot_rp57.py b/...xamples/reliability/problems/plot_rp57.py → ...xamples/reliability_problems/plot_rp57.py
diff --git a/...xamples/reliability/problems/plot_rp75.py → ...xamples/reliability_problems/plot_rp75.py b/...xamples/reliability/problems/plot_rp75.py → ...xamples/reliability_problems/plot_rp75.py
diff --git a/...examples/reliability/problems/plot_rp8.py → ...examples/reliability_problems/plot_rp8.py b/...examples/reliability/problems/plot_rp8.py → ...examples/reliability_problems/plot_rp8.py
diff --git a/...xamples/reliability/problems/plot_rp89.py → ...xamples/reliability_problems/plot_rp89.py b/...xamples/reliability/problems/plot_rp89.py → ...xamples/reliability_problems/plot_rp89.py
diff --git a/doc/examples/sensitivity/README.txt b/doc/examples/sensitivity/README.txt
diff --git a/...ods/plot_benchmark_sensitivity_methods.py → ...ods/plot_benchmark_sensitivity_methods.py b/...ods/plot_benchmark_sensitivity_methods.py → ...ods/plot_benchmark_sensitivity_methods.py
diff --git a/...vity/methods/plot_convergence_ishigami.py → ...vity_methods/plot_convergence_ishigami.py b/...vity/methods/plot_convergence_ishigami.py → ...vity_methods/plot_convergence_ishigami.py
diff --git a/...ensitivity/methods/plot_print_problems.py → ...ensitivity_methods/plot_print_problems.py b/...ensitivity/methods/plot_print_problems.py → ...ensitivity_methods/plot_print_problems.py
diff --git a/...plot_sensitivity_distribution_ishigami.py → ...plot_sensitivity_distribution_ishigami.py b/...plot_sensitivity_distribution_ishigami.py → ...plot_sensitivity_distribution_ishigami.py
diff --git a/...ity/problems/plot_borehole_sensitivity.py → ...ity_problems/plot_borehole_sensitivity.py b/...ity/problems/plot_borehole_sensitivity.py → ...ity_problems/plot_borehole_sensitivity.py
diff --git a/...ty/problems/plot_borgonovo_sensitivity.py → ...ty_problems/plot_borgonovo_sensitivity.py b/...ty/problems/plot_borgonovo_sensitivity.py → ...ty_problems/plot_borgonovo_sensitivity.py
diff --git a/...ty/problems/plot_dirichlet_sensitivity.py → ...ty_problems/plot_dirichlet_sensitivity.py b/...ty/problems/plot_dirichlet_sensitivity.py → ...ty_problems/plot_dirichlet_sensitivity.py
diff --git a/...tivity/problems/plot_flood_sensitivity.py → ...tivity_problems/plot_flood_sensitivity.py b/...tivity/problems/plot_flood_sensitivity.py → ...tivity_problems/plot_flood_sensitivity.py
diff --git a/...lems/plot_gaussian_product_sensitivity.py → ...lems/plot_gaussian_product_sensitivity.py b/...lems/plot_gaussian_product_sensitivity.py → ...lems/plot_gaussian_product_sensitivity.py
diff --git a/...sensitivity/problems/plot_gaussian_sum.py → ...sensitivity_problems/plot_gaussian_sum.py b/...sensitivity/problems/plot_gaussian_sum.py → ...sensitivity_problems/plot_gaussian_sum.py
diff --git a/...ivity/problems/plot_gsobol_sensitivity.py → ...ivity_problems/plot_gsobol_sensitivity.py b/...ivity/problems/plot_gsobol_sensitivity.py → ...ivity_problems/plot_gsobol_sensitivity.py
diff --git a/...ity/problems/plot_ishigami_sensitivity.py → ...ity_problems/plot_ishigami_sensitivity.py b/...ity/problems/plot_ishigami_sensitivity.py → ...ity_problems/plot_ishigami_sensitivity.py
diff --git a/...ivity/problems/plot_morris_sensitivity.py → ...ivity_problems/plot_morris_sensitivity.py b/...ivity/problems/plot_morris_sensitivity.py → ...ivity_problems/plot_morris_sensitivity.py
diff --git a/...problems/plot_nloscillator_sensitivity.py → ...problems/plot_nloscillator_sensitivity.py b/...problems/plot_nloscillator_sensitivity.py → ...problems/plot_nloscillator_sensitivity.py
diff --git a/...problems/plot_oakleyohagan_sensitivity.py → ...problems/plot_oakleyohagan_sensitivity.py b/...problems/plot_oakleyohagan_sensitivity.py → ...problems/plot_oakleyohagan_sensitivity.py
diff --git a/otbenchmark/ReliabilityLibrary.py b/otbenchmark/ReliabilityLibrary.py
@@ -7,20 +7,26 @@
 
 
 def ComputeLogRelativeError(exact, computed, basis=10.0):
-    """
+    r"""
     Compute the log-relative error between exact and computed.
 
     The log-relative error (LRE) is defined by:
 
+    .. math::
+
         LRE = -logB(relativeError)
 
     where relativeError is the relative error:
 
-        relativeError = abs(exact - computed) / abs(exact)
+    .. math::
+
+        relativeError = \frac{|exact - computed|}{|exact|}
 
     and logB is the base-b logarithm:
 
-        logB(x) = log(x) / log(basis)
+    .. math::
+
+        logB(x) = \frac{log(x)}{log(basis)}
 
     where log is the natural logarithm.
     This assumes that exact is different from zero.

diff --git a/otbenchmark/_FloodingSensitivity.py b/otbenchmark/_FloodingSensitivity.py
@@ -11,12 +11,14 @@ class FloodingSensitivity(SensitivityBenchmarkProblem):
     """Class to define a Flooding sensitivity benchmark problem."""
 
     def __init__(self):
-        """
+        r"""
         Create a Flooding sensitivity problem.
 
         The function is defined by the equation:
 
-        g(x) = (Q/(Ks*B*sqrt((Zm-Zv)/L)))^(3.0/5.0)+Zv-Zb-Hd
+        .. math::
+
+            g(x) = (\frac{Q}{K_s B \sqrt{\frac{Z_m-Z_v}{L}}})^{\frac{3}{5}}+Z_v-Z_b-H_d
 
         with:
 

diff --git a/otbenchmark/_FourBranchSerialSystemReliability.py b/otbenchmark/_FourBranchSerialSystemReliability.py
@@ -15,18 +15,14 @@ def __init__(self):
         References
         ----------
 
-        Waarts, P.-H. (2000). Structural reliability using finite element
-        methods: an appraisal of DARS: Directional Adaptive Response Surface
-        Sampling. Ph. D. thesis, Technical University of Delft, The
-        Netherlands. Pages 58, 69, 160.
-
-        Thèse Vincent Dubourg 2011, Méta-modèles adaptatifs pour l’analyse
-        de fiabilité et l’optimisation sous contrainte fiabiliste,
-        section "A two-dimensional four-branch serial system", page 182
-
-        Parameters
-        ----------
-        None.
+        - Waarts, P.-H. (2000). Structural reliability using finite element
+          methods: an appraisal of DARS: Directional Adaptive Response Surface
+          Sampling. Ph. D. thesis, Technical University of Delft, The
+          Netherlands. Pages 58, 69, 160.
+
+        - Thèse Vincent Dubourg 2011, Méta-modèles adaptatifs pour l’analyse
+          de fiabilité et l’optimisation sous contrainte fiabiliste,
+          section "A two-dimensional four-branch serial system", page 182
 
         Examples
         --------

diff --git a/otbenchmark/_NLOscillatorSensitivity.py b/otbenchmark/_NLOscillatorSensitivity.py
@@ -12,15 +12,15 @@ class NLOscillatorSensitivity(SensitivityBenchmarkProblem):
     """Class to define a Oscillator sensitivity benchmark problem."""
 
     def __init__(self):
-        """
+        r"""
         Create a nonlinear oscillator sensitivity problem.
 
         The function is defined by the equation:
 
         .. math::
-            g(x) = fs - 3*ks*np.sqrt(np.pi*S0/(4.*xis*omegas**3)*
-                xi_a*xis/(xip*xis*(4.*xi_a**2+theta**2)+gamma*xi_a**2)*
-                (xip*omegap**3+xis*omegas**3)*omegap/(4.*xi_a*omegaa**4))
+            g(x) = fs - 3*ks*\sqrt{\pi*S0/(4.*xis*omegas^3)*
+                xi_a*xis/(xip*xis*(4.*xi_a^2+theta^2)+gamma*xi_a^2)*
+                (xip*omegap^3+xis*omegas^3)*omegap/(4.*xi_a*omegaa^4)}
 
         where
         * omegap = np.sqrt(kp/mp)