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Expand Up @@ -78,6 +78,28 @@
"source": [
"The plot compare two distributions.\n\n- The \"Computed\" distribution is the one computed by OpenTURNS.\n- The \"Sample\" distribution is the one generated by Monte-Carlo sampling.\n\nThe fact that the \"Computed\" distribution is not centered on the true value is an\nexpected property of the way the distribution is computed.\nWhat must be checked, instead, is the the variance of the distribution.\nMore precisely, we check that the asymptotic covariance is correctly computed by the library.\nIn other words, we focus on the spread of the distribution and check that it is consistent with the actual spread.\nThis comparison is, however, restricted by the fact that the re-sampling size has a limited size\nequal to the `numberOfRepetitions` parameter. Increasing this parameter allows the check to be more accurate,\nbut increases the simulation elapsed time.\n\nWe see that these distributions are never far away from each other.\nThis proves that the computation of the distribution is correct, for both the asymptotic and bootstrap options.\n\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"otv.View.ShowAll()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ot.ResourceMap.Reload()"
]
}
],
"metadata": {
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Expand Up @@ -123,3 +123,9 @@
#
# We see that these distributions are never far away from each other.
# This proves that the computation of the distribution is correct, for both the asymptotic and bootstrap options.

# %%
otv.View.ShowAll()

# %%
ot.ResourceMap.Reload()
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Expand Up @@ -183,3 +183,6 @@
result = algoMC.getResult()
probability = result.getProbabilityEstimate()
print("Pf = ", probability)

# %%
otv.View.ShowAll()
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Expand Up @@ -317,6 +317,17 @@
"source": [
"result = algoMC.getResult()\nprobability = result.getProbabilityEstimate()\nprint(\"Pf = \", probability)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"otv.View.ShowAll()"
]
}
],
"metadata": {
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Expand Up @@ -644,7 +644,7 @@ in absolute value, to the Monte-Carlo estimator.

.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 0.246 seconds)
**Total running time of the script:** (0 minutes 0.498 seconds)


.. _sphx_glr_download_auto_examples_plot_check_reliability_reference_probabilities.py:
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Expand Up @@ -242,7 +242,7 @@ Create a Punk distribution
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 2.467 seconds)
**Total running time of the script:** (0 minutes 4.500 seconds)


.. _sphx_glr_download_auto_examples_plot_conditionaldistribution.py:
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Expand Up @@ -152,7 +152,7 @@ Plot cross-cuts of the distribution

.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 1.982 seconds)
**Total running time of the script:** (0 minutes 2.020 seconds)


.. _sphx_glr_download_auto_examples_plot_crosscut_distribution_2d.py:
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Expand Up @@ -146,7 +146,7 @@ Print the iso-values of the distribution

.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 7.550 seconds)
**Total running time of the script:** (0 minutes 8.155 seconds)


.. _sphx_glr_download_auto_examples_plot_crosscut_distribution_3d.py:
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Expand Up @@ -213,7 +213,7 @@ Let :math:`\bar{x}\in\mathbb{R}^3` be the reference point.
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 1.100 seconds)
**Total running time of the script:** (0 minutes 1.145 seconds)


.. _sphx_glr_download_auto_examples_plot_crosscut_function.py:
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Expand Up @@ -359,7 +359,7 @@ See https://github.com/mbaudin47/otbenchmark/issues/47 for details.
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 10.372 seconds)
**Total running time of the script:** (0 minutes 10.592 seconds)


.. _sphx_glr_download_auto_examples_plot_draw_cross_cuts.py:
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4 changes: 2 additions & 2 deletions otbenchmark/master/_sources/auto_examples/plot_drawevent.rst
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Expand Up @@ -446,7 +446,7 @@ In this case, we can use the `drawInputOutputSample` method.
.. code-block:: none
class=Graph name=Points X s.t. g(X) < 0.0 implementation=class=GraphImplementation name=Points X s.t. g(X) < 0.0 title=Points X s.t. g(X) < 0.0 xTitle=x1 yTitle=x2 axes=ON grid=ON legendposition=topright legendFontSize=1 drawables=[class=Drawable name=In implementation=class=Cloud name=In derived from class=DrawableImplementation name=In legend=In data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=40 dimension=2 data=[[1.71237,2.85486],[1.66792,2.31783],[2.69441,1.34366],[1.86644,2.24982],[2.02031,1.92003],[1.37012,2.49056],[2.09796,1.7934],[1.51539,2.21068],[1.65414,2.24108],[2.38439,1.58069],[2.09313,1.52526],[1.88487,2.12252],[1.53307,3.17321],[3.35848,1.22148],[1.73253,2.64634],[2.53091,1.47052],[1.76564,1.90677],[2.22299,1.66299],[2.72437,1.52226],[1.87608,1.75339],[1.20151,2.79605],[1.61561,1.94388],[1.97895,2.3215],[1.45782,3.05815],[1.98593,1.87883],[2.16331,1.7884],[0.998138,3.66056],[2.15616,1.83874],[1.47851,2.3263],[2.55846,1.62646],[3.36152,1.47219],[2.65572,2.43453],[2.02096,1.72365],[1.94358,2.18157],[1.99646,2.14285],[3.05755,1.43522],[2.17683,2.15387],[1.77961,2.17732],[1.32333,3.19999],[2.03815,1.59132]] color=lightsalmon3 isColorExplicitlySet=true fillStyle=solid lineStyle=solid pointStyle=fsquare lineWidth=1,class=Drawable name=Out implementation=class=Cloud name=Out derived from class=DrawableImplementation name=Out legend=Out data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=9960 dimension=2 data=[[-0.173501,-0.0297064],[-1.61099,1.88273],[0.280493,-1.76397],...,[-0.501814,-2.23713],[1.12524,0.218319],[-1.00681,0.0682829]] color=darkseagreen3 isColorExplicitlySet=true fillStyle=solid lineStyle=solid pointStyle=fsquare lineWidth=1]
class=Graph name=Points X s.t. g(X) < 0.0 implementation=class=GraphImplementation name=Points X s.t. g(X) < 0.0 title=Points X s.t. g(X) < 0.0 xTitle=x1 yTitle=x2 axes=ON grid=ON legendposition=topright legendFontSize=1 drawables=[class=Drawable name=In implementation=class=Cloud name=In derived from class=DrawableImplementation name=In legend=In data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=48 dimension=2 data=[[1.75206,2.1331],[2.65402,1.25186],[3.05344,1.37844],[1.51339,2.51736],[2.54761,1.37642],[2.12316,2.55392],[2.9651,1.10725],[1.56455,2.53366],[1.25938,2.77634],[1.23662,2.82189],[2.59475,1.45159],[1.99746,2.53124],[2.14658,1.89942],[2.13898,1.76489],[2.80095,1.14849],[1.42333,2.50344],[1.99307,1.70834],[2.23565,2.336],[2.30481,2.06017],[2.76317,2.07778],[2.05894,1.8149],[2.06568,1.57253],[2.00174,1.65279],[1.83384,2.53628],[2.2881,1.73489],[1.22935,2.86777],[1.72694,2.19741],[2.66474,1.49464],[1.95762,1.64623],[2.33063,1.58673],[2.5289,1.45325],[1.91649,2.14158],[1.37821,2.3388],[1.32028,2.72169],[1.97745,1.67481],[2.35367,1.72189],[1.94211,2.20454],[2.44141,2.16931],[1.88873,1.90417],[3.05892,2.42918],[2.10954,2.835],[1.74686,1.89147],[1.31915,3.10624],[1.46469,2.3849],[2.32639,1.46009],[2.85151,1.6471],[2.47383,2.06196],[2.64109,1.62487]] color=lightsalmon3 isColorExplicitlySet=true fillStyle=solid lineStyle=solid pointStyle=fsquare lineWidth=1,class=Drawable name=Out implementation=class=Cloud name=Out derived from class=DrawableImplementation name=Out legend=Out data=class=Sample name=Unnamed implementation=class=SampleImplementation name=Unnamed size=9952 dimension=2 data=[[0.83378,-1.49686],[-1.03462,-0.611822],[2.66921,-0.140542],...,[1.3881,-0.559157],[-1.22664,0.216045],[0.683437,0.589782]] color=darkseagreen3 isColorExplicitlySet=true fillStyle=solid lineStyle=solid pointStyle=fsquare lineWidth=1]
Expand All @@ -465,7 +465,7 @@ In this case, we can use the `drawInputOutputSample` method.
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 7.739 seconds)
**Total running time of the script:** (0 minutes 9.512 seconds)


.. _sphx_glr_download_auto_examples_plot_drawevent.py:
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Expand Up @@ -453,7 +453,7 @@ This corresponds to the following code and comments:

.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 0.240 seconds)
**Total running time of the script:** (0 minutes 0.293 seconds)


.. _sphx_glr_download_auto_examples_plot_lognormal_bbrc.py:
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Expand Up @@ -331,7 +331,7 @@ Create a LHS algorithm
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 9.459 seconds)
**Total running time of the script:** (0 minutes 5.246 seconds)


.. _sphx_glr_download_auto_examples_plot_methodFactory.py:
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Expand Up @@ -455,7 +455,7 @@ ThresholdEvent
.. GENERATED FROM PYTHON SOURCE LINES 183-186
.. GENERATED FROM PYTHON SOURCE LINES 183-187
.. code-block:: Python
Expand All @@ -466,19 +466,32 @@ ThresholdEvent
.. rst-class:: sphx-glr-script-out

.. code-block:: none
Pf = 0.15821596244131447
Pf = 0.1497584541062803
.. GENERATED FROM PYTHON SOURCE LINES 188-189
.. code-block:: Python
otv.View.ShowAll()
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (1 minutes 35.870 seconds)
**Total running time of the script:** (1 minutes 40.251 seconds)


.. _sphx_glr_download_auto_examples_plot_uncecomp_ot_examples.py:
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Expand Up @@ -138,8 +138,8 @@ Get the results
.. code-block:: none
Number of function calls = 1000
Failure Probability = 0.0760
95.0 % confidence interval :[0.0596,0.0924]
Failure Probability = 0.0880
95.0 % confidence interval :[0.0704,0.1056]
Expand Down Expand Up @@ -438,7 +438,7 @@ Fill the event domain with a color
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 1.688 seconds)
**Total running time of the script:** (0 minutes 1.764 seconds)


.. _sphx_glr_download_auto_examples_reliability_problems_plot_case_rs.py:
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Expand Up @@ -418,9 +418,9 @@ From integration
<tr><td></td><th>y0</th></tr>
<tr><th>0</th><td>0.25</td></tr>
<tr><th>1</th><td>0.25</td></tr>
<tr><th>2</th><td>0</td></tr>
<tr><th>3</th><td>0</td></tr>
<tr><th>4</th><td>0.25</td></tr>
<tr><th>2</th><td>0.25</td></tr>
<tr><th>3</th><td>0.25</td></tr>
<tr><th>4</th><td>0</td></tr>
</table>
</div>
<br />
Expand Down Expand Up @@ -1049,7 +1049,7 @@ The area of each polygon is computed based on the shapely module.
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 3.622 seconds)
**Total running time of the script:** (0 minutes 3.814 seconds)


.. _sphx_glr_download_auto_examples_reliability_problems_plot_compute_reference_rp55_pf.py:
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Expand Up @@ -238,7 +238,7 @@ Fill the event domain with a color
.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 1.156 seconds)
**Total running time of the script:** (0 minutes 1.355 seconds)


.. _sphx_glr_download_auto_examples_reliability_problems_plot_four_branch_serial_system_waarts.py:
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Expand Up @@ -261,7 +261,7 @@ Print a reliability benchmark problem

.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 0.003 seconds)
**Total running time of the script:** (0 minutes 0.004 seconds)


.. _sphx_glr_download_auto_examples_reliability_problems_plot_print_reliability_benchmark.py:
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Expand Up @@ -246,7 +246,7 @@ The LHS method
.. code-block:: none
'computedProbability = 0.0007000000000000013\nexactProbability = 0.0007897927545597477\nabsoluteError = 8.979275455974639e-05\nnumberOfCorrectDigits = 0.9442718507112124\nnumberOfFunctionEvaluations = 10000\nnumberOfDigitsPerEvaluation = 9.442718507112124e-05'
'computedProbability = 0.0006999999999999989\nexactProbability = 0.0007897927545597477\nabsoluteError = 8.979275455974877e-05\nnumberOfCorrectDigits = 0.9442718507112009\nnumberOfFunctionEvaluations = 10000\nnumberOfDigitsPerEvaluation = 9.442718507112009e-05'
Expand All @@ -271,7 +271,7 @@ The MonteCarloSampling method
.. code-block:: none
'computedProbability = 0.0006999999999999989\nexactProbability = 0.0007897927545597477\nabsoluteError = 8.979275455974877e-05\nnumberOfCorrectDigits = 0.9442718507112009\nnumberOfFunctionEvaluations = 10000\nnumberOfDigitsPerEvaluation = 9.442718507112009e-05'
'computedProbability = 0.0006000000000000008\nexactProbability = 0.0007897927545597477\nabsoluteError = 0.00018979275455974687\nnumberOfCorrectDigits = 0.619233516283543\nnumberOfFunctionEvaluations = 10000\nnumberOfDigitsPerEvaluation = 6.192335162835429e-05'
Expand All @@ -296,7 +296,7 @@ The FORM - Importance Sampling method
.. code-block:: none
'computedProbability = 0.0007629026630847465\nexactProbability = 0.0007897927545597477\nabsoluteError = 2.6890091475001193e-05\nnumberOfCorrectDigits = 1.4679208656529377\nnumberOfFunctionEvaluations = 380\nnumberOfDigitsPerEvaluation = 0.003862949646455099'
'computedProbability = 0.0007687158730375458\nexactProbability = 0.0007897927545597477\nabsoluteError = 2.1076881522201886e-05\nnumberOfCorrectDigits = 1.5737067909975317\nnumberOfFunctionEvaluations = 335\nnumberOfDigitsPerEvaluation = 0.004697632211932931'
Expand All @@ -321,7 +321,7 @@ The Subset method
.. code-block:: none
'computedProbability = 0.0005690000000000008\nexactProbability = 0.0007897927545597477\nabsoluteError = 0.00022079275455974686\nnumberOfCorrectDigits = 0.5535283275966657\nnumberOfFunctionEvaluations = 4000\nnumberOfDigitsPerEvaluation = 0.00013838208189916642'
'computedProbability = 0.0007543799999999997\nexactProbability = 0.0007897927545597477\nabsoluteError = 3.541275455974798e-05\nnumberOfCorrectDigits = 1.3483534358601093\nnumberOfFunctionEvaluations = 4000\nnumberOfDigitsPerEvaluation = 0.00033708835896502734'
Expand Down Expand Up @@ -450,10 +450,10 @@ In addition, it returns the performance of these methods.
Exact probability: 0.0007897927545597477
------------------------------------------------------------------
SubsetSampling
Estimated probability: 0.0007430000000000004
Estimated probability: 0.0007590000000000005
Number of function calls: 4000
Number of correct digits=1.2
Performance=3.07e-04 (correct digits/evaluation)
Number of correct digits=1.4
Performance=3.52e-04 (correct digits/evaluation)
------------------------------------------------------------------
FORM
Estimated probability: 0.000659887791408224
Expand All @@ -468,36 +468,36 @@ In addition, it returns the performance of these methods.
Performance=2.65e-01 (correct digits/evaluation)
------------------------------------------------------------------
FORM-IS
Estimated probability: 0.0008395999875129127
Number of function calls: 338
Number of correct digits=1.2
Performance=3.55e-03 (correct digits/evaluation)
Estimated probability: 0.0008521464618589394
Number of function calls: 362
Number of correct digits=1.1
Performance=3.05e-03 (correct digits/evaluation)
------------------------------------------------------------------
MonteCarloSampling
Estimated probability: 0.0006999999999999957
Estimated probability: 0.0011000000000000005
Number of function calls: 10000
Number of correct digits=0.9
Performance=9.44e-05 (correct digits/evaluation)
Number of correct digits=0.4
Performance=4.06e-05 (correct digits/evaluation)
------------------------------------------------------------------
LHS
Estimated probability: 0.0
Estimated probability: 0.001999999999999997
Number of function calls: 1000
Number of correct digits=0.0
Performance=0.00e+00 (correct digits/evaluation)
------------------------------------------------------------------------
Scoring by number of correct digits
5 : LHS (0.0)
4 : MonteCarloSampling (0.4)
1 : FORM (0.8)
4 : MonteCarloSampling (0.9)
3 : FORM-IS (1.2)
0 : SubsetSampling (1.2)
3 : FORM-IS (1.1)
0 : SubsetSampling (1.4)
2 : SORM (2.1)
------------------------------------------------------------------------
Scoring by performance (digits/evaluation)
5 : LHS (0.0e+00)
4 : MonteCarloSampling (9.4e-05)
0 : SubsetSampling (3.1e-04)
3 : FORM-IS (3.6e-03)
4 : MonteCarloSampling (4.1e-05)
0 : SubsetSampling (3.5e-04)
3 : FORM-IS (3.0e-03)
1 : FORM (9.8e-02)
2 : SORM (2.7e-01)
Expand All @@ -518,7 +518,7 @@ Remarks

.. rst-class:: sphx-glr-timing

**Total running time of the script:** (0 minutes 2.735 seconds)
**Total running time of the script:** (0 minutes 1.466 seconds)


.. _sphx_glr_download_auto_examples_reliability_problems_plot_reliability_benchmark.py:
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