.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_meta_modeling/kriging_metamodel/plot_draw_covariance_models.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_meta_modeling_kriging_metamodel_plot_draw_covariance_models.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_meta_modeling_kriging_metamodel_plot_draw_covariance_models.py:


Kriging : draw covariance models
================================

.. GENERATED FROM PYTHON SOURCE LINES 5-10

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv
    from matplotlib import pylab as plt
    import pylab as pl








.. GENERATED FROM PYTHON SOURCE LINES 11-20

Abstract
--------

Gaussian processes are a common fixture in UQ.
They are defined by their covariance function and the library implements several of them.
In this example we should depict covariance functions and play with parameters
for two families of models: the generalized exponential model and the Matern models.

For visualization sake we should limit ourselves to the dimension 1.

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.. code-block:: Python

    dimension = 1








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We set the lower bound to zero for stationary kernels

.. GENERATED FROM PYTHON SOURCE LINES 24-27

.. code-block:: Python

    ot.ResourceMap.SetAsScalar("CovarianceModel-DefaultTMin", 0.0)









.. GENERATED FROM PYTHON SOURCE LINES 28-35

The generalized exponential model
---------------------------------

The :class:`~openturns.GeneralizedExponential` class implements a generalized exponential with a
parameter :math:`p < 0 \leq 2` exponent. The case :math:`p=1` is the standard exponential model
while :math:`p=2` is the squared exponential.


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Various parameters p and a fixed correlation length of 0.1
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

In this part we set the correlation length to :math:`\theta = 0.1` and study three different models
with parameters :math:`p=0.25`, :math:`p=1` and :math:`p=2` and trajectories from gaussian processes
based on these models.

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We define the :math:`p = 0.25` generalized exponential model :

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.. code-block:: Python

    covarianceModel = ot.GeneralizedExponential([0.1], 0.25)








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We define the :math:`p = 1` generalized exponential model :

.. GENERATED FROM PYTHON SOURCE LINES 50-52

.. code-block:: Python

    covarianceModel2 = ot.GeneralizedExponential([0.1], 1.0)








.. GENERATED FROM PYTHON SOURCE LINES 53-54

We define the :math:`p = 2` generalized exponential model :

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: Python

    covarianceModel3 = ot.GeneralizedExponential([0.1], 2.0)








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We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 58-67

.. code-block:: Python

    graphModel = covarianceModel.draw()
    graphModel.add(covarianceModel2.draw())
    graphModel.add(covarianceModel3.draw())
    graphModel.setColors(["green", "orange", "blue"])
    graphModel.setXTitle(r"$\tau = \|s-t\|$")
    graphModel.setYTitle(r"$C(\tau)$")
    graphModel.setLegends([r"$p = 0.25$", r"$p = 1$", r"$p = 2$"])









.. GENERATED FROM PYTHON SOURCE LINES 68-71

For each covariance model we build a gaussian process and generate a random trajectory of
on :math:`[-1,1]`.
We first build a discretization of this interval with a regular grid with step 0.01.

.. GENERATED FROM PYTHON SOURCE LINES 71-77

.. code-block:: Python

    xmin = -1.0
    step = 0.01
    n = 200
    grid1D = ot.RegularGrid(xmin, step, n + 1)
    nbTrajectories = 1








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We define the first gaussian process and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 79-82

.. code-block:: Python

    process = ot.GaussianProcess(covarianceModel, grid1D)
    sample = process.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 83-84

then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 84-87

.. code-block:: Python

    process2 = ot.GaussianProcess(covarianceModel2, grid1D)
    sample2 = process2.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 88-89

and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 89-92

.. code-block:: Python

    process3 = ot.GaussianProcess(covarianceModel3, grid1D)
    sample3 = process3.getSample(nbTrajectories)








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We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 94-103

.. code-block:: Python

    graphTraj = sample.drawMarginal(0)
    graphTraj.add(sample2.drawMarginal(0))
    graphTraj.add(sample3.drawMarginal(0))
    graphTraj.setXTitle(r"$x$")
    graphTraj.setYTitle(r"$GP_{\nu}(x)$")
    graphTraj.setTitle("Random realization from the covariance model")
    graphTraj.setColors(["green", "orange", "blue"])
    graphTraj.setLegends([r"$p = 0.25$", r"$p = 1$", r"$p = 2$"])








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We present each covariance model and the corresponding tracjectory side by side.

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.. code-block:: Python

    fig = pl.figure(figsize=(12, 4))
    ax_pdf = fig.add_subplot(1, 2, 1)
    _ = otv.View(graphModel, figure=fig, axes=[ax_pdf])
    ax_cdf = fig.add_subplot(1, 2, 2)
    _ = otv.View(graphTraj, figure=fig, axes=[ax_cdf])
    _ = fig.suptitle(r"Generalized Exponential Model : influence of the p parameter")




.. image-sg:: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_001.png
   :alt: Generalized Exponential Model : influence of the p parameter
   :srcset: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_001.png
   :class: sphx-glr-single-img





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The blue trajectory corresponding to the parameter :math:`p=2` is smooth as expected as compared with
the :math:`p=0.25` process which is less regular.

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The exponential model (:math:`p=1`)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

In the case of the exponential model (:math:`p=1`) we show the influence of the correlation length on
the trajectories.


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with correlation length :math:`\theta = 0.01`  :

.. GENERATED FROM PYTHON SOURCE LINES 127-129

.. code-block:: Python

    covarianceModel = ot.GeneralizedExponential([0.01], 1.0)








.. GENERATED FROM PYTHON SOURCE LINES 130-131

with correlation length :math:`\theta = 0.1` :

.. GENERATED FROM PYTHON SOURCE LINES 131-133

.. code-block:: Python

    covarianceModel2 = ot.GeneralizedExponential([0.1], 1.0)








.. GENERATED FROM PYTHON SOURCE LINES 134-135

with correlation length :math:`\theta = 1.0`

.. GENERATED FROM PYTHON SOURCE LINES 135-137

.. code-block:: Python

    covarianceModel3 = ot.GeneralizedExponential([1.0], 1.0)








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We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 139-148

.. code-block:: Python

    graphModel = covarianceModel.draw()
    graphModel.add(covarianceModel2.draw())
    graphModel.add(covarianceModel3.draw())
    graphModel.setColors(["green", "orange", "blue"])
    graphModel.setXTitle(r"$\tau = \|s-t\|$")
    graphModel.setYTitle(r"$C(\tau)$")
    graphModel.setLegends([r"$\theta = 0.01$", r"$\theta = 0.1$", r"$\theta = 1$"])









.. GENERATED FROM PYTHON SOURCE LINES 149-152

For each covariance model we build a gaussian process and generate a random trajectory of
on :math:`[-1,1]`.
We first build a discretization of this interval with a regular grid with step 0.01.

.. GENERATED FROM PYTHON SOURCE LINES 152-158

.. code-block:: Python

    xmin = -1.0
    step = 0.01
    n = 200
    grid1D = ot.RegularGrid(xmin, step, n + 1)
    nbTrajectories = 1








.. GENERATED FROM PYTHON SOURCE LINES 159-160

We define the first gaussian process and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 160-163

.. code-block:: Python

    process = ot.GaussianProcess(covarianceModel, grid1D)
    sample = process.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 164-165

then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 165-168

.. code-block:: Python

    process2 = ot.GaussianProcess(covarianceModel2, grid1D)
    sample2 = process2.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 169-170

and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 170-173

.. code-block:: Python

    process3 = ot.GaussianProcess(covarianceModel3, grid1D)
    sample3 = process3.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 174-175

We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 175-184

.. code-block:: Python

    graphTraj = sample.drawMarginal(0)
    graphTraj.add(sample2.drawMarginal(0))
    graphTraj.add(sample3.drawMarginal(0))
    graphTraj.setXTitle(r"$x$")
    graphTraj.setYTitle(r"$GP_{\theta}(x)$")
    graphTraj.setTitle("Random realization from the covariance model")
    graphTraj.setColors(["green", "orange", "blue"])
    graphTraj.setLegends([r"$\theta = 0.01$", r"$\theta = 0.1$", r"$\theta = 1$"])








.. GENERATED FROM PYTHON SOURCE LINES 185-186

We present each covariance model and the corresponding tracjectory side by side.

.. GENERATED FROM PYTHON SOURCE LINES 186-193

.. code-block:: Python

    fig = pl.figure(figsize=(12, 4))
    ax_pdf = fig.add_subplot(1, 2, 1)
    _ = otv.View(graphModel, figure=fig, axes=[ax_pdf])
    ax_cdf = fig.add_subplot(1, 2, 2)
    _ = otv.View(graphTraj, figure=fig, axes=[ax_cdf])
    _ = fig.suptitle(r"Exponential Model : influence of correlation length $\theta$")




.. image-sg:: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_002.png
   :alt: Exponential Model : influence of correlation length $\theta$
   :srcset: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_002.png
   :class: sphx-glr-single-img





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We observe a smoother trajectory with a high correlation value.

.. GENERATED FROM PYTHON SOURCE LINES 198-205

The squared exponential (:math:`p=2`)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


In the case of the squared exponential model (:math:`p=2`) we show the influence of the correlation length on
the trajectories.


.. GENERATED FROM PYTHON SOURCE LINES 207-208

with correlation length :math:`\theta = 0.01`  :

.. GENERATED FROM PYTHON SOURCE LINES 208-210

.. code-block:: Python

    covarianceModel = ot.GeneralizedExponential([0.01], 2.0)








.. GENERATED FROM PYTHON SOURCE LINES 211-212

with correlation length :math:`\theta = 0.1` :

.. GENERATED FROM PYTHON SOURCE LINES 212-214

.. code-block:: Python

    covarianceModel2 = ot.GeneralizedExponential([0.1], 2.0)








.. GENERATED FROM PYTHON SOURCE LINES 215-216

with correlation length :math:`\theta = 1.0`

.. GENERATED FROM PYTHON SOURCE LINES 216-218

.. code-block:: Python

    covarianceModel3 = ot.GeneralizedExponential([1.0], 2.0)








.. GENERATED FROM PYTHON SOURCE LINES 219-220

We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 220-229

.. code-block:: Python

    graphModel = covarianceModel.draw()
    graphModel.add(covarianceModel2.draw())
    graphModel.add(covarianceModel3.draw())
    graphModel.setColors(["green", "orange", "blue"])
    graphModel.setXTitle(r"$\tau = \|s-t\|$")
    graphModel.setYTitle(r"$C(\tau)$")
    graphModel.setLegends([r"$\theta = 0.01$", r"$\theta = 0.1$", r"$\theta = 1$"])









.. GENERATED FROM PYTHON SOURCE LINES 230-233

For each covariance model we build a gaussian process and generate a random trajectory of
on :math:`[-1,1]`.
We first build a discretization of this interval with a regular grid with step 0.01.

.. GENERATED FROM PYTHON SOURCE LINES 233-239

.. code-block:: Python

    xmin = -1.0
    step = 0.01
    n = 200
    grid1D = ot.RegularGrid(xmin, step, n + 1)
    nbTrajectories = 1








.. GENERATED FROM PYTHON SOURCE LINES 240-241

We define the first gaussian process and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 241-244

.. code-block:: Python

    process = ot.GaussianProcess(covarianceModel, grid1D)
    sample = process.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 245-246

then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 246-249

.. code-block:: Python

    process2 = ot.GaussianProcess(covarianceModel2, grid1D)
    sample2 = process2.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 250-251

and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 251-254

.. code-block:: Python

    process3 = ot.GaussianProcess(covarianceModel3, grid1D)
    sample3 = process3.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 255-256

We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 256-265

.. code-block:: Python

    graphTraj = sample.drawMarginal(0)
    graphTraj.add(sample2.drawMarginal(0))
    graphTraj.add(sample3.drawMarginal(0))
    graphTraj.setXTitle(r"$x$")
    graphTraj.setYTitle(r"$GP_{\theta}(x)$")
    graphTraj.setTitle("Random realization from the covariance model")
    graphTraj.setColors(["green", "orange", "blue"])
    graphTraj.setLegends([r"$\theta = 0.01$", r"$\theta = 0.1$", r"$\theta = 1$"])








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We present each covariance model and the corresponding tracjectory side by side.

.. GENERATED FROM PYTHON SOURCE LINES 267-277

.. code-block:: Python


    fig = pl.figure(figsize=(12, 4))
    ax_pdf = fig.add_subplot(1, 2, 1)
    _ = otv.View(graphModel, figure=fig, axes=[ax_pdf])
    ax_cdf = fig.add_subplot(1, 2, 2)
    _ = otv.View(graphTraj, figure=fig, axes=[ax_cdf])
    _ = fig.suptitle(
        r"Squared exponential model : influence of correlation length $\theta$"
    )




.. image-sg:: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_003.png
   :alt: Squared exponential model : influence of correlation length $\theta$
   :srcset: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 278-280

Execpt for very small values of the correlation length, trajectories are usually smooth. It is the
main effect of the squared exponential model which leads to smooth process.

.. GENERATED FROM PYTHON SOURCE LINES 283-289

The Matern covariance model
---------------------------

The :class:`~openturns.MaternModel` class implements the Matern model of parameter :math:`\nu`.
This parameter controls the smoothness of the process : for any :math:`\nu = n + \frac{1}{2}` the
process is :math:`n` times continuously differentiable.

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Influence of the regularity
^^^^^^^^^^^^^^^^^^^^^^^^^^^

In this paragraph we represent three models with different regularity and generate the
corresponding random trajectories. We shall use :math:`\nu = 0.5`, :math:`\nu = 1.5` and
:math:`\nu = 2.5` and observe the regularity.


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We define the :math:`\nu = 0.5` Matern model :

.. GENERATED FROM PYTHON SOURCE LINES 301-303

.. code-block:: Python

    covarianceModel = ot.MaternModel([1.0], 0.5)








.. GENERATED FROM PYTHON SOURCE LINES 304-305

We define the :math:`\nu = 1.5` Matern model :

.. GENERATED FROM PYTHON SOURCE LINES 305-307

.. code-block:: Python

    covarianceModel2 = ot.MaternModel([1.0], 1.5)








.. GENERATED FROM PYTHON SOURCE LINES 308-309

We define the :math:`\nu = 2.5` Matern model :

.. GENERATED FROM PYTHON SOURCE LINES 309-311

.. code-block:: Python

    covarianceModel3 = ot.MaternModel([1.0], 2.5)








.. GENERATED FROM PYTHON SOURCE LINES 312-313

We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 313-322

.. code-block:: Python

    graphModel = covarianceModel.draw()
    graphModel.add(covarianceModel2.draw())
    graphModel.add(covarianceModel3.draw())
    graphModel.setColors(["green", "orange", "blue"])
    graphModel.setXTitle(r"$\tau = \|s-t\|$")
    graphModel.setYTitle(r"$C(\tau)$")
    graphModel.setLegends([r"$\nu = 1/2$", r"$\nu = 3/2$", r"$\nu = 5/2$"])









.. GENERATED FROM PYTHON SOURCE LINES 323-326

For each covariance model we build a gaussian process and generate a random trajectory of
on :math:`[-1,1]`.
We first build a discretization of this interval with a regular grid with step 0.001.

.. GENERATED FROM PYTHON SOURCE LINES 326-332

.. code-block:: Python

    xmin = -5.0
    step = 0.01
    n = 1000
    grid1D = ot.RegularGrid(xmin, step, n + 1)
    nbTrajectories = 1








.. GENERATED FROM PYTHON SOURCE LINES 333-334

We define the first gaussian process and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 334-337

.. code-block:: Python

    process = ot.GaussianProcess(covarianceModel, grid1D)
    sample = process.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 338-339

then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 339-342

.. code-block:: Python

    process2 = ot.GaussianProcess(covarianceModel2, grid1D)
    sample2 = process2.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 343-344

and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 344-347

.. code-block:: Python

    process3 = ot.GaussianProcess(covarianceModel3, grid1D)
    sample3 = process3.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 348-349

We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 349-358

.. code-block:: Python

    graphTraj = sample.drawMarginal(0)
    graphTraj.add(sample2.drawMarginal(0))
    graphTraj.add(sample3.drawMarginal(0))
    graphTraj.setXTitle(r"$x$")
    graphTraj.setYTitle(r"$GP_{\nu}(x)$")
    graphTraj.setTitle("Random realization from the covariance model")
    graphTraj.setColors(["green", "orange", "blue"])
    graphTraj.setLegends([r"$\nu = 1/2$", r"$\nu = 3/2$", r"$\nu = 5/2$"])








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We present each covariance model and the corresponding tracjectory side by side.

.. GENERATED FROM PYTHON SOURCE LINES 360-367

.. code-block:: Python

    fig = pl.figure(figsize=(12, 4))
    ax_pdf = fig.add_subplot(1, 2, 1)
    _ = otv.View(graphModel, figure=fig, axes=[ax_pdf])
    ax_cdf = fig.add_subplot(1, 2, 2)
    _ = otv.View(graphTraj, figure=fig, axes=[ax_cdf])
    _ = fig.suptitle(r"Matern model : influence of the regularity $\nu$ parameter")




.. image-sg:: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_004.png
   :alt: Matern model : influence of the regularity $\nu$ parameter
   :srcset: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_004.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 368-370

The red trajectory is the least regular (:math:`nu = 0.5`) as it is only continuous. We see that the
the blue trajectory is more smooth as expected.

.. GENERATED FROM PYTHON SOURCE LINES 373-381

Variation of the correlation length
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

In this paragraph we fix the regularity by choosing :math:`\nu = 1.5` so we expect a continuously
differentiable realization.
We then use three different correlation lengths :math:`\theta = 0.01`, :math:`\theta = 0.1` and
:math:`\theta = 1.0` and observe the impact on realizations of gaussian processes based on these
covariance models.

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We define the Matern model with :math:`\theta = 0.01` :

.. GENERATED FROM PYTHON SOURCE LINES 384-386

.. code-block:: Python

    covarianceModel = ot.MaternModel([0.01], 1.5)








.. GENERATED FROM PYTHON SOURCE LINES 387-388

We define the Matern model with :math:`\theta = 0.1` :

.. GENERATED FROM PYTHON SOURCE LINES 388-390

.. code-block:: Python

    covarianceModel2 = ot.MaternModel([0.1], 1.5)








.. GENERATED FROM PYTHON SOURCE LINES 391-392

We define the Matern model with :math:`\theta = 1.0` :

.. GENERATED FROM PYTHON SOURCE LINES 392-394

.. code-block:: Python

    covarianceModel3 = ot.MaternModel([1.0], 1.5)








.. GENERATED FROM PYTHON SOURCE LINES 395-396

We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 396-405

.. code-block:: Python

    graphModel = covarianceModel.draw()
    graphModel.add(covarianceModel2.draw())
    graphModel.add(covarianceModel3.draw())
    graphModel.setColors(["green", "orange", "blue"])
    graphModel.setXTitle(r"$\tau = \|s-t\|$")
    graphModel.setYTitle(r"$C(\tau)$")
    graphModel.setTitle("Matern covariance model with \nu = 3/2")
    graphModel.setLegends([r"$\theta = 0.01$", r"$\theta = 0.1$", r"$\theta = 1.0$"])








.. GENERATED FROM PYTHON SOURCE LINES 406-409

For each covariance model we build a gaussian process and generate a random trajectory of
on :math:`[-1,1]`.
We build a discretization of this interval with a regular grid with step 0.01.

.. GENERATED FROM PYTHON SOURCE LINES 409-415

.. code-block:: Python

    xmin = -1.0
    step = 0.01
    n = 200
    grid1D = ot.RegularGrid(xmin, step, n + 1)
    nbTrajectories = 1








.. GENERATED FROM PYTHON SOURCE LINES 416-417

We define the first gaussian process and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 417-420

.. code-block:: Python

    process = ot.GaussianProcess(covarianceModel, grid1D)
    sample = process.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 421-422

then the second process :

.. GENERATED FROM PYTHON SOURCE LINES 422-425

.. code-block:: Python

    process2 = ot.GaussianProcess(covarianceModel2, grid1D)
    sample2 = process2.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 426-427

and the third one :

.. GENERATED FROM PYTHON SOURCE LINES 427-430

.. code-block:: Python

    process3 = ot.GaussianProcess(covarianceModel3, grid1D)
    sample3 = process3.getSample(nbTrajectories)








.. GENERATED FROM PYTHON SOURCE LINES 431-432

We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 432-440

.. code-block:: Python

    graphTraj = sample.drawMarginal(0)
    graphTraj.add(sample2.drawMarginal(0))
    graphTraj.add(sample3.drawMarginal(0))
    graphTraj.setXTitle(r"$x$")
    graphTraj.setYTitle(r"$GP_{\theta}(x)$")
    graphTraj.setColors(["green", "orange", "blue"])
    graphTraj.setLegends([r"$\theta = 0.01$", r"$\theta = 0.1$", r"$\theta = 1.0$"])








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We present each covariance model and the corresponding tracjectory side by side.

.. GENERATED FROM PYTHON SOURCE LINES 442-449

.. code-block:: Python

    fig = pl.figure(figsize=(12, 4))
    ax_pdf = fig.add_subplot(1, 2, 1)
    _ = otv.View(graphModel, figure=fig, axes=[ax_pdf])
    ax_cdf = fig.add_subplot(1, 2, 2)
    _ = otv.View(graphTraj, figure=fig, axes=[ax_cdf])
    _ = fig.suptitle("The Matern model : variation of the correlation length")




.. image-sg:: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_005.png
   :alt: The Matern model : variation of the correlation length
   :srcset: /auto_meta_modeling/kriging_metamodel/images/sphx_glr_plot_draw_covariance_models_005.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 450-452

From the previous figure we see that the trajectory of the gaussian process is smoother with large
correlation length.

.. GENERATED FROM PYTHON SOURCE LINES 454-455

Display figures

.. GENERATED FROM PYTHON SOURCE LINES 455-457

.. code-block:: Python

    plt.show()








.. GENERATED FROM PYTHON SOURCE LINES 458-459

Reset default settings

.. GENERATED FROM PYTHON SOURCE LINES 459-460

.. code-block:: Python

    ot.ResourceMap.Reload()








.. _sphx_glr_download_auto_meta_modeling_kriging_metamodel_plot_draw_covariance_models.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_draw_covariance_models.ipynb <plot_draw_covariance_models.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_draw_covariance_models.py <plot_draw_covariance_models.py>`