.. 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
================================

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.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 11-17

Abstract
--------

Gaussian processes are a common fixture in UQ and in OpenTURNS. They are defined by their covariance function and OpenTURNS 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:: default

    dimension = 1








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We set the lower bound to zero for stationary kernels

.. GENERATED FROM PYTHON SOURCE LINES 21-24

.. code-block:: default

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









.. GENERATED FROM PYTHON SOURCE LINES 25-32

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:: default

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








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

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.. code-block:: default

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








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

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.. code-block:: default

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








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We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 55-64

.. code-block:: default

    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"$p = 2$"])









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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 68-74

.. code-block:: default

    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 76-79

.. code-block:: default

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








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then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 81-84

.. code-block:: default

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








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and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 86-89

.. code-block:: default

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








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We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 91-100

.. code-block:: default

    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:: default

    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 124-126

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 127-128

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

.. GENERATED FROM PYTHON SOURCE LINES 128-130

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 131-132

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

.. GENERATED FROM PYTHON SOURCE LINES 132-134

.. code-block:: default

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








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We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 136-145

.. code-block:: default

    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"$\theta = 1$"])









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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 149-155

.. code-block:: default

    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 157-160

.. code-block:: default

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








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then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 162-165

.. code-block:: default

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








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and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 167-170

.. code-block:: default

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








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We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 172-181

.. code-block:: default

    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 183-190

.. code-block:: default

    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.

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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 204-205

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

.. GENERATED FROM PYTHON SOURCE LINES 205-207

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 208-209

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

.. GENERATED FROM PYTHON SOURCE LINES 209-211

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 212-213

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

.. GENERATED FROM PYTHON SOURCE LINES 213-215

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 216-217

We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 217-226

.. code-block:: default

    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 227-230

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 230-236

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 237-238

We define the first gaussian process and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 238-241

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 242-243

then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 243-246

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 247-248

and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 248-251

.. code-block:: default

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








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We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 253-262

.. code-block:: default

    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 264-274

.. code-block:: default


    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 275-277

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

.. GENERATED FROM PYTHON SOURCE LINES 280-286

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 298-300

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 301-302

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

.. GENERATED FROM PYTHON SOURCE LINES 302-304

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 305-306

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

.. GENERATED FROM PYTHON SOURCE LINES 306-308

.. code-block:: default

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








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We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 310-319

.. code-block:: default

    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 320-323

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 323-329

.. code-block:: default

    xmin = -5.0
    step = 0.01
    n = 1000
    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 331-334

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 335-336

then the second one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 336-339

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 340-341

and finally the third one and its trajectory :

.. GENERATED FROM PYTHON SOURCE LINES 341-344

.. code-block:: default

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








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We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 346-355

.. code-block:: default

    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 357-364

.. code-block:: default

    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 365-367

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 370-378

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 381-383

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 384-385

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

.. GENERATED FROM PYTHON SOURCE LINES 385-387

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 388-389

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

.. GENERATED FROM PYTHON SOURCE LINES 389-391

.. code-block:: default

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








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We draw the covariance models :

.. GENERATED FROM PYTHON SOURCE LINES 393-402

.. code-block:: default

    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"$\theta = 1.0$"])








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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 406-412

.. code-block:: default

    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 414-417

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 418-419

then the second process :

.. GENERATED FROM PYTHON SOURCE LINES 419-422

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 423-424

and the third one :

.. GENERATED FROM PYTHON SOURCE LINES 424-427

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 428-429

We draw the trajectories :

.. GENERATED FROM PYTHON SOURCE LINES 429-437

.. code-block:: default

    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 439-446

.. code-block:: default

    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





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

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Display figures

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.. code-block:: default

    plt.show()








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

   **Total running time of the script:** ( 0 minutes  1.224 seconds)


.. _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-python

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

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

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