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

.. only:: html

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

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

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

.. _sphx_glr_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py:


Estimate an integral
====================

.. GENERATED FROM PYTHON SOURCE LINES 6-13

In this example we are going to evaluate an integral of the form.

.. math::
   I_f = \int_{a}^{b}\, \int_{l_1(x_0)}^{u_1(x_0)}\, \int_{l_2(x_0, x_1)}^{u_2(x_0,x_1)}\, \int_{l_{n-1}(x_0, \dots, x_{n-2})}^{u_{n-1}(x_0, \dots, x_{n-2})}
   \, f(x_0, \dots, x_{n-1})\mathrm{d}{x_{n-1}}\dots\mathrm{d}{x_0}

with the iterated quadrature algorithm.

.. GENERATED FROM PYTHON SOURCE LINES 15-22

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    import math as m

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 23-24

define the integrand and the bounds

.. GENERATED FROM PYTHON SOURCE LINES 24-30

.. code-block:: Python

    a = -m.pi
    b = m.pi
    f = ot.SymbolicFunction(["x", "y"], ["1+cos(x)*sin(y)"])
    ll = [ot.SymbolicFunction(["x"], [" 2+cos(x)"])]
    u = [ot.SymbolicFunction(["x"], ["-2-cos(x)"])]








.. GENERATED FROM PYTHON SOURCE LINES 31-32

Draw the graph of the integrand and the bounds

.. GENERATED FROM PYTHON SOURCE LINES 32-44

.. code-block:: Python

    g = ot.Graph("Integration nodes", "x", "y", True, "upper right")
    g.add(f.draw([a, a], [b, b]))
    curve = ll[0].draw(a, b).getDrawable(0)
    curve.setLineWidth(2)
    curve.setColor("red")
    g.add(curve)
    curve = u[0].draw(a, b).getDrawable(0)
    curve.setLineWidth(2)
    curve.setColor("red")
    g.add(curve)
    view = viewer.View(g)




.. image-sg:: /auto_numerical_methods/general_methods/images/sphx_glr_plot_estimate_integral_iterated_quadrature_001.png
   :alt: Integration nodes
   :srcset: /auto_numerical_methods/general_methods/images/sphx_glr_plot_estimate_integral_iterated_quadrature_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 45-46

compute the integral value

.. GENERATED FROM PYTHON SOURCE LINES 46-49

.. code-block:: Python

    I2 = ot.IteratedQuadrature().integrate(f, a, b, ll, u)
    print(I2)
    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [-25.1327]





.. _sphx_glr_download_auto_numerical_methods_general_methods_plot_estimate_integral_iterated_quadrature.py:

.. only:: html

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

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

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

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

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