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

.. only:: html

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

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

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

.. _sphx_glr_auto_data_analysis_manage_data_and_samples_plot_quick_start_point_and_sample.py:


A quick start guide to the `Point` and `Sample` classes
=======================================================

.. GENERATED FROM PYTHON SOURCE LINES 6-13

Abstract
--------

In this example, we present the :class:`~openturns.Point` and :class:`~openturns.Sample` classes, two fundamental objects in the library.
We present the principles behind these classes and the way to create and use these objects.
We show how to extract a row or a column with the slicing operator.
We show how these objects interacts with Python variables and with the `numpy` module.

.. GENERATED FROM PYTHON SOURCE LINES 15-23

Introduction
------------

Two fundamental objects in the library are:

* `Point`: a multidimensional point in :math:`D` dimensions (:math:`\in \mathbb{R}^D`) ;
* `Sample`: a multivariate sample made of :math:`N` points in :math:`D` dimensions.


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.. code-block:: Python

    import numpy as np
    import openturns as ot

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








.. GENERATED FROM PYTHON SOURCE LINES 31-40

The `Point` class
-----------------

In this section, we see how to:

* create a point in :math:`\mathbb{R}^3`,
* access its components,
* update its components.


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By default, points are filled with zeros.

.. GENERATED FROM PYTHON SOURCE LINES 45-48

.. code-block:: Python

    p = ot.Point(3)
    p






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=3 values=[0,0,0]
    </div>
    <br />
    <br />

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The following statement returns the value of the second component (with index 1).
Python beginners should remember that Python indices start at zero.

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: Python

    p[1]





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

 .. code-block:: none


    0.0



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The following statements sets the second component.

.. GENERATED FROM PYTHON SOURCE LINES 59-62

.. code-block:: Python

    p[1] = 2
    p






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=3 values=[0,2,0]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: Python

    p.getDimension()





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

 .. code-block:: none


    3



.. GENERATED FROM PYTHON SOURCE LINES 66-78

The `Sample` class
------------------

The `Sample` class represents a multivariate sample made of :math:`N` points in :math:`\mathbb{R}^D`.

* :math:`D` is the *dimension* of the sample,
* :math:`N` is the *size* of the sample.


A `Sample` can be seen as an array of with :math:`N` rows and :math:`D` columns.

*Remark.* The :class:`~openturns.ProcessSample` class can be used to manage a sample of stochastic processes.

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The script below creates a `Sample` with size :math:`N=5` and dimension :math:`D=3`.

.. GENERATED FROM PYTHON SOURCE LINES 83-86

.. code-block:: Python

    data = ot.Sample(5, 3)
    data






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th><th>v2</th></tr>
      <tr><th>0</th><td>0</td><td>0</td><td>0</td></tr>
      <tr><th>1</th><td>0</td><td>0</td><td>0</td></tr>
      <tr><th>2</th><td>0</td><td>0</td><td>0</td></tr>
      <tr><th>3</th><td>0</td><td>0</td><td>0</td></tr>
      <tr><th>4</th><td>0</td><td>0</td><td>0</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: Python

    data.getSize()





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

 .. code-block:: none


    5



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.. code-block:: Python

    data.getDimension()





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

 .. code-block:: none


    3



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The following statement sets the third component (with index 2) of the fourth point (with index 3) in the `Sample`.

.. GENERATED FROM PYTHON SOURCE LINES 96-99

.. code-block:: Python

    data[3, 2] = 32
    data






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th><th>v2</th></tr>
      <tr><th>0</th><td>0</td><td>0</td><td>0</td></tr>
      <tr><th>1</th><td>0</td><td>0</td><td>0</td></tr>
      <tr><th>2</th><td>0</td><td>0</td><td>0</td></tr>
      <tr><th>3</th><td>0</td><td>0</td><td>32</td></tr>
      <tr><th>4</th><td>0</td><td>0</td><td>0</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 100-101

Notice that the rendering is different when we use the `print` statement.

.. GENERATED FROM PYTHON SOURCE LINES 103-105

.. code-block:: Python

    print(data)





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

 .. code-block:: none

    0 : [  0  0  0 ]
    1 : [  0  0  0 ]
    2 : [  0  0  0 ]
    3 : [  0  0 32 ]
    4 : [  0  0  0 ]




.. GENERATED FROM PYTHON SOURCE LINES 106-108

We can customize the format used to print the floating point numbers
with the `Sample-PrintFormat` key of the :class:`~openturns.ResourceMap`.

.. GENERATED FROM PYTHON SOURCE LINES 110-115

Get a row or a column of a `Sample`
-----------------------------------

As with `numpy` arrays, we can extract a row or a column with the `:` slicing operator.
As a reminder for Python beginners, *slicing* is the fact of extracting a part of an array with one single statement; this avoids `for` loops and improves performance and readability.

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.. code-block:: Python

    row = data[3, :]
    row






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=3 values=[0,0,32]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 121-123

.. code-block:: Python

    print(type(row))





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

 .. code-block:: none

    <class 'openturns.typ.Point'>




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.. code-block:: Python

    column = data[:, 2]
    column






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v2</th></tr>
      <tr><th>0</th><td>0</td></tr>
      <tr><th>1</th><td>0</td></tr>
      <tr><th>2</th><td>0</td></tr>
      <tr><th>3</th><td>32</td></tr>
      <tr><th>4</th><td>0</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 128-130

.. code-block:: Python

    print(type(column))





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

 .. code-block:: none

    <class 'openturns.typ.Sample'>




.. GENERATED FROM PYTHON SOURCE LINES 131-137

We see that:

* the `row` is a `Point`,
* the `column` is a `Sample`.

This is consistent with the fact that, in a dimension :math:`D` `Sample`, a row is a :math:`D`-dimensional `Point`.

.. GENERATED FROM PYTHON SOURCE LINES 139-140

The following statement extracts several columns (with indices 0 and 2) and creates a new `Sample`.

.. GENERATED FROM PYTHON SOURCE LINES 142-144

.. code-block:: Python

    data.getMarginal([0, 2])






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th></tr>
      <tr><th>0</th><td>0</td><td>0</td></tr>
      <tr><th>1</th><td>0</td><td>0</td></tr>
      <tr><th>2</th><td>0</td><td>0</td></tr>
      <tr><th>3</th><td>0</td><td>32</td></tr>
      <tr><th>4</th><td>0</td><td>0</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 145-146

Slicing can also be used to set a `Sample` row or column.

.. GENERATED FROM PYTHON SOURCE LINES 148-153

.. code-block:: Python

    sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
    p = [8.0, 10.0]
    sample[2, :] = p
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th></tr>
      <tr><th>0</th><td>1</td><td>2</td></tr>
      <tr><th>1</th><td>3</td><td>4</td></tr>
      <tr><th>2</th><td>8</td><td>10</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 154-159

.. code-block:: Python

    sample = ot.Sample([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
    s = ot.Sample([[3.0], [5.0], [7.0]])
    sample[:, 1] = s
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th></tr>
      <tr><th>0</th><td>1</td><td>3</td></tr>
      <tr><th>1</th><td>3</td><td>5</td></tr>
      <tr><th>2</th><td>5</td><td>7</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 160-164

Create a `Point` or a `Sample` from a Python list
-------------------------------------------------

The following statement creates a `Point` from a Python list.

.. GENERATED FROM PYTHON SOURCE LINES 166-169

.. code-block:: Python

    p1 = ot.Point([2, 3])
    p1






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[2,3]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 170-173

.. code-block:: Python

    p2 = ot.Point(range(2))
    p2






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[0,1]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 174-177

The first useful *Pythonism* that we will review is the *list comprehension*. This creates a list from a `for` loop.
This kind of statements is often used in the examples, so that they can be as short as possible.
In the following statement, we create a point by iterating over the components of a `Point`.

.. GENERATED FROM PYTHON SOURCE LINES 179-182

.. code-block:: Python

    p3 = ot.Point([i * i for i in p1])
    p3






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[4,9]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 183-186

The second useful *Pythonism* is the repetition with the `*` operator.

The following statements creates a list with three 5s.

.. GENERATED FROM PYTHON SOURCE LINES 188-191

.. code-block:: Python

    p4 = [5] * 3
    p4





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

 .. code-block:: none


    [5, 5, 5]



.. GENERATED FROM PYTHON SOURCE LINES 192-193

We can also create a `Sample` from a list of `Point`.

.. GENERATED FROM PYTHON SOURCE LINES 195-198

.. code-block:: Python

    sample = ot.Sample([p1, p2, p3])
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th></tr>
      <tr><th>0</th><td>2</td><td>3</td></tr>
      <tr><th>1</th><td>0</td><td>1</td></tr>
      <tr><th>2</th><td>4</td><td>9</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 199-200

We can loop over the points in a sample, using a list comprehension. In the following example, we compute the Euclidian norm of the points in the previous sample.

.. GENERATED FROM PYTHON SOURCE LINES 202-204

.. code-block:: Python

    [point.norm() for point in sample]





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

 .. code-block:: none


    [3.605551275463989, 1.0, 9.848857801796104]



.. GENERATED FROM PYTHON SOURCE LINES 205-206

We can also create a `Sample` based on a `Point`, repeated three times.

.. GENERATED FROM PYTHON SOURCE LINES 208-211

.. code-block:: Python

    sample = ot.Sample([p4] * 3)
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th><th>v2</th></tr>
      <tr><th>0</th><td>5</td><td>5</td><td>5</td></tr>
      <tr><th>1</th><td>5</td><td>5</td><td>5</td></tr>
      <tr><th>2</th><td>5</td><td>5</td><td>5</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 212-213

A nested list of floats is the easiest way to create a non-trivial `Sample`.

.. GENERATED FROM PYTHON SOURCE LINES 215-218

.. code-block:: Python

    sample = ot.Sample([[0, 1], [2, 3], [4, 5]])
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th></tr>
      <tr><th>0</th><td>0</td><td>1</td></tr>
      <tr><th>1</th><td>2</td><td>3</td></tr>
      <tr><th>2</th><td>4</td><td>5</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 219-224

Interactions with Numpy
-----------------------

The Python classes defined in Python modules are unknown to OpenTURNS and hence cannot be used by the library.
This is why it is useful to know how to convert to and from more basic Python variable types, especially Numpy arrays.

.. GENERATED FROM PYTHON SOURCE LINES 226-227

The following statement creates a `Sample` and converts it into a bidimensional Numpy `array`.

.. GENERATED FROM PYTHON SOURCE LINES 229-233

.. code-block:: Python

    sample = ot.Sample(5, 3)
    array = np.array(sample)
    array





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

 .. code-block:: none


    array([[0., 0., 0.],
           [0., 0., 0.],
           [0., 0., 0.],
           [0., 0., 0.],
           [0., 0., 0.]])



.. GENERATED FROM PYTHON SOURCE LINES 234-236

.. code-block:: Python

    type(array)








.. GENERATED FROM PYTHON SOURCE LINES 237-238

Conversely, the following script creates a Numpy `array`, then converts it into a `Sample`.

.. GENERATED FROM PYTHON SOURCE LINES 240-244

.. code-block:: Python

    array = 3.14 * np.ones((5, 3))
    sample = ot.Sample(array)
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th><th>v2</th></tr>
      <tr><th>0</th><td>3.14</td><td>3.14</td><td>3.14</td></tr>
      <tr><th>1</th><td>3.14</td><td>3.14</td><td>3.14</td></tr>
      <tr><th>2</th><td>3.14</td><td>3.14</td><td>3.14</td></tr>
      <tr><th>3</th><td>3.14</td><td>3.14</td><td>3.14</td></tr>
      <tr><th>4</th><td>3.14</td><td>3.14</td><td>3.14</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 245-247

.. code-block:: Python

    sample.getSize()





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

 .. code-block:: none


    5



.. GENERATED FROM PYTHON SOURCE LINES 248-250

.. code-block:: Python

    sample.getDimension()





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

 .. code-block:: none


    3



.. GENERATED FROM PYTHON SOURCE LINES 251-261

There is an ambiguous situation: a `Sample` based on several scalar values.

For example, is a `Sample` based on 5 values:

* a `Sample` with size 5 in 1 dimension or
* a `Sample` with size 1 in 5 dimensions?

In order to solve the case, we can use the second input argument of the `Sample` constructor, which specifies the dimension.

The following statement creates an array containing 5 values from 0 to 1.

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.. code-block:: Python

    u = np.linspace(0, 1, 5)
    u





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

 .. code-block:: none


    array([0.  , 0.25, 0.5 , 0.75, 1.  ])



.. GENERATED FROM PYTHON SOURCE LINES 267-268

Choice A: we create a `Sample` with size 5 in 1 dimension.

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.. code-block:: Python

    sample = ot.Sample([[ui] for ui in u])
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th></tr>
      <tr><th>0</th><td>0</td></tr>
      <tr><th>1</th><td>0.25</td></tr>
      <tr><th>2</th><td>0.5</td></tr>
      <tr><th>3</th><td>0.75</td></tr>
      <tr><th>4</th><td>1</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 274-275

Choice B: we create a `Sample` with size 1 in 5 dimensions.

.. GENERATED FROM PYTHON SOURCE LINES 277-280

.. code-block:: Python

    sample = ot.Sample([u[i: i + 5] for i in range(len(u) // 5)])
    sample






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th><th>v2</th><th>v3</th><th>v4</th></tr>
      <tr><th>0</th><td>0</td><td>0.25</td><td>0.5</td><td>0.75</td><td>1</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 281-291

If we do not set the optional `size` parameter, the library cannot solve the
case and an `InvalidArgumentException` is generated.
More precisely, the code::

    sample = ot.Sample(u)

produces the exception::

    TypeError: InvalidArgumentException : Invalid array dimension: 1



.. _sphx_glr_download_auto_data_analysis_manage_data_and_samples_plot_quick_start_point_and_sample.py:

.. only:: html

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

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

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

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

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