.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "intro/scipy/auto_examples/solutions/plot_curvefit_temperature_data.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

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

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

.. _sphx_glr_intro_scipy_auto_examples_solutions_plot_curvefit_temperature_data.py:


==============================================================
Curve fitting: temperature as a function of month of the year
==============================================================

We have the min and max temperatures in Alaska for each months of the
year. We would like to find a function to describe this yearly evolution.

For this, we will fit a periodic function.

.. GENERATED FROM PYTHON SOURCE LINES 13-15

The data
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 15-27

.. code-block:: default

    import numpy as np

    temp_max = np.array([17,  19,  21,  28,  33,  38, 37,  37,  31,  23,  19,  18])
    temp_min = np.array([-62, -59, -56, -46, -32, -18, -9, -13, -25, -46, -52, -58])

    import matplotlib.pyplot as plt
    months = np.arange(12)
    plt.plot(months, temp_max, 'ro')
    plt.plot(months, temp_min, 'bo')
    plt.xlabel('Month')
    plt.ylabel('Min and max temperature')




.. image-sg:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_curvefit_temperature_data_001.png
   :alt: plot curvefit temperature data
   :srcset: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_curvefit_temperature_data_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(35.472222222222214, 0.5, 'Min and max temperature')



.. GENERATED FROM PYTHON SOURCE LINES 28-30

Fitting it to a periodic function
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 30-41

.. code-block:: default


    import scipy as sp
    def yearly_temps(times, avg, ampl, time_offset):
        return (avg
                + ampl * np.cos((times + time_offset) * 2 * np.pi / times.max()))

    res_max, cov_max = sp.optimize.curve_fit(yearly_temps, months,
                                          temp_max, [20, 10, 0])
    res_min, cov_min = sp.optimize.curve_fit(yearly_temps, months,
                                          temp_min, [-40, 20, 0])








.. GENERATED FROM PYTHON SOURCE LINES 42-44

Plotting the fit
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 44-56

.. code-block:: default


    days = np.linspace(0, 12, num=365)

    plt.figure()
    plt.plot(months, temp_max, 'ro')
    plt.plot(days, yearly_temps(days, *res_max), 'r-')
    plt.plot(months, temp_min, 'bo')
    plt.plot(days, yearly_temps(days, *res_min), 'b-')
    plt.xlabel('Month')
    plt.ylabel(r'Temperature ($^\circ$C)')

    plt.show()



.. image-sg:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_curvefit_temperature_data_002.png
   :alt: plot curvefit temperature data
   :srcset: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_curvefit_temperature_data_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.100 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_solutions_plot_curvefit_temperature_data.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_curvefit_temperature_data.py <plot_curvefit_temperature_data.py>`

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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_