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

    Click :ref:`here <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.


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



.. code-block:: python

    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:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_curvefit_temperature_data_001.png
    :class: sphx-glr-single-img




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



.. code-block:: python


    from scipy import optimize
    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 = optimize.curve_fit(yearly_temps, months,
                                          temp_max, [20, 10, 0])
    res_min, cov_min = optimize.curve_fit(yearly_temps, months,
                                          temp_min, [-40, 20, 0])







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



.. code-block:: python


    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('Temperature ($^\circ$C)')

    plt.show()



.. image:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_curvefit_temperature_data_002.png
    :class: sphx-glr-single-img




**Total running time of the script:** ( 0 minutes  0.027 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_solutions_plot_curvefit_temperature_data.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

     :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.readthedocs.io>`_