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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_fit_complex_with_transform.py:


Fit complex data with transform
===============================

Using lmfitdata, fit a complex data set.

Use a transform to allow us to fit a peak in the
frequency domain while leaving the definition of the
peak in the time domain.

Why is this useful?
Remember that for noiseless spectra, the norm
of the residual might not be the same, but
when we consider noisy spectra, it's better
to use the domain where the peak rises
clearly above the noise.
Also, in the "transform" we can do other
things, such as masking, etc.

.. GENERATED FROM PYTHON SOURCE LINES 20-108



.. image-sg:: /auto_examples/images/sphx_glr_fit_complex_with_transform_001.png
   :alt: fit complex with transform
   :srcset: /auto_examples/images/sphx_glr_fit_complex_with_transform_001.png, /auto_examples/images/sphx_glr_fit_complex_with_transform_001_2_00x.png 2.00x
   :class: sphx-glr-single-img


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

 .. code-block:: none

    ----------  logging output to /home/jmfranck/pyspecdata.0.log  ----------
    --> fit_complex_with_transform.py(44):pyspecdata.core             <module> 2025-01-22 14:37:30,483
    INFO: Functional Form: A*exp(-6.28318530717959*I*nu*(t - t_origin))*exp(-pi*R*Abs(t - t_origin))






|

.. code-block:: Python

    import matplotlib.pyplot as plt
    from numpy import pi
    import sympy as sp
    import numpy as np
    from numpy import r_
    import pyspecdata as psd

    # initialize logging and set a seed so this runs the same every time
    psd.init_logging(level="debug")
    np.random.seed(15816)
    A, R, nu, t, t_origin = sp.symbols("A R nu t t_origin", real=True)
    # {{{ create an empty dataset and drop the fake data into it
    thisfit = psd.lmfitdata(psd.nddata(r_[-0.05:1:1001j], "t"))

    @thisfit.define_residual_transform
    def my_transform(d):
        d.ft("t")
        return d

    thisfit.functional_form = (
        A
        * sp.exp(-1j * 2 * pi * nu * (t - t_origin))
        * sp.exp(-R * sp.pi * abs(t - t_origin))
    )
    psd.logger.info(psd.strm("Functional Form:", thisfit.functional_form))
    # {{{ if you set only_real to True, it previously worked -- this
    #     example demonstrates that this also works when set to False
    only_real = False
    if only_real:
        thisfit.functional_form = sp.re(thisfit.functional_form)
    # }}}
    # {{{ create the "true" parameters for the fake data by pretending like
    #     the true values are a guess, and then outputting the guess data
    true_values = {"A": 14.0, "R": 30, "nu": 25, "t_origin": 0.01}
    thisfit.set_guess(true_values)
    # {{{ here, just set the ft startpoints -- as noted
    #     elsewhere, we should have a function to do this
    #     without actually doing the transform
    thisfit.ft("t", shift=True).ift("t")
    # }}}
    # }}}
    mydata = thisfit.settoguess().eval()
    mydata.add_noise(0.01)
    fig, ((ax3, ax1), (ax4, ax2)) = plt.subplots(2, 2)
    psd.plot(mydata, "r", label="data", ax=ax1)
    psd.plot(mydata.imag, "r", label="data", ax=ax2)
    mydata.ift("t")
    psd.plot(mydata, "r", label="data", ax=ax3)
    psd.plot(mydata.imag, "r", label="data", ax=ax4)
    # }}}
    # {{{ set up the fit object using the "simulated" data
    #     here we need to IFT above, since "eval" above
    #     generates in the frequency domain
    newfit = psd.lmfitdata(mydata.C)
    newfit.functional_form = thisfit.functional_form
    newfit.set_guess(
        A=dict(value=13.0, max=20, min=0.0),
        R=dict(value=10, max=1000, min=0),
        nu=dict(value=20),
        t_origin=dict(value=0.0, min=-0.1, max=0.1),
    )
    newfit.residual_transform = thisfit.residual_transform # use the same
    #                                                        transform
    # }}}
    # {{{ show the guess
    guess = newfit.settoguess().eval()
    psd.plot(guess, "g--", label="guess", ax=ax1)
    psd.plot(guess.imag, "g--", label="guess", ax=ax2)
    guess.ift("t")
    psd.plot(guess, "g--", label="guess", ax=ax3)
    psd.plot(guess.imag, "g--", label="guess", ax=ax4)
    # }}}
    # {{{ run the fit and generate nddata
    newfit.fit()
    plotdata = newfit.eval()
    psd.plot(plotdata, "b", alpha=0.5, label="fit", ax=ax1)
    psd.plot(plotdata.imag, "b", alpha=0.5, label="fit", ax=ax2)
    plotdata.ift("t")
    psd.plot(plotdata, "b", alpha=0.5, label="fit", ax=ax3)
    psd.plot(plotdata.imag, "b", alpha=0.5, label="fit", ax=ax4)
    # }}}
    ax1.set_ylabel("real components")
    ax2.set_ylabel("imag components")
    ax3.set_ylabel("real components")
    ax4.set_ylabel("imag components")
    ax1.legend()
    ax2.legend()
    plt.show()


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

   **Total running time of the script:** (0 minutes 1.086 seconds)


.. _sphx_glr_download_auto_examples_fit_complex_with_transform.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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