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

.. only:: html

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

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

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

.. _sphx_glr_examples_generated_scripts_synth_data_three_survey_lines_smt_neighpy.py:


Invert three surveys line for a thin plate using the surrogate model
====================================================================

.. raw:: html

   <!-- Please leave the cell below as it is -->

.. GENERATED FROM PYTHON SOURCE LINES 13-18

|Open In Colab|

.. |Open In Colab| image:: https://img.shields.io/badge/open%20in-Colab-b5e2fa?logo=googlecolab&style=flat-square&color=ffd670
   :target: https://colab.research.google.com/github/inlab-geo/cofi-examples/blob/main/examples/airborne_em/airborne_em_three_lines_transmitters.ipynb


.. GENERATED FROM PYTHON SOURCE LINES 21-40

.. raw:: html

   <!-- Again, please don't touch the markdown cell above. We'll generate badge 
        automatically from the above cell. -->

.. raw:: html

   <!-- This cell describes things related to environment setup, so please add more text 
        if something special (not listed below) is needed to run this notebook -->

..

   If you are running this notebook locally, make sure you’ve followed
   `steps
   here <https://github.com/inlab-geo/cofi-examples#run-the-examples-with-cofi-locally>`__
   to set up the environment. (This
   `environment.yml <https://github.com/inlab-geo/cofi-examples/blob/main/envs/environment.yml>`__
   file specifies a list of packages required to run the notebooks)


.. GENERATED FROM PYTHON SOURCE LINES 43-49

This notebook assumes that you have created a surrogate model by
executing the following two notebooks: - `Latin Hypercube
Sampling <./three_survey_lines_latin_hypercube_sampling.ipynb>`__ -
`Surrogate model
creation <./three_survey_lines_surrogate_model_creation.ipynb>`__


.. GENERATED FROM PYTHON SOURCE LINES 49-62

.. code-block:: Python


    # -------------------------------------------------------- #
    #                                                          #
    #     Uncomment below to set up environment on "colab"     #
    #                                                          #
    # -------------------------------------------------------- #

    # !pip install -U cofi
    # !pip install git+https://github.com/JuergHauser/PyP223.git
    # !pip install smt
    # !git clone https://github.com/inlab-geo/cofi-examples.git
    # %cd cofi-examples/examples/vtem_max








.. GENERATED FROM PYTHON SOURCE LINES 64-70

.. code-block:: Python


    # If this notebook is run locally PyP223 and smt need to be installed separately by uncommenting the following lines, 
    # that is by removing the # and the white space between it and the exclamation mark.
    # !pip install git+https://github.com/JuergHauser/PyP223.git
    # !pip install smt








.. GENERATED FROM PYTHON SOURCE LINES 72-92

.. code-block:: Python


    import pickle
    import numpy
    import matplotlib.pyplot as plt
    from matplotlib.lines import Line2D
    import cofi
    import arviz
    from vtem_max_forward_lib import (
        problem_setup, 
        system_spec, 
        survey_setup, 
        ForwardWrapper, 
        plot_predicted_profile, 
        plot_transient, 
        plot_plate_faces, 
        plot_plate_faces_single
    )

    numpy.random.seed(42)








.. GENERATED FROM PYTHON SOURCE LINES 97-111

Background
----------

This example inverts three survey line of VTEM max data using the
vertical component for a thin plate target. It thus becomes possible to
invert for the easting,northing, depth of the plate reference point, the
plate dip and plate azimuth. Solving the forward problem, that is
calculating the objective function, usess the surrogate model that has
been created by the `Kriging
approach <./three_survey_lines_surrogate_model_creation.ipynb>`__
applied to the `latin hypercube
samples <three_survey_lines_latin_hypercube_sampling.ipynb>`__ of the
objective function.


.. GENERATED FROM PYTHON SOURCE LINES 114-117

Problem definition
------------------


.. GENERATED FROM PYTHON SOURCE LINES 117-131

.. code-block:: Python


    tx_min = 115
    tx_max = 281
    tx_interval = 15
    ty_min = 25
    ty_max = 176
    ty_interval = 75
    tx_points = numpy.arange(tx_min, tx_max, tx_interval)
    ty_points = numpy.arange(ty_min, ty_max, ty_interval)
    n_transmitters = len(tx_points) * len(ty_points)
    tx, ty = numpy.meshgrid(tx_points, ty_points)
    tx = tx.flatten()
    ty = ty.flatten()








.. GENERATED FROM PYTHON SOURCE LINES 133-140

.. code-block:: Python


    fiducial_id = numpy.arange(len(tx))
    line_id = numpy.zeros(len(tx), dtype=int)
    line_id[ty==ty_points[0]] = 0
    line_id[ty==ty_points[1]] = 1
    line_id[ty==ty_points[2]] = 2








.. GENERATED FROM PYTHON SOURCE LINES 142-159

.. code-block:: Python


    survey_setup = {
        "tx": tx,                                                   # transmitter easting/x-position
        "ty": ty,                                                   # transmitter northing/y-position
        "tz": numpy.array([50]*n_transmitters),                     # transmitter height/z-position
        "tazi": numpy.deg2rad(numpy.array([90]*n_transmitters)),    # transmitter azimuth
        "tincl": numpy.deg2rad(numpy.array([6]*n_transmitters)),    # transmitter inclination
        "rx": tx,                                                   # receiver easting/x-position
        "ry": numpy.array([100]*n_transmitters),                    # receiver northing/y-position
        "rz": numpy.array([50]*n_transmitters),                     # receiver height/z-position
        "trdx": numpy.array([0]*n_transmitters),                    # transmitter receiver separation inline
        "trdy": numpy.array([0]*n_transmitters),                    # transmitter receiver separation crossline
        "trdz": numpy.array([0]*n_transmitters),                    # transmitter receiver separation vertical
        "fiducial_id": fiducial_id,                                 # unique id for each transmitter
        "line_id": line_id                  # id for each line
    }








.. GENERATED FROM PYTHON SOURCE LINES 161-177

.. code-block:: Python


    true_model = {
        "res": numpy.array([300, 1000]), 
        "thk": numpy.array([20]), 
        "peast": numpy.array([175]), 
        "pnorth": numpy.array([100]), 
        "ptop": numpy.array([30]), 
        "pres": numpy.array([0.1]), 
        "plngth1": numpy.array([100]), 
        "plngth2": numpy.array([100]), 
        "pwdth1": numpy.array([0.1]), 
        "pwdth2": numpy.array([90]), 
        "pdzm": numpy.array([75]),
        "pdip": numpy.array([60])
    }








.. GENERATED FROM PYTHON SOURCE LINES 179-183

.. code-block:: Python


    forward = ForwardWrapper(true_model, problem_setup, system_spec, survey_setup,
                             ["pdip","pdzm", "peast", "ptop", "pwdth2"], data_returned=["vertical"])





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

 .. code-block:: none

    ['pdip', 'pdzm', 'peast', 'ptop', 'pwdth2']




.. GENERATED FROM PYTHON SOURCE LINES 185-189

.. code-block:: Python


    # check the order of parameters in a model vector
    forward.params_to_invert





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

 .. code-block:: none


    ['pdip', 'pdzm', 'peast', 'ptop', 'pwdth2']



.. GENERATED FROM PYTHON SOURCE LINES 191-194

.. code-block:: Python


    true_param_value = numpy.array([60.,65., 175., 30., 90.])








.. GENERATED FROM PYTHON SOURCE LINES 199-202

Ensemble method using the surrogate model
-----------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 202-208

.. code-block:: Python


    sm = None
    filename = "kriging_surrogate_model.pkl"
    with open(filename, "rb") as f:
       sm = pickle.load(f)








.. GENERATED FROM PYTHON SOURCE LINES 213-215

**Initialise a model for inversion**


.. GENERATED FROM PYTHON SOURCE LINES 215-220

.. code-block:: Python


    init_param_value = numpy.array([45, 90, 160, 35, 80])
    m_min = numpy.array([15, 35, 155, 30, 65])
    m_max = numpy.array([75, 145, 185, 40, 115])








.. GENERATED FROM PYTHON SOURCE LINES 225-227

**Define helper functions for CoFI**


.. GENERATED FROM PYTHON SOURCE LINES 227-243

.. code-block:: Python


    def my_objective(model):
        val=sm.predict_values(numpy.array([model]))[0][0]
        if val<1e-3:
            return 1e-3
        else:
            return val
        
    def my_log_likelihood(model):
        return -0.5 * my_objective(model)

    def my_log_prior(model):    # uniform distribution
        for i in range(len(model)):
            if model[i] < m_min[i] or model[i] > m_max[i]: return -numpy.inf
        return 0.0 # model lies within bounds -> return log(1)








.. GENERATED FROM PYTHON SOURCE LINES 248-250

**Define CoFI problem**


.. GENERATED FROM PYTHON SOURCE LINES 250-254

.. code-block:: Python


    my_problem = cofi.BaseProblem()
    my_problem.set_objective(my_objective)








.. GENERATED FROM PYTHON SOURCE LINES 259-261

**Define CoFI options**


.. GENERATED FROM PYTHON SOURCE LINES 261-266

.. code-block:: Python


    inv_options = cofi.InversionOptions()
    inv_options.set_tool("neighpy")
    inv_options.suggest_solver_params()





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

 .. code-block:: none

    Current backend tool neighpy has the following solver-specific parameters:
    Required parameters:
    {'n_cells_to_resample', 'n_initial_samples', 'n_walkers', 'bounds', 'n_resample', 'n_iterations', 'n_samples_per_iteration'}
    Optional parameters & default settings:
    {'serial': False}




.. GENERATED FROM PYTHON SOURCE LINES 268-286

.. code-block:: Python


    inv_options.set_params(
        n_samples_per_iteration=100,
        n_initial_samples=10,
        n_resample=8000,
        n_iterations=100,
        bounds=numpy.array([m_min, m_max]).T,
        n_cells_to_resample=10,
        n_walkers=4
    )
    ######## Run it
    inv = cofi.Inversion(my_problem, inv_options)
    inv_result = inv.run()

    ######## Check result
    print(f"The inversion result from `neighpy`:")
    inv_result.summary()





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

 .. code-block:: none

    NAI - Initial Random Search

    NAI - Optimisation Loop:   0%|          | 0/100 [00:00<?, ?it/s]
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    NAI - Optimisation Loop: 100%|██████████| 100/100 [00:06<00:00, 16.18it/s]
    The inversion result from `neighpy`:
    ============================
    Summary for inversion result
    ============================
    SUCCESS
    ----------------------------
    model: [ 60.54890045  68.21943427 179.34874008  38.03067502 102.4513261 ]
    direct_search_samples: [[ 56.6912376   61.72943964 165.30224057  39.25708288  65.24360417]
     [ 64.07747464  94.20427513 166.36617511  32.13264507 111.92329337]
     [ 39.33555312  55.25951694 156.03017994  39.42022733  84.52241171]
     ...
     [ 60.32016867  68.21948407 179.35088011  38.03887313 102.45475841]
     [ 60.32017207  68.21948739 179.35087916  38.03887312 102.45475954]
     [ 60.32017157  68.21948501 179.35088322  38.03887402 102.45475897]]
    direct_search_objectives: [4.12243928e+04 2.48002996e+04 3.03365076e+04 ... 1.00000000e-03
     1.00000000e-03 1.00000000e-03]
    appraisal_samples: [[ 56.72072038  52.22306732 176.15083527  38.19021261 111.16926771]
     [ 55.22087425  49.68086801 176.86884413  38.41193374 110.4078104 ]
     [ 56.62957613  55.41558994 173.9893494   35.65224388 108.4636213 ]
     ...
     [ 45.08009491  61.27801175 181.71420978  38.51149541  97.89571622]
     [ 52.81663461  50.63049815 184.57462469  34.88042899  98.21648662]
     [ 53.89568914  60.7444161  181.90052107  33.99459004 107.94323154]]




.. GENERATED FROM PYTHON SOURCE LINES 291-294

Plotting
--------


.. GENERATED FROM PYTHON SOURCE LINES 294-324

.. code-block:: Python


    import arviz_base
    arviz.style.use("arviz-variat")
    display_names = [
        "Dip (°)", 
        "Dip azimuth (°)", 
        "Easting (m)", 
        "Depth (m)", 
        "Width (m)"
    ]
    clean_names = ["Dip_deg", "Dip_azimuth_deg", "Easting_m", "Depth_m", "Width_m"]

    true_values = [60, 65, 175, 30, 90]
    d = {k: v[numpy.newaxis, :] for k, v in zip(clean_names, inv_result.appraisal_samples.T)}
    az_idata = arviz_base.from_dict({"posterior": d})
    pc = arviz.plot_trace_dist(
        az_idata.sel(draw=slice(2000, None)),
        visuals={"xlabel_trace": False, "trace": {"color": "C0"}, "dist": {"color": "C0"}},
        figure_kwargs={"figsize": (12, 20), "constrained_layout": True},
    )
    for i, dname in enumerate(display_names):
        ax_kde = pc.iget_target(i, 0)
        ax_trace = pc.iget_target(i, 1)
        ax_kde.set_title(dname)
        ax_trace.set_title(dname)
        ax_kde.axvline(true_values[i], color="green", linestyle="--", lw=1, alpha=0.5)
        ax_trace.axhline(true_values[i], color="green", linestyle="--", lw=1, alpha=0.5)
        ax_trace.margins(x=0)





.. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_neighpy_001.png
   :alt: Dip (°), Dip (°), Dip azimuth (°), Dip azimuth (°), Easting (m), Easting (m), Depth (m), Depth (m), Width (m), Width (m)
   :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_neighpy_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 326-390

.. code-block:: Python


    from scipy.stats import gaussian_kde

    true_values_dict = {
        display_names[i]: true_param_value[i] for i in range(init_param_value.size)
    }

    # Set to True for KDE contours (old style), False for scatter (arviz 1.0 default)
    USE_KDE_CONTOURS = True

    arviz_base.rcParams["plot.max_subplots"] = 80

    if USE_KDE_CONTOURS:
        pm = arviz.plot_pair(
            az_idata.sel(draw=slice(4000, None)),
            marginal=True,
            triangle="lower",
            visuals={"scatter": False},
        )
        # Add KDE contours to off-diagonal panels
        posterior = az_idata.posterior.sel(draw=slice(4000, None))
        n = len(clean_names)
        for i in range(n):
            for j in range(n):
                if i <= j:
                    continue
                try:
                    ax = pm.iget_target(i, j)
                except (ValueError, IndexError):
                    continue
                x = posterior[clean_names[j]].values.flatten()
                y = posterior[clean_names[i]].values.flatten()
                kde = gaussian_kde(numpy.vstack([x, y]))
                xmin, xmax = x.min(), x.max()
                ymin, ymax = y.min(), y.max()
                xx, yy = numpy.mgrid[xmin:xmax:100j, ymin:ymax:100j]
                zz = kde(numpy.vstack([xx.ravel(), yy.ravel()])).reshape(xx.shape)
                ax.contourf(xx, yy, zz, levels=10, cmap="Blues")
                ax.contour(xx, yy, zz, levels=10, colors="grey", linewidths=0.5, alpha=0.5)
    else:
        pm = arviz.plot_pair(
            az_idata.sel(draw=slice(4000, None)),
            marginal=True,
            triangle="lower",
        )

    # Add reference values
    ref_vals = list(true_values_dict.values())
    n = len(ref_vals)
    for i in range(n):
        for j in range(n):
            try:
                ax = pm.iget_target(i, j)
            except (ValueError, IndexError):
                continue
            if i == j:
                ax.axvline(ref_vals[i], color="green", linestyle="--", lw=1, alpha=0.5)
            elif i > j:
                ax.plot(
                    ref_vals[j], ref_vals[i], "o",
                    color="yellow", markeredgecolor="k", ms=10, zorder=5,
                )





.. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_neighpy_002.png
   :alt: three survey lines smt neighpy
   :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_neighpy_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 392-452

.. code-block:: Python


    arviz.style.use("arviz-variat")

    _, axes = plt.subplots(2, 2)
    axes[1,1].axis("off")
    plot_plate_faces(
        "plate_true", forward, true_param_value, 
        axes[0,0], axes[0,1], axes[1,0], color="purple", label="True model"
    )
    plot_plate_faces(
        "plate_init", forward, init_param_value, 
        axes[0,0], axes[0,1], axes[1,0], color="green", label="Starting model"
    )

    plt.tight_layout()

    posterior = az_idata.posterior
    has_chain = "chain" in posterior.dims
    n_chains = int(posterior.sizes["chain"]) if has_chain else 1
    n_draws = int(posterior.sizes["draw"])

    ichain = 0
    idraw = min(2500, n_draws - 1)
    sample = numpy.zeros(5)

    if has_chain:
        for idx, cn in enumerate(clean_names):
            sample[idx] = float(posterior[cn].isel(chain=ichain, draw=idraw))
    else:
        for idx, cn in enumerate(clean_names):
            sample[idx] = float(posterior[cn].isel(draw=idraw))

    plot_plate_faces(
        "plate_inverted", forward, sample, 
        axes[0,0], axes[0,1], axes[1,0], color="red", label="Posterior sample", linestyle="dotted"
    )

    point = Line2D([0], [0], label='Fiducial', marker='o', markersize=5, 
             markeredgecolor='orange', markerfacecolor='orange', linestyle='')

    handles, labels = axes[1,0].get_legend_handles_labels()
    handles.extend([point])

    axes[1,0].legend(handles=handles,bbox_to_anchor=(1.04, 0), loc="lower left")

    # plot 10 randomly selected samples of the posterior distribution
    for i in range(10):
        idraw = numpy.random.randint(min(2000, n_draws), n_draws)
        if has_chain:
            for idx, cn in enumerate(clean_names):
                sample[idx] = float(posterior[cn].isel(chain=ichain, draw=idraw))
        else:
            for idx, cn in enumerate(clean_names):
                sample[idx] = float(posterior[cn].isel(draw=idraw))
        plot_plate_faces(
            "plate_inverted", forward, sample, 
            axes[0,0], axes[0,1], axes[1,0], color="red", label="Posterior sample", linestyle="dotted"
        )





.. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_neighpy_003.png
   :alt: three survey lines smt neighpy
   :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_three_survey_lines_smt_neighpy_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 457-470

--------------

Watermark
---------

.. raw:: html

   <!-- Feel free to add more modules in the watermark_list below, if more packages are used -->

.. raw:: html

   <!-- Otherwise please leave the below code cell unchanged -->


.. GENERATED FROM PYTHON SOURCE LINES 470-476

.. code-block:: Python


    watermark_list = ["cofi", "numpy", "scipy", "matplotlib"]
    for pkg in watermark_list:
        pkg_var = __import__(pkg)
        print(pkg, getattr(pkg_var, "__version__"))





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

 .. code-block:: none

    cofi 0.2.11+71.gb28b5b0
    numpy 2.2.6
    scipy 1.17.1
    matplotlib 3.10.9




.. GENERATED FROM PYTHON SOURCE LINES 477-477

sphinx_gallery_thumbnail_number = -1


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

   **Total running time of the script:** (0 minutes 44.679 seconds)


.. _sphx_glr_download_examples_generated_scripts_synth_data_three_survey_lines_smt_neighpy.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: three_survey_lines_smt_neighpy.zip <three_survey_lines_smt_neighpy.zip>`


.. only:: html

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

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