.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "_examples/02_simple_inversion/plot_03_adding_data_noise.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr__examples_02_simple_inversion_plot_03_adding_data_noise.py: Adding data noise to measurements ================================= Especially for synthetic modeling/inversion studies it is important to add data noise to the data. While CRTomo contains built-in functionality to add data noise, we now recommend to add noise manually for better control. Note that error parameters in the inversion context usually refer to standard deviations in the statistical sense. This implies that the actual realization of a given data noise component can be smaller or larger than the specified noise level. As such it **may** be possible/useful to sometimes reduce a given noise estimate below the actual noise level added to synthetic data. For further reading, see: https://en.wikipedia.org/wiki/Pseudorandom_number_generator .. GENERATED FROM PYTHON SOURCE LINES 23-24 Imports .. GENERATED FROM PYTHON SOURCE LINES 24-27 .. code-block:: Python import numpy as np import crtomo .. GENERATED FROM PYTHON SOURCE LINES 28-29 Setup: Generate some synthetic data .. GENERATED FROM PYTHON SOURCE LINES 29-37 .. code-block:: Python mesh = crtomo.crt_grid.create_surface_grid(nr_electrodes=10, spacing=1) tdm = crtomo.tdMan(grid=mesh) tdm.add_homogeneous_model(100, 0) tdm.configs.gen_dipole_dipole(skipc=0) rmag = tdm.measurements()[:, 0] rpha = tdm.measurements()[:, 1] .. rst-class:: sphx-glr-script-out .. code-block:: none This grid was sorted using CutMcK. The nodes were resorted! Triangular grid found attempting modeling b' ######### CMod ############\nLicence:\nCopyright \xc2\xa9 1990-2020 Andreas Kemna \nCopyright \xc2\xa9 2008-2020 CRTomo development team (see AUTHORS file)\nPermission is hereby granted, free of charge, to any person obtaining a copy of\nthis software and associated documentation files (the \xe2\x80\x9cSoftware\xe2\x80\x9d), to deal in\nthe Software without restriction, including without limitation the rights to\nuse, copy, modify, merge, publish, distribute, sublicense, and/or sell copies\nof the Software, and to permit persons to whom the Software is furnished to do\nso, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \xe2\x80\x9cAS IS\xe2\x80\x9d, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n \n \n CRMod Process_ID :: 5125\n OpenMP max threads: 4\n Git-Branch master\n Commit-ID cb89ccd2c4341b9b08bbe7bb08f5aea0d60916ee\n Created Mon-Mar-25-14:34:56-2024\n Compiler \n OS GNU/Linux\n\n Reading Input-Files\n++ check 1\r++ check 2 done!\n\rGetting voltage 1\rGetting voltage 2\rGetting voltage 3\rGetting voltage 4\rGetting voltage 5\rGetting voltage 6\rGetting voltage 7\rGetting voltage 8\rGetting voltage 9\rGetting voltage 10\rGetting voltage 11\rGetting voltage 12\rGetting voltage 13\rGetting voltage 14\rGetting voltage 15\rGetting voltage 16\rGetting voltage 17\rGetting voltage 18\rGetting voltage 19\rGetting voltage 20\rGetting voltage 21\rGetting voltage 22\rGetting voltage 23\rGetting voltage 24\rGetting voltage 25\rGetting voltage 26\rGetting voltage 27\rGetting voltage 28 No electrode cap file\n \n Rescheduling..\n less nodes than wavenumbers\n OpenMP threads: 3( 4)\n\n\r Calculating Potentials : Wavenumber 2 \r Calculating Potentials : Wavenumber 3 \r Calculating Potentials : Wavenumber 3 \r Calculating Potentials : Wavenumber 4 \r Calculating Potentials : Wavenumber 6 \r Calculating Potentials : Wavenumber 6 \r Calculating Potentials : Wavenumber 7 \r Calculating Potentials : Wavenumber 8 \r Calculating Potentials : Wavenumber 9 done, now processing\n solution time 0d/ 0h/ 0m/ 0s/ 29ms\n\n Modelling completedSTOP 0\n' reading voltages .. GENERATED FROM PYTHON SOURCE LINES 38-44 Generate data noise ------------------- For synthetic studies a good starting point is that the structure of the actual noise should be the same as used in the inversion error model. As such we use a linear model for the magnitude noise components, and an absolute standard deviation for the phase values. .. GENERATED FROM PYTHON SOURCE LINES 44-73 .. code-block:: Python # Important: ALWAYS initialize the random number generator using a seed! np.random.seed(2048) # absolute component in [Ohm ] noise_level_rmag_absolute = 0.01 # relative component [0, 1] noise_level_rmag_relative = 0.05 noise_rmag = np.random.normal( loc=0, scale=rmag * noise_level_rmag_relative + noise_level_rmag_absolute ) rmag_with_noise = rmag + noise_rmag # 0.5 mrad absolute noise level noise_level_phases = 0.5 noise_rpha = np.random.normal( loc=0, scale=noise_level_phases ) rpha_with_noise = rpha + noise_rpha # register the noise-added data as new measurements and mark them for use in a # subsequent inversion tdm.register_measurements(rmag_with_noise, rpha_with_noise) .. GENERATED FROM PYTHON SOURCE LINES 74-75 Remove physically implausible negative magnitude values .. GENERATED FROM PYTHON SOURCE LINES 75-77 .. code-block:: Python indices = np.where(rmag_with_noise <= 0)[0] tdm.configs.delete_data_points(indices) .. rst-class:: sphx-glr-script-out .. code-block:: none Deleting configurations: [] .. _sphx_glr_download__examples_02_simple_inversion_plot_03_adding_data_noise.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_03_adding_data_noise.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_03_adding_data_noise.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_03_adding_data_noise.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_