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==================
Examples
==================

Here you can find some examples of how to use the library.


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1 | Single-Set Analysis
=======================



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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates Extended EOF (EEOF) analysis on xarray tutorial data. EEOF analysis, also termed as Multivariate/Multichannel Singular Spectrum Analysis, advances traditional EOF analysis to capture propagating signals or oscillations in multivariate datasets. At its core, this involves the formulation of a lagged covariance matrix that encapsulates both spatial and temporal correlations. Subsequently, this matrix is decomposed to yield its eigenvectors (components) and eigenvalues (explained variance).">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_eeof_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_eeof.py`

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      <div class="sphx-glr-thumbnail-title">Extented EOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this tutorial, we&#x27;ll walk through how to perform a Complex EOF analysis on the zonal and meridional wind components.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_complex_eof_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_complex_eof.py`

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      <div class="sphx-glr-thumbnail-title">Complex EOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="EOF analysis in T-mode maximises the spatial variance.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_eof-tmode_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_eof-tmode.py`

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      <div class="sphx-glr-thumbnail-title">EOF analysis (T-mode)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="We demonstrate how to execute a Hilbert EOF analysis [1]_ [2]_ [3]_. This method extends traditional EOF analysis into the complex domain, allowing the EOF components to have real and imaginary parts. This capability can reveal oscillatory patterns in datasets, which are common in Earth observations. For example, beyond typical examples like seasonal cycles, you can think of internal waves in the ocean, or the Quasi-Biennial Oscillation in the atmosphere.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_hilbert_eof_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_hilbert_eof.py`

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      <div class="sphx-glr-thumbnail-title">Hilbert EOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the application of sparse PCA [1]_ to sea surface temperature data. Sparse PCA is an alternative to rotated PCA, where the components are sparse, often providing a more interpretable solution.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_eof-smode_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_eof-smode.py`

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      <div class="sphx-glr-thumbnail-title">Sparse PCA</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This tutorial illustrates the application of Extended EOF (EEOF) analysis to isolate and remove nonlinear trends within a dataset.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_eeof_trend_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_eeof_trend.py`

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      <div class="sphx-glr-thumbnail-title">Removing nonlinear trends with EEOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Multivariate EOF analysis.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_multivariate-eof_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_multivariate-eof.py`

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      <div class="sphx-glr-thumbnail-title">Multivariate EOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Multivariate EOF analysis with additional Varimax rotation.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_mreof_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_mreof.py`

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      <div class="sphx-glr-thumbnail-title">Varimax-rotated Multivariate EOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="EOF (Empirical Orthogonal Function) analysis is commonly used in climate science, interpreting the derived eigenvectors (EOFs) as climatic variability patterns. However, due to the inherent orthogonality constraint in EOF analysis, the interpretation of all but the first EOF can be problematic. Rotated EOF analysis, using optimization criteria like Varimax and Promax, offers a solution by releasing this orthogonality constraint, thus enabling a more accurate interpretation of variability patterns.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_rotated_eof_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_rotated_eof.py`

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      <div class="sphx-glr-thumbnail-title">Rotated EOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Weighted EOF analysis (in S-mode) maximises the temporal variance considering each gridpoint with a different weight. We compare the results for an EOF analysis based on (1) the covariance matrix, (2) area weighting based on latitude (coslat weighting), (3) the correlation matrix and finally (4) correlation matrix + coslat weighting.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_weighted-eof_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_weighted-eof.py`

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      <div class="sphx-glr-thumbnail-title">Weighted EOF analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="TIn this demonstration, we&#x27;ll apply GWPCA to a dataset detailing the chemical compositions of soils from countries around the Baltic Sea [1]_. This example is inspired by a tutorial originally crafted and published by Chris Brunsdon [2]_. The dataset comprises 10 variables (chemical elements) and spans 768 samples. Here, each sample refers to a pair of latitude and longitude coordinates, representing specific sampling stations.">

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  .. image:: /content/user_guide/auto_examples/1single/images/thumb/sphx_glr_plot_gwpca_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_1single_plot_gwpca.py`

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      <div class="sphx-glr-thumbnail-title">Geographically weighted PCA</div>
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2 | Cross-Set Analysis
========================



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    <div class="sphx-glr-thumbcontainer" tooltip="Maximum Covariance Analysis (MCA) between two data sets.">

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  .. image:: /content/user_guide/auto_examples/2cross/images/thumb/sphx_glr_plot_mca_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_2cross_plot_mca.py`

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      <div class="sphx-glr-thumbnail-title">Maximum Covariance Analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Rotated Maximum Covariance Analysis (MCA) between two data sets.">

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  .. image:: /content/user_guide/auto_examples/2cross/images/thumb/sphx_glr_plot_rotated_mca_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_2cross_plot_rotated_mca.py`

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      <div class="sphx-glr-thumbnail-title">Rotated Maximum Covariance Analysis</div>
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3 | Multi-Set Analysis
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we&#x27;re going to perform a Canonical Correlation Analysis (CCA) on three datasets using the ERSSTv5 monthly sea surface temperature (SST) data from 1970 to 2022. We divide this data into three areas: the Indian Ocean, the Pacific Ocean, and the Atlantic Ocean. Our goal is to perform CCA on these regions.">

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  .. image:: /content/user_guide/auto_examples/3multi/images/thumb/sphx_glr_plot_cca_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_3multi_plot_cca.py`

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      <div class="sphx-glr-thumbnail-title">Canonical Correlation Analysis</div>
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4 | Validation
===============


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    <div class="sphx-glr-thumbcontainer" tooltip="Test the significance of individual modes and obtain confidence intervals for both EOFs and PCs.">

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  .. image:: /content/user_guide/auto_examples/4validation/images/thumb/sphx_glr_plot_bootstrap_thumb.png
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  :ref:`sphx_glr_content_user_guide_auto_examples_4validation_plot_bootstrap.py`

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      <div class="sphx-glr-thumbnail-title">Significance testing of EOF analysis via bootstrap</div>
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.. toctree::
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   :includehidden:


   /content/user_guide/auto_examples/1single/index.rst
   /content/user_guide/auto_examples/2cross/index.rst
   /content/user_guide/auto_examples/3multi/index.rst
   /content/user_guide/auto_examples/4validation/index.rst


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

      :download:`Download all examples in Python source code: auto_examples_python.zip </content/user_guide/auto_examples/auto_examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </content/user_guide/auto_examples/auto_examples_jupyter.zip>`


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