.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/2multi/plot_rotated_mca.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_auto_examples_2multi_plot_rotated_mca.py: Rotated Maximum Covariance Analysis =================================== Rotated Maximum Covariance Analysis (MCA) between two data sets. .. GENERATED FROM PYTHON SOURCE LINES 7-18 .. code-block:: Python # Load packages and data: import numpy as np import xarray as xr import matplotlib.pyplot as plt from matplotlib.gridspec import GridSpec from cartopy.crs import Orthographic, PlateCarree from cartopy.feature import LAND from xeofs.models import MCA, MCARotator .. GENERATED FROM PYTHON SOURCE LINES 19-20 Create 2 different DataArrays .. GENERATED FROM PYTHON SOURCE LINES 20-25 .. code-block:: Python t2m = xr.tutorial.load_dataset("air_temperature")["air"] da1 = t2m.isel(lon=slice(0, 26)) da2 = t2m.isel(lon=slice(27, None)) .. GENERATED FROM PYTHON SOURCE LINES 26-27 Perform MCA .. GENERATED FROM PYTHON SOURCE LINES 27-31 .. code-block:: Python mca = MCA(n_modes=20, standardize=False, use_coslat=True) mca.fit(da1, da2, dim="time") .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 32-33 Apply Varimax-rotation to MCA solution .. GENERATED FROM PYTHON SOURCE LINES 33-37 .. code-block:: Python rot = MCARotator(n_modes=10) rot.fit(mca) .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 38-40 Get rotated singular vectors, projections (PCs), homogeneous and heterogeneous patterns: .. GENERATED FROM PYTHON SOURCE LINES 40-46 .. code-block:: Python singular_vectors = rot.components() scores = rot.scores() hom_pats, pvals_hom = rot.homogeneous_patterns() het_pats, pvals_het = rot.heterogeneous_patterns() .. GENERATED FROM PYTHON SOURCE LINES 47-51 When two fields are expected, the output of the above methods is a list of length 2, with the first and second entry containing the relevant object for ``X`` and ``Y``. For example, the p-values obtained from the two-sided t-test for the homogeneous patterns of ``X`` are: .. GENERATED FROM PYTHON SOURCE LINES 51-54 .. code-block:: Python pvals_hom[0] .. raw:: html 
<xarray.DataArray 'pvalues_of_left_homogeneous_patterns' (mode: 10, lat: 25,
                                                              lon: 26)> Size: 52kB
    5.921e-81 4.092e-64 6.235e-58 5.975e-49 ... 0.001974 0.005479 0.01494 0.03604
    Coordinates:
      * lat      (lat) float32 100B 15.0 17.5 20.0 22.5 25.0 ... 67.5 70.0 72.5 75.0
      * lon      (lon) float32 104B 200.0 202.5 205.0 207.5 ... 257.5 260.0 262.5
      * mode     (mode) int64 80B 1 2 3 4 5 6 7 8 9 10
    Attributes:
        model:             Rotated MCA
        n_modes:           10
        power:             1
        max_iter:          1000
        rtol:              1e-08
        squared_loadings:  False
        compute:           True
        software:          xeofs
        version:           2.3.2
        date:              2024-03-31 21:13:29


.. GENERATED FROM PYTHON SOURCE LINES 55-56 Create a mask to identifiy where p-values are below 0.05 .. GENERATED FROM PYTHON SOURCE LINES 56-61 .. code-block:: Python hom_mask = [values < 0.05 for values in pvals_hom] het_mask = [values < 0.05 for values in pvals_het] .. GENERATED FROM PYTHON SOURCE LINES 62-63 Plot some relevant quantities of mode 2. .. GENERATED FROM PYTHON SOURCE LINES 63-119 .. code-block:: Python lonlats = [ np.meshgrid(pvals_hom[0].lon.values, pvals_hom[0].lat.values), np.meshgrid(pvals_hom[1].lon.values, pvals_hom[1].lat.values), ] proj = [ Orthographic(central_latitude=30, central_longitude=-120), Orthographic(central_latitude=30, central_longitude=-60), ] kwargs1 = {"cmap": "BrBG", "vmin": -0.05, "vmax": 0.05, "transform": PlateCarree()} kwargs2 = {"cmap": "RdBu", "vmin": -1, "vmax": 1, "transform": PlateCarree()} mode = 2 fig = plt.figure(figsize=(7, 14)) gs = GridSpec(5, 2) ax1 = [fig.add_subplot(gs[0, i], projection=proj[i]) for i in range(2)] ax2 = [fig.add_subplot(gs[1, i], projection=proj[i]) for i in range(2)] ax3 = [fig.add_subplot(gs[2, i], projection=proj[i]) for i in range(2)] ax4 = [fig.add_subplot(gs[3, i]) for i in range(2)] for i, a in enumerate(ax1): singular_vectors[i].sel(mode=mode).plot(ax=a, **kwargs1) for i, a in enumerate(ax2): hom_pats[i].sel(mode=mode).plot(ax=a, **kwargs2) a.scatter( lonlats[i][0], lonlats[i][1], hom_mask[i].sel(mode=mode).values * 0.5, color="k", alpha=0.5, transform=PlateCarree(), ) for i, a in enumerate(ax3): het_pats[i].sel(mode=mode).plot(ax=a, **kwargs2) a.scatter( lonlats[i][0], lonlats[i][1], het_mask[i].sel(mode=mode).values * 0.5, color="k", alpha=0.5, transform=PlateCarree(), ) for i, a in enumerate(ax4): scores[i].sel(mode=mode).plot(ax=a) a.set_xlabel("") for a in np.ravel([ax1, ax2, ax3]): a.coastlines(color=".5") a.add_feature(LAND) plt.tight_layout() plt.savefig("rotated_mca.jpg") .. image-sg:: /auto_examples/2multi/images/sphx_glr_plot_rotated_mca_001.png :alt: mode = 2, mode = 2, mode = 2, mode = 2, mode = 2, mode = 2, mode = 2, mode = 2 :srcset: /auto_examples/2multi/images/sphx_glr_plot_rotated_mca_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 2.207 seconds) .. _sphx_glr_download_auto_examples_2multi_plot_rotated_mca.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_rotated_mca.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_rotated_mca.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_