feat: add MCA

docs/auto_examples/1eof/plot_bootstrap.ipynb

@@ -0,0 +1,137 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n# Significance teting of EOF analysis via bootstrap\n\nTesting the significance of individual modes and obtain confidence intervals\nfor both EOFs and PCs.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# Load packages and data:\nimport numpy as np\nimport xarray as xr\nimport matplotlib.pyplot as plt\nfrom matplotlib.gridspec import GridSpec\nfrom cartopy.crs import Orthographic, PlateCarree\n\nfrom xeofs.xarray import EOF, Bootstrapper"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "t2m = xr.tutorial.load_dataset('air_temperature')['air']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Perform EOF analysis\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "model = EOF(t2m, n_modes=25, norm=False, dim='time')\nmodel.solve()\nexpvar = model.explained_variance_ratio()\neofs = model.eofs()\npcs = model.pcs()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Perform bootstrapping of the model to identy the number of significant modes.\nWe choose a significance level of alpha=0.05 and perform 25 bootstraps.\nNote - if computationallly feasible - you typically want to choose higher\nnumbers of bootstraps e.g. 100 or 1000.\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "alpha = .05\nn_boot = 25\n\nbs = Bootstrapper(n_boot=n_boot, alpha=alpha)\nbs.bootstrap(model)\nn_significant_modes = bs.n_significant_modes()\nprint('{:} modes are significant at alpha={:.2}'.format(n_significant_modes, alpha))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The bootstrapping procedure identifies 5 significant modes. We can also\ncompute the 95 % confidence intervals of the EOFs/PCs and mask out\ninsignificant elements of the obtained EOFs.\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "eofs_ci, eofs_mask = bs.eofs()\npcs_ci, pcs_mask = bs.pcs()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Summarize the results in a figure.\n\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "lons, lats = np.meshgrid(eofs_mask.lon.values, eofs_mask.lat.values)\nproj = Orthographic(central_latitude=30, central_longitude=-80)\nkwargs = {\n 'cmap' : 'RdBu', 'vmin' : -.05, 'vmax': .05, 'transform': PlateCarree()\n}\n\nfig = plt.figure(figsize=(10, 16))\ngs = GridSpec(5, 2)\nax1 = [fig.add_subplot(gs[i, 0], projection=proj) for i in range(5)]\nax2 = [fig.add_subplot(gs[i, 1]) for i in range(5)]\n\nfor i, (a1, a2) in enumerate(zip(ax1, ax2)):\n a1.coastlines(color='.5')\n eofs.isel(mode=i).plot(ax=a1, **kwargs)\n a1.scatter(\n lons, lats, eofs_mask.isel(mode=i).values * .5,\n color='k', alpha=.5, transform=PlateCarree()\n )\n pcs_ci.isel(mode=i, quantile=0).plot(ax=a2, color='.3', lw='.5', label='2.5%')\n pcs_ci.isel(mode=i, quantile=1).plot(ax=a2, color='.3', lw='.5', label='97.5%')\n pcs.isel(mode=i).plot(ax=a2, lw='.5', alpha=.5, label='PC')\n a2.legend(loc=2)\n\nplt.tight_layout()\nplt.savefig('bootstrap.jpg')"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.13"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}

examples/3significance/plot_bootstrap.py → docs/auto_examples/1eof/plot_bootstrap.py

@@ -1,6 +1,6 @@
 """
-Significance via bootstrap
-==========================
+Significance teting of EOF analysis via bootstrap
+=================================================
 
 Testing the significance of individual modes and obtain confidence intervals
 for both EOFs and PCs.

docs/auto_examples/1eof/plot_bootstrap.py.md5

@@ -0,0 +1 @@
+b574b07fccf1b8340da617a56baf5ea3

docs/auto_examples/1eof/plot_bootstrap.rst

@@ -0,0 +1,221 @@
+
+.. DO NOT EDIT.
+.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
+.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
+.. "auto_examples/1eof/plot_bootstrap.py"
+.. LINE NUMBERS ARE GIVEN BELOW.
+
+.. only:: html
+
+ .. note::
+ :class: sphx-glr-download-link-note
+
+ Click :ref:`here <sphx_glr_download_auto_examples_1eof_plot_bootstrap.py>`
+ to download the full example code
+
+.. rst-class:: sphx-glr-example-title
+
+.. _sphx_glr_auto_examples_1eof_plot_bootstrap.py:
+
+
+Significance teting of EOF analysis via bootstrap
+=================================================
+
+Testing the significance of individual modes and obtain confidence intervals
+for both EOFs and PCs.
+
+.. GENERATED FROM PYTHON SOURCE LINES 8-19
+
+.. code-block:: default
+
+
+
+ # 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 xeofs.xarray import EOF, Bootstrapper
+
+
+
+
+
+
+
+
+.. GENERATED FROM PYTHON SOURCE LINES 20-23
+
+.. code-block:: default
+
+
+ t2m = xr.tutorial.load_dataset('air_temperature')['air']
+
+
+
+
+
+
+
+
+.. GENERATED FROM PYTHON SOURCE LINES 24-25
+
+Perform EOF analysis
+
+.. GENERATED FROM PYTHON SOURCE LINES 25-33
+
+.. code-block:: default
+
+
+ model = EOF(t2m, n_modes=25, norm=False, dim='time')
+ model.solve()
+ expvar = model.explained_variance_ratio()
+ eofs = model.eofs()
+ pcs = model.pcs()
+
+
+
+
+
+
+
+
+
+.. GENERATED FROM PYTHON SOURCE LINES 34-38
+
+Perform bootstrapping of the model to identy the number of significant modes.
+We choose a significance level of alpha=0.05 and perform 25 bootstraps.
+Note - if computationallly feasible - you typically want to choose higher
+numbers of bootstraps e.g. 100 or 1000.
+
+.. GENERATED FROM PYTHON SOURCE LINES 38-47
+
+.. code-block:: default
+
+
+ alpha = .05
+ n_boot = 25
+
+ bs = Bootstrapper(n_boot=n_boot, alpha=alpha)
+ bs.bootstrap(model)
+ n_significant_modes = bs.n_significant_modes()
+ print('{:} modes are significant at alpha={:.2}'.format(n_significant_modes, alpha))
+
+
+
+
+
+.. rst-class:: sphx-glr-script-out
+
+ Out:
+
+ .. code-block:: none
+
+ Bootstrap: 0%| | 0/25 [00:00<?, ?it/s] Bootstrap: 4%|4 | 1/25 [00:00<00:06, 3.44it/s] Bootstrap: 8%|8 | 2/25 [00:00<00:08, 2.87it/s] Bootstrap: 12%|#2 | 3/25 [00:01<00:07, 2.91it/s] Bootstrap: 16%|#6 | 4/25 [00:01<00:07, 2.81it/s] Bootstrap: 20%|## | 5/25 [00:01<00:07, 2.69it/s] Bootstrap: 24%|##4 | 6/25 [00:02<00:06, 2.83it/s] Bootstrap: 28%|##8 | 7/25 [00:02<00:06, 2.78it/s] Bootstrap: 32%|###2 | 8/25 [00:03<00:07, 2.21it/s] Bootstrap: 36%|###6 | 9/25 [00:03<00:07, 2.16it/s] Bootstrap: 40%|#### | 10/25 [00:03<00:06, 2.39it/s] Bootstrap: 44%|####4 | 11/25 [00:04<00:05, 2.50it/s] Bootstrap: 48%|####8 | 12/25 [00:04<00:05, 2.45it/s] Bootstrap: 52%|#####2 | 13/25 [00:05<00:05, 2.33it/s] Bootstrap: 56%|#####6 | 14/25 [00:05<00:05, 2.17it/s] Bootstrap: 60%|###### | 15/25 [00:06<00:04, 2.39it/s] Bootstrap: 64%|######4 | 16/25 [00:06<00:03, 2.42it/s] Bootstrap: 68%|######8 | 17/25 [00:06<00:03, 2.25it/s] Bootstrap: 72%|#######2 | 18/25 [00:07<00:03, 2.27it/s] Bootstrap: 76%|#######6 | 19/25 [00:07<00:02, 2.36it/s] Bootstrap: 80%|######## | 20/25 [00:08<00:02, 2.45it/s] Bootstrap: 84%|########4 | 21/25 [00:08<00:01, 2.22it/s] Bootstrap: 88%|########8 | 22/25 [00:09<00:01, 2.25it/s] Bootstrap: 92%|#########2| 23/25 [00:09<00:00, 2.46it/s] Bootstrap: 96%|#########6| 24/25 [00:09<00:00, 2.65it/s] Bootstrap: 100%|##########| 25/25 [00:10<00:00, 2.75it/s] Bootstrap: 100%|##########| 25/25 [00:10<00:00, 2.47it/s]
+ 3 modes are significant at alpha=0.05
+
+
+
+
+.. GENERATED FROM PYTHON SOURCE LINES 48-51
+
+The bootstrapping procedure identifies 5 significant modes. We can also
+compute the 95 % confidence intervals of the EOFs/PCs and mask out
+insignificant elements of the obtained EOFs.
+
+.. GENERATED FROM PYTHON SOURCE LINES 51-55
+
+.. code-block:: default
+
+
+ eofs_ci, eofs_mask = bs.eofs()
+ pcs_ci, pcs_mask = bs.pcs()
+
+
+
+
+
+
+
+
+.. GENERATED FROM PYTHON SOURCE LINES 56-57
+
+Summarize the results in a figure.
+
+.. GENERATED FROM PYTHON SOURCE LINES 57-84
+
+.. code-block:: default
+
+
+
+ lons, lats = np.meshgrid(eofs_mask.lon.values, eofs_mask.lat.values)
+ proj = Orthographic(central_latitude=30, central_longitude=-80)
+ kwargs = {
+ 'cmap' : 'RdBu', 'vmin' : -.05, 'vmax': .05, 'transform': PlateCarree()
+ }
+
+ fig = plt.figure(figsize=(10, 16))
+ gs = GridSpec(5, 2)
+ ax1 = [fig.add_subplot(gs[i, 0], projection=proj) for i in range(5)]
+ ax2 = [fig.add_subplot(gs[i, 1]) for i in range(5)]
+
+ for i, (a1, a2) in enumerate(zip(ax1, ax2)):
+ a1.coastlines(color='.5')
+ eofs.isel(mode=i).plot(ax=a1, **kwargs)
+ a1.scatter(
+ lons, lats, eofs_mask.isel(mode=i).values * .5,
+ color='k', alpha=.5, transform=PlateCarree()
+ )
+ pcs_ci.isel(mode=i, quantile=0).plot(ax=a2, color='.3', lw='.5', label='2.5%')
+ pcs_ci.isel(mode=i, quantile=1).plot(ax=a2, color='.3', lw='.5', label='97.5%')
+ pcs.isel(mode=i).plot(ax=a2, lw='.5', alpha=.5, label='PC')
+ a2.legend(loc=2)
+
+ plt.tight_layout()
+ plt.savefig('bootstrap.jpg')
+
+
+
+.. image-sg:: /auto_examples/1eof/images/sphx_glr_plot_bootstrap_001.png
+ :alt: mode = 1, mode = 2, mode = 3, mode = 4, mode = 5, mode = 1, mode = 2, mode = 3, mode = 4, mode = 5
+ :srcset: /auto_examples/1eof/images/sphx_glr_plot_bootstrap_001.png
+ :class: sphx-glr-single-img
+
+
+
+
+
+
+.. rst-class:: sphx-glr-timing
+
+ **Total running time of the script:** ( 0 minutes 12.438 seconds)
+
+
+.. _sphx_glr_download_auto_examples_1eof_plot_bootstrap.py:
+
+
+.. only :: html
+
+ .. container:: sphx-glr-footer
+ :class: sphx-glr-footer-example
+
+
+
+ .. container:: sphx-glr-download sphx-glr-download-python
+
+ :download:`Download Python source code: plot_bootstrap.py <plot_bootstrap.py>`
+
+
+
+ .. container:: sphx-glr-download sphx-glr-download-jupyter
+
+ :download:`Download Jupyter notebook: plot_bootstrap.ipynb <plot_bootstrap.ipynb>`
+
+
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+ `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_

docs/auto_examples/1eof/sg_execution_times.rst

@@ -5,14 +5,16 @@
 
 Computation times
 =================
-**00:01.629** total execution time for **auto_examples_1eof** files:
+**00:12.438** total execution time for **auto_examples_1eof** files:
 
 +--------------------------------------------------------------------------------------------+-----------+--------+
-| :ref:`sphx_glr_auto_examples_1eof_plot_multivariate-eof.py` (``plot_multivariate-eof.py``) | 00:01.629 | 0.0 MB |
+| :ref:`sphx_glr_auto_examples_1eof_plot_bootstrap.py` (``plot_bootstrap.py``)  | 00:12.438 | 0.0 MB |
 +--------------------------------------------------------------------------------------------+-----------+--------+
 | :ref:`sphx_glr_auto_examples_1eof_plot_eof-smode.py` (``plot_eof-smode.py``) | 00:00.000 | 0.0 MB |
 +--------------------------------------------------------------------------------------------+-----------+--------+
 | :ref:`sphx_glr_auto_examples_1eof_plot_eof-tmode.py` (``plot_eof-tmode.py``) | 00:00.000 | 0.0 MB |
 +--------------------------------------------------------------------------------------------+-----------+--------+
+| :ref:`sphx_glr_auto_examples_1eof_plot_multivariate-eof.py` (``plot_multivariate-eof.py``) | 00:00.000 | 0.0 MB |
++--------------------------------------------------------------------------------------------+-----------+--------+
 | :ref:`sphx_glr_auto_examples_1eof_plot_weighted-eof.py` (``plot_weighted-eof.py``) | 00:00.000 | 0.0 MB |
 +--------------------------------------------------------------------------------------------+-----------+--------+