Project Name | Stars | Downloads | Repos Using This | Packages Using This | Most Recent Commit | Total Releases | Latest Release | Open Issues | License | Language |
---|---|---|---|---|---|---|---|---|---|---|
Quaternion | 540 | 17 | 37 | a month ago | 186 | April 28, 2022 | 3 | mit | Python | |
Add built-in support for quaternions to numpy | ||||||||||
Alyn | 174 | 4 years ago | 15 | mit | Python | |||||
Detect and fix skew in images containing text | ||||||||||
Quaternionic | 61 | 2 | 2 months ago | 39 | March 27, 2022 | 4 | mit | Python | ||
Interpret numpy arrays as quaternionic arrays with numba acceleration | ||||||||||
Eigen3topython | 38 | 4 months ago | 4 | bsd-2-clause | Python | |||||
Provide Eigen3 to numpy conversion | ||||||||||
Pymesh | 28 | 3 | 6 years ago | 7 | October 16, 2015 | 3 | mit | Python | ||
Library for manipulating (Translate, Rotate and Scale) 3D data using numpy. Currently, this library supports STL & OBJ. | ||||||||||
Xmca | 20 | a year ago | 6 | mit | Python | |||||
Maximum Covariance Analysis in Python | ||||||||||
Rowan | 11 | 4 months ago | 1 | other | Python | |||||
A Python package for working with quaternions. | ||||||||||
Models | 10 | 3 years ago | R | |||||||
NLP models | ||||||||||
Rotnist | 8 | 5 years ago | mit | Python | ||||||
Rotated MNIST dataset | ||||||||||
Infogan Tensorflow | 5 | 4 years ago | Python | |||||||
InfoGAN implementation using tensorflow |
The aim of this package is to provide a flexible tool for the climate science community to perform Maximum Covariance Analysis (MCA) in a simple and consistent way. Given the huge popularity of xarray
in the climate science community, xmca
supports xarray.DataArray
as well as numpy.ndarray
as input formats.
_{Mode 2 of complex rotated Maximum Covariance Analysis showing the shared dynamics of SST and continental precipitation associated to ENSO between 1980 and 2020.}
MCA maximises the temporal covariance between two different data fields and is closely related to Principal Component Analysis (PCA) / Empirical Orthogonal Function analysis (EOF analysis). While EOF analysis maximises the variance within a single data field, MCA allows to extract the dominant co-varying patterns between two different data fields. When the two input fields are the same, MCA reduces to standard EOF analysis.
For the mathematical understanding please have a look at e.g. Bretherton et al. or the lecture material written by C. Bretherton.
solve
method provides more flexibility to exponential extension, making complex MCA more stableStandard | Rotated | Complex | Complex Rotated | |
---|---|---|---|---|
EOF analysis | ✔️ | ✔️ | ✔️ | ✔️ |
MCA | ✔️ | ✔️ | ✔️ | ✔️ |
* click on check marks for reference
** Complex rotated MCA is also available as a pre-print on arXiv.
Installation is simply done via
pip install xmca
If you have problems during the installation please consult the documentation or raise an issue here on Github.
A tutorial to get you started as well as the full API can be found in the documentation.
Import the package
from xmca.array import MCA # use with np.ndarray
from xmca.xarray import xMCA # use with xr.DataArray
As an example, we take North American surface temperatures shipped with
xarray
. Note: only works with xr.DataArray
, not xr.Dataset
.
import xarray as xr # only needed to obtain test data
# split data arbitrarily into west and east coast
data = xr.tutorial.open_dataset('air_temperature').air
west = data.sel(lon=slice(200, 260))
east = data.sel(lon=slice(260, 360))
Construct a model with only one field and solve it to perform standard PCA / EOF analysis.
pca = xMCA(west) # PCA of west coast
pca.solve(complexify=False) # True for complex PCA
svals = pca.singular_values() # singular vales = eigenvalues for PCA
expvar = pca.explained_variance() # explained variance
pcs = pca.pcs() # Principal component scores (PCs)
eofs = pca.eofs() # spatial patterns (EOFs)
Obtaining a Varimax/Promax-rotated solution can be achieved by rotating
the model choosing the number of EOFs to be rotated (n_rot
) as well as the
Promax parameter (power
). Here, power=1
equals a Varimax-rotated solution.
pca.rotate(n_rot=10, power=1)
expvar_rot = pca.explained_variance() # explained variance
pcs_rot = pca.pcs() # Principal component scores (PCs)
eofs_rot = pca.eofs() # spatial patterns (EOFs)
Same as for PCA / EOF analysis, but with two input fields instead of one.
mca = xMCA(west, east) # MCA of field A and B
mca.solve(complexify=False) # True for complex MCA
eigenvalues = mca.singular_values() # singular vales
pcs = mca.pcs() # expansion coefficient (PCs)
eofs = mca.eofs() # spatial patterns (EOFs)
A simple way of estimating the significance of the obtained modes is by running Monte Carlo simulations based on uncorrelated Gaussian white noise known as Rule N (Overland and Preisendorfer 1982). Here we create 200 of such synthetic data sets and compare the synthetic with the real singular spectrum to assess significance.
surr = mca.rule_n(200)
median = surr.median('run')
q99 = surr.quantile(.99, dim='run')
q01 = surr.quantile(.01, dim='run')
cutoff = np.sum((svals - q99 > 0)).values # first 8 modes significant
fig = plt.figure(figsize=(10, 4))
ax = fig.add_subplot(111)
svals.plot(ax=ax, yscale='log', label='true')
median.plot(ax=ax, yscale='log', color='.5', label='rule N')
q99.plot(ax=ax, yscale='log', color='.5', ls=':')
q01.plot(ax=ax, yscale='log', color='.5', ls=':')
ax.axvline(cutoff + 0.5, ls=':')
ax.set_xlim(-2, 200)
ax.set_ylim(1e-1, 2.5e4)
ax.set_title('Significance based on Rule N')
ax.legend()
The first 8 modes are significant according to rule N using 200 synthetic runs.
mca.save_analysis('my_analysis') # this will save the data and a respective
# info file. The files will be stored in a
# special directory
mca2 = xMCA() # create a new, empty instance
mca2.load_analysis('my_analysis/info.xmca') # analysis can be
# loaded via specifying the path to the
# info file created earlier
The package provides a method to plot individual modes.
mca2.set_field_names('West', 'East')
pkwargs = {'orientation' : 'vertical'}
mca2.plot(mode=1, **pkwargs)
Result of default plot method after performing MCA on T2m of North American west and east coast showing mode 1.
You may want to modify the plot for some better optics:
from cartopy.crs import EqualEarth # for different map projections
# map projections for "left" and "right" field
projections = {
'left': EqualEarth(),
'right': EqualEarth()
}
pkwargs = {
"figsize" : (8, 5),
"orientation" : 'vertical',
'cmap_eof' : 'BrBG', # colormap amplitude
"projection" : projections,
}
mca2.plot(mode=3, **pkwargs)
You can save the plot to your local disk as a .png
file via
skwargs={'dpi':200}
mca2.save_plot(mode=3, plot_kwargs=pkwargs, save_kwargs=skwargs)
I am just starting my career as a scientist. Feedback on my scientific work is therefore important to me in order to assess which of my work advances the scientific community. As such, if you use the package for your own research and find it helpful, I would appreciate feedback here on Github, via email, or as a citation:
Niclas Rieger, 2021: nicrie/xmca: version x.y.z. doi:10.5281/zenodo.4749830.
Kudos to the developers and contributors of the following Github projects which I initially used myself and used as an inspiration:
And of course credits to the developers of the extremely useful packages