Zeit: Change Detection and Time Series for Python

Zeit is a high-performance Python package for Earth Observation (EO) data cube processing and time series analysis. It bridges the gap between modern cloud-native data formats (STAC, Xarray, Dask) and state-of-the-art pixel-based trajectory algorithms (TWDTW, CCDC, LandTrendr).

Built with highly optimized C++ extensions (OpenMP and Eigen SIMD) bound to Python via pybind11, Zeit is designed to handle massive multi-spectral satellite image time series efficiently while keeping memory footprints strictly bounded.

Key Capabilities

• ARD Data Cube Ingestion: Fetch cloud-native STAC catalogs (via MGRS/WRS tiles or Bounding Boxes) or parse local TIFF directories into lazy Dask-backed xarray Datacubes.
• Semantic Cloud Masking: Automated extraction and translation of Quality Assessment (QA) bands for Landsat and Sentinel-2 directly inside the query pipeline, plus a temporal Tmask harmonic baseline model to catch clouds/shadows missed by the native QA mask.
• Sensor Harmonization: harmonize puts Sentinel-2 reflectance on Landsat 8's OLI scale with the HLS bandpass adjustment of each Sentinel-2 unit (A, B, C), and optionally Landsat 5/7 with Roy et al. (2016), so a dense series that mixes sensors has no step for CCDC or BFAST to read as a break.
• Temporal Regularization: Mathematical composite generation (e.g., Medoid, Median) to align irregular satellite acquisitions into uniform time steps (crucial for Deep Learning and DTW).
• High-Performance C++ Algorithms:
  • TWDTW (Time-Weighted Dynamic Time Warping): Highly optimized with LB_Keogh lower bounding, early abandonment, Sakoe-Chiba constraints, and multivariate Eigen vectorization.
  • Batch SOM (Self-Organizing Maps): Unsupervised multi-threaded clustering of massive spectral-temporal arrays.
  • CCDC / COLD: Continuous Change Detection and Classification via robust harmonic modeling.
  • LandTrendr: Trajectory-based disturbance and recovery detection.
  • BFAST, BFAST Monitor & BFAST Lite: Classic iterative trend+season break detection, near-real-time monitoring, and single-pass multiple-breakpoint detection (ported from R's bfast/strucchangeRcpp).
  • One map of events for every algorithm: extract_events turns the result of LandTrendr, CCDC or any BFAST into the same maps (year, date, magnitude, DSNR of the change per pixel), and agreement shows where and when the algorithms agree.
  • Phenology Extraction: 19 simultaneous phenological metrics from optimized curve-fitting models (Beck, Elmore, Gu, Zhang, Asymmetric Gaussian, Double Logistic), with QA-based per-observation weighting.
  • CODED: forest degradation and deforestation from the NDFI of a spectral unmixing (unmix, Souza et al. 2005) of every Landsat observation.
  • Mann-Kendall / Theil-Sen: Pixel-wise non-parametric trend test and slope estimation for detecting statistically significant greening/browning trends.
  • SNIC Segmentation: Superpixel segmentation of images and whole time series cubes (one segment = similar trajectories), matching the original SNIC's labels pixel for pixel, with tile-parallel processing for large scenes.
• Validation: sampling_design, stratified_sample and accuracy follow the good practices of Olofsson et al. (2014): a stratified random sample of any map, then its accuracies and error-adjusted areas with confidence intervals (checked against the paper's example and R's sits). interpret labels the sample by eye, point after point, with yearly image chips, the pixel's series, the keyboard, and a review of the error matrix.
• Foundation-model embeddings: load_embeddings reads the yearly embeddings of TESSERA (128 dimensions) and Google's AlphaEarth Foundations (64) at 10 m as a (time, band, y, x) cube, on the products' own grids, lazily. Classify them from few samples, cluster or segment them as any cube; similarity finds places like a sample, and embedding_change follows each pixel from year to year into the same events as LandTrendr or CCDC. The cube remembers which embeddings it holds, and a model refuses another product's.
• Deep Learning (zeit.ai): PyTorch architectures for spatio-temporal Earth Observation (U-TAE, LightTAE, TempCNN, Siamese Networks) and a wrapper for Geospatial Foundation Models (ViT), with samples, train and predict to go from a cube and labelled samples to a georeferenced map.
• Visualisation (zeit.plot): One function to look at any cube, map or result: an interactive viewer in Jupyter (or its own window from a script) that pages through dense time series at the display's frame rate, with a click-a-pixel inspector showing each algorithm's fit, satellite basemaps and vector outlines; or a matplotlib figure for reports.
• Command-Line Interface: Every core algorithm is also available as a zeit subcommand, for running change detection on GeoTIFF stacks from bash scripts, cron jobs, or HPC environments without writing Python.

Installation

pip install zeit-cdts

(Note: Wheels are provided for Windows, Linux, and macOS. macOS runs in single-threaded mode by default due to Apple Clang lacking OpenMP).

For zeit.plot (matplotlib and anywidget), install the plot extra: pip install zeit-cdts[plot]. The TESSERA and AlphaEarth embeddings need nothing extra (TESSERA's reader, geotessera, comes with zeit on Python 3.12+).

For macOS users who want C++ OpenMP multi-threading: Apple's default Clang compiler disables OpenMP. To achieve maximum performance and enable multi-threading, you must install the libomp library and manually export the compilation flags before forcing a local compilation:

brew install libomp
export CFLAGS="-I$(brew --prefix libomp)/include"
export CXXFLAGS="-I$(brew --prefix libomp)/include"
export LDFLAGS="-L$(brew --prefix libomp)/lib -lomp"
pip install --no-binary zeit-cdts zeit-cdts

Quickstart: load, run, export

Every algorithm is one function that understands its input, and the dates and georeferencing travel with the data:

import zeit

ndvi = zeit.load_raster("LT_Stack_NDVI_Rondonia.tif")   # (time, y, x) cube, years from the band names
lt = zeit.landtrendr(ndvi)                               # or zeit.ccdc, zeit.bfast_monitor, zeit.mann_kendall, zeit.phenology...
loss = zeit.extract_events(lt)                           # greatest NDVI loss per pixel
zeit.save_raster(loss, "lt_rondonia")                    # one georeferenced GeoTIFF per metric
zeit.plot(ndvi, fit=lt)                                  # look: page through the years, click a pixel to see its fit

Visualisation

zeit.plot shows any cube, map, result Dataset or pixel's series. In a notebook (JupyterLab, VS Code, Colab) it returns an interactive viewer; in a script it opens the same viewer in its own window; with static=True or save= it draws a matplotlib figure.

ndvi = zeit.load_raster("LT_Stack_NDVI_Rondonia.tif")
zeit.plot(ndvi)                                          # space plays the 40 years, wheel zooms, hover reads values
zeit.plot(ndvi, fit=zeit.landtrendr(ndvi))               # click a pixel: its series and LandTrendr's segments
zeit.plot(zeit.extract_events(zeit.landtrendr(ndvi)), basemap="satellite", vector="aoi.gpkg")
zeit.plot(ndvi, time=["1985", "2000", "2024"], save="ndvi.png")   # a figure for a report

It is fast because each frame travels to the browser once, as one byte per cell, and is coloured by the GPU: paging through time then runs at the display's refresh rate without touching Python, and the cube is only ever read at screen resolution. See the plotting tutorial.

Cloud-Native ARD Cubes (STAC)

Fetch lazy evaluated, Dask-backed analysis-ready data cubes directly from STAC providers (e.g., Earth Search, Planetary Computer, Brazil Data Cube).

import zeit

# Build a lazy DataArray using MGRS/WRS tiles or Bounding Boxes
cube = zeit.build_time_series(
    source="earth_search",
    collection="sentinel-2-l2a",
    tiles=["22JFQ"], # Sentinel-2 MGRS or Landsat WRS-2 (e.g., "215065")
    start_date="2022-01-01",
    end_date="2022-12-31",
    bands=["red", "green", "blue", "nir"],
    apply_cloud_mask=True # Automatically fetches QA band and natively masks clouds/shadows
)

print(cube) # Returns an xarray.DataArray (Time, Band, Y, X)

Sensor Harmonization

A dense series that mixes Landsat and Sentinel-2 has a step wherever the sensor changes. zeit.harmonize takes each Sentinel-2 date to Landsat 8's OLI with the bandpass adjustment of HLS (one line per band and Sentinel-2 unit, from the HLS v2.0 User Guide), reading each date's sensor from the platform coordinate STAC provides. Given cubes of several collections on one grid, it joins them into one series, matching the bands by role:

grid = dict(source="planetary_computer", bbox=bbox, start_date="2019-01-01", end_date="2024-12-31",
            apply_cloud_mask=True, resolution=30, epsg=32722)
s2 = zeit.build_time_series(collection="sentinel-2-l2a", bands=["B02", "B03", "B04", "B8A", "B11", "B12"], **grid)
landsat = zeit.build_time_series(collection="landsat-c2-l2", bands=["blue", "green", "red", "nir08", "swir16", "swir22"], **grid)
mixed = zeit.harmonize([s2, landsat])            # S2A, S2B and S2C dates each by its own lines; Landsat 8/9 as they are
zeit.ccdc(mixed)

It is the bandpass step of HLS only, not its common atmospheric correction or BRDF normalization; see the reference for what that leaves.

Temporal Regularization

Algorithms like TWDTW, SOM, and Deep Learning expect temporally aligned data. zeit natively regularizes irregular STAC acquisitions.

from zeit import regularize_time_series

# Aggregate observations into 16-day Medoid composites 
# (Maintains xarray lazy evaluation via Dask graphs)
cube_16d = regularize_time_series(cube, freq="16D", method="medoid")

Change Detection (LandTrendr & CCDC)

Continuous structural monitoring using robust breakpoint and harmonic regression models directly on xarray Datacubes (zeit.landtrendr(cube), zeit.ccdc(cube), or pandas-like accessors such as cube.zeit.ccdc(...)).

LandTrendr (Trajectory-based Disturbance)

Identify structural breakpoints in time-series (e.g., detecting exactly when deforestation occurred). One function, zeit.landtrendr, takes a raster file, an in-memory or Dask cube, a NumPy stack or a single pixel's series, and scales LandTrendr to massive datasets using C++ OpenMP and Dask.

import zeit

# 1. An annual index stack: one band per year (years read from band names such as yr1985)
ndvi = zeit.load_raster("LT_Stack_NDVI_Rondonia.tif")   # georeferenced (time, y, x) cube

# 2. Segment every pixel. direction="loss" (the default) looks for drops of the index
#    (NDVI/NBR vegetation loss); use direction="gain" for indices that rise (e.g. SWIR).
lt = zeit.landtrendr(ndvi, max_segments=6)
# xarray.Dataset: vertex_year, vertex_value (vertex, y, x), n_vertices, rmse (y, x)
# Dask cubes stay lazy; zeit.landtrendr("big.tif", chunks="auto") works block by block.

# 3. Analyze disturbances (e.g., finding the biggest drop in NDVI)
loss = zeit.extract_events(
    lt,
    sort_by="greatest",     # Get the segment with the largest magnitude
    min_magnitude=1500      # Optional noise filter (NDVI x 10000)
)

# Georeferenced maps, ready to be exported to GeoTIFF
yod_map = loss["yod"]         # Year of Disturbance (YOD)
mag_map = loss["magnitude"]   # Magnitude of the disturbance
dur_map = loss["duration"]    # How many years the disturbance took
zeit.save_raster(loss, "lt_rondonia")   # one GeoTIFF per map: yod.tif, magnitude.tif, ...

CCDC / COLD (Harmonic Modeling)

Extracts harmonic coefficients (Intercept, Slopes, Sine, Cosine) and detects intra-annual changes by fitting mathematical curves to multi-spectral data. Like LandTrendr, one function, zeit.ccdc, takes a raster file, an in-memory or Dask cube, a NumPy stack or a single pixel's series.

import zeit

# 1. A dense multi-band stack: surface reflectance x 10000 (Blue, Green, Red, NIR, SWIR1, SWIR2)
#    plus a band of Fmask codes (0 clear, 1 water, 2 shadow, 3 snow, 4 cloud, 255 fill)
cube = zeit.load_raster("landsat_sr.tif")   # (time, band, y, x); dates from band names 2020-01-15_blue ...

# 2. Run CCDC on every pixel; the QA band is named, and left out of the spectral bands
segments = zeit.ccdc(cube, qa="fmask", max_segments=6)
# xarray.Dataset: t_start, t_end, t_break (segment, y, x), n_segments (y, x),
# rmse (segment, band, y, x), coefs (segment, band, coef, y, x)
# Dask cubes stay lazy; zeit.ccdc("big.tif", qa="fmask", chunks="auto") works block by block.

first_break = segments.t_break.isel(segment=0)   # date of the first change (NaT = none)
zeit.save_raster(segments, "ccdc_out")           # one GeoTIFF per variable, dates as decimal years

# 3. Generate Synthetic Images (Harmonic Reconstruction)
# Predict what the surface should look like on any arbitrary date without clouds!
synthetic_image = zeit.predict_synthetic_image(segments, "2020-07-15")   # (band, y, x)

# 4. Land Cover Classification using the harmonic models
# Each pixel's model on a date (coefficients and RMSE) as features, a Random Forest
# trained at labelled points, and every pixel classified
rf_model = zeit.train_classifier(segments, "samples.gpkg", label="class", date="2020-07-01")
land_cover = zeit.classify(segments, rf_model, date="2020-07-01")
zeit.save_raster(land_cover, "output/land_cover")     # label.tif; class names in label's flag_meanings

Phenology Extraction

Extract 19 simultaneous phenological metrics (Gu, Zhang, Thresholds, Derivatives, LOS, POP) across massive datasets using optimized C++ curve-fitting models (Beck, Elmore, Gu, Zhang, Asymmetric Gaussian, Double Logistic) over Dask clusters.

The smoothing, curve-fitting, and metric-extraction methodology is based on the R package phenofit (Kong et al., 2022, Methods in Ecology and Evolution, doi:10.1111/2041-210X.13870), reimplemented in C++/Eigen/OpenMP. See the Phenology tutorial for the full reference list and a real-world walkthrough.

import zeit

# cube_16d: (time, y, x) DataArray of 16-day NDVI composites; the day numbering
# and the years are read from its dates
pheno = zeit.phenology(
    cube_16d,
    curve="beck",                   # Beck's double logistic
    annual=False,                   # one value per detected season, not per calendar year
    max_seasons=2,                  # up to 2 growing seasons per pixel

    # Smoothing Configuration
    apply_whittaker=False,          # Turn off Whittaker
    apply_hants=True,               # Use HANTS (Fourier-based) instead
    hants_frequencies=3,

    # Fine-Grained Season Control
    min_season_length=90,           # Ignore noisy peaks shorter than 90 days
    min_amplitude=0.2,              # Ignore seasons with less than 0.2 NDVI growth

    n_jobs=-1                       # C++ multithreading (leave cores for OS)
)

# An xarray.Dataset: 19 metrics + R2 + RMSE, each (season, y, x).
# Lazy for a Dask cube: computed by .compute() or while save_raster writes it.
greenup_map = pheno["Greenup"].sel(season=1)    # Zhang's Greenup, first season
zeit.save_raster(pheno, "output/phenology")      # one GeoTIFF per metric

Down-weighting cloud/snow-contaminated observations: zeit.qc decodes a sensor's QA/QC band into per-observation reliability weights in [0, 1] (ported from phenofit's qcFUN.R), which feed the Whittaker/HANTS smoothing and the iterative curve fit instead of trusting every observation equally:

from zeit.qc import qc_modis_summary

# qa_cube: (time, y, x) MOD13 SummaryQA band, aligned with cube_16d
weights = qc_modis_summary(qa_cube)  # 0=good, 1=marginal, 2=snow/ice, 3=cloudy -> [1.0, 0.5, 0.2, 0.2]

pheno = zeit.phenology(
    cube_16d,
    weights=weights,       # down-weights unreliable observations during smoothing/fitting
    season_retry=True,     # relax the trough threshold once if a pixel finds no season at all
)

Trend Analysis (Mann-Kendall)

Pixel-wise Mann-Kendall trend test + Theil-Sen slope, ported from pymannkendall (Hussain & Mahmud, 2019) to a C++/OpenMP backend, with the same Dask distribution strategy as Phenology Extraction. Useful for "is there a statistically significant greening/browning trend at this pixel?" questions on multi-year composite stacks. See the Mann-Kendall tutorial for the full method comparison (autocorrelation-corrected variants, seasonal test) and a real-world walkthrough.

# annual_ndvi: (time, y, x) DataArray, one max-NDVI composite per year (or a GeoTIFF path)
result = zeit.mann_kendall(
    annual_ndvi,
    method="hamed_rao",  # autocorrelation-corrected (recommended for annual composites)
    alpha=0.05,
)

slope_map = result.slope                      # NDVI change per year
significant = result.h == 1.0                 # statistically significant at alpha=0.05
declining = (result.trend == -1) & significant
zeit.save_raster(result, "output/mann_kendall")   # one GeoTIFF per metric

Change Monitoring (BFAST Monitor)

Pixel-wise near-real-time structural change monitoring, ported from the R package bfast (Verbesselt et al.) to a C++/OpenMP backend, with the same Dask distribution strategy as Mann-Kendall. Unlike LandTrendr/CCDC (retrospective, whole-series segmentation), bfastmonitor fits a trend+harmonic model on a stable history period and asks "is a disturbance happening right now, in the most recent observations?" — verified bit-for-bit-scale accurate against R's bfastmonitor(). See the BFAST Monitor tutorial for the full method background and scope (only type="OLS-MOSUM" + history="all" are ported so far).

# ndvi_16d: (time, y, x) DataArray of 16-day composites from 2010 (or a GeoTIFF path);
# start_time=2010.0 and frequency=23 are read from its dates
result = zeit.bfast_monitor(ndvi_16d, "2022-01-01")   # monitor everything from 2022 onward

disturbed = result.has_break == 1.0
break_time = result.breakpoint  # fractional-year time of the first detected break

Change Detection (BFAST Lite)

Pixel-wise, single-pass multiple-breakpoint detection, ported from the R package bfast's bfastlite() and its strucchangeRcpp dependency's breakpoints() (the Bai & Perron optimal multiple-breakpoint dynamic program) to a C++/OpenMP backend. Unlike bfastmonitor above (single break, near-real-time), this retrospectively segments the whole series into the optimal number of pieces (via the LWZ model-selection criterion) — no STL decomposition needed. Verified exactly against R's bfastlite() across 6 scenarios (~3.1x faster single-threaded than R; n_jobs=-1 adds a further ~5.5x on top of that by reserving one CPU core and parallelizing across the rest — a smaller gap than bfastmonitor's, since this workload is genuinely CPU-bound dynamic programming on both sides, not dominated by R's per-call overhead). See the BFAST Lite tutorial for the full method background, scope, and validation details (including two real numerical bugs caught and fixed along the way).

# ndvi_16d: (time, y, x) DataArray of 16-day composites
result = zeit.bfast_lite(ndvi_16d, max_breaks=5)

n_breaks = result.n_breaks
first_break_idx = result.breakpoint_idx_1  # NaN where n_breaks == 0

Time-Series Classification (TWDTW)

Classify pixels by their likeness to a few reference series, one per class, with Time-Weighted Dynamic Time Warping. The distances are those of the R package twdtw (checked to 1e-12), computed in C++ with OpenMP; a pattern of one year matches the same season of any year, and cloudy dates are left out of each pixel's series.

import pandas as pd
import zeit

# Patterns: a typical series per class, indexed by dates (a DataFrame for several bands)
patterns = {"Forest": forest_ndvi, "Soy": soy_ndvi, "Pasture": pasture_ndvi}

ndvi = zeit.load_raster("S2_ndvi_2022.tif")          # (time, y, x)
classes = zeit.twdtw(ndvi, patterns)                  # label, distance, distances

# Pixels that matched poorly with every pattern: unknown (0)
known = classes.label.where(classes.distance < 15, 0)
classes.label.zeit.plot()                             # legend: Forest, Soy, Pasture
zeit.plot(ndvi, fit=classes)                          # click a pixel: its series and best match

Unsupervised Clustering (SOM)

Unsupervised classification of whole trajectories: zeit.som trains a self-organizing map on a sample of the pixels and puts every pixel in its best-matching neuron. The engine is a C++ port of Python minisom (online and Batch SOM) that reproduces its results bit-for-bit, 30-190x faster.

ndvi = zeit.load_raster("LT_Stack_NDVI_Rondonia.tif")
clusters = zeit.som(ndvi, x=3, y=3, sample=50_000)   # label, distance, prototypes (neuron, time)
clusters.prototypes.sel(neuron=1).plot()              # a typical trajectory
zeit.plot(ndvi, fit=clusters)                         # click a pixel: its series and its prototype

# Before training a classifier: flag samples whose class is not their neuron's
checked = zeit.clean_samples(cube, "samples.gpkg", label="class")

Foundation-Model Embeddings (TESSERA, AlphaEarth)

TESSERA and Google's AlphaEarth Foundations turn a year of Sentinel-1/2 (and, for AlphaEarth, Landsat and more) into one vector per 10 m pixel, every year since 2017. zeit.load_embeddings reads them as a cube on their own UTM grids (the two products line up cell by cell), and the rest of zeit takes it as it is:

emb = zeit.load_embeddings("aoi.gpkg", source="tessera", years=range(2017, 2026))     # or source="alphaearth"
zeit.plot(emb)                                                 # the first 3 principal components, the same colours every year
rf = zeit.train_classifier(emb.sel(time="2024"), "samples.gpkg")
classes = zeit.classify(emb.sel(time="2024"), rf)              # refuses another product's embeddings
like_these = zeit.similarity(emb, "known_mines.gpkg", year=2024)
events = zeit.extract_events(zeit.embedding_change(emb), min_magnitude=0.3)   # yod, date, magnitude, dsnr

Deep Learning (zeit.ai)

PyTorch models for satellite image time series (TempCNN, LightTAE, U-TAE, a Siamese change detector and a foundation-model wrapper), with the path from a cube to a map: samples from labelled points or polygons (validated in spatial blocks), a ready-made training loop, and prediction over the whole cube, lazily and without seams between windows.

from zeit import ai

samples = ai.samples(cube, "samples.gpkg", label="class")   # pixels; patch=64 for U-TAE
model = ai.train(ai.TempCNN, samples, epochs=50)
classes = ai.predict(model, cube)                          # label (y, x), georeferenced
ai.save(model, "tempcnn.pt")

Pre and Post-Processing

Before classifying, it is highly recommended to smooth temporal trajectories. After classifying, pixel-based maps often suffer from noise. Zeit provides fast functions to regularize your data in both dimensions:

import zeit
from zeit import apply_majority_filter, apply_mmu_filter, save_raster

# Temporal smoothing: Whittaker (uneven dates, NaN gaps filled, per-observation weights)...
smoothed = zeit.smooth(cube, lmbda=10.0, weights=clear_sky_weights)

# ...or Savitzky-Golay, for evenly spaced series
smoothed = zeit.smooth(cube, method="savgol", window=5, polyorder=2)

# Spatial Regularization (Mode filter): maps in, maps out, georeferencing kept
regularized_map = apply_majority_filter(land_cover.label, size=3)

# Minimum Mapping Unit (MMU): erase isolated patches smaller than 11 pixels
final_map = apply_mmu_filter(regularized_map, mmu_pixels=11)
save_raster(final_map, "results/classified_final.tif")

Exporting Geospatial Data

save_raster writes any map, stack or result back to disk with its georeferencing, NoData, band names and dates, so GIS software and load_raster read it back as it was.

from zeit import save_raster

save_raster(final_map, "output/land_cover.tif", like=cube, nodata=255)   # numpy: CRS and transform from cube
save_raster(ndvi_cube, "output/ndvi.tif")      # a DataArray brings its own georeferencing and dates
save_raster(events, "output/loss")             # a dict/Dataset of maps: one GeoTIFF per map

Command-Line Interface

Every core algorithm is also available as a zeit subcommand, so you can run change detection directly on GeoTIFF stacks from bash scripts, cron jobs, or HPC batch systems without writing any Python:

zeit landtrendr input_stack.tif output_dir/ --max-segments 6 --jobs -1   # years from the band names, or --start-year

See the CLI reference for the full list of subcommands and options.

Architecture & Threading Safety

Zeit safely blends Python-based distributed workflows (Dask) with highly parallel C++ routines:

• OpenMP CPU Scaling: All C++ algorithms expose the n_jobs parameter, and default to it (n_jobs=-1) in their Python entry points. n_jobs=-1 reserves one CPU core (std::max(1, max_threads - 1)) so the host OS stays responsive during intensive workloads — standardized across every parallel algorithm (LandTrendr, CCDC, TWDTW, SOM, Phenology, Mann-Kendall, BFAST Monitor, BFAST Lite). Pass an explicit positive integer to use a specific thread count instead (e.g. all cores with no reservation, or fewer to leave more headroom).
• Memory Footprint: Algorithms like TWDTW are strictly optimized via a 2-Row Dynamic Programming algorithm, restricting mathematical matrices to the CPU's L1 cache and avoiding heavy allocations.
• Cross-Platform Compatibility: Uses safe #ifdef _OPENMP boundaries to gracefully fallback to single-threaded operations on macOS environments using Apple Clang (which lacks native libomp), allowing pip install to succeed universally.

Versioning

From 1.0, Zeit follows semantic versioning: a minor version adds features, a patch fixes bugs, and neither changes what an existing call returns. A function or argument to be removed first warns with a DeprecationWarning for at least one minor version, and only goes in the next major version.

License

Zeit is free software, licensed under the GNU General Public License v2.0 or later (GPL-2.0-or-later). Several algorithms are ports of existing open-source implementations (bfast, strucchangeRcpp, GLMnet, pymannkendall, GERSL/CCDC, ...); their origins, licenses and copyright notices are listed in THIRD_PARTY_NOTICES.md. Because the CCDC lasso solver derives from GPL-2.0-only code, the compiled extension as a whole is distributed under GPL version 2.