scientific-computing-system-2.0
CDS v2 is a scientific computing platform built on the scientific Python stack: NumPy, SciPy, pandas and matplotlib. The algorithms proven in the pure-Python scientific-computing-system (v1.x) form its foundation; v2 rebuilds them for speed and adds new domain modules on top.
Installation
pip install scientific-computing-system-2.0
From source:
git clone https://github.com/Furox-Art/scientific-computing-system-2.0.git
cd scientific-computing-system-2.0
pip install -e .[dev]
Quick start
import numpy as np
import cds2
# Linear algebra
A = [[3.0, 1.0], [1.0, 2.0]]
b = [9.0, 8.0]
x = cds2.linalg.solve(A, b)
# Statistics
r = cds2.stats.independent_t_test([1, 2, 3, 4, 5], [3, 4, 5, 6, 7])
# Optimization
res = cds2.optimize.minimize(lambda v: (v[0] - 2) ** 2 + (v[1] + 1) ** 2, x0=[0.0, 0.0])
print(res.x) # ~ [2.0, -1.0]
# Signals
freqs, psd = cds2.signals.power_spectrum(np.sin(np.linspace(0, 100, 1024)), fs=256.0)
# Graphs with PageRank
adj = cds2.graph.from_edges(4, [(0, 1), (0, 2), (1, 3), (2, 3)], directed=True)
scores = cds2.graph.pagerank(adj)
# Information theory
h = cds2.infotheory.entropy([0.25, 0.25, 0.25, 0.25])
mi = cds2.infotheory.mutual_information([[0.5, 0.0], [0.0, 0.5]])
# Chaos / nonlinear dynamics
series = cds2.chaos.logistic_map(3.99, length=400, seed=1)
lyap = cds2.chaos.largest_lyapunov_exponent(series)
# Bayesian conjugate updates
post = cds2.bayes.beta_binomial_update(successes=7, failures=3)
print(post.mean) # 0.7
# Metaheuristics
res = cds2.metaheuristics.pso_minimize(lambda v: (v[0] - 3) ** 2, [(-10, 10)], seed=1)
# Geometry
area = cds2.geometry.hull_area([(0, 0), (1, 0), (0, 1)])
# Reinforcement learning
q_values, returns = cds2.rl.q_learn(cds2.rl.GridWorld(4, 4), episodes=300, seed=1)
Modules
| Module | Built on | Highlights |
|---|---|---|
cds2.linalg |
NumPy | solve, det, inv, pinv, eig/eigh, SVD, least squares, cholesky, cond |
cds2.stats |
scipy.stats | t-tests, ANOVA, non-parametrics, correlations, chi-square, effect sizes, normal dist helpers |
cds2.optimize |
scipy.optimize | minimize, roots (brentq/newton/system), linprog, least squares, curve fit |
cds2.integrate |
scipy.integrate | quad, 2-D/3-D integration, ODE solvers, trapezoid/simpson |
cds2.interpolate |
scipy.interpolate | linear/cubic/pchip, lagrange, griddata, regular grids |
cds2.signals |
scipy.signal | FFT, PSD/welch/spectrogram, Butterworth filters, peaks, envelope |
cds2.montecarlo |
NumPy Generator | pi estimate, MC integration/expectation, hit-or-miss (all seedable) |
cds2.graph |
scipy.sparse.csgraph | components, Dijkstra/Bellman-Ford/Floyd-Warshall, MST, topological order, PageRank |
cds2.ml |
NumPy/SciPy | LinearRegression, LogisticRegression, KMeans++, PCA, KNN, metrics, data generators |
cds2.timeseries |
pandas | moving average, EWM, differencing, seasonal decomposition, ACF/PACF, Ljung-Box |
cds2.viz |
matplotlib | series/histogram/scatter/heatmap/spectrum/regression/confusion plots |
cds2.io |
pandas | CSV/JSON read-write, optional Excel/Parquet bridges, DataFrame summaries |
cds2.calculus |
NumPy | derivative, complex-step gradient, jacobian, hessian |
cds2.special |
scipy.special | gamma, erf family, beta, Bessels, zeta |
cds2.sparse |
scipy.sparse.linalg | CG/GMRES/BiCGSTAB solvers, Lanczos eigenpairs, truncated SVD |
cds2.distributions |
scipy.stats | t, chi2, F, exponential, uniform, lognormal, poisson, binomial (pdf/cdf/ppf) |
cds2.spectral |
scipy.sparse | Laplacians, Fiedler vector, algebraic connectivity, spectral clustering |
cds2.infotheory |
NumPy | Shannon/joint/conditional entropy, KL & Jensen-Shannon divergence, mutual information, permutation entropy |
cds2.chaos |
NumPy | delay embedding, false nearest neighbours, Lyapunov exponent, correlation dimension, sample entropy, Hurst exponent, bifurcation scans |
cds2.bayes |
scipy.stats | Beta-Binomial / Normal-Normal / Gamma-Poisson conjugate updates, credible intervals, naive Bayes, Metropolis posteriors |
cds2.bayesopt |
scipy.optimize | Gaussian Process, expected improvement, UCB, Bayesian optimization |
cds2.data_analysis |
pandas | DataSet / DataFrame bridge, describe/summarize, group-by, NaN-aware |
cds2.metaheuristics |
NumPy | real-coded genetic algorithm, particle swarm optimization, simulated annealing |
cds2.geometry |
scipy.spatial | convex hull, closest pair, point-in-polygon, polygon area/perimeter, line-segment intersection, rotations |
cds2.rl |
NumPy | Bernoulli bandits (epsilon-greedy, UCB1), tabular Q-learning, grid-world environment |
cds2.quality |
NumPy + scipy.stats | Shewhart/EWMA/CUSUM/p control charts, Cp/Cpk capability indices, defective PPM |
cds2.design |
NumPy | full & fractional factorial DOE, Latin hypercube sampling, central composite designs |
cds2.wavelets |
NumPy | Haar DWT/IDWT, multi-level decomposition, wavelet denoising |
cds2.epidemiology |
NumPy | SIR/SEIR compartmental models (RK4), herd immunity, final-size iteration |
cds2.image |
NumPy | 2-D convolution, Gaussian blur, Sobel edges, pooling, binary morphology |
cds2.genetics |
pure Python | GC content, k-mers, reverse complement, Needleman-Wunsch alignment, ORF finder |
cds2.reliability |
scipy.stats | Kaplan-Meier survival curves, Weibull fitting, MTBF/availability, bathtub hazard |
cds2.finance |
NumPy + scipy.stats | returns, Sharpe/Sortino, max drawdown, Black-Scholes greeks, Monte Carlo VaR |
cds2.text |
NumPy | tokenization, TF-IDF matrix, cosine & Jaccard similarity, term summaries |
cds2.game_theory |
scipy.optimize | Nash equilibria, iterated dominance elimination, zero-sum minimax, IPD tournaments |
cds2.combinatorial |
scipy.optimize | nearest-neighbor TSP + 2-opt, 0/1 knapsack DP, optimal assignment, LCS |
cds2.spatial |
scipy.spatial | Moran's I, Geary's C, row-standardized weights, nearest-neighbor index |
cds2.modeling |
pure Python | expression trees, symbolic diff/integral, polynomial solving, MathModel |
cds2.hypothesis |
pure Python | heuristic hypothesis generation: trend, periodicity, outlier, correlation |
cds2.knowledge |
pure Python | knowledge graph with typed relations, notebook, ranked search |
cds2.pde |
NumPy | heat/wave 1D/2D FTCS/leapfrog, CFL-guarded, Dirichlet/Neumann |
cds2.sde |
NumPy | Euler-Maruyama / Milstein ensembles, ensemble statistics |
cds2.scientific |
pure Python | CODATA constants, mechanics/EM/thermo formulas, unit conversion |
cds2.quantum |
NumPy | statevector circuit simulator up to 16 qubits |
cds2.nlp |
NumPy | scalar autograd, BPE tokenizer, multi-head attention, mini-GPT forward pass |
cds2.cli |
argparse | cds2 console entry point (info/stats/integrate/linsolve/entropy/units/solve/plot) |
Facade vs Real Capability
Some cds2.* modules are thin convenience wrappers that only coerce args and unify return types; others contain CDS-native science with no SciPy equivalent. Knowing which is which tells you when cds2 saves time and when to import upstream directly.
| Class | What it means | Modules | Guidance |
|---|---|---|---|
| Convenience re-export | Thin numpy/scipy/pandas wrappers that only coerce args / unify return types. No new math; lags upstream by one release. |
cds2.special¹, cds2.distributions¹ |
Prefer upstream. from scipy import special, stats |
| Convenience re-export, kept | Same pattern, but the typed dataclass DX justifies the import. |
cds2.linalg, cds2.interpolate, cds2.io (thin part), cds2.scientific² |
Use cds2 for uniform result types; docs state Convenience re-export — see SciPy/pandas for full API. |
| Thin + CDS companion | Module keeps its wrappers but its reason to exist is a companion with no SciPy equivalent. | cds2.integrate + cds2.sde, cds2.optimize + cds2.metaheuristics, cds2.signals + cds2.wavelets/cds2.spectral/cds2.chaos, cds2.sparse³ |
Keep cds2. Deterministic integrate pairs with SDE ensembles; optimize pairs with global search. |
| Native | Pure CDS: constants, formulas, C kernels, ML, etc. | cds2.graph (C kernel), cds2.ml, cds2.sde, cds2.quality, … |
Always use cds2. |
¹ Deprecated since 4.3.0, removed in 5.0.0: DeprecationWarning. ² cds2.scientific is 100% native (CODATA CONSTANTS, physics formulas, convert_units). ³ cds2.sparse already has real value: jacobi_preconditioner/ilu_preconditioner → LinearOperator, residual_norm diagnostics.
# Convenience re-export — use SciPy
from scipy import special as sps
from scipy import stats
sps.gamma([0.5, 1, 2])
stats.norm.pdf(0.0, loc=0, scale=1)
# CDS-native — use cds2
from cds2 import sde
ens = sde.sde_milstein(
lambda y, t: 0.05 * y,
lambda y, t: 0.20 * y,
y0=[100.0],
t_span=(0, 1),
dt=1e-3,
n_paths=8192,
seed=0,
)
CLI
cds2 info
cds2 stats 1,2,3,4,5
cds2 integrate sin --a 0 --b 3.14159
cds2 linsolve --a "3,1;1,2" --b "9,8"
cds2 entropy "0.25,0.25,0.25,0.25"
cds2 units 5 --from-unit km --to-unit mile
cds2 solve --coeffs "1,-5,6"
cds2 plot 1,3,2,5,4 --file out.png
Relationship to CDS v1.x
The original zero-dependency pure-Python line lives at Furox-Art/scientific-computing-system and remains available. v2 is an independent project that trades that constraint for the speed and breadth of the scientific Python ecosystem.
Runnable case studies live in examples/ - see the docs page for details.
Benchmarks
cds2 races the scientific stack head-to-head, and ships its own compiled C kernels where they help. Current scoreboard (full methodology in docs/benchmarks.md):
| Race | Baseline | cds2/baseline |
|---|---|---|
| PageRank 400n (C kernel) | NetworkX | 0.18x |
| K-Means 4k×2 k=8 (C kernel) | scikit-learn | 0.72x |
| Linear regression 20k×10 | scikit-learn | 0.74x |
| Monte Carlo pi 2M | hand-vectorized NumPy | 0.77x |
| solve / eigh / rfft / welch / minimize | NumPy & SciPy | ~1.00x |
| describe 500k (adds quartiles) | SciPy | 1.10x |
Wrapper APIs hold parity with raw NumPy/SciPy; the KMeans Lloyd loop and
PageRank power iteration are from-scratch C extensions (cds2._fast_kmeans,
cds2._fast_pagerank) that beat the specialist libraries. A pure-Python
fallback wheel keeps compiler-less installs working.
python benchmarks/run_benchmarks.py # full run
python benchmarks/run_benchmarks.py --quick # smoke run
Development
pip install -e .[dev]
pytest # run the test suite
ruff check . # lint
License
MIT: see LICENSE.
1 maintainer
Release files for scientific-computing-system-2.0 5.1.0
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