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scipy.interpolate.make_interp_spline: modern 1-D splines Returns a callable BSpline. k=3 is cubic. Extrapolation is a choice.

scipy.integrate.quad: integrate a Python function Returns integral and error estimate. Singularities need points= or weight=.

scipy.linalg.solve: Ax=b with SciPy's solvers Prefer solve over inv. assume_a= when you know structure. scipy.linalg.solve — one ...

scipy.optimize.minimize: find a minimum with a method you choose Pass fun, x0, method=. jac= helps. Check success before ...

scipy.stats.ttest_ind: two-sample t-test without Excel equal_var=False is Welch. p-value is not effect size. scipy.stats.ttest_ind ...

scipy.linalg.lstsq: least squares when A is rectangular Under/over-determined systems. Residuals tell you fit quality.

scipy.fft.fft: discrete Fourier transform Complex output. fftfreq labels bins. rfft for real input. scipy.fft.fft — one API, about 75 seconds.

scipy.special.expit: stable sigmoid Prefer expit over hand-rolled 1/(1+exp(-x)). logit is the inverse. scipy.special.expit — one API, ...

scipy.spatial.ConvexHull: convex envelope of points vertices and simplices. Degenerate inputs raise QhullError. scipy.spatial.

scipy.signal.butter: design a Butterworth filter Returns ba or sos. Prefer sos for stability. Wn is normalized to Nyquist unless fs=.

scipy.stats.bootstrap: confidence intervals without a formula Pass data and statistic. method= and confidence_level= matter.

scipy.stats.pearsonr: linear correlation and its p-value r near 0 is not "independent". Outliers own Pearson. Spearman for ranks.

scipy.io.loadmat: read MATLAB .mat into Python Returns a dict. squeeze_me and struct_as_record shape the pain.

scipy.signal.sosfiltfilt: zero-phase filter forward and back No phase distortion. Not for realtime. Pair with butter(sos).

scipy.optimize.curve_fit: fit a parametric curve to data Returns popt and pcov. Bounds= stop wild parameters. Scale your x.

scipy.stats.norm: pdf, cdf, ppf for the Gaussian loc and scale are mean and std. ppf is the inverse cdf. scipy.stats.norm — one API, ...

scipy.stats.spearmanr: rank correlation when shapes are weird Monotonic, not linear. Ties matter. Still not causation.

scipy.signal.find_peaks: pick peaks with prominence height, distance, prominence beat a raw argmax loop.

scipy.sparse.csr_matrix: store mostly-zeros without melting RAM CSR loves row slices and matvecs. Build with coo then convert.

scipy.optimize.root: solve f(x)=0 in N dimensions method= hybr or lm. Need a residual vector. Check success. scipy.optimize.root ...