name: scipy-best-practices
description: Best practices for SciPy scientific computing, optimization, signal processing, and statistical analysis in Python

SciPy Best Practices

Expert guidelines for SciPy development, focusing on scientific computing, optimization, signal processing, and statistical analysis.

Code Style and Structure

• Write concise, technical Python code with accurate SciPy examples
• Prioritize numerical accuracy and computational efficiency
• Use functional programming patterns for mathematical operations
• Prefer vectorized operations over explicit loops
• Use descriptive variable names reflecting scientific context
• Follow PEP 8 style guidelines

scipy.optimize - Optimization

• Use scipy.optimize.minimize() for general-purpose optimization
• Choose appropriate method based on problem characteristics:
• 'BFGS' for smooth, unconstrained problems
• 'L-BFGS-B' for bounded problems
• 'SLSQP' for constrained optimization
• 'Nelder-Mead' for non-differentiable functions
• Provide gradients when available for faster convergence
• Use scipy.optimize.curve_fit() for nonlinear least squares fitting
• Use scipy.optimize.root() for finding roots of equations

scipy.linalg - Linear Algebra

• Prefer scipy.linalg over numpy.linalg for additional functionality
• Use scipy.linalg.solve() instead of computing matrix inverse
• Leverage specialized solvers for structured matrices (banded, triangular)
• Use scipy.linalg.lu_factor() and lu_solve() for multiple right-hand sides
• Use sparse matrix solvers from scipy.sparse.linalg for large sparse systems

scipy.stats - Statistics

• Use distribution objects for probability calculations
• Leverage scipy.stats.describe() for summary statistics
• Use hypothesis testing functions: ttest_ind(), chi2_contingency(), mannwhitneyu()
• Generate random samples with .rvs() method on distributions
• Use .fit() for parameter estimation from data

scipy.interpolate - Interpolation

• Use scipy.interpolate.interp1d() for 1D interpolation
• Use scipy.interpolate.griddata() for scattered data interpolation
• Choose appropriate interpolation method: 'linear', 'cubic', 'nearest'
• Use spline functions for smooth interpolation: UnivariateSpline, BSpline
• Consider RegularGridInterpolator for regular grid data

scipy.integrate - Integration

• Use scipy.integrate.quad() for single integrals
• Use scipy.integrate.dblquad(), tplquad() for multiple integrals
• Use scipy.integrate.solve_ivp() for ordinary differential equations
• Choose appropriate ODE method: 'RK45', 'BDF', 'LSODA'
• Provide Jacobian for stiff systems to improve performance

scipy.signal - Signal Processing

• Use scipy.signal.butter(), cheby1(), ellip() for filter design
• Apply filters with scipy.signal.filtfilt() for zero-phase filtering
• Use scipy.signal.welch() for power spectral density estimation
• Use scipy.signal.find_peaks() for peak detection
• Leverage scipy.signal.convolve() and correlate() for convolution

scipy.sparse - Sparse Matrices

• Use appropriate sparse format for your use case:
• csr_matrix for efficient row slicing and matrix-vector products
• csc_matrix for efficient column slicing
• coo_matrix for constructing sparse matrices
• lil_matrix for incremental construction
• Convert to optimal format before operations
• Use scipy.sparse.linalg solvers for sparse linear systems

Performance Optimization

• Use appropriate data types (float64 for precision, float32 for memory)
• Leverage BLAS/LAPACK through SciPy for optimized linear algebra
• Pre-allocate arrays when possible
• Use in-place operations when available

Error Handling and Validation

• Check convergence status of optimization routines
• Validate numerical results for reasonableness
• Handle ill-conditioned problems gracefully
• Use appropriate tolerances for convergence criteria

Testing Scientific Code

• Test against known analytical solutions
• Use np.testing.assert_allclose() for numerical comparisons
• Test edge cases and boundary conditions
• Verify conservation laws and invariants

Key Conventions

• Import specific submodules: from scipy import optimize, stats, linalg
• Use snake_case for variables and functions
• Document algorithm choices and parameters
• Include convergence diagnostics in output