7. Numerical Stability¶

This chapter covers NLSQ’s numerical stability features and how to handle ill-conditioned problems.

7.1. Chapter Overview¶

Numerical Guards (10 min): NumericalStabilityGuard for detecting and fixing issues.
SVD Fallback (10 min): Fallback strategies when standard methods fail.
Condition Monitoring (5 min): Tracking condition numbers during optimization.
Recovery (10 min): Automatic recovery from optimization failures.

7.2. Stability Features¶

NLSQ includes multiple stability layers:

Input Validation: Check for NaN, inf, invalid shapes
Condition Monitoring: Track Jacobian condition number
SVD Fallback: Switch to stable SVD when needed
Auto-Recovery: Retry with different strategies

from nlsq import fit

# Enable stability features
popt, pcov = fit(
    model,
    x,
    y,
    p0=[...],
    stability="auto",  # Auto-detect issues
    fallback=True,  # Enable fallbacks
    rescale_data=True,
)  # Normalize data