Least squares fitting with Numpy and Scipy

Abstraction: Python code tutorial for linear and nonlinear least-squares data fitting

Key points:

• Three NumPy approaches to linear least squares: direct matrix inversion, np.linalg.lstsq, and np.polyfit; direct inversion is fastest (~16 µs) but lstsq and polyfit are more idiomatic
• Polynomial fitting uses np.polyfit which internally builds a Vandermonde matrix
• Non-linear least squares uses SciPy's optimize.leastsq with the Levenberg-Marquardt algorithm; requires an initial parameter guess
• scipy.optimize.curve_fit wraps leastsq with a simpler interface but is ~70% slower than calling leastsq directly
• Poor initial guesses (e.g., for trigonometric functions) cause bad fits; domain knowledge is needed to set reasonable starting values

Connections: Numpy · Scipy · Least Squares · Curve Fitting

Source: https://mmas.github.io/least-squares-fitting-numpy-scipy