CurveFit.jl

CurveFit.jl is a high-performance curve fitting library for Julia that provides linear, polynomial, special function, and nonlinear least squares fitting algorithms. It is part of the SciML ecosystem and implements the common solve interface from CommonSolve.jl.

Installation

To install CurveFit.jl, use the Julia package manager:

using Pkg
Pkg.add("CurveFit")

Features

CurveFit.jl provides the following fitting algorithms:

• Linear fitting: LinearCurveFitAlgorithm - General linear fits with customizable transformations
• Log fitting: LogCurveFitAlgorithm - Fits y = a*log(x) + b
• Power fitting: PowerCurveFitAlgorithm - Fits y = b*x^a
• Exponential fitting: ExpCurveFitAlgorithm - Fits y = b*exp(a*x)
• Polynomial fitting: PolynomialFitAlgorithm - Fits polynomials of arbitrary degree
• Rational polynomial fitting: RationalPolynomialFitAlgorithm - Fits rational functions p(x)/q(x)
• Sum of exponentials: ExpSumFitAlgorithm - Fits y = k + p1*exp(λ1*t) + p2*exp(λ2*t) + ...
• King's law: KingCurveFitAlgorithm, ModifiedKingCurveFitAlgorithm - For hotwire anemometry
• Nonlinear least squares: Via NonlinearCurveFitProblem with any user-defined function

Quick Start

Linear Fit

using CurveFit

x = 1.0:10.0
y = @. 1.0 + 2.0 * x  # y = 1 + 2x

prob = CurveFitProblem(x, y)
sol = solve(prob, LinearCurveFitAlgorithm())

sol.u  # (2.0, 1.0) - coefficients (slope, intercept)
sol(5.0)  # Evaluate fitted curve at x=5

Polynomial Fit

using CurveFit

x = 1.0:10.0
y = @. 1.0 + 2.0*x + 0.5*x^2

prob = CurveFitProblem(x, y)
sol = solve(prob, PolynomialFitAlgorithm(degree=2))

sol.u  # [1.0, 2.0, 0.5] - polynomial coefficients
sol(3.0)  # Evaluate at x=3

Nonlinear Fit

using CurveFit

x = 1.0:10.0
fn(a, x) = @. a[1] + a[2] * x^a[3]  # Nonlinear model
y = fn([3.0, 2.0, 0.7], x)  # Generate data

prob = NonlinearCurveFitProblem(fn, [0.5, 0.5, 0.5], x, y)  # Initial guess
sol = solve(prob)

sol.u  # Fitted parameters ≈ [3.0, 2.0, 0.7]
sol(5.0)  # Evaluate at x=5

Statistical Analysis

CurveFit.jl provides statistical functions compatible with StatsAPI.jl:

using CurveFit

# ... after fitting ...
coef(sol)        # Fitted coefficients
residuals(sol)   # Residuals
fitted(sol)      # Fitted values
rss(sol)         # Residual sum of squares
stderror(sol)    # Standard errors
confint(sol)     # Confidence intervals

Documentation

For more details, see the documentation.