NLCF — Non-Linear Curve Fitting

V2026.2 Web · G. Argraves · runs entirely in your browser; nothing is uploaded

WARNING: the model block is real JavaScript and runs in your browser. Only run model code you wrote or have read and trust.

1 · Data

2 · model.js (equation and parameters)

3 · Fit

Method Speed Weighting log x INFO: ready

datafit · lower strip: residuals (y − fit)

Param	Initial	Current	Bounds

Iteration

Method

χ² (weighted SSE)

χ²/df (reduced)

R²

χ² evaluations

4 · Report

Press Report after a fit (Ctrl+Enter is GO / STOP).

Instructions

Data formats

1. MRA style, with an optional sigma column for instrumental weighting:

any notes, ignored until the first double colon...
:: Title of the run           <- text after the marker becomes the title
1 2 3    x, y, sigma columns  <- sigma column optional (leave it off or 0 = none)
0.0    11.52   0.40           <- RAW data rows: spaces, tabs or commas
...
15.0    1.53   0.12  :: End   <- a double colon ends the data; this row is kept

2. Raw / AD3 files (as GRIDFIT 1990 read them): with no double colon anywhere, every line that starts with two numbers is a data point (x, y) and everything else is skipped. AD3 acquisition files (ADCHAN-A.DAT) load directly; their "Experiment Title:" line becomes the title.

Do not type a double colon in notes above the start marker of an MRA-style file.

Weighting (GRIDFIT mode)

Weighting	w per point	Use for	Std errors
none (mode 0)	1	equal, unknown noise	scaled by χ²/df
statistical (mode −1)	1/\|y\| (y = 0 → 1)	counts, Poisson noise σ² = y	scaled by χ²/df
instrumental (mode +1)	1/σ² from the sigma column	known measurement errors	absolute; χ²/df ≈ 1 means model and σ agree

All methods minimise χ² = Σ w·(y − f)². With instrumental weighting the report adds P(χ² ≥ observed): a very small value means the model or the stated σs are wrong.

Model block contract (model.js)

The block is the body of a function and must return an object:

return {
  TITLE: "Exponential decay",
  EQUATION: "y = A·exp(−k·x) + C",     // shown under the parameter table
  LABEL_X: "time (s)",  LABEL_Y: "signal",
  LOG_X: false,                         // start with a log x axis
  PARAMS: [                             // order = order of p[] in f()
    { name: "A", init: 5 },
    { name: "k", init: 1, min: 0 },     // optional min / max bounds,
                                        // optional step (Bevington DELTAA)
    { name: "C", init: 0 },
  ],
  f: function (x, p) {
    const [A, k, C] = p;
    return A * Math.exp(-k * x) + C;
  },
};

Methods and switching

GO runs the selected method; STOP halts it. Change the Method menu at any time: while running the switch is immediate, or STOP → switch → GO. Every method continues from the current parameters. Step runs one iteration of the selected method.

Method	Use it when	Notes
AUTO	you do not know which to pick	global search first (DE if every parameter has min and max, otherwise NM) until progress stops, then hands over to LM by itself; the log shows the handover
LM Levenberg-Marquardt	almost always	blends gradient descent (far) and Gauss-Newton (near) through its damping λ
GN Gauss-Newton	already close to the answer	fastest near the minimum; step-halving keeps it stable, but it can stall far away
NM Nelder-Mead	poor starting values, rough models	no derivatives; its simplex follows correlated valleys; finish with LM
DE Differential Evolution	several local minima (oscillations, peaks)	global search inside the bounds; unbounded parameters search ±(2·\|value\|+1); finish with LM
GRIDLS (Bevington)	teaching, comparison	one parameter at a time with a parabola through the last 3 points; slow when parameters are correlated (zig-zags across the valley)
GRADLS (Bevington)	teaching, comparison	steepest descent with a line search; also zig-zags in narrow valleys
CHIFIT (Bevington)	teaching, comparison	Newton step on a numerical χ² Hessian (many evaluations per step), damped by 0.2 and a line search
CURFIT (Bevington)	same job as LM	Marquardt's method; the 1990 port evaluated χ² at the old parameters, so the λ test never fired. Restored here, with a finer derivative step

The Bevington methods step each parameter by an increment Δa (Bevington's DELTAA): a parameter's step in PARAMS, else 10% of its starting value (0.1 if it starts at 0). GRIDLS adapts Δa as it goes. The χ² evaluations counter (full passes over the data) lets you compare how much work each method needs; Reset clears it.

Report

Standard errors come from (J′WJ)⁻¹ at the final parameters: scaled by χ²/df for none and statistical weighting, absolute for instrumental weighting. This is the usual asymptotic (linearised) estimate, matching SciPy curve_fit (absolute_sigma False / True).
Confidence intervals and p-values assume independent, normally distributed errors. Points along one smooth trace are correlated, so treat them as optimistic there.
High parameter correlations (|r| > 0.95) mean the data cannot separate those parameters well.
AIC = n·ln(SSE/n) + 2p compares models on the same data: lower is better.

Lua / Pascal to JavaScript

x ^ 2	x ** 2
exp(x), ln(x)	Math.exp(x), Math.log(x)
arrays from 1	arrays from 0: p[0] is the first parameter