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Fitting (Desktop)

The fitting module fits explicit models to your data. It outputs parameters, uncertainties, and goodness-of-fit metrics, and can generate curve/residual plots.

Data and Uncertainties

  • Inputs support x, y (and optional σ)
  • When σ is detected, you can choose whether to use statistical weighting (to avoid double-counting statistical and systematic errors)

Model Selection

The desktop app provides explicit fitting models:

  • Polynomial models
  • Inverse-power series
  • Padé and power-limit models
  • Custom nonlinear and self-consistent/implicit models
  • Explicit selected-fit comparison

Model-specific parameters appear dynamically on the left.

Explicit Selected-Fit Comparison

The explicit selected-fit comparison mode runs only the fits you enter in the candidate JSON editor. Each entry must provide its own identifier, label, and model settings. Supported candidate families are polynomial, inverse_power, and custom.

Example candidate JSON:

[
  {
    "candidate_id": "linear",
    "label": "Linear",
    "model_type": "polynomial",
    "poly_degree": 1
  },
  {
    "candidate_id": "inverse_1_2",
    "label": "Inverse powers 1-2",
    "model_type": "inverse_power",
    "inverse_min": 1,
    "inverse_max": 2
  },
  {
    "candidate_id": "custom_a",
    "label": "Custom a*x+b",
    "model_type": "custom",
    "model_expr": "a*x+b"
  }
]

The result panel shows a comparison table for the listed fits. CSV export uses the same comparison row order, and LaTeX output writes a comparison table when LaTeX generation is enabled. Workspaces save the candidate JSON under config.fitting.comparison_candidates so the same explicit list is restored with the project.

Custom and Self-Consistent/Implicit Models

Custom formulas and self-consistent/implicit models share the workbench formula card, parameter table, and constants table. Formula input uses DataLab/Mathematica-compatible syntax, and the preview button renders the current expression as LaTeX-style math. Preview is display-only and does not change computation. The parameter table is still populated from the active formula and can be edited manually; disabled constants are not substituted into the fit.

Self-consistent/implicit models cover problems such as u = g(x, u, parameters) and y = f(x, u, parameters). For each data point, DataLab solves the self-consistent variable first and then evaluates the output expression for the fit target. Start with stable initial guesses and bounds before adding more parameters or increasing precision.

Plots and Log Axes

When plots are enabled, the result area can show:

  • Fit curve and data points
  • Residual plot

You can also enable log-x / log-y:

  • If the data contains non-positive values, the corresponding log axis is automatically disabled with a log message

Outputs and Export

  • Parameters and metrics are shown and can be exported as CSV
  • LaTeX table generation and optional PDF compilation are available (depending on the TeX engine and settings)