Frida is a collection of methods that operate on data files and curve files held in memory.

Data files

A data file is an ordered array of spectra. Each spectrum contains x, y data pairs, or x, y, dy triples when measurement errors are provided.

The physical meaning of x and y is stored as coordinate metadata: a name and a unit, e.g. energy (meV) or counts (Hz).

Z coordinates

If a data file contains more than one spectrum, each spectrum must have one or more z coordinates (denoted z0, z1, …). These carry per-spectrum scalar metadata such as scattering angle or temperature. Each z coordinate also has a name and a unit.

File-level metadata

Each data file also carries:

• File name — a short identifier
• Documentation (doc) — a cumulative log of operations applied to the data
• File constants (r0, r1, …) — named scalar parameters, each a coordinate-value pair, e.g. r0 = T (K) = 320

Example

A neutron scattering experiment might produce a file where:

• x is energy transfer E (μeV)
• y is the scattering law S(E, q)
• z0 is the momentum transfer q (Å⁻¹)
• one spectrum per q value

Curve files

A curve file stores a fit model together with its fitted results. It contains:

• A curve definition — an expression, e.g. p0 * gnn(t-p1, p2).
• A set of curves, one per spectrum in the associated data file. Each curve carries parameters, parameter flags, and quality metrics.

The running variable t

In a curve expression, t is the independent variable — the equivalent of x in data. When Frida evaluates the curve for plotting, t runs over an equidistant grid. When Frida fits the curve to data, t is equated with the x values of the data points.

All other expression syntax (file constants, z coordinates, parameters) works exactly as in data expressions.

Parameter flags

Each parameter p0, p1, … carries a flag that controls its role during fitting:

• Free — the parameter is adjusted by the least-squares solver to minimise the residuals. This is the default.
• Fixed — the parameter is held at its current value and not changed by the solver. Use cx <n> to fix parameter n; cu <n> to release it.

Fixing a parameter is useful when its value is known from physics or when a preliminary fit has converged and you want to refine only the remaining parameters.

Quality metrics

After a fit, three quality metrics are stored:

• cq0 — the weighted sum of squared residuals (χ² = Σ ((y_data − y_curve) / dy)²). A smaller value means a better fit to the data.

• cq1 — the number of data points included in the fit (after any range restriction set by cr).

• cq2 — the number of free parameters (those not fixed).

The reduced chi-squared χ²_red = cq0 / (cq1 − cq2) should be close to 1 for a statistically good fit. A value much larger than 1 indicates the model does not describe the data well (or the error bars are underestimated); a value much smaller than 1 suggests the error bars are overestimated.

Use ci * to extract the quality metrics into a new workspace for further analysis.

History

The data model has been stable for decades. Major changes were:

• 1996 — Added multi-z coordinates
• 2006 — Inserted abstraction layer for x-y-dy
• 2010 — Full support for file constants (r parameters)

Backward compatibility is always maintained by providing import methods for older file formats.