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docs/nodes/Relate Fields.md
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# Relate Fields
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Fit a functional relationship between two data fields: b = f(a). Outputs the predicted field_b from the fit and a table of fitted parameters with R-squared goodness-of-fit. Equivalent to Gwyddion's relate.c module.
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## Inputs
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| Name | Type | Required | Description |
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|------|------|----------|-------------|
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| field_a | DATA_FIELD | Yes | Independent variable field |
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| field_b | DATA_FIELD | Yes | Dependent variable field |
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## Outputs
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| Name | Type | Description |
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|------|------|-------------|
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| predicted | DATA_FIELD | Predicted field_b values from the fitted function |
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| fit_params | RECORD_TABLE | Fitted coefficients and R-squared statistic |
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## Controls
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| Name | Type | Default | Description |
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|------|------|---------|-------------|
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| function | dropdown | linear | Functional form to fit: linear, quadratic, cubic, power, or logarithmic |
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## Notes
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- **Linear**: b = slope * a + intercept. Reports slope and intercept.
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- **Quadratic**: b = a2*a^2 + a1*a + a0. Reports a2, a1, a0.
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- **Cubic**: b = a3*a^3 + a2*a^2 + a1*a + a0. Reports a3, a2, a1, a0.
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- **Power**: b = c * a^n (fitted via log-log regression). Reports exponent and coefficient. Requires positive values in both fields.
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- **Logarithmic**: b = log_coeff * log(a) + intercept. Requires positive values in field_a.
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- R-squared is always reported as the last row: values near 1.0 indicate a good fit.
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- Both fields are flattened and truncated to the shorter length when they differ in total pixel count.
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- The predicted output retains field_b's shape and metadata.
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