# SmoothInfo


Metadata describing where one smooth term lives inside a [ModelMatrix](ModelMatrix.md#whittaker.ModelMatrix).


Usage

``` python
SmoothInfo(
    term,
    basis,
    col_start,
    col_end,
    null_space_dim,
    penalty_indices=list(),
    by_var=None,
    by_level=None,
)
```


Each `~whittaker.formula.terms.SmoothTerm` in a formula (an `s()`, `te()`, `ti()`, or `t2()` call) expands into several columns of the full design matrix `X` -- one per basis function of the fitted [SmoothBasis](SmoothBasis.md#whittaker.SmoothBasis). A [SmoothInfo](SmoothInfo.md#whittaker.SmoothInfo) records the bookkeeping needed to make sense of that expansion after the fact: which contiguous slice `X[:, col_start:col_end]` belongs to this term, the fitted [SmoothBasis](SmoothBasis.md#whittaker.SmoothBasis) instance itself (so the exact same knots and constraints can be reused later), and which entries of `ModelMatrix.penalties` hold this term's own penalty block(s). [build_model_matrix](build_model_matrix.md#whittaker.build_model_matrix) creates one [SmoothInfo](SmoothInfo.md#whittaker.SmoothInfo) per smooth term (or per `by=` level, for factor-by smooths) and stores the list on `ModelMatrix.smooths`; [predict_matrix](predict_matrix.md#whittaker.predict_matrix) later reads these back to evaluate each smooth's basis on new data without needing the original [Formula](Formula.md#whittaker.Formula) object.


## Attributes


`term: SmoothTerm`  
The parsed [SmoothTerm](SmoothTerm.md#whittaker.SmoothTerm) this info belongs to.

`basis: SmoothBasis`  
The fitted [SmoothBasis](SmoothBasis.md#whittaker.SmoothBasis) instance for this term. Retained so that [predict_matrix](predict_matrix.md#whittaker.predict_matrix) can call `basis.basis_matrix()` on new covariate values using the exact knots, degrees of freedom, and identifiability constraints learned during fitting, rather than re-fitting a new basis.

`col_start: int`  
Start column index (inclusive) in the full model matrix `X`.

`col_end: int`  
End column index (exclusive) in the full model matrix `X`.

`null_space_dim: int`  
Dimension of the penalty null space for this smooth, i.e. the number of basis directions (after identifiability constraints) that the penalty does not shrink at all. For an ordinary cubic or thin-plate spline this is typically the "linear" part of the smooth; for shrinkage bases (`bs="ts"`, `bs="cs"`) and random-effect/factor-smooth bases (`bs="re"`, `bs="fs"`) it is `0` because every direction is already penalized.

`penalty_indices: list of int`  
Indices into `ModelMatrix.penalties` that belong to this smooth. For `s()` terms this is usually a single index (or two, if `select=True` added a null-space penalty); for `te()` terms it is one index per marginal direction.

`by_var: str or None`  
Name of the `by=` variable for this term, or `None` if the term has no `by=` modifier.

`by_level: str or None`  
For factor `by=` variables, the specific level this [SmoothInfo](SmoothInfo.md#whittaker.SmoothInfo) corresponds to (one [SmoothInfo](SmoothInfo.md#whittaker.SmoothInfo) is created per level); `None` for continuous `by=` variables or terms without a `by=` modifier.