# packRepeatTile

Loads a saved 2D packing and tiles it `scalXMult` times in x and `scalYMult`
times in y, producing a larger periodic packing. If `calc_eig` is set it
removes rattlers, builds the 2D Hessian, and saves the eigenvectors/eigenvalues
of the tiled packing. Called automatically at the end of `pack` when
`x_mult` or `y_mult` are not 1.

## Default Syntax

```matlab
N = 400; K = 100; P_target = 0.05; widthFactor = 22; seed = 1;
scalXMult = 2; scalYMult = 2; calc_eig = false;
strInPath  = "data/packings/2d/hooke/";   % directory of the base tile .mat
strSavePath = "data/packings/2d/hooke/";  % directory for the tiled output .mat
packRepeatTile(N, K, P_target, widthFactor, seed, scalXMult, scalYMult, calc_eig, strInPath, strSavePath)
```

The base tile file is located by name:
`2D_N<N>_P<P_target>_Width<widthFactor>_Seed<seed>.mat` — so the first five
arguments must match the `pack` call that generated it (Width = `round(sqrt(N))`).
Output is saved as `2D_N<N*xMult*yMult>_P<P_target>_Width<widthFactor*yMult>_Seed<seed>.mat`.

## Arguments

| Arg | Type | Meaning |
|---|---|---|
| `N` | double | Particles in the base tile |
| `K` | double | Spring constant (loaded from the base file, passed through) |
| `P_target` | double | Target pressure (must match base filename) |
| `widthFactor` | double | Width factor in the base filename (`round(sqrt(N))` for 2D) |
| `seed` | double | Seed in the base filename |
| `scalXMult` | double | Number of tile copies in x |
| `scalYMult` | double | Number of tile copies in y |
| `calc_eig` | logical | Remove rattlers + compute and save the tiled Hessian's eigenvectors/eigenvalues |
| `strInPath` | string | Directory containing the base tile |
| `strSavePath` | string | Directory to save the tiled packing |

## Examples

```matlab
% Tile a 400-particle packing 2x2 -> 1600 particles
packRepeatTile(400, 100, 0.05, 20, 1, 2, 2, false, ...
               'data/packings/2d/hooke/', 'data/packings/2d/hooke/');

% Tile 3x1 in x only and compute the tiled eigenmodes
packRepeatTile(100, 100, 0.1, 10, 1, 3, 1, true, ...
               'data/packings/2d/hooke/', 'data/junkyard/');

% Usually you don't call this directly — pack() does it for you:
pack(100, 100, 1, 1.4, 1, 0.1, 1, false, 2, 2, 0, false, 'data/packings/2d/hooke/');
```