> ## Documentation Index
> Fetch the complete documentation index at: https://tsim.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# linalg

> Linear algebra utilities for GF(2) operations.

## `find_basis`

```python theme={null}
find_basis(vectors: np.ndarray) -> tuple[np.ndarray, np.ndarray]
```

Decompose a set of binary vectors into a basis subset and a transformation matrix over GF(2).

Given a set of vectors V, this function finds a maximal linearly independent subset B
(the basis) and computes a transformation matrix T such that the original vectors can be
reconstructed from the basis via matrix multiplication over GF(2):

V = T @ B (mod 2)

**Parameters:**

* `vectors` (`np.ndarray`) — Input binary vectors of shape `(N, D)`. Can be a list of lists or a numpy array. Elements should be 0 or 1 (or convertible to them).

**Returns:**

* `tuple[np.ndarray, np.ndarray]` — A tuple `(basis, transform)` where: basis: The subset of independent vectors, shape `(K, D)`, where `K` is the rank. transform: The transformation matrix, shape `(N, K)`.

## `matmul_gf2`

```python theme={null}
matmul_gf2(a: Array, b: Array) -> Array
```

Compute binary dot products mod 2 as `a_GTP x b_BP -\> b_BGT`.

Uses float32 matmul (integer matmul does not have BLAS support on CPU)
then casts back to uint8.

**Parameters:**

* `a` (`Array`) — Parameter bit-masks, shape `(G, T, P)` — G graphs, T terms, P parameters.
* `b` (`Array`) — Binary parameter values, shape `(B, P)` — B batch elements.

**Returns:**

* `Array` — Binary row-sums mod 2, shape `(B, G, T)`.