FAQ¤
How does this differ from jax.numpy.solve
, jax.scipy.{...}
etc.?¤
Lineax offers several improvements. Most notably:

Several new solvers. For example,
lineax.QR
has no counterpart in core JAX. (And it is much faster thanjax.numpy.linalg.lstsq
, which is the closest equivalent, and uses an SVD decomposition instead.) 
Several new operators. For example,
lineax.JacobianLinearOperator
has no counterpart in core JAX. 
A consistent API. The builtin JAX operations all differ from each other slightly, and are split across
jax.numpy
,jax.scipy
, andjax.scipy.sparse
. 
Numerically stable gradients. The existing JAX implementations will sometimes return
NaN
s! 
Some faster compile times and run times in a few places.
Most of these are because JAX aims to mimic the existing NumPy/SciPy APIs. (I.e. it's not JAX's fault that it doesn't take the approach that Lineax does!)
How do I represent a {lower, upper} triangular matrix?¤
Typically: create a full matrix, with the {lower, upper} part containing your values, and the converse {upper, lower} part containing all zeros. Then use, e.g., operator = lx.MatrixLinearOperator(matrix, lx.lower_triangular_tag)
.
This is the most efficient way to store a triangular matrix in JAX's ndarraybased programming model.
What about other operations from linear algebra? (Determinants, eigenvalues, etc.)¤
See jax.numpy.linalg
and jax.scipy.linalg
.
How do I solve multiple systems of equations (i.e. AX = B
)?¤
Solvers implemented in Lineax target single systems of linear equations (i.e., Ax = b
), however, using jax.vmap
or equinox.filter_vmap
, it can solve multiple systems with minimal effort.
multi_linear_solve = eqx.filter_vmap(lx.linear_solve, in_axes=(None, 1))
# or
multi_linear_solve = jax.vmap(lx.linear_solve, in_axes=(None, 1))