klujax.factor(Ai, Aj, Ax, symbolic) -> KLUHandleManager

Perform numeric LU factorization using a pre-computed symbolic analysis. This computes A = LU (lower × upper triangular decomposition) using the actual matrix values, given the structural information from analyze.

Parameters¶

Returns¶

How It Fits In¶

Example¶

import klujax
import jax.numpy as jnp

Ai = jnp.array([0, 1, 2], dtype=jnp.int32)
Aj = jnp.array([0, 1, 2], dtype=jnp.int32)
Ax = jnp.array([2.0, 3.0, 4.0])
n_col = 3

# Step 1: Analyze pattern
symbolic = klujax.analyze(Ai, Aj, n_col)

# Step 2: Factor with specific values
numeric = klujax.factor(Ai, Aj, Ax, symbolic)

# Step 3: Solve many b's with the same factorization
for b_t in right_hand_sides:
    x = klujax.solve_with_numeric(numeric, b_t, symbolic)

Batched Factorization¶

If Ax has shape (n_lhs, n_nz), factor creates one numeric factorization per batch element:

# 5 different matrices, same sparsity pattern
Ax_batch = jnp.ones((5, 3)) * jnp.arange(1, 6)[:, None]

numeric = klujax.factor(Ai, Aj, Ax_batch, symbolic)
# numeric wraps 5 separate LU factorizations

Memory Management¶

Same rules as analyze — the handle cleans up automatically outside JIT, but needs explicit free_numeric inside JIT.

When to Use factor vs. solve_with_symbol¶

• Use factor when you need to solve the same matrix against many different b vectors. Factor once, solve many times.
• Use solve_with_symbol when both Ax and b change together — it factors and solves in one step.