From 3603b119998cb8ef3dd78ba4518cae2606492315 Mon Sep 17 00:00:00 2001
From: cdaunt <chris.ll.m.daunt@gmail.com>
Date: Thu, 26 Feb 2026 17:06:04 +0100
Subject: [PATCH 1/6] modify sax dependency

---
 pixi.lock      | 813 ++-----------------------------------------------
 pyproject.toml |   2 +-
 2 files changed, 19 insertions(+), 796 deletions(-)

diff --git a/pixi.lock b/pixi.lock
index 79420d7..76b208c 100644
--- a/pixi.lock
+++ b/pixi.lock
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-  - pycodestyle~=2.11.0 ; extra == 'test'
-  - pyopenssl~=25.3.0 ; extra == 'test'
-  - mypy>=0.800 ; extra == 'test'
-  - setuptools>=60 ; extra == 'dev'
-  - cython~=3.0 ; extra == 'dev'
-  - sphinx~=4.1.2 ; extra == 'docs'
-  - sphinxcontrib-asyncio~=0.3.0 ; extra == 'docs'
-  - sphinx-rtd-theme~=0.5.2 ; extra == 'docs'
-  requires_python: '>=3.8.1'
-- pypi: https://files.pythonhosted.org/packages/c7/d5/69900f7883235562f1f50d8184bb7dd84a2fb61e9ec63f3782546fdbd057/uvloop-0.22.1-cp311-cp311-macosx_10_9_universal2.whl
-  name: uvloop
-  version: 0.22.1
-  sha256: c60ebcd36f7b240b30788554b6f0782454826a0ed765d8430652621b5de674b9
-  requires_dist:
-  - aiohttp>=3.10.5 ; extra == 'test'
-  - flake8~=6.1 ; extra == 'test'
-  - psutil ; extra == 'test'
-  - pycodestyle~=2.11.0 ; extra == 'test'
-  - pyopenssl~=25.3.0 ; extra == 'test'
-  - mypy>=0.800 ; extra == 'test'
-  - setuptools>=60 ; extra == 'dev'
-  - cython~=3.0 ; extra == 'dev'
-  - sphinx~=4.1.2 ; extra == 'docs'
-  - sphinxcontrib-asyncio~=0.3.0 ; extra == 'docs'
-  - sphinx-rtd-theme~=0.5.2 ; extra == 'docs'
-  requires_python: '>=3.8.1'
 - pypi: https://files.pythonhosted.org/packages/fa/6e/3e955517e22cbdd565f2f8b2e73d52528b14b8bcfdb04f62466b071de847/validators-0.35.0-py3-none-any.whl
   name: validators
   version: 0.35.0
@@ -6797,30 +6044,6 @@ packages:
   - multidict>=4.0
   - propcache>=0.2.1
   requires_python: '>=3.9'
-- pypi: https://files.pythonhosted.org/packages/2e/54/647ade08bf0db230bfea292f893923872fd20be6ac6f53b2b936ba839d75/zipp-3.23.0-py3-none-any.whl
-  name: zipp
-  version: 3.23.0
-  sha256: 071652d6115ed432f5ce1d34c336c0adfd6a884660d1e9712a256d3d3bd4b14e
-  requires_dist:
-  - pytest>=6,!=8.1.* ; extra == 'test'
-  - jaraco-itertools ; extra == 'test'
-  - jaraco-functools ; extra == 'test'
-  - more-itertools ; extra == 'test'
-  - big-o ; extra == 'test'
-  - pytest-ignore-flaky ; extra == 'test'
-  - jaraco-test ; extra == 'test'
-  - sphinx>=3.5 ; extra == 'doc'
-  - jaraco-packaging>=9.3 ; extra == 'doc'
-  - rst-linker>=1.9 ; extra == 'doc'
-  - furo ; extra == 'doc'
-  - sphinx-lint ; extra == 'doc'
-  - jaraco-tidelift>=1.4 ; extra == 'doc'
-  - pytest-checkdocs>=2.4 ; extra == 'check'
-  - pytest-ruff>=0.2.1 ; sys_platform != 'cygwin' and extra == 'check'
-  - pytest-cov ; extra == 'cover'
-  - pytest-enabler>=2.2 ; extra == 'enabler'
-  - pytest-mypy ; extra == 'type'
-  requires_python: '>=3.9'
 - conda: https://conda.anaconda.org/conda-forge/linux-64/zstd-1.5.7-hb78ec9c_6.conda
   sha256: 68f0206ca6e98fea941e5717cec780ed2873ffabc0e1ed34428c061e2c6268c7
   md5: 4a13eeac0b5c8e5b8ab496e6c4ddd829
diff --git a/pyproject.toml b/pyproject.toml
index d77e05e..45ab5ab 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -23,7 +23,7 @@ dependencies = [
     "jax>=0.7.1,<0.8",
     "jaxlib>=0.7.1,<0.8",
     "diffrax>=0.7.0,<0.8",
-    "sax>=0.15.15,<0.16",
+    "sax>=0.15.15",
     "matplotlib",
     "typing-extensions>=4.13.2",
     "lineax",

From 8647495a98cd9c48f00bc658c06c8b3e6e3c4d8d Mon Sep 17 00:00:00 2001
From: cdaunt <chris.ll.m.daunt@gmail.com>
Date: Thu, 26 Feb 2026 17:36:20 +0100
Subject: [PATCH 2/6] fixed python closures in assembly

---
 circulax/solvers/assembly.py | 34 ++++++++++++++++++----------------
 1 file changed, 18 insertions(+), 16 deletions(-)

diff --git a/circulax/solvers/assembly.py b/circulax/solvers/assembly.py
index c2086fe..8f55107 100644
--- a/circulax/solvers/assembly.py
+++ b/circulax/solvers/assembly.py
@@ -20,11 +20,25 @@
 algebra kernels.
 """
 
+import functools
+
 import jax
 import jax.numpy as jnp
 from jax import Array
 
 
+def _real_physics(v: Array, p: Array, group, t1: float) -> tuple[Array, Array]:
+    return group.physics_func(y=v, args=p, t=t1)
+
+
+def _complex_physics(
+    vr: Array, vi: Array, p: Array, group, t1: float
+) -> tuple[Array, Array, Array, Array]:
+    v = vr + 1j * vi
+    f, q = group.physics_func(y=v, args=p, t=t1)
+    return f.real, f.imag, q.real, q.imag
+
+
 def assemble_system_real(
     y_guess: Array,
     component_groups: dict,
@@ -67,8 +81,7 @@ def assemble_system_real(
         group = component_groups[k]
         v_locs = y_guess[group.var_indices]
 
-        def physics_at_t1(v: Array, p: Array) -> tuple[Array, Array]:
-            return group.physics_func(y=v, args=p, t=t1)
+        physics_at_t1 = functools.partial(_real_physics, group=group, t1=t1)
 
         (f_l, q_l) = jax.vmap(physics_at_t1)(v_locs, group.params)
         (df_l, dq_l) = jax.vmap(jax.jacfwd(physics_at_t1))(v_locs, group.params)
@@ -116,8 +129,7 @@ def assemble_residual_only_real(
         group = component_groups[k]
         v = y_guess[group.var_indices]
 
-        def physics_at_t1(v: Array, p: Array) -> tuple[Array, Array]:
-            return group.physics_func(y=v, args=p, t=t1)
+        physics_at_t1 = functools.partial(_real_physics, group=group, t1=t1)
 
         f_l, q_l = jax.vmap(physics_at_t1)(v, group.params)
 
@@ -179,12 +191,7 @@ def assemble_system_complex(
         group = component_groups[k]
         v_r, v_i = y_real[group.var_indices], y_imag[group.var_indices]
 
-        def physics_split(
-            vr: Array, vi: Array, p: Array
-        ) -> tuple[Array, Array, Array, Array]:
-            v = vr + 1j * vi
-            f, q = group.physics_func(y=v, args=p, t=t1)
-            return f.real, f.imag, q.real, q.imag
+        physics_split = functools.partial(_complex_physics, group=group, t1=t1)
 
         fr, fi, qr, qi = jax.vmap(physics_split)(v_r, v_i, group.params)
 
@@ -243,12 +250,7 @@ def assemble_residual_only_complex(
         group = component_groups[k]
         v_r, v_i = y_real[group.var_indices], y_imag[group.var_indices]
 
-        def physics_split(
-            vr: Array, vi: Array, p: Array
-        ) -> tuple[Array, Array, Array, Array]:
-            v = vr + 1j * vi
-            f, q = group.physics_func(y=v, args=p, t=t1)
-            return f.real, f.imag, q.real, q.imag
+        physics_split = functools.partial(_complex_physics, group=group, t1=t1)
 
         fr, fi, qr, qi = jax.vmap(physics_split)(v_r, v_i, group.params)
 

From f713c05f610dde24692d719f54248d40845176e5 Mon Sep 17 00:00:00 2001
From: cdaunt <chris.ll.m.daunt@gmail.com>
Date: Thu, 26 Feb 2026 17:52:03 +0100
Subject: [PATCH 3/6] call jacfwd only once

---
 circulax/solvers/assembly.py | 62 +++++++++++++++++++++++++++++++-----
 1 file changed, 54 insertions(+), 8 deletions(-)

diff --git a/circulax/solvers/assembly.py b/circulax/solvers/assembly.py
index 8f55107..218d8d8 100644
--- a/circulax/solvers/assembly.py
+++ b/circulax/solvers/assembly.py
@@ -39,6 +39,52 @@ def _complex_physics(
     return f.real, f.imag, q.real, q.imag
 
 
+def _primal_and_jac_real(
+    f, v: Array, p: Array
+) -> tuple[tuple[Array, Array], tuple[Array, Array]]:
+    """Compute f(v,p) and its Jacobian w.r.t. v in a single forward sweep.
+
+    Sweeps n unit tangents via ``jax.jvp``, extracting the primal from the
+    first sweep rather than computing it separately.  Jacobian is returned in
+    ``(n_eqs, n_vars)`` shape to match ``jax.jacfwd`` convention.
+    """
+    n = v.shape[0]
+    g = lambda v_: f(v_, p)  # close over p; differentiate w.r.t. v only
+    (f_vals, q_vals), (dfs, dqs) = jax.vmap(
+        lambda e: jax.jvp(g, (v,), (e,))
+    )(jnp.eye(n))
+    return (f_vals[0], q_vals[0]), (dfs.T, dqs.T)
+
+
+def _primal_and_jac_complex(
+    f, vr: Array, vi: Array, p: Array
+) -> tuple[
+    tuple[Array, Array, Array, Array],
+    tuple[Array, Array, Array, Array],
+    tuple[Array, Array, Array, Array],
+]:
+    """Compute f(vr,vi,p) and its Jacobian w.r.t. (vr, vi) in two forward sweeps.
+
+    Mirrors ``jax.jacfwd(f, argnums=(0, 1))``: sweeps unit tangents for vr
+    then vi, extracting the primal from the first sweep.  Each Jacobian block
+    is returned in ``(n_eqs, n_vars)`` shape.
+    """
+    n = vr.shape[0]
+    zeros_vr = jnp.zeros_like(vr)
+    zeros_vi = jnp.zeros_like(vi)
+    g = lambda vr_, vi_: f(vr_, vi_, p)  # close over p; differentiate w.r.t. vr, vi only
+    (fr_s, fi_s, qr_s, qi_s), (dfr_r, dfi_r, dqr_r, dqi_r) = jax.vmap(
+        lambda e: jax.jvp(g, (vr, vi), (e, zeros_vi))
+    )(jnp.eye(n))
+    _, (dfr_i, dfi_i, dqr_i, dqi_i) = jax.vmap(
+        lambda e: jax.jvp(g, (vr, vi), (zeros_vr, e))
+    )(jnp.eye(n))
+    primal = (fr_s[0], fi_s[0], qr_s[0], qi_s[0])
+    jac_r = (dfr_r.T, dfi_r.T, dqr_r.T, dqi_r.T)
+    jac_i = (dfr_i.T, dfi_i.T, dqr_i.T, dqi_i.T)
+    return primal, jac_r, jac_i
+
+
 def assemble_system_real(
     y_guess: Array,
     component_groups: dict,
@@ -83,8 +129,9 @@ def assemble_system_real(
 
         physics_at_t1 = functools.partial(_real_physics, group=group, t1=t1)
 
-        (f_l, q_l) = jax.vmap(physics_at_t1)(v_locs, group.params)
-        (df_l, dq_l) = jax.vmap(jax.jacfwd(physics_at_t1))(v_locs, group.params)
+        (f_l, q_l), (df_l, dq_l) = jax.vmap(
+            functools.partial(_primal_and_jac_real, physics_at_t1)
+        )(v_locs, group.params)
 
         total_f = total_f.at[group.eq_indices].add(f_l)
         total_q = total_q.at[group.eq_indices].add(q_l)
@@ -193,17 +240,16 @@ def assemble_system_complex(
 
         physics_split = functools.partial(_complex_physics, group=group, t1=t1)
 
-        fr, fi, qr, qi = jax.vmap(physics_split)(v_r, v_i, group.params)
+        (fr, fi, qr, qi), (dfr_r, dfi_r, dqr_r, dqi_r), (dfr_i, dfi_i, dqr_i, dqi_i) = (
+            jax.vmap(functools.partial(_primal_and_jac_complex, physics_split))(
+                v_r, v_i, group.params
+            )
+        )
 
         idx_r, idx_i = group.eq_indices, group.eq_indices + half_size
         total_f = total_f.at[idx_r].add(fr).at[idx_i].add(fi)
         total_q = total_q.at[idx_r].add(qr).at[idx_i].add(qi)
 
-        jac_res = jax.vmap(jax.jacfwd(physics_split, argnums=(0, 1)))(
-            v_r, v_i, group.params
-        )
-        ((dfr_r, dfr_i), (dfi_r, dfi_i), (dqr_r, dqr_i), (dqi_r, dqi_i)) = jac_res
-
         vals_blocks[0].append((dfr_r + dqr_r / dt).reshape(-1))  # RR
         vals_blocks[1].append((dfr_i + dqr_i / dt).reshape(-1))  # RI
         vals_blocks[2].append((dfi_r + dqi_r / dt).reshape(-1))  # IR

From 3400dbe3f5b2c69643b90635ac2f92b4f10df9c8 Mon Sep 17 00:00:00 2001
From: cdaunt <chris.ll.m.daunt@gmail.com>
Date: Thu, 26 Feb 2026 18:08:35 +0100
Subject: [PATCH 4/6] modified constants used in circulus

---
 circulax/solvers/assembly.py  | 12 +++++-----
 circulax/solvers/linear.py    | 43 +++++++++++++++++++++++------------
 circulax/solvers/transient.py | 15 ++++++++----
 3 files changed, 45 insertions(+), 25 deletions(-)

diff --git a/circulax/solvers/assembly.py b/circulax/solvers/assembly.py
index 218d8d8..d414201 100644
--- a/circulax/solvers/assembly.py
+++ b/circulax/solvers/assembly.py
@@ -165,12 +165,12 @@ def assemble_residual_only_real(
 
     Returns:
         A two-tuple ``(total_f, total_q)`` where both arrays have shape
-        ``(sys_size,)`` and ``dtype=float64``.
+        ``(sys_size,)`` and ``dtype`` matching ``y_guess.dtype``.
 
     """
     sys_size = y_guess.shape[0]
-    total_f = jnp.zeros(sys_size, dtype=jnp.float64)
-    total_q = jnp.zeros(sys_size, dtype=jnp.float64)
+    total_f = jnp.zeros(sys_size, dtype=y_guess.dtype)
+    total_q = jnp.zeros(sys_size, dtype=y_guess.dtype)
 
     for k in sorted(component_groups.keys()):
         group = component_groups[k]
@@ -282,15 +282,15 @@ def assemble_residual_only_complex(
 
     Returns:
         A two-tuple ``(total_f, total_q)`` where both arrays have shape
-        ``(2 * num_vars,)`` and ``dtype=float64``.
+        ``(2 * num_vars,)`` and ``dtype`` matching ``y_guess.dtype``.
 
     """
     sys_size = y_guess.shape[0]
     half_size = sys_size // 2
     y_real, y_imag = y_guess[:half_size], y_guess[half_size:]
 
-    total_f = jnp.zeros(sys_size, dtype=jnp.float64)
-    total_q = jnp.zeros(sys_size, dtype=jnp.float64)
+    total_f = jnp.zeros(sys_size, dtype=y_guess.dtype)
+    total_q = jnp.zeros(sys_size, dtype=y_guess.dtype)
 
     for k in sorted(component_groups.keys()):
         group = component_groups[k]
diff --git a/circulax/solvers/linear.py b/circulax/solvers/linear.py
index d7ee403..29acb62 100644
--- a/circulax/solvers/linear.py
+++ b/circulax/solvers/linear.py
@@ -29,6 +29,21 @@
 
 from circulax.solvers.assembly import assemble_system_complex, assemble_system_real
 
+# ---------------------------------------------------------------------------
+# Solver constants
+# ---------------------------------------------------------------------------
+GROUND_STIFFNESS: float = 1e9
+"""Penalty added to ground-node diagonal entries to enforce V=0."""
+
+DC_DT: float = 1e18
+"""Effective timestep used for DC analysis; makes capacitor stamps vanish (C/dt → 0)."""
+
+DAMPING_FACTOR: float = 0.5
+"""Newton-step damping coefficient: limits each step to at most ``DAMPING_FACTOR / |δy|_max``."""
+
+DAMPING_EPS: float = 1e-9
+"""Small additive epsilon that prevents division by zero in the damping formula."""
+
 # Check if split solver available — KLUHandleManager was added in a later version of klujax.
 split_solver_available = True
 try:
@@ -132,22 +147,22 @@ def solve_dc(
         """
 
         def dc_step(y: jax.Array, _: Any) -> jax.Array:
-            # 1. Assemble System (dt=1e18 effectively removes time-dependent terms like C*dv/dt)
+            # 1. Assemble System (DC_DT effectively removes time-dependent terms like C*dv/dt)
             if self.is_complex:
                 total_f, _, all_vals = assemble_system_complex(
-                    y, component_groups, t1=0.0, dt=1e18
+                    y, component_groups, t1=0.0, dt=DC_DT
                 )
             else:
                 total_f, _, all_vals = assemble_system_real(
-                    y, component_groups, t1=0.0, dt=1e18
+                    y, component_groups, t1=0.0, dt=DC_DT
                 )
 
             # 2. Apply Ground Constraints to Residual
-            #    We add a massive penalty (1e9 * V) to the residual at ground nodes.
+            #    We add a massive penalty (GROUND_STIFFNESS * V) to the residual at ground nodes.
             #    This forces the solver to drive V -> 0.
             total_f_grounded = total_f
             for idx in self.ground_indices:
-                total_f_grounded = total_f_grounded.at[idx].add(1e9 * y[idx])
+                total_f_grounded = total_f_grounded.at[idx].add(GROUND_STIFFNESS * y[idx])
 
             # 3. Solve Linear System (J * delta = -R)
             sol = self._solve_impl(all_vals, -total_f_grounded)
@@ -156,7 +171,7 @@ def dc_step(y: jax.Array, _: Any) -> jax.Array:
             # 4. Apply Voltage Limiting (Damping)
             #    Prevents the solver from taking huge steps that crash exponentials (diodes/transistors).
             max_change = jnp.max(jnp.abs(delta))
-            damping = jnp.minimum(1.0, 0.5 / (max_change + 1e-9))
+            damping = jnp.minimum(1.0, DAMPING_FACTOR / (max_change + DAMPING_EPS))
 
             return y + delta * damping
 
@@ -205,7 +220,7 @@ def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
 
         # 3. Apply Ground Constraints (Stiff Diagonal)
         for idx in self.ground_indices:
-            J = J.at[idx, idx].add(1e9)
+            J = J.at[idx, idx].add(GROUND_STIFFNESS)
 
         # 4. Dense Solve (LU)
         x = jnp.linalg.solve(J, residual)
@@ -287,7 +302,7 @@ def cleanup(self) -> None:  # noqa: D102
 
     def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         # 1. Prepare raw value vector including Ground and Leakage entries
-        g_vals = jnp.full(self.ground_indices.shape[0], 1e9, dtype=all_vals.dtype)
+        g_vals = jnp.full(self.ground_indices.shape[0], GROUND_STIFFNESS, dtype=all_vals.dtype)
         l_vals = jnp.full(self.sys_size, self.g_leak, dtype=all_vals.dtype)
 
         raw_vals = jnp.concatenate([all_vals, g_vals, l_vals])
@@ -387,7 +402,7 @@ class KlursSplitSolver(KLUSplitSolver):
 
     def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         # 1. Prepare raw value vector including Ground and Leakage entries
-        g_vals = jnp.full(self.ground_indices.shape[0], 1e9, dtype=all_vals.dtype)
+        g_vals = jnp.full(self.ground_indices.shape[0], GROUND_STIFFNESS, dtype=all_vals.dtype)
         l_vals = jnp.full(self.sys_size, self.g_leak, dtype=all_vals.dtype)
 
         raw_vals = jnp.concatenate([all_vals, g_vals, l_vals])
@@ -503,7 +518,7 @@ def cleanup(self) -> None:  # noqa: D102
 
     def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         """Regular solve - does full factor + solve."""
-        g_vals = jnp.full(self.ground_indices.shape[0], 1e9, dtype=all_vals.dtype)
+        g_vals = jnp.full(self.ground_indices.shape[0], GROUND_STIFFNESS, dtype=all_vals.dtype)
         l_vals = jnp.full(self.sys_size, self.g_leak, dtype=all_vals.dtype)
 
         raw_vals = jnp.concatenate([all_vals, g_vals, l_vals])
@@ -542,7 +557,7 @@ def solve_with_frozen_jacobian(
 
     def factor_jacobian(self, all_vals: jax.Array) -> jax.Array:
         """Factor the Jacobian and return numeric handle."""
-        g_vals = jnp.full(self.ground_indices.shape[0], 1e9, dtype=all_vals.dtype)
+        g_vals = jnp.full(self.ground_indices.shape[0], GROUND_STIFFNESS, dtype=all_vals.dtype)
         l_vals = jnp.full(self.sys_size, self.g_leak, dtype=all_vals.dtype)
 
         raw_vals = jnp.concatenate([all_vals, g_vals, l_vals])
@@ -597,7 +612,7 @@ class KLUSolver(CircuitLinearSolver):
 
     def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         # 1. Prepare raw value vector including Ground and Leakage entries
-        g_vals = jnp.full(self.ground_indices.shape[0], 1e9, dtype=all_vals.dtype)
+        g_vals = jnp.full(self.ground_indices.shape[0], GROUND_STIFFNESS, dtype=all_vals.dtype)
         l_vals = jnp.full(self.sys_size, self.g_leak, dtype=all_vals.dtype)
 
         raw_vals = jnp.concatenate([all_vals, g_vals, l_vals])
@@ -699,7 +714,7 @@ def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         #    Add Leakage & Ground stiffness to diagonal
         diag_vals = diag_vals + self.g_leak
         for idx in self.ground_indices:
-            diag_vals = diag_vals.at[idx].add(1e9)
+            diag_vals = diag_vals.at[idx].add(GROUND_STIFFNESS)
 
         #    Invert diagonal for Jacobi Preconditioner
         inv_diag = jnp.where(jnp.abs(diag_vals) < 1e-12, 1.0, 1.0 / diag_vals)
@@ -716,7 +731,7 @@ def matvec(x: jax.Array) -> jax.Array:
             # Add Leakage & Ground contributions
             Ax = Ax + (x * self.g_leak)
             for idx in self.ground_indices:
-                Ax = Ax.at[idx].add(1e9 * x[idx])
+                Ax = Ax.at[idx].add(GROUND_STIFFNESS * x[idx])
             return Ax
 
         # 3. Solve (BiCGStab)
diff --git a/circulax/solvers/transient.py b/circulax/solvers/transient.py
index a2b685c..d6107a8 100644
--- a/circulax/solvers/transient.py
+++ b/circulax/solvers/transient.py
@@ -17,7 +17,12 @@
     assemble_system_complex,
     assemble_system_real,
 )
-from circulax.solvers.linear import CircuitLinearSolver
+from circulax.solvers.linear import (
+    DAMPING_EPS,
+    DAMPING_FACTOR,
+    GROUND_STIFFNESS,
+    CircuitLinearSolver,
+)
 
 
 def _compute_history(component_groups, y_c, t, num_vars) -> ArrayLike:
@@ -111,7 +116,7 @@ def newton_update_step(y, _) -> float:
 
             # C. Apply Ground Constraints (RHS)
             for idx in ground_indices:
-                residual = residual.at[idx].add(1e9 * y[idx])
+                residual = residual.at[idx].add(GROUND_STIFFNESS * y[idx])
 
             # D. Solve Linear System
             #    Strategy handles the flat 2N system automatically
@@ -120,7 +125,7 @@ def newton_update_step(y, _) -> float:
 
             # E. Damping
             max_change = jnp.max(jnp.abs(delta))
-            damping = jnp.minimum(1.0, 0.5 / (max_change + 1e-9))
+            damping = jnp.minimum(1.0, DAMPING_FACTOR / (max_change + DAMPING_EPS))
 
             return y + delta * damping
 
@@ -215,7 +220,7 @@ def func(self, terms, t0, y0, args):
 #             residual = total_f + (total_q - q_prev) / dt
 
 #             for idx in ground_indices:
-#                 residual = residual.at[idx].add(1e9 * y[idx])
+#                 residual = residual.at[idx].add(GROUND_STIFFNESS * y[idx])
 
 #             sol = self.linear_solver.solve_with_frozen_jacobian(
 #                 -residual, numeric_handle
@@ -223,7 +228,7 @@ def func(self, terms, t0, y0, args):
 #             delta = sol.value
 
 #             max_change = jnp.max(jnp.abs(delta))
-#             damping = jnp.minimum(1.0, 0.5 / (max_change + 1e-9))
+#             damping = jnp.minimum(1.0, DAMPING_FACTOR / (max_change + DAMPING_EPS))
 
 #             return y + delta * damping
 

From ee48b9893d9a90a9a5e698bb02200e168af1cab6 Mon Sep 17 00:00:00 2001
From: cdaunt <chris.ll.m.daunt@gmail.com>
Date: Sun, 1 Mar 2026 15:58:22 +0100
Subject: [PATCH 5/6] refactor: deduplicate solver factory methods and rename
 from_circuit

Extract _build_index_arrays and _klu_deduplicate as module-level helpers,
eliminating ~25 lines of copy-pasted index-building and KLU coalescence
logic from DenseSolver, KLUSolver, KLUSplitSolver, KlursSplitSolver, and
SparseSolver.

Rename from_circuit -> from_component_groups across all solver classes and
call sites to reflect the actual input type and leave room for future
parsers from other formats.

Also fix wrong return type hints on KLUSplitSolver and KlursSplitSolver,
and add the missing * keyword-only separator in KlursSplitSolver.
---
 circulax/solvers/linear.py | 266 +++++++++++++------------------------
 tests/test_dc.py           |   4 +-
 tests/test_transient.py    |   4 +-
 3 files changed, 96 insertions(+), 178 deletions(-)

diff --git a/circulax/solvers/linear.py b/circulax/solvers/linear.py
index 29acb62..acf7bbb 100644
--- a/circulax/solvers/linear.py
+++ b/circulax/solvers/linear.py
@@ -61,6 +61,63 @@
     KLUHandleManager = object  # type: ignore[assignment,misc]
     KLURSHandleManager = object  # type: ignore[assignment,misc]
 
+# ---------------------------------------------------------------------------
+# Index-building helpers shared across all solver factory classmethods
+# ---------------------------------------------------------------------------
+
+
+def _build_index_arrays(
+    component_groups: dict, num_vars: int, is_complex: bool
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, int]:
+    """Extract COO row/col index arrays from component groups and expand for complex systems.
+
+    Returns:
+        (static_rows, static_cols, ground_idxs, sys_size) as numpy arrays.
+    """
+    all_rows, all_cols = [], []
+    for k in sorted(component_groups.keys()):
+        g = component_groups[k]
+        all_rows.append(np.array(g.jac_rows).reshape(-1))
+        all_cols.append(np.array(g.jac_cols).reshape(-1))
+
+    static_rows = np.concatenate(all_rows)
+    static_cols = np.concatenate(all_cols)
+    sys_size = num_vars
+    ground_idxs = np.array([0], dtype=np.int32)
+
+    if is_complex:
+        # Expand to 2N x 2N block structure:  [ RR  RI ]
+        #                                      [ IR  II ]
+        N = num_vars
+        static_rows = np.concatenate([static_rows, static_rows, static_rows + N, static_rows + N])
+        static_cols = np.concatenate([static_cols, static_cols + N, static_cols, static_cols + N])
+        sys_size = N * 2
+        ground_idxs = np.array([0, num_vars], dtype=np.int32)
+
+    return static_rows, static_cols, ground_idxs, sys_size
+
+
+def _klu_deduplicate(
+    static_rows: np.ndarray,
+    static_cols: np.ndarray,
+    ground_idxs: np.ndarray,
+    sys_size: int,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, int]:
+    """Build unique COO index arrays for KLU, coalescing circuit + ground + leakage entries.
+
+    Returns:
+        (u_rows, u_cols, map_idx, n_unique)
+    """
+    leak_diag = np.arange(sys_size, dtype=np.int32)
+    full_rows = np.concatenate([static_rows, ground_idxs, leak_diag])
+    full_cols = np.concatenate([static_cols, ground_idxs, leak_diag])
+    rc_hashes = full_rows.astype(np.int64) * sys_size + full_cols.astype(np.int64)
+    unique_hashes, map_indices = np.unique(rc_hashes, return_inverse=True)
+    u_rows = (unique_hashes // sys_size).astype(np.int32)
+    u_cols = (unique_hashes % sys_size).astype(np.int32)
+    return u_rows, u_cols, map_indices, len(unique_hashes)
+
+
 class CircuitLinearSolver(lx.AbstractLinearSolver):
     """Abstract Base Class for all circuit linear solvers.
 
@@ -227,37 +284,16 @@ def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         return lx.Solution(value=x, result=lx.RESULTS.successful, state=None, stats={})
 
     @classmethod
-    def from_circuit(
+    def from_component_groups(
         cls, component_groups: dict[str, Any], num_vars: int, *, is_complex: bool = False
     ) -> "DenseSolver":
         """Factory method to pre-calculate indices for the dense matrix."""
-        all_rows, all_cols = [], []
-        for k in sorted(component_groups.keys()):
-            g = component_groups[k]
-            all_rows.append(np.array(g.jac_rows).reshape(-1))
-            all_cols.append(np.array(g.jac_cols).reshape(-1))
-
-        static_rows = np.concatenate(all_rows)
-        static_cols = np.concatenate(all_cols)
-
-        sys_size = num_vars
-        ground_idxs = np.array([0], dtype=np.int32)
-
-        if is_complex:
-            # Expand to 2N x 2N Block Structure:
-            # [ RR  RI ]
-            # [ IR  II ]
-            sys_size = num_vars * 2
-            r, c = static_rows, static_cols
-            N = num_vars
-
-            static_rows = np.concatenate([r, r, r + N, r + N])
-            static_cols = np.concatenate([c, c + N, c, c + N])
-            ground_idxs = np.array([0, num_vars], dtype=np.int32)
-
+        rows, cols, ground_idxs, sys_size = _build_index_arrays(
+            component_groups, num_vars, is_complex
+        )
         return cls(
-            static_rows=jnp.array(static_rows),
-            static_cols=jnp.array(static_cols),
+            static_rows=jnp.array(rows),
+            static_cols=jnp.array(cols),
             sys_size=sys_size,
             ground_indices=jnp.array(ground_idxs),
             is_complex=is_complex,
@@ -325,52 +361,19 @@ def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         )
 
     @classmethod
-    def from_circuit(
+    def from_component_groups(
         cls, component_groups: dict[str, Any], num_vars: int, *, is_complex: bool = False
-    ) -> "KLUSolver":
+    ) -> "KLUSplitSolver":
         """Factory method to pre-hash indices for sparse coalescence."""
-        all_rows, all_cols = [], []
-        for k in sorted(component_groups.keys()):
-            g = component_groups[k]
-            all_rows.append(np.array(g.jac_rows).reshape(-1))
-            all_cols.append(np.array(g.jac_cols).reshape(-1))
-
-        static_rows = np.concatenate(all_rows)
-        static_cols = np.concatenate(all_cols)
-
-        sys_size = num_vars
-        ground_idxs = np.array([0], dtype=np.int32)
-
-        if is_complex:
-            sys_size = num_vars * 2
-            r, c = static_rows, static_cols
-            N = num_vars
-            static_rows = np.concatenate([r, r, r + N, r + N])
-            static_cols = np.concatenate([c, c + N, c, c + N])
-            ground_idxs = np.array([0, num_vars], dtype=np.int32)
-
-        # We must include indices for the full leakage diagonal
-        leak_rows = np.arange(sys_size, dtype=np.int32)
-        leak_cols = np.arange(sys_size, dtype=np.int32)
-
-        # Combine Circuit + Ground + Leakage indices
-        full_rows = np.concatenate([static_rows, ground_idxs, leak_rows])
-        full_cols = np.concatenate([static_cols, ground_idxs, leak_cols])
-
-        # Hashing to find unique entries for coalescence
-        rc_hashes = full_rows.astype(np.int64) * sys_size + full_cols.astype(np.int64)
-        unique_hashes, map_indices = np.unique(rc_hashes, return_inverse=True)
-
-        u_rows = (unique_hashes // sys_size).astype(np.int32)
-        u_cols = (unique_hashes % sys_size).astype(np.int32)
-        n_unique = len(unique_hashes)
-
+        rows, cols, ground_idxs, sys_size = _build_index_arrays(
+            component_groups, num_vars, is_complex
+        )
+        u_rows, u_cols, map_idx, n_unique = _klu_deduplicate(rows, cols, ground_idxs, sys_size)
         symbolic = klujax.analyze(u_rows, u_cols, sys_size)
-
         return cls(
             u_rows=jnp.array(u_rows),
             u_cols=jnp.array(u_cols),
-            map_idx=jnp.array(map_indices),
+            map_idx=jnp.array(map_idx),
             n_unique=n_unique,
             _handle_wrapper=symbolic,
             ground_indices=jnp.array(ground_idxs),
@@ -427,52 +430,19 @@ def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
 
 
     @classmethod
-    def from_circuit(
-        cls, component_groups: dict[str, Any], num_vars: int, is_complex: bool = False
-    ) -> "KLUSolver":
+    def from_component_groups(
+        cls, component_groups: dict[str, Any], num_vars: int, *, is_complex: bool = False
+    ) -> "KlursSplitSolver":
         """Factory method to pre-hash indices for sparse coalescence."""
-        all_rows, all_cols = [], []
-        for k in sorted(component_groups.keys()):
-            g = component_groups[k]
-            all_rows.append(np.array(g.jac_rows).reshape(-1))
-            all_cols.append(np.array(g.jac_cols).reshape(-1))
-
-        static_rows = np.concatenate(all_rows)
-        static_cols = np.concatenate(all_cols)
-
-        sys_size = num_vars
-        ground_idxs = np.array([0], dtype=np.int32)
-
-        if is_complex:
-            sys_size = num_vars * 2
-            r, c = static_rows, static_cols
-            N = num_vars
-            static_rows = np.concatenate([r, r, r + N, r + N])
-            static_cols = np.concatenate([c, c + N, c, c + N])
-            ground_idxs = np.array([0, num_vars], dtype=np.int32)
-
-        # We must include indices for the full leakage diagonal
-        leak_rows = np.arange(sys_size, dtype=np.int32)
-        leak_cols = np.arange(sys_size, dtype=np.int32)
-
-        # Combine Circuit + Ground + Leakage indices
-        full_rows = np.concatenate([static_rows, ground_idxs, leak_rows])
-        full_cols = np.concatenate([static_cols, ground_idxs, leak_cols])
-
-        # Hashing to find unique entries for coalescence
-        rc_hashes = full_rows.astype(np.int64) * sys_size + full_cols.astype(np.int64)
-        unique_hashes, map_indices = np.unique(rc_hashes, return_inverse=True)
-
-        u_rows = (unique_hashes // sys_size).astype(np.int32)
-        u_cols = (unique_hashes % sys_size).astype(np.int32)
-        n_unique = len(unique_hashes)
-
+        rows, cols, ground_idxs, sys_size = _build_index_arrays(
+            component_groups, num_vars, is_complex
+        )
+        u_rows, u_cols, map_idx, n_unique = _klu_deduplicate(rows, cols, ground_idxs, sys_size)
         symbol = klurs.analyze(u_rows, u_cols, sys_size)
-
         return cls(
             u_rows=jnp.array(u_rows),
             u_cols=jnp.array(u_cols),
-            map_idx=jnp.array(map_indices),
+            map_idx=jnp.array(map_idx),
             n_unique=n_unique,
             _handle_wrapper=symbol,
             ground_indices=jnp.array(ground_idxs),
@@ -629,50 +599,18 @@ def _solve_impl(self, all_vals: jax.Array, residual: jax.Array) -> lx.Solution:
         )
 
     @classmethod
-    def from_circuit(
+    def from_component_groups(
         cls, component_groups: dict[str, Any], num_vars: int, *, is_complex: bool = False
     ) -> "KLUSolver":
         """Factory method to pre-hash indices for sparse coalescence."""
-        all_rows, all_cols = [], []
-        for k in sorted(component_groups.keys()):
-            g = component_groups[k]
-            all_rows.append(np.array(g.jac_rows).reshape(-1))
-            all_cols.append(np.array(g.jac_cols).reshape(-1))
-
-        static_rows = np.concatenate(all_rows)
-        static_cols = np.concatenate(all_cols)
-
-        sys_size = num_vars
-        ground_idxs = np.array([0], dtype=np.int32)
-
-        if is_complex:
-            sys_size = num_vars * 2
-            r, c = static_rows, static_cols
-            N = num_vars
-            static_rows = np.concatenate([r, r, r + N, r + N])
-            static_cols = np.concatenate([c, c + N, c, c + N])
-            ground_idxs = np.array([0, num_vars], dtype=np.int32)
-
-        # We must include indices for the full leakage diagonal
-        leak_rows = np.arange(sys_size, dtype=np.int32)
-        leak_cols = np.arange(sys_size, dtype=np.int32)
-
-        # Combine Circuit + Ground + Leakage indices
-        full_rows = np.concatenate([static_rows, ground_idxs, leak_rows])
-        full_cols = np.concatenate([static_cols, ground_idxs, leak_cols])
-
-        # Hashing to find unique entries for coalescence
-        rc_hashes = full_rows.astype(np.int64) * sys_size + full_cols.astype(np.int64)
-        unique_hashes, map_indices = np.unique(rc_hashes, return_inverse=True)
-
-        u_rows = (unique_hashes // sys_size).astype(np.int32)
-        u_cols = (unique_hashes % sys_size).astype(np.int32)
-        n_unique = len(unique_hashes)
-
+        rows, cols, ground_idxs, sys_size = _build_index_arrays(
+            component_groups, num_vars, is_complex
+        )
+        u_rows, u_cols, map_idx, n_unique = _klu_deduplicate(rows, cols, ground_idxs, sys_size)
         return cls(
             u_rows=jnp.array(u_rows),
             u_cols=jnp.array(u_cols),
-            map_idx=jnp.array(map_indices),
+            map_idx=jnp.array(map_idx),
             n_unique=n_unique,
             ground_indices=jnp.array(ground_idxs),
             sys_size=sys_size,
@@ -748,37 +686,17 @@ def matvec(x: jax.Array) -> jax.Array:
         return lx.Solution(value=x, result=lx.RESULTS.successful, state=None, stats={})
 
     @classmethod
-    def from_circuit(
+    def from_component_groups(
         cls, component_groups: dict[str, Any], num_vars: int, *, is_complex: bool = False
     ) -> "SparseSolver":
         """Factory method to prepare indices and diagonal mask."""
-        all_rows, all_cols = [], []
-        for k in sorted(component_groups.keys()):
-            g = component_groups[k]
-            all_rows.append(np.array(g.jac_rows).reshape(-1))
-            all_cols.append(np.array(g.jac_cols).reshape(-1))
-
-        static_rows = np.concatenate(all_rows)
-        static_cols = np.concatenate(all_cols)
-
-        sys_size = num_vars
-        ground_idxs = np.array([0], dtype=np.int32)
-
-        if is_complex:
-            sys_size = num_vars * 2
-            r, c = static_rows, static_cols
-            N = num_vars
-            static_rows = np.concatenate([r, r, r + N, r + N])
-            static_cols = np.concatenate([c, c + N, c, c + N])
-            ground_idxs = np.array([0, num_vars], dtype=np.int32)
-
-        # Create mask to identify diagonal elements (row == col) efficiently
-        diag_mask = static_rows == static_cols
-
+        rows, cols, ground_idxs, sys_size = _build_index_arrays(
+            component_groups, num_vars, is_complex
+        )
         return cls(
-            static_rows=jnp.array(static_rows),
-            static_cols=jnp.array(static_cols),
-            diag_mask=jnp.array(diag_mask),
+            static_rows=jnp.array(rows),
+            static_cols=jnp.array(cols),
+            diag_mask=jnp.array(rows == cols),
             sys_size=sys_size,
             ground_indices=jnp.array(ground_idxs),
             is_complex=is_complex,
@@ -838,6 +756,6 @@ def analyze_circuit(
             msg
         )
 
-    linear_strategy = solver_class.from_circuit(groups, num_vars, is_complex=is_complex)
+    linear_strategy = solver_class.from_component_groups(groups, num_vars, is_complex=is_complex)
 
     return linear_strategy
diff --git a/tests/test_dc.py b/tests/test_dc.py
index 47f438a..8d0721f 100644
--- a/tests/test_dc.py
+++ b/tests/test_dc.py
@@ -31,7 +31,7 @@ def test_solve_operation_point_residual_small(simple_lrc_netlist: Netlist, solve
     net_dict, models_map = simple_lrc_netlist
     groups, sys_size, _ = compile_netlist(net_dict, models_map)
 
-    linear_strat = solver.from_circuit(groups, sys_size, is_complex=False)
+    linear_strat = solver.from_component_groups(groups, sys_size, is_complex=False)
     y_guess = jnp.zeros(sys_size)
     y_op = linear_strat.solve_dc(groups, y_guess)
 
@@ -50,7 +50,7 @@ def test_solve_operation_point_residual_small_complex(simple_optical_netlist: Ne
     net_dict, models_map = simple_optical_netlist
     groups, sys_size, _ = compile_netlist(net_dict, models_map)
 
-    linear_strat = solver.from_circuit(groups, sys_size, is_complex=True)
+    linear_strat = solver.from_component_groups(groups, sys_size, is_complex=True)
     y_guess = jnp.ones(2 * sys_size)
     y_op = linear_strat.solve_dc(groups, y_guess)
 
diff --git a/tests/test_transient.py b/tests/test_transient.py
index 2bc8319..296f11b 100644
--- a/tests/test_transient.py
+++ b/tests/test_transient.py
@@ -16,7 +16,7 @@ def test_short_transient_runs_float(simple_lrc_netlist, solver):
     groups, sys_size, _ = compile_netlist(net_dict, models_map)
 
     # Solve DC operating point and run a very short transient with zero forcing
-    linear_strat = solver.from_circuit(groups, sys_size, is_complex=False)
+    linear_strat = solver.from_component_groups(groups, sys_size, is_complex=False)
     y_guess = jnp.zeros(sys_size)
     y_op = linear_strat.solve_dc(groups, y_guess)
 
@@ -51,7 +51,7 @@ def test_short_transient_runs_complex(simple_optical_netlist, solver):
     groups, sys_size, port_map = compile_netlist(net_dict, models_map)
 
     # Solve DC operating point and run a very short transient with zero forcing
-    linear_strat = solver.from_circuit(groups, sys_size, is_complex=True)
+    linear_strat = solver.from_component_groups(groups, sys_size, is_complex=True)
 
     y_guess_flat = jnp.zeros(sys_size * 2, dtype=jnp.float64)
     y_op_flat = linear_strat.solve_dc(groups, y_guess_flat)

From 95f7bb841520dbb974d29996965ef03ca3a71d06 Mon Sep 17 00:00:00 2001
From: cdaunt <chris.ll.m.daunt@gmail.com>
Date: Sun, 1 Mar 2026 16:04:55 +0100
Subject: [PATCH 6/6] update pixi lock

---
 pixi.lock | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/pixi.lock b/pixi.lock
index 76b208c..ca38a1c 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -1369,8 +1369,8 @@ packages:
   requires_python: '>=3.7'
 - pypi: ./
   name: circulax
-  version: 0.1.1.dev2+g405bc2b2f.d20260226
-  sha256: 815b322f1050d476978adb57f093492587a156bc9af6c275535f518279ca5769
+  version: 0.1.1.dev3+g3603b1199.d20260226
+  sha256: a457c3003a815f37af62c21aa22560180e68265c5521aded99d68a779f6a49a8
   requires_dist:
   - diffrax>=0.7.0,<0.8
   - jax>=0.7.1,<0.8
@@ -1379,7 +1379,7 @@ packages:
   - lineax
   - matplotlib
   - numpy
-  - sax==0.16.11
+  - sax>=0.15.15
   - typing-extensions>=4.13.2
   - black ; extra == 'dev'
   - hippogriffe==0.2.2 ; extra == 'dev'