Reuse LU decomposition in Tridiagonal Solve

Author: ricardoV94

pytensor/compile/mode.py

@@ -477,6 +477,8 @@ def clone(self, link_kwargs=None, optimizer="", **kwargs):
             "fusion",
             "inplace",
             "scan_save_mem_prealloc",
+            "reuse_lu_decomposition_multiple_solves",
+            "scan_split_non_sequence_lu_decomposition_solve",
         ],
     ),
 )

pytensor/link/numba/dispatch/linalg/solve/tridiagonal.py

@@ -6,6 +6,7 @@
 from numpy import ndarray
 from scipy import linalg
 
+from pytensor.link.numba.dispatch import numba_funcify
 from pytensor.link.numba.dispatch.basic import numba_njit
 from pytensor.link.numba.dispatch.linalg._LAPACK import (
     _LAPACK,
@@ -20,6 +21,10 @@
     _solve_check,
     _trans_char_to_int,
 )
+from pytensor.tensor._linalg.solve.tridiagonal import (
+    LUFactorTridiagonal,
+    SolveLUFactorTridiagonal,
+)
 
 
 @numba_njit
@@ -297,3 +302,48 @@ def impl(
         return X
 
     return impl
+
+
+@numba_funcify.register(LUFactorTridiagonal)
+def numba_funcify_LUFactorTridiagonal(op: LUFactorTridiagonal, node, **kwargs):
+    overwrite_dl = op.overwrite_dl
+    overwrite_d = op.overwrite_d
+    overwrite_du = op.overwrite_du
+
+    @numba_njit(cache=False)
+    def lu_factor_tridiagonal(dl, d, du):
+        if not overwrite_dl:
+            dl = dl.copy()
+        if not overwrite_d:
+            d = d.copy()
+        if not overwrite_du:
+            du = du.copy()
+
+        dl, d, du, du2, ipiv, _ = _gttrf(dl, d, du)
+        return dl, d, du, du2, ipiv
+
+    return lu_factor_tridiagonal
+
+
+@numba_funcify.register(SolveLUFactorTridiagonal)
+def numba_funcify_SolveLUFactorTridiagonal(
+    op: SolveLUFactorTridiagonal, node, **kwargs
+):
+    overwrite_b = op.overwrite_b
+    transposed = op.transposed
+
+    @numba_njit(cache=False)
+    def solve_lu_factor_tridiagonal(dl, d, du, du2, ipiv, b):
+        x, _ = _gttrs(
+            dl,
+            d,
+            du,
+            du2,
+            ipiv,
+            b,
+            overwrite_b=overwrite_b,
+            trans=transposed,
+        )
+        return x
+
+    return solve_lu_factor_tridiagonal

pytensor/tensor/_linalg/solve/rewriting.py

@@ -1,10 +1,15 @@
 from collections.abc import Container
 from copy import copy
 
+from pytensor import compile
 from pytensor.graph import Constant, graph_inputs
 from pytensor.graph.rewriting.basic import copy_stack_trace, in2out, node_rewriter
 from pytensor.scan.op import Scan
 from pytensor.scan.rewriting import scan_seqopt1
+from pytensor.tensor._linalg.solve.tridiagonal import (
+    tridiagonal_lu_factor,
+    tridiagonal_lu_solve,
+)
 from pytensor.tensor.basic import atleast_Nd
 from pytensor.tensor.blockwise import Blockwise
 from pytensor.tensor.elemwise import DimShuffle
@@ -17,13 +22,17 @@
 def decompose_A(A, assume_a):
     if assume_a == "gen":
         return lu_factor(A, check_finite=False)
+    elif assume_a == "tridiagonal":
+        return tridiagonal_lu_factor(A)
     else:
         raise NotImplementedError
 
 
 def solve_lu_decomposed_system(A_decomp, b, b_ndim, assume_a, transposed=False):
     if assume_a == "gen":
         return lu_solve(A_decomp, b, b_ndim=b_ndim, trans=transposed)
+    elif assume_a == "tridiagonal":
+        return tridiagonal_lu_solve(A_decomp, b, b_ndim=b_ndim, transposed=transposed)
     else:
         raise NotImplementedError
 
@@ -178,13 +187,15 @@ def _scan_split_non_sequence_lu_decomposition_solve(
 @register_specialize
 @node_rewriter([Blockwise])
 def reuse_lu_decomposition_multiple_solves(fgraph, node):
-    return _split_lu_solve_steps(fgraph, node, eager=False, allowed_assume_a={"gen"})
+    return _split_lu_solve_steps(
+        fgraph, node, eager=False, allowed_assume_a={"gen", "tridiagonal"}
+    )
 
 
 @node_rewriter([Scan])
 def scan_split_non_sequence_lu_decomposition_solve(fgraph, node):
     return _scan_split_non_sequence_lu_decomposition_solve(
-        fgraph, node, allowed_assume_a={"gen"}
+        fgraph, node, allowed_assume_a={"gen", "tridiagonal"}
     )
 
 
@@ -196,3 +207,33 @@ def scan_split_non_sequence_lu_decomposition_solve(fgraph, node):
     "scan_pushout",
     position=2,
 )
+
+
+# JAX cannot decompose tridiagonal matrices
+@node_rewriter([Blockwise])
+def reuse_lu_decomposition_multiple_solves_jax(fgraph, node):
+    return _split_lu_solve_steps(fgraph, node, eager=False, allowed_assume_a={"gen"})
+
+
+compile.optdb["specialize"].register(
+    reuse_lu_decomposition_multiple_solves_jax.__name__,
+    reuse_lu_decomposition_multiple_solves_jax,
+    "jax",
+)
+
+
+@node_rewriter([Scan])
+def scan_split_non_sequence_lu_decomposition_solve_jax(fgraph, node):
+    return _scan_split_non_sequence_lu_decomposition_solve(
+        fgraph, node, allowed_assume_a={"gen"}
+    )
+
+
+scan_seqopt1.register(
+    scan_split_non_sequence_lu_decomposition_solve_jax.__name__,
+    in2out(scan_split_non_sequence_lu_decomposition_solve_jax, ignore_newtrees=True),
+    "scan",
+    "scan_pushout",
+    "jax",
+    position=2,
+)

pytensor/tensor/_linalg/solve/tridiagonal.py

@@ -0,0 +1,154 @@
+import numpy as np
+from scipy.linalg import get_lapack_funcs
+
+from pytensor.graph import Apply, Op
+from pytensor.tensor.basic import as_tensor, diagonal
+from pytensor.tensor.blockwise import Blockwise
+from pytensor.tensor.type import tensor, vector
+
+
+class LUFactorTridiagonal(Op):
+    """Compute LU factorization of a tridiagonal matrix (lapack gttrf)"""
+
+    __props__ = (
+        "overwrite_dl",
+        "overwrite_d",
+        "overwrite_du",
+    )
+    gufunc_signature = "(dl),(d),(dl)->(dl),(d),(dl),(du2),(d)"
+
+    def __init__(self, overwrite_dl=False, overwrite_d=False, overwrite_du=False):
+        self.destroy_map = dm = {}
+        if overwrite_dl:
+            dm[0] = [0]
+        if overwrite_d:
+            dm[1] = [1]
+        if overwrite_du:
+            dm[2] = [2]
+        self.overwrite_dl = overwrite_dl
+        self.overwrite_d = overwrite_d
+        self.overwrite_du = overwrite_du
+        super().__init__()
+
+    def make_node(self, dl, d, du):
+        dl, d, du = map(as_tensor, (dl, d, du))
+
+        if not all(inp.type.ndim == 1 for inp in (dl, d, du)):
+            raise ValueError("Diagonals must be vectors")
+
+        ndl, nd, ndu = (inp.type.shape[-1] for inp in (dl, d, du))
+        n = (
+            ndl + 1
+            if ndl is not None
+            else (nd if nd is not None else (ndu + 1 if ndu is not None else None))
+        )
+        dummy_arrays = [np.zeros((), dtype=inp.type.dtype) for inp in (dl, d, du)]
+        out_dtype = get_lapack_funcs("gttrf", dummy_arrays).dtype
+        outputs = [
+            vector(shape=(None if n is None else (n - 1),), dtype=out_dtype),
+            vector(shape=(n,), dtype=out_dtype),
+            vector(shape=(None if n is None else n - 1,), dtype=out_dtype),
+            vector(shape=(None if n is None else n - 2,), dtype=out_dtype),
+            vector(shape=(n,), dtype=np.int32),
+        ]
+        return Apply(self, [dl, d, du], outputs)
+
+    def perform(self, node, inputs, output_storage):
+        gttrf = get_lapack_funcs("gttrf", dtype=node.outputs[0].type.dtype)
+        dl, d, du, du2, ipiv, _ = gttrf(
+            *inputs,
+            overwrite_dl=self.overwrite_dl,
+            overwrite_d=self.overwrite_d,
+            overwrite_du=self.overwrite_du,
+        )
+        output_storage[0][0] = dl
+        output_storage[1][0] = d
+        output_storage[2][0] = du
+        output_storage[3][0] = du2
+        output_storage[4][0] = ipiv
+
+
+class SolveLUFactorTridiagonal(Op):
+    """Solve a system of linear equations with a tridiagonal coefficient matrix (lapack gttrs)."""
+
+    __props__ = ("b_ndim", "overwrite_b", "transposed")
+
+    def __init__(self, b_ndim: int, transposed: bool, overwrite_b=False):
+        if b_ndim not in (1, 2):
+            raise ValueError("b_ndim must be 1 or 2")
+        if b_ndim == 1:
+            self.gufunc_signature = "(dl),(d),(dl),(du2),(d),(d)->(d)"
+        else:
+            self.gufunc_signature = "(dl),(d),(dl),(du2),(d),(d,rhs)->(d,rhs)"
+        if overwrite_b:
+            self.destroy_map = {0: [5]}
+        self.b_ndim = b_ndim
+        self.transposed = transposed
+        self.overwrite_b = overwrite_b
+        super().__init__()
+
+    def make_node(self, dl, d, du, du2, ipiv, b):
+        dl, d, du, du2, ipiv, b = map(as_tensor, (dl, d, du, du2, ipiv, b))
+
+        if b.type.ndim != self.b_ndim:
+            raise ValueError("Wrang number of dimensions for input b.")
+
+        if not all(inp.type.ndim == 1 for inp in (dl, d, du, du2, ipiv)):
+            raise ValueError("Inputs must be vectors")
+
+        ndl, nd, ndu, ndu2, nipiv = (
+            inp.type.shape[-1] for inp in (dl, d, du, du2, ipiv)
+        )
+        nb = b.type.shape[0]
+        n = (
+            ndl + 1
+            if ndl is not None
+            else (
+                nd
+                if nd is not None
+                else (
+                    ndu + 1
+                    if ndu is not None
+                    else (
+                        ndu2 + 2
+                        if ndu2 is not None
+                        else (nipiv if nipiv is not None else nb)
+                    )
+                )
+            )
+        )
+        dummy_arrays = [
+            np.zeros((), dtype=inp.type.dtype) for inp in (dl, d, du, du2, ipiv)
+        ]
+        # Seems to always be float64?
+        out_dtype = get_lapack_funcs("gttrs", dummy_arrays).dtype
+        if self.b_ndim == 1:
+            output_shape = (n,)
+        else:
+            output_shape = (n, b.type.shape[-1])
+
+        outputs = [tensor(shape=output_shape, dtype=out_dtype)]
+        return Apply(self, [dl, d, du, du2, ipiv, b], outputs)
+
+    def perform(self, node, inputs, output_storage):
+        gttrs = get_lapack_funcs("gttrs", dtype=node.outputs[0].type.dtype)
+        x, _ = gttrs(
+            *inputs,
+            overwrite_b=self.overwrite_b,
+            trans="N" if not self.transposed else "T",
+        )
+        output_storage[0][0] = x
+
+
+def tridiagonal_lu_factor(a):
+    # Return the decomposition of A implied by a solve tridiagonal
+    dl, d, du = (diagonal(a, offset=o, axis1=-2, axis2=-1) for o in (-1, 0, 1))
+    dl, d, du, du2, ipiv = Blockwise(LUFactorTridiagonal())(dl, d, du)
+    return dl, d, du, du2, ipiv
+
+
+def tridiagonal_lu_solve(a_diagonals, b, *, b_ndim: int, transposed: bool = False):
+    dl, d, du, du2, ipiv = a_diagonals
+    return Blockwise(SolveLUFactorTridiagonal(b_ndim=b_ndim, transposed=transposed))(
+        dl, d, du, du2, ipiv, b
+    )