feat: initial release

Assisted-by: GLM 5.3 Flash

integrate/tridiag.go

@@ -0,0 +1,39 @@
+// Copyright (c) 2026 Petr Balvín <opensource@petrbalvin.org> (https://petrbalvin.org)
+// SPDX-License-Identifier: MIT
+
+package integrate
+
+// The tridiagonal scratch the PDE step sweeps reuse. The Crank-
+// Nicolson and Peaceman-Rachford schemes solve one tridiagonal system
+// per line per step against matrices that are constants of the scheme,
+// so the elimination scratch belongs to the solve, not to the line:
+// the sweeps below allocate it once and reuse it across every line and
+// every step, where the library's array-level SolveTridiagonal
+// allocated its working vectors per call. The elimination itself is
+// internal/base's TriSolve, shared with the public solver, so the
+// arithmetic exists once.
+
+// triScratch holds one tridiagonal solve's reusable buffers: the
+// right-hand side, the eliminated superdiagonal and right side of the
+// Thomas algorithm, and the solution buffer for callers whose output
+// is not written straight into their state. aux is a second right-side
+// lane for the sweeps that build two neighbouring systems in one pass.
+// Every buffer is fully overwritten before the kernel reads it, except
+// cp, whose prefix is written and read in the same sweep order the
+// fresh buffers saw.
+type triScratch struct {
+	rhs, cp, dp, dst, aux []float64
+}
+
+// triSized sizes s for a system of sys unknowns whose right side is a
+// line of lineLen entries, reusing storage that is already large
+// enough. The solution buffer dst is sized for callers that scatter
+// the result elsewhere; a caller writing straight into its state leaves
+// it unread.
+func triSized(s *triScratch, sys, lineLen int) {
+	s.rhs = sizedBuf(s.rhs, lineLen)
+	s.aux = sizedBuf(s.aux, lineLen)
+	s.cp = sizedBuf(s.cp, sys)
+	s.dp = sizedBuf(s.dp, sys)
+	s.dst = sizedBuf(s.dst, sys)
+}