feat: initial release

Assisted-by: GLM 5.3 Flash

internal/base/tridiag.go

@@ -0,0 +1,51 @@
+// Copyright (c) 2026 Petr Balvín <opensource@petrbalvin.org> (https://petrbalvin.org)
+// SPDX-License-Identifier: MIT
+
+package base
+
+// The tridiagonal Thomas elimination, one kernel for every caller. The
+// linalg package's public SolveTridiagonal and the integrate package's
+// PDE step sweeps solve the same systems; both call TriSolve, so the
+// arithmetic and the refusal texts exist once. The messages name
+// SolveTridiagonal because both public surfaces publish that text
+// today, and a message a caller matches is part of the contract.
+
+// TriSolve solves the tridiagonal system with lower diagonal a
+// (length n-1), main diagonal b (length n), upper diagonal c (length
+// n-1) and right side d (length n), writing the solution into dst. The
+// scratch cp and dp must hold at least n elements. A zero pivot is
+// refused. Every buffer is fully overwritten before the kernel reads
+// it, except cp, whose prefix is written and read in the same sweep
+// order a fresh buffer saw, so reused scratch and fresh allocations
+// solve bit-identically. dst must not alias any diagonal or d.
+func TriSolve(dst, cp, dp, a, b, c, d []float64) error {
+	n := len(b)
+	if n == 0 {
+		return Errf("SolveTridiagonal: empty system")
+	}
+	b0 := b[0]
+	if b0 == 0 {
+		return Errf("SolveTridiagonal: zero pivot at row 0")
+	}
+	// For n = 1 the c diagonal is empty per the length contract, so the
+	// seed must not read it; the single unknown falls out of dp[0].
+	if n > 1 {
+		cp[0] = c[0] / b0
+	}
+	dp[0] = d[0] / b0
+	for i := 1; i < n; i++ {
+		den := b[i] - a[i-1]*cp[i-1]
+		if den == 0 {
+			return Errf("SolveTridiagonal: zero pivot at row %d", i)
+		}
+		if i < n-1 {
+			cp[i] = c[i] / den
+		}
+		dp[i] = (d[i] - a[i-1]*dp[i-1]) / den
+	}
+	dst[n-1] = dp[n-1]
+	for i := n - 2; i >= 0; i-- {
+		dst[i] = dp[i] - cp[i]*dst[i+1]
+	}
+	return nil
+}