Add Tridiagonal construction rule

src/rulesets/LinearAlgebra/structured.jl

@@ -268,3 +268,16 @@ function rrule(::typeof(logdet), X::Union{Diagonal, AbstractTriangular})
     end
     return y, logdet_pullback
 end
+
+#####
+##### Tridiagonal
+#####
+
+function rrule(::Type{Tridiagonal}, dl, d, du)
+    y = Tridiagonal(dl, d, du)
+    @views function ∇Tridiagonal(∂y)
+        return (NoTangent(), diag(∂y[2:end, 1:(end - 1)]), diag(∂y),
+            diag(∂y[1:(end - 1), 2:end]))
+    end
+    return y, ∇Tridiagonal
+end