Fix eigvals(:::SymTridagonal) with longer off-diagonal vector (#40165)

* Fix eigvals(:::SymTridagonal) with longer off-diagonal vector

* Update tridiag.jl

* Update lapack.jl

* Revert "Update lapack.jl"

This reverts commit 5c40476.

* Update lapack.jl

Author: dlfivefifty

stdlib/LinearAlgebra/src/lapack.jl

@@ -3775,8 +3775,8 @@ for (stev, stebz, stegr, stein, elty) in
             require_one_based_indexing(dv, ev)
             chkstride1(dv, ev)
             n = length(dv)
-            if length(ev) != n - 1
-                throw(DimensionMismatch("ev has length $(length(ev)) but needs one less than dv's length, $n)"))
+            if length(ev) != n - 1 && length(ev) != n
+                throw(DimensionMismatch("ev has length $(length(ev)) but needs one less than or equal to dv's length, $n)"))
             end
             Zmat = similar(dv, $elty, (n, job != 'N' ? n : 0))
             work = Vector{$elty}(undef, max(1, 2n-2))

stdlib/LinearAlgebra/test/lapack.jl

@@ -407,7 +407,7 @@ end
     @testset for elty in (Float32, Float64)
         d = rand(elty,10)
         e = rand(elty,9)
-        @test_throws DimensionMismatch LAPACK.stev!('U',d,rand(elty,10))
+        @test_throws DimensionMismatch LAPACK.stev!('U',d,rand(elty,11))
         @test_throws DimensionMismatch LAPACK.stebz!('A','B',zero(elty),zero(elty),0,0,-1.,d,rand(elty,10))
         @test_throws DimensionMismatch LAPACK.stegr!('N','A',d,rand(elty,11),zero(elty),zero(elty),0,0)
         @test_throws DimensionMismatch LAPACK.stein!(d,zeros(elty,10),zeros(elty,10),zeros(BlasInt,10),zeros(BlasInt,10))

stdlib/LinearAlgebra/test/tridiag.jl

@@ -589,7 +589,7 @@ end
     A2 = SymTridiagonal(fill(1.0, 3), fill(-1.0, 2))
     F2 = eigen(A2)
     test_approx_eq_modphase(F.vectors, F2.vectors)
-    @test F.values ≈ F2.values
+    @test F.values ≈ F2.values ≈ eigvals(A) ≈ eigvals(A2)
 end
 
 @testset "non-commutative algebra (#39701)" begin