Fix eigvecs(:::SymTridiagonal) with longer off-diagonal vector (#40526)

Co-authored-by: Marcelo Forets <[email protected]>

Author: dkarrasch

stdlib/LinearAlgebra/src/lapack.jl

@@ -3835,7 +3835,7 @@ for (stev, stebz, stegr, stein, elty) in
                 eev = copy(ev)
                 eev[n] = zero($elty)
             else
-                throw(DimensionMismatch("ev has length $(length(ev)) but should be either $(length(dv) - 1) or $(length(dv))"))
+                throw(DimensionMismatch("ev has length $ne but needs one less than or equal to dv's length, $n)"))
             end
 
             abstol = Vector{$elty}(undef, 1)
@@ -3878,10 +3878,15 @@ for (stev, stebz, stegr, stein, elty) in
             require_one_based_indexing(dv, ev_in, w_in, iblock_in, isplit_in)
             chkstride1(dv, ev_in, w_in, iblock_in, isplit_in)
             n = length(dv)
-            if length(ev_in) != n - 1
-                throw(DimensionMismatch("ev_in has length $(length(ev_in)) but needs one less than dv's length, $n)"))
+            ne = length(ev_in)
+            if ne == n - 1
+                ev = [ev_in; zero($elty)]
+            elseif ne == n
+                ev = copy(ev_in)
+                ev[n] = zero($elty)
+            else
+                throw(DimensionMismatch("ev_in has length $ne but needs one less than or equal to dv's length, $n)"))
             end
-            ev = [ev_in; zeros($elty,1)]
             ldz = n #Leading dimension
             #Number of eigenvalues to find
             if !(1 <= length(w_in) <= n)

stdlib/LinearAlgebra/test/lapack.jl

@@ -410,7 +410,7 @@ end
         @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))
+        @test_throws DimensionMismatch LAPACK.stein!(d,zeros(elty,11),zeros(elty,10),zeros(BlasInt,10),zeros(BlasInt,10))
         @test_throws DimensionMismatch LAPACK.stein!(d,e,zeros(elty,11),zeros(BlasInt,10),zeros(BlasInt,10))
     end
 end

stdlib/LinearAlgebra/test/tridiag.jl

@@ -590,6 +590,8 @@ end
     F2 = eigen(A2)
     test_approx_eq_modphase(F.vectors, F2.vectors)
     @test F.values ≈ F2.values ≈ eigvals(A) ≈ eigvals(A2)
+    @test eigvecs(A) ≈ eigvecs(A2)
+    @test eigvecs(A, eigvals(A)[1:1]) ≈ eigvecs(A2, eigvals(A2)[1:1])
 end
 
 @testset "non-commutative algebra (#39701)" begin