Fix orientation of right vectors in svds (#19974)

Author: andreasnoack

base/linalg/arnoldi.jl

@@ -388,9 +388,12 @@ function _svds(X; nsv::Int = 6, ritzvec::Bool = true, tol::Float64 = 0.0, maxite
         # calculating singular vectors
         left_sv  = sqrt(2) * ex[2][ 1:size(X,1),     ind ] .* sign(ex[1][ind]')
         right_sv = sqrt(2) * ex[2][ size(X,1)+1:end, ind ]
-        return (SVD(left_sv, sval, right_sv), ex[3], ex[4], ex[5], ex[6])
+        return (SVD(left_sv, sval, right_sv'), ex[3], ex[4], ex[5], ex[6])
     else
         #The sort is necessary to work around #10329
-        return (SVD(zeros(eltype(sval),n,0),sort!(sval, by=real, rev=true),zeros(eltype(sval),0,m)), ex[2], ex[3], ex[4], ex[5])
+        return (SVD(zeros(eltype(sval), n, 0),
+                    sort!(sval, by=real, rev=true),
+                    zeros(eltype(sval), 0, m)),
+                    ex[2], ex[3], ex[4], ex[5])
     end
 end

test/linalg/arnoldi.jl

@@ -167,7 +167,7 @@ end
             @test s1_left ≈ s2_left
 
             ## 1st right singular vector
-            s1_right = sign(S1[1][:Vt][3,1]) * S1[1][:Vt][:,1]
+            s1_right = sign(S1[1][:V][3,1]) * S1[1][:V][:,1]
             s2_right = sign(S2[3][3,1]) * S2[3][:,1]
             @test s1_right ≈ s2_right
         end
@@ -212,7 +212,7 @@ end
             @test s1_left ≈ s2_left
 
             ## right singular vectors
-            s1_right = abs.(S1[1][:Vt][:,1:2])
+            s1_right = abs.(S1[1][:V][:,1:2])
             s2_right = abs.(S2[3][:,1:2])
             @test s1_right ≈ s2_right
         end