batched - dense: Testing and fixing Serial QR

The serial QR algorithms does not have unit-tests and is failing
for non square matrices. See issue kokkos#2328.
This first commit fixes the issue with rectangular matrices and
adds a basic test for that use case. Next will work on adding a
test that exercises the interfaces on multiple matrices of different
sizes within a parallel_for. Finally equivalent tests will be added
for the square case as well.

batched/dense/impl/KokkosBatched_QR_FormQ_Serial_Internal.hpp

@@ -49,12 +49,16 @@ struct SerialQR_FormQ_Internal {
     ///   B is m x m
 
     // set identity
-    if (is_Q_zero)
-      SerialSetInternal::invoke(m, value_type(1), Q, qs0 + qs1);
-    else
+    if (is_Q_zero) {
+      for (int idx = 0; idx < m; ++idx) {
+        Q[(qs0 + qs1) * idx] = value_type(1);
+        // SerialSetInternal::invoke(m, value_type(1), Q, qs0 + qs1);
+      }
+    } else {
       SerialSetIdentityInternal::invoke(m, Q, qs0, qs1);
+    }
 
-    return SerialApplyQ_LeftNoTransForwardInternal ::invoke(m, m, k, A, as0, as1, t, ts, Q, qs0, qs1, w);
+    return SerialApplyQ_LeftForwardInternal::invoke(m, m, k, A, as0, as1, t, ts, Q, qs0, qs1, w);
   }
 };
 

batched/dense/impl/KokkosBatched_QR_Serial_Internal.hpp

@@ -53,7 +53,7 @@ struct SerialQR_Internal {
     A_part2x2.partWithATL(A, m, n, 0, 0);
     t_part2x1.partWithAT(t, m, 0);
 
-    for (int m_atl = 0; m_atl < m; ++m_atl) {
+    for (int m_atl = 0; m_atl < Kokkos::min(m, n); ++m_atl) {
       // part 2x2 into 3x3
       A_part3x3.partWithABR(A_part2x2, 1, 1);
       const int m_A22 = m - m_atl - 1;

batched/dense/unit_test/Test_Batched_Dense.hpp

@@ -30,6 +30,7 @@
 #include "Test_Batched_SerialLU.hpp"
 #include "Test_Batched_SerialLU_Real.hpp"
 #include "Test_Batched_SerialLU_Complex.hpp"
+#include "Test_Batched_SerialQR.hpp"
 #include "Test_Batched_SerialSolveLU.hpp"
 #include "Test_Batched_SerialSolveLU_Real.hpp"
 #include "Test_Batched_SerialSolveLU_Complex.hpp"