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.
Fixing unused variable error
It looks like the Left NoTranspose ApplyQ is not doing the correct
thing. Will have a look at that next.

Signed-off-by: Luc <[email protected]>

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
-      SerialSetIdentityInternal::invoke(m, Q, qs0, qs1);
+    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, 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"