diff --git a/Eigen/src/Core/products/TriangularMatrixMatrix.h b/Eigen/src/Core/products/TriangularMatrixMatrix.h
index 967deaffb..a099160c2 100644
--- a/Eigen/src/Core/products/TriangularMatrixMatrix.h
+++ b/Eigen/src/Core/products/TriangularMatrixMatrix.h
@@ -75,14 +75,14 @@ struct ei_product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
     Scalar alpha)
   {
     ei_product_triangular_matrix_matrix<Scalar, Index,
-      (Mode&UnitDiag) | (Mode&Upper) ? Lower : Upper,
+      (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper),
       (!LhsIsTriangular),
       RhsStorageOrder==RowMajor ? ColMajor : RowMajor,
       ConjugateRhs,
       LhsStorageOrder==RowMajor ? ColMajor : RowMajor,
       ConjugateLhs,
       ColMajor>
-      ::run(rows, cols, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
+      ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
   }
 };
 
@@ -138,6 +138,7 @@ struct ei_product_triangular_matrix_matrix<Scalar,Index,Mode,true,
       Index actual_kc = std::min(IsLower ? k2 : depth-k2, kc);
       Index actual_k2 = IsLower ? k2-actual_kc : k2;
 
+      // align blocks with the end of the triangular part for trapezoidal lhs
       if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
       {
         actual_kc = rows-k2;
@@ -191,7 +192,7 @@ struct ei_product_triangular_matrix_matrix<Scalar,Index,Mode,true,
       // the part below the diagonal => GEPP
       {
         Index start = IsLower ? k2 : 0;
-        Index end   = IsLower ? rows : actual_k2;
+        Index end   = IsLower ? rows : std::min(actual_k2,rows);
         for(Index i2=start; i2<end; i2+=mc)
         {
           const Index actual_mc = std::min(i2+mc,end)-i2;
@@ -258,14 +259,27 @@ struct ei_product_triangular_matrix_matrix<Scalar,Index,Mode,false,
         IsLower ? k2<depth  : k2>0;
         IsLower ? k2+=kc   : k2-=kc)
     {
-      const Index actual_kc = std::min(IsLower ? depth-k2 : k2, kc);
+      Index actual_kc = std::min(IsLower ? depth-k2 : k2, kc);
       Index actual_k2 = IsLower ? k2 : k2-actual_kc;
-      Index rs = IsLower ? actual_k2 : depth - k2;
-      Scalar* geb = blockB+actual_kc*actual_kc;
+
+      // align blocks with the end of the triangular part for trapezoidal rhs
+      if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
+      {
+        actual_kc = cols-k2;
+        k2 = actual_k2 + actual_kc - kc;
+      }
+
+      // remaining size
+      Index rs = IsLower ? std::min(cols,actual_k2) : cols - k2;
+      // size of the triangular part
+      Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
+      
+      Scalar* geb = blockB+ts*ts;
 
       pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, alpha, actual_kc, rs);
 
       // pack the triangular part of the rhs padding the unrolled blocks with zeros
+      if(ts>0)
       {
         for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
         {
@@ -301,6 +315,7 @@ struct ei_product_triangular_matrix_matrix<Scalar,Index,Mode,false,
         pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
 
         // triangular kernel
+        if(ts>0)
         {
           for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
           {
diff --git a/test/product_trmm.cpp b/test/product_trmm.cpp
index e8580cbd2..a689deba6 100644
--- a/test/product_trmm.cpp
+++ b/test/product_trmm.cpp
@@ -24,48 +24,54 @@
 
 #include "main.h"
 
-template<typename Scalar> void trmm(int size,int othersize)
+template<typename Scalar> void trmm(int size,int /*othersize*/)
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
 
-  typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixType;
+  typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixColMaj;
+  typedef Matrix<Scalar,Dynamic,Dynamic,RowMajor> MatrixRowMaj;
 
-  MatrixType tri(size,size), upTri(size,size), loTri(size,size),
-             unitUpTri(size,size), unitLoTri(size,size);
-  MatrixType ge1(size,othersize), ge2(10,size), ge3;
-  Matrix<Scalar,Dynamic,Dynamic,RowMajor> rge3;
+  int rows = size;
+  int cols = ei_random<int>(1,size);
+
+  MatrixColMaj  triV(rows,cols), triH(cols,rows), upTri(cols,rows), loTri(rows,cols),
+                unitUpTri(cols,rows), unitLoTri(rows,cols);
+  MatrixColMaj  ge1(rows,cols), ge2(cols,rows), ge3;
+  MatrixRowMaj  rge3;
 
   Scalar s1 = ei_random<Scalar>(),
          s2 = ei_random<Scalar>();
 
-  tri.setRandom();
-  loTri = tri.template triangularView<Lower>();
-  upTri = tri.template triangularView<Upper>();
-  unitLoTri = tri.template triangularView<UnitLower>();
-  unitUpTri = tri.template triangularView<UnitUpper>();
+  triV.setRandom();
+  triH.setRandom();
+  loTri = triV.template triangularView<Lower>();
+  upTri = triH.template triangularView<Upper>();
+  unitLoTri = triV.template triangularView<UnitLower>();
+  unitUpTri = triH.template triangularView<UnitUpper>();
   ge1.setRandom();
   ge2.setRandom();
 
-  VERIFY_IS_APPROX( ge3 = tri.template triangularView<Lower>() * ge1, loTri * ge1);
-  VERIFY_IS_APPROX(rge3 = tri.template triangularView<Lower>() * ge1, loTri * ge1);
-  VERIFY_IS_APPROX( ge3 = tri.template triangularView<Upper>() * ge1, upTri * ge1);
-  VERIFY_IS_APPROX(rge3 = tri.template triangularView<Upper>() * ge1, upTri * ge1);
-  VERIFY_IS_APPROX( ge3 = (s1*tri.adjoint()).template triangularView<Upper>() * (s2*ge1), s1*loTri.adjoint() * (s2*ge1));
-  VERIFY_IS_APPROX(rge3 = tri.adjoint().template triangularView<Upper>() * ge1, loTri.adjoint() * ge1);
-  VERIFY_IS_APPROX( ge3 = tri.adjoint().template triangularView<Lower>() * ge1, upTri.adjoint() * ge1);
-  VERIFY_IS_APPROX(rge3 = tri.adjoint().template triangularView<Lower>() * ge1, upTri.adjoint() * ge1);
-  VERIFY_IS_APPROX( ge3 = tri.template triangularView<Lower>() * ge2.adjoint(), loTri * ge2.adjoint());
-  VERIFY_IS_APPROX(rge3 = tri.template triangularView<Lower>() * ge2.adjoint(), loTri * ge2.adjoint());
-  VERIFY_IS_APPROX( ge3 = tri.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
-  VERIFY_IS_APPROX(rge3 = tri.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
-  VERIFY_IS_APPROX( ge3 = (s1*tri).adjoint().template triangularView<Upper>() * ge2.adjoint(), ei_conj(s1) * loTri.adjoint() * ge2.adjoint());
-  VERIFY_IS_APPROX(rge3 = tri.adjoint().template triangularView<Upper>() * ge2.adjoint(), loTri.adjoint() * ge2.adjoint());
-  VERIFY_IS_APPROX( ge3 = tri.adjoint().template triangularView<Lower>() * ge2.adjoint(), upTri.adjoint() * ge2.adjoint());
-  VERIFY_IS_APPROX(rge3 = tri.adjoint().template triangularView<Lower>() * ge2.adjoint(), upTri.adjoint() * ge2.adjoint());
+  VERIFY_IS_APPROX( ge3 = triV.template triangularView<Lower>() * ge2, loTri * ge2);
+  VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<Lower>(), ge2 * loTri);
+  VERIFY_IS_APPROX( ge3 = triH.template triangularView<Upper>() * ge1, upTri * ge1);
+  VERIFY_IS_APPROX( ge3 = ge1 * triH.template triangularView<Upper>(), ge1 * upTri);
+  VERIFY_IS_APPROX( ge3 = (s1*triV.adjoint()).template triangularView<Upper>() * (s2*ge1), s1*loTri.adjoint() * (s2*ge1));
+  VERIFY_IS_APPROX( ge3 = ge1 * triV.adjoint().template triangularView<Upper>(), ge1 * loTri.adjoint());
+  VERIFY_IS_APPROX( ge3 = triH.adjoint().template triangularView<Lower>() * ge2, upTri.adjoint() * ge2);
+  VERIFY_IS_APPROX( ge3 = ge2 * triH.adjoint().template triangularView<Lower>(), ge2 * upTri.adjoint());
+  VERIFY_IS_APPROX( ge3 = triV.template triangularView<Lower>() * ge1.adjoint(), loTri * ge1.adjoint());
+  VERIFY_IS_APPROX( ge3 = ge1.adjoint() * triV.template triangularView<Lower>(), ge1.adjoint() * loTri);
+  VERIFY_IS_APPROX( ge3 = triH.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
+  VERIFY_IS_APPROX(rge3.noalias() = triH.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
+  VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<Upper>() * ge2.adjoint(), ei_conj(s1) * loTri.adjoint() * ge2.adjoint());
+  VERIFY_IS_APPROX(rge3.noalias() = triV.adjoint().template triangularView<Upper>() * ge2.adjoint(), loTri.adjoint() * ge2.adjoint());
+  VERIFY_IS_APPROX( ge3 = triH.adjoint().template triangularView<Lower>() * ge1.adjoint(), upTri.adjoint() * ge1.adjoint());
+  VERIFY_IS_APPROX(rge3.noalias() = triH.adjoint().template triangularView<Lower>() * ge1.adjoint(), upTri.adjoint() * ge1.adjoint());
 
-  VERIFY_IS_APPROX( ge3 = tri.template triangularView<UnitLower>() * ge1, unitLoTri * ge1);
-  VERIFY_IS_APPROX(rge3 = tri.template triangularView<UnitLower>() * ge1, unitLoTri * ge1);
-  VERIFY_IS_APPROX( ge3 = (s1*tri).adjoint().template triangularView<UnitUpper>() * ge2.adjoint(), ei_conj(s1) * unitLoTri.adjoint() * ge2.adjoint());
+  VERIFY_IS_APPROX( ge3 = triV.template triangularView<UnitLower>() * ge2, unitLoTri * ge2);
+  VERIFY_IS_APPROX( rge3.noalias() = ge2 * triV.template triangularView<UnitLower>(), ge2 * unitLoTri);
+  VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<UnitLower>(), ge2 * unitLoTri);
+  VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<UnitUpper>() * ge2.adjoint(), ei_conj(s1) * unitLoTri.adjoint() * ge2.adjoint());
 }
 
 void test_product_trmm()