Re-enable products with triangular views of sparse matrices: we simply have to treat them as a sparse matrix.

Eigen/src/Core/TriangularMatrix.h

@@ -247,7 +247,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
     inline const AdjointReturnType adjoint() const
     { return AdjointReturnType(m_matrix.adjoint()); }
 
-    typedef TriangularView<Transpose<MatrixType>,TransposeMode> TransposeReturnType;
+    typedef TriangularView<typename MatrixType::TransposeReturnType,TransposeMode> TransposeReturnType;
      /** \sa MatrixBase::transpose() */
     EIGEN_DEVICE_FUNC
     inline TransposeReturnType transpose()
@@ -255,11 +255,13 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
       EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
       return TransposeReturnType(m_matrix.const_cast_derived().transpose());
     }
+    
+    typedef TriangularView<const typename MatrixType::ConstTransposeReturnType,TransposeMode> ConstTransposeReturnType;
     /** \sa MatrixBase::transpose() const */
     EIGEN_DEVICE_FUNC
-    inline const TransposeReturnType transpose() const
+    inline const ConstTransposeReturnType transpose() const
     {
-      return TransposeReturnType(m_matrix.transpose());
+      return ConstTransposeReturnType(m_matrix.transpose());
     }
 
     template<typename Other>

Eigen/src/SparseCore/ConservativeSparseSparseProduct.h

@@ -141,6 +141,8 @@ struct conservative_sparse_sparse_product_selector<Lhs,Rhs,ResultType,ColMajor,C
     typedef SparseMatrix<typename ResultType::Scalar,ColMajor,typename ResultType::Index> ColMajorMatrixAux;
     typedef typename sparse_eval<ColMajorMatrixAux,ResultType::RowsAtCompileTime,ResultType::ColsAtCompileTime>::type ColMajorMatrix;
     
+    // If the result is tall and thin (in the extreme case a column vector)
+    // then it is faster to sort the coefficients inplace instead of transposing twice.
     // FIXME, the following heuristic is probably not very good.
     if(lhs.rows()>=rhs.cols())
     {

Eigen/src/SparseCore/SparseDenseProduct.h

@@ -146,6 +146,11 @@ struct generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType>
   }
 };
 
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseTriangularShape, DenseShape, ProductType>
+  : generic_product_impl<Lhs, Rhs, SparseShape, DenseShape, ProductType>
+{};
+
 template<typename Lhs, typename Rhs, int ProductType>
 struct generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>
 {
@@ -158,12 +163,17 @@ struct generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>
     RhsNested rhsNested(rhs);
     
     dst.setZero();
-    // transpoe everything
+    // transpose everything
     Transpose<Dest> dstT(dst);
     internal::sparse_time_dense_product(rhsNested.transpose(), lhsNested.transpose(), dstT, typename Dest::Scalar(1));
   }
 };
 
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, DenseShape, SparseTriangularShape, ProductType>
+  : generic_product_impl<Lhs, Rhs, DenseShape, SparseShape, ProductType>
+{};
+
 template<typename LhsT, typename RhsT, bool NeedToTranspose>
 struct sparse_dense_outer_product_evaluator
 {

Eigen/src/SparseCore/SparseProduct.h

@@ -33,6 +33,7 @@ SparseMatrixBase<Derived>::operator*(const SparseMatrixBase<OtherDerived> &other
 
 namespace internal {
 
+// sparse * sparse
 template<typename Lhs, typename Rhs, int ProductType>
 struct generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>
 {
@@ -48,6 +49,18 @@ struct generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>
   }
 };
 
+// sparse * sparse-triangular
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseShape, SparseTriangularShape, ProductType>
+ : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>
+{};
+
+// sparse-triangular * sparse
+template<typename Lhs, typename Rhs, int ProductType>
+struct generic_product_impl<Lhs, Rhs, SparseTriangularShape, SparseShape, ProductType>
+ : public generic_product_impl<Lhs, Rhs, SparseShape, SparseShape, ProductType>
+{};
+
 template<typename Lhs, typename Rhs, int Options>
 struct evaluator<SparseView<Product<Lhs, Rhs, Options> > > 
  : public evaluator<typename Product<Lhs, Rhs, DefaultProduct>::PlainObject>::type

test/sparse_product.cpp

@@ -194,7 +194,7 @@ template<typename SparseMatrixType> void sparse_product()
     VERIFY_IS_APPROX(d3=d1*m2.transpose(), refM3=d1*refM2.transpose());
   }
 
-  // test self adjoint products
+  // test self-adjoint and traingular-view products
   {
     DenseMatrix b = DenseMatrix::Random(rows, rows);
     DenseMatrix x = DenseMatrix::Random(rows, rows);
@@ -202,9 +202,12 @@ template<typename SparseMatrixType> void sparse_product()
     DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
     DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
     DenseMatrix refS = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refA = DenseMatrix::Zero(rows, rows);
     SparseMatrixType mUp(rows, rows);
     SparseMatrixType mLo(rows, rows);
     SparseMatrixType mS(rows, rows);
+    SparseMatrixType mA(rows, rows);
+    initSparse<Scalar>(density, refA, mA);
     do {
       initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
     } while (refUp.isZero());
@@ -224,19 +227,30 @@ template<typename SparseMatrixType> void sparse_product()
     VERIFY_IS_APPROX(mS, refS);
     VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
 
+    // sparse selfadjointView with dense matrices
     VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
     VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
     VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
     
-    // sparse selfadjointView * sparse 
+    // sparse selfadjointView with sparse matrices
     SparseMatrixType mSres(rows,rows);
     VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,
                      refX = refLo.template selfadjointView<Lower>()*refS);
-    // sparse * sparse selfadjointview
     VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),
                      refX = refS * refLo.template selfadjointView<Lower>());
+    
+    // sparse triangularView with dense matrices
+    VERIFY_IS_APPROX(x=mA.template triangularView<Upper>()*b, refX=refA.template triangularView<Upper>()*b);
+    VERIFY_IS_APPROX(x=mA.template triangularView<Lower>()*b, refX=refA.template triangularView<Lower>()*b);
+    VERIFY_IS_APPROX(x=b*mA.template triangularView<Upper>(), refX=b*refA.template triangularView<Upper>());
+    VERIFY_IS_APPROX(x=b*mA.template triangularView<Lower>(), refX=b*refA.template triangularView<Lower>());
+    
+    // sparse triangularView with sparse matrices
+    VERIFY_IS_APPROX(mSres = mA.template triangularView<Lower>()*mS,   refX = refA.template triangularView<Lower>()*refS);
+    VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Lower>(), refX = refS * refA.template triangularView<Lower>());
+    VERIFY_IS_APPROX(mSres = mA.template triangularView<Upper>()*mS,   refX = refA.template triangularView<Upper>()*refS);
+    VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Upper>(), refX = refS * refA.template triangularView<Upper>());
   }
-  
 }
 
 // New test for Bug in SparseTimeDenseProduct