Clean up informal language, vague TODOs, and dead code in comments

libeigen/eigen!2191

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>

Eigen/src/SparseLU/SparseLU.h

@@ -51,7 +51,7 @@ class SparseLUTransposeView : public SparseSolverBase<SparseLUTransposeView<Conj
     eigen_assert(m_sparseLU->info() == Success && "The matrix should be factorized first");
     EIGEN_STATIC_ASSERT((Dest::Flags & RowMajorBit) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
 
-    // this ugly const_cast_derived() helps to detect aliasing when applying the permutations
+    // const_cast_derived() is needed to enable aliasing detection when applying the permutations.
     for (Index j = 0; j < B.cols(); ++j) {
       X.col(j) = m_sparseLU->colsPermutation() * B.const_cast_derived().col(j);
     }
@@ -344,7 +344,7 @@ class SparseLU : public SparseSolverBase<SparseLU<MatrixType_, OrderingType_>>,
     // on return, X is overwritten by the computed solution
     X.resize(B.rows(), B.cols());
 
-    // this ugly const_cast_derived() helps to detect aliasing when applying the permutations
+    // const_cast_derived() is needed to enable aliasing detection when applying the permutations.
     for (Index j = 0; j < B.cols(); ++j) X.col(j) = rowsPermutation() * B.const_cast_derived().col(j);
 
     // Forward substitution with L
@@ -603,7 +603,7 @@ void SparseLU<MatrixType, OrderingType>::analyzePattern(const MatrixType& mat) {
  * > A->ncol: number of bytes allocated when memory allocation failure occurred, plus A->ncol.
  * If lwork = -1, it is the estimated amount of space needed, plus A->ncol.
  *
- * It seems that A was the name of the matrix in the past.
+ * Note: 'A' in the above description refers to the factored matrix (historical naming from SuperLU).
  *
  * \sa analyzePattern(), compute(), SparseLU(), info(), lastErrorMessage()
  */
@@ -616,7 +616,6 @@ void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix) {
   m_isInitialized = true;
 
   // Apply the column permutation computed in analyzepattern()
-  //   m_mat = matrix * m_perm_c.inverse();
   m_mat = matrix;
   if (m_perm_c.size()) {
     m_mat.uncompress();  // NOTE: The effect of this command is only to create the InnerNonzeros pointers.
@@ -779,7 +778,7 @@ void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix) {
       }
 
       // Update the determinant of the row permutation matrix
-      // FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not
+      // FIXME: the following test is not correct; it should account for iperm_c, and pivrow is not
       // directly the row pivot.
       if (pivrow != jj) m_detPermR = -m_detPermR;
 

Eigen/src/SparseLU/SparseLU_SupernodalMatrix.h

@@ -27,11 +27,7 @@ namespace internal {
  * NOTE : This class corresponds to the SCformat structure in SuperLU
  *
  */
-/* TODO
- * InnerIterator as for sparsematrix
- * SuperInnerIterator to iterate through all supernodes
- * Function for triangular solve
- */
+// TODO: add InnerIterator, SuperInnerIterator, and triangular solve support.
 template <typename Scalar_, typename StorageIndex_>
 class MappedSuperNodalMatrix {
  public:

Eigen/src/SparseLU/SparseLU_heap_relax_snode.h

@@ -52,7 +52,7 @@ void SparseLUImpl<Scalar, StorageIndex>::heap_relax_snode(const Index n, IndexVe
   IndexVector post;
   internal::treePostorder(StorageIndex(n), et, post);  // Post order etree
   IndexVector inv_post(n + 1);
-  for (StorageIndex i = 0; i < n + 1; ++i) inv_post(post(i)) = i;  // inv_post = post.inverse()???
+  for (StorageIndex i = 0; i < n + 1; ++i) inv_post(post(i)) = i;  // Compute the inverse postorder permutation.
 
   // Renumber etree in postorder
   IndexVector iwork(n);

Eigen/src/SparseLU/SparseLU_panel_dfs.h

@@ -136,12 +136,9 @@ void SparseLUImpl<Scalar, StorageIndex>::dfs_kernel(const StorageIndex jj, Index
         //    segment is seen for the first time. (Note that
         //    "repfnz(krep)" may change later.)
         //    Baktrack dfs to its parent
-        if (traits.update_segrep(krep, jj))
-        // if (marker1(krep) < jcol )
-        {
+        if (traits.update_segrep(krep, jj)) {
           segrep(nseg) = krep;
           ++nseg;
-          // marker1(krep) = jj;
         }
 
         kpar = parent(krep);            // Pop recursion, mimic recursion