Index: include/polly/ScheduleOptimizer.h
===================================================================
--- include/polly/ScheduleOptimizer.h
+++ include/polly/ScheduleOptimizer.h
@@ -148,6 +148,9 @@
   ///
   /// @param Node The schedule node to (possibly) optimize.
   /// @param User A pointer to forward some use information (currently unused).
+  static isl_schedule_node *
+  standardBandOpts(__isl_take isl_schedule_node *Node);
+
   static isl_schedule_node *optimizeBand(isl_schedule_node *Node, void *User);
 };
 
Index: lib/Transform/ScheduleOptimizer.cpp
===================================================================
--- lib/Transform/ScheduleOptimizer.cpp
+++ lib/Transform/ScheduleOptimizer.cpp
@@ -166,6 +166,11 @@
                       cl::Hidden, cl::ZeroOrMore, cl::CommaSeparated,
                       cl::cat(PollyCategory));
 
+static cl::opt<bool>
+    PMBasedOpts("polly-pm-based-opts",
+                cl::desc("Perform optimizations based on pattern matching"),
+                cl::init(false), cl::ZeroOrMore, cl::cat(PollyCategory));
+
 /// @brief Create an isl_union_set, which describes the isolate option based
 ///        on IsoalteDomain.
 ///
@@ -359,11 +364,7 @@
 }
 
 __isl_give isl_schedule_node *
-ScheduleTreeOptimizer::optimizeBand(__isl_take isl_schedule_node *Node,
-                                    void *User) {
-  if (!isTileableBandNode(Node))
-    return Node;
-
+ScheduleTreeOptimizer::standardBandOpts(__isl_take isl_schedule_node *Node) {
   if (FirstLevelTiling)
     Node = tileNode(Node, "1st level tiling", FirstLevelTileSizes,
                     FirstLevelDefaultTileSize);
@@ -396,6 +397,87 @@
   return Node;
 }
 
+static bool isInputDimUsed(__isl_take isl_map *IslMap, unsigned DimNum) {
+  auto *CheckedAccessRelation =
+      isl_map_project_out(isl_map_copy(IslMap), isl_dim_in, DimNum, 1);
+  CheckedAccessRelation =
+      isl_map_add_dims(CheckedAccessRelation, isl_dim_in, 1);
+  auto *InputDimsId = isl_map_get_tuple_id(IslMap, isl_dim_in);
+  CheckedAccessRelation =
+      isl_map_set_tuple_id(CheckedAccessRelation, isl_dim_in, InputDimsId);
+  InputDimsId = isl_map_get_tuple_id(IslMap, isl_dim_out);
+  CheckedAccessRelation =
+      isl_map_set_tuple_id(CheckedAccessRelation, isl_dim_out, InputDimsId);
+  auto res = !isl_map_is_equal(CheckedAccessRelation, IslMap);
+  isl_map_free(CheckedAccessRelation);
+  isl_map_free(IslMap);
+  return res;
+}
+
+static bool containsMatrMult(__isl_keep isl_map *PartialSchedule) {
+  auto InputDimsId = isl_map_get_tuple_id(PartialSchedule, isl_dim_in);
+  auto *ScpStmt = static_cast<ScopStmt *>(isl_id_get_user(InputDimsId));
+  isl_id_free(InputDimsId);
+  if (ScpStmt->size() <= 1)
+    return false;
+  auto MemA = ScpStmt->begin();
+  for (unsigned i = 0; i < ScpStmt->size() - 2 && MemA != ScpStmt->end();
+       i++, MemA++)
+    if (!(*MemA)->isRead() or
+        ((*MemA)->isArrayKind() and
+         !((*MemA)->isStrideOne(isl_map_copy(PartialSchedule)) or
+           (*MemA)->isStrideZero(isl_map_copy(PartialSchedule)))))
+      return false;
+  MemA++;
+  if (!(*MemA)->isWrite() or !(*MemA)->isArrayKind() or
+      !((*MemA)->isStrideOne(isl_map_copy(PartialSchedule)) or
+        (*MemA)->isStrideZero(isl_map_copy(PartialSchedule))))
+    return false;
+  auto DimNum = isl_map_dim(PartialSchedule, isl_dim_in);
+  return !isInputDimUsed((*MemA)->getAccessRelation(), DimNum - 1);
+}
+
+static __isl_give isl_map *interchangeInputDims(__isl_take isl_map *IslMap,
+                                                unsigned DstPos,
+                                                unsigned SrcPos) {
+  auto InputDimsId = isl_map_get_tuple_id(IslMap, isl_dim_in);
+  IslMap = isl_map_move_dims(IslMap, isl_dim_in, 0, isl_dim_out, SrcPos, 1);
+  IslMap = isl_map_move_dims(IslMap, isl_dim_out, 0, isl_dim_in, DstPos, 1);
+  return isl_map_set_tuple_id(IslMap, isl_dim_in, InputDimsId);
+}
+
+bool static isMatrMultPattern(__isl_keep isl_schedule_node *Node) {
+  auto *PartialSchedule =
+      isl_schedule_node_band_get_partial_schedule_union_map(Node);
+  if (isl_union_map_n_map(PartialSchedule) != 1)
+    return false;
+  auto *NewPartialSchedule = isl_map_from_union_map(PartialSchedule);
+  auto DimNum = isl_map_dim(NewPartialSchedule, isl_dim_in);
+  if (DimNum != 3) {
+    isl_map_free(NewPartialSchedule);
+    return false;
+  }
+  NewPartialSchedule = interchangeInputDims(NewPartialSchedule, 0, DimNum - 1);
+  if (containsMatrMult(NewPartialSchedule)) {
+    isl_map_free(NewPartialSchedule);
+    return true;
+  }
+  isl_map_free(NewPartialSchedule);
+  return false;
+}
+
+__isl_give isl_schedule_node *
+ScheduleTreeOptimizer::optimizeBand(__isl_take isl_schedule_node *Node,
+                                    void *User) {
+  if (!isTileableBandNode(Node))
+    return Node;
+
+  if (PMBasedOpts && isMatrMultPattern(Node))
+    dbgs() << "The matrix multiplication pattern was detected\n";
+
+  return standardBandOpts(Node);
+}
+
 __isl_give isl_schedule *
 ScheduleTreeOptimizer::optimizeSchedule(__isl_take isl_schedule *Schedule) {
   isl_schedule_node *Root = isl_schedule_get_root(Schedule);