[SYSTEMDS-3909] Final framework for einsum expressions

Closes #2391.

Author: HubertKrawczyk

src/main/java/org/apache/sysds/hops/NaryOp.java

@@ -165,7 +165,7 @@ else if ( areDimsBelowThreshold() )
 		setRequiresRecompileIfNecessary();
 
 		//ensure cp exec type for single-node operations
-		if ( _op == OpOpN.PRINTF  || _op == OpOpN.EVAL || _op == OpOpN.LIST
+		if ( _op == OpOpN.PRINTF  || _op == OpOpN.EVAL || _op == OpOpN.LIST || _op == OpOpN.EINSUM
 			//TODO: cbind/rbind of lists only support in CP right now
 			|| (_op == OpOpN.CBIND && getInput().get(0).getDataType().isList())
 			|| (_op == OpOpN.RBIND && getInput().get(0).getDataType().isList())

src/main/java/org/apache/sysds/hops/rewrite/RewriteMatrixMultChainOptimization.java

@@ -210,7 +210,7 @@ protected void optimizeMMChain(Hop hop, List<Hop> mmChain, List<Hop> mmOperators
 	 * Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein
 	 * Introduction to Algorithms, Third Edition, MIT Press, page 395.
 	 */
-	private static int[][] mmChainDP(double[] dimArray, int size) 
+	public static int[][] mmChainDP(double[] dimArray, int size)
 	{
 		double[][] dpMatrix = new double[size][size]; //min cost table
 		int[][] split = new int[size][size]; //min cost index table

src/main/java/org/apache/sysds/runtime/einsum/EOpNode.java

@@ -0,0 +1,69 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+package org.apache.sysds.runtime.einsum;
+
+import org.apache.commons.logging.Log;
+import org.apache.sysds.runtime.matrix.data.MatrixBlock;
+import scala.Int;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+public abstract class EOpNode {
+    public Character c1;
+    public Character c2;
+	public Integer dim1;
+	public Integer dim2;
+    public EOpNode(Character c1, Character c2, Integer dim1, Integer dim2) {
+        this.c1 = c1;
+        this.c2 = c2;
+		this.dim1 = dim1;
+		this.dim2 = dim2;
+    }
+
+    public String getOutputString() {
+        if(c1 == null) return "''";
+        if(c2 == null) return c1.toString();
+        return c1.toString() + c2.toString();
+    }
+	public abstract List<EOpNode> getChildren();
+
+	public String[] recursivePrintString(){
+		ArrayList<String[]> inpStrings = new ArrayList<>();
+		for (EOpNode node : getChildren()) {
+			inpStrings.add(node.recursivePrintString());
+		}
+		String[] inpRes = inpStrings.stream().flatMap(Arrays::stream).toArray(String[]::new);
+		String[] res = new String[1 + inpRes.length];
+
+		res[0] = this.toString();
+
+		for  (int i=0; i<inpRes.length; i++) {
+			res[i+1] = (i==0 ?  "┌  " : (i==inpRes.length-1 ?  "└  " : "|  "))+inpRes[i];
+		}
+		return res;
+	};
+
+    public abstract MatrixBlock computeEOpNode(ArrayList<MatrixBlock> inputs, int numOfThreads, Log LOG);
+
+    public abstract EOpNode reorderChildrenAndOptimize(EOpNode parent, Character outChar1, Character outChar2);
+}
+