[SYSTEMDS-3889] New simplification rewrite for matrix-scalar ops

e.g., a-A-b -> (a-b)-A; a+A-b -> (a-b)+A
Closes #2272.

Author: aarnaty

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

@@ -202,6 +202,7 @@ private void rule_AlgebraicSimplification(Hop hop, boolean descendFirst)
 			hi = simplifyNegatedSubtraction(hop, hi, i);         //e.g., -(B-A)->A-B
 			hi = simplifyTransposeAddition(hop, hi, i);          //e.g., t(A+s1)+s2 -> t(A)+(s1+s2) + potential constant folding
 			hi = simplifyNotOverComparisons(hop, hi, i);         //e.g., !(A>B) -> (A<=B)
+			hi = simplifyMatrixScalarPMOperation(hop, hi, i);    //e.g., a-A-b -> (a-b)-A; a+A-b -> (a-b)+A
 			//hi = removeUnecessaryPPred(hop, hi, i);            //e.g., ppred(X,X,"==")->matrix(1,rows=nrow(X),cols=ncol(X))
 
 			//process childs recursively after rewrites (to investigate pattern newly created by rewrites)
@@ -212,6 +213,40 @@ private void rule_AlgebraicSimplification(Hop hop, boolean descendFirst)
 		hop.setVisited();
 	}
 
+	private Hop simplifyMatrixScalarPMOperation(Hop parent, Hop hi, int pos) {
+		if (!(hi instanceof BinaryOp))
+			return hi;
+
+		BinaryOp outer = (BinaryOp) hi;
+		Hop left = outer.getInput(0);
+		Hop right = outer.getInput(1);
+		OpOp2 outerOp = outer.getOp();
+
+		if((outerOp != OpOp2.PLUS && outerOp != OpOp2.MINUS) || !(left instanceof BinaryOp))
+			return hi;
+
+		Hop a = left.getInput(0);
+		Hop A = left.getInput(1);
+		Hop b = right;
+		
+		java.util.function.Predicate<Hop> isScalar = h -> h.getDataType().isScalar();
+		if (!isScalar.test(a) || !isScalar.test(b) || A.getDataType() != DataType.MATRIX)
+			return hi;
+
+		// Determine the scalarOp (between a and b) and matrixOp (with A)
+		OpOp2 innerOp = ((BinaryOp)left).getOp();
+		if( innerOp != OpOp2.PLUS && innerOp != OpOp2.MINUS )
+			return hi;
+		OpOp2 scalarOp = (outerOp == OpOp2.PLUS) ? OpOp2.PLUS : OpOp2.MINUS;
+		OpOp2 matrixOp = (innerOp == OpOp2.PLUS) ? OpOp2.PLUS : OpOp2.MINUS;
+		Hop scalarCombined = HopRewriteUtils.createBinary(a, b, scalarOp);
+		Hop result = HopRewriteUtils.createBinary(scalarCombined, A, matrixOp);
+
+		HopRewriteUtils.replaceChildReference(parent, hi, result, pos);
+		LOG.debug("Applied simplifyMatrixScalarPMOperation");
+		return result;
+	}
+
 	private static Hop simplifyTransposeAddition(Hop parent, Hop hi, int pos) {
 		//pattern: t(A+s1)+s2 -> t(A)+(s1+s2), and subsequent constant folding
 		if (HopRewriteUtils.isBinary(hi, OpOp2.PLUS) 

src/test/java/org/apache/sysds/test/functions/rewrite/RewriteSimplifyScalarMatrixPMOperationTest.java

@@ -0,0 +1,98 @@
+/*
+ * 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.test.functions.rewrite;
+
+import org.apache.sysds.hops.OptimizerUtils;
+import org.apache.sysds.runtime.matrix.data.MatrixValue;
+import org.apache.sysds.test.AutomatedTestBase;
+import org.apache.sysds.test.TestConfiguration;
+import org.apache.sysds.test.TestUtils;
+import org.junit.Test;
+
+import java.util.HashMap;
+
+public class RewriteSimplifyScalarMatrixPMOperationTest extends AutomatedTestBase {
+	private static final String TEST_NAME1 = "RewriteScalarMinusMatrixMinusScalar";
+	private static final String TEST_NAME2 = "RewriteScalarPlusMatrixMinusScalar";
+	private static final String TEST_DIR = "functions/rewrite/";
+	private static final String TEST_CLASS_DIR = TEST_DIR + RewriteSimplifyScalarMatrixPMOperationTest.class.getSimpleName() + "/";
+	private static final int rows = 100;
+	private static final int cols = 100;
+	private static final double eps = 1e-6;
+
+	@Override
+	public void setUp() {
+		TestUtils.clearAssertionInformation();
+		addTestConfiguration(TEST_NAME1, new TestConfiguration(TEST_CLASS_DIR, TEST_NAME1, new String[]{"A", "a", "b", "R"}));
+		addTestConfiguration(TEST_NAME2, new TestConfiguration(TEST_CLASS_DIR, TEST_NAME2, new String[]{"A", "a", "b", "R"}));
+	}
+
+	@Test
+	public void testScalarMinusMatrixMinusScalarRewriteEnabled() {
+		runRewriteTest(TEST_NAME1, true);
+	}
+
+	@Test
+	public void testScalarMinusMatrixMinusScalarRewriteDisabled() {
+		runRewriteTest(TEST_NAME1, false);
+	}
+
+	@Test
+	public void testScalarPlusMatrixMinusScalarRewriteEnabled() {
+		runRewriteTest(TEST_NAME2, true);
+	}
+
+	@Test
+	public void testScalarPlusMatrixMinusScalarRewriteDisabled() {
+		runRewriteTest(TEST_NAME2, false);
+	}
+
+	private void runRewriteTest(String testName, boolean rewriteEnabled) {
+		boolean oldFlag = OptimizerUtils.ALLOW_ALGEBRAIC_SIMPLIFICATION;
+		try {
+			TestConfiguration config = getTestConfiguration(testName);
+			loadTestConfiguration(config);
+
+			String HOME = SCRIPT_DIR + TEST_DIR;
+			fullDMLScriptName = HOME + testName + ".dml";
+			fullRScriptName = HOME + testName + ".R";
+			programArgs = new String[]{"-stats", "-args", input("A"), input("a"), input("b"), output("R")};
+			rCmd = getRCmd(inputDir(), expectedDir());
+
+			OptimizerUtils.ALLOW_ALGEBRAIC_SIMPLIFICATION = rewriteEnabled;
+
+			double[][] A = getRandomMatrix(rows, cols, -100, 100, 0.9, 3);
+			double[][] a = getRandomMatrix(1, 1, -10, 10, 1.0, 7);
+			double[][] b = getRandomMatrix(1, 1, -10, 10, 1.0, 5);
+
+			writeInputMatrixWithMTD("A", A, true);
+			writeInputMatrixWithMTD("a", a, true);
+			writeInputMatrixWithMTD("b", b, true);
+
+			runTest(true, false, null, -1);
+			runRScript(true);
+
+			HashMap<MatrixValue.CellIndex, Double> dml = readDMLMatrixFromOutputDir("R");
+			HashMap<MatrixValue.CellIndex, Double> r = readRMatrixFromExpectedDir("R");
+			TestUtils.compareMatrices(dml, r, eps, "Stat-DML", "Stat-R");
+		} finally {
+			OptimizerUtils.ALLOW_ALGEBRAIC_SIMPLIFICATION = oldFlag;
+		}
+	}
+}

src/test/scripts/functions/rewrite/RewriteScalarMinusMatrixMinusScalar.R

@@ -0,0 +1,30 @@
+#-------------------------------------------------------------
+#
+# 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.
+#
+#-------------------------------------------------------------
+args <- commandArgs(TRUE)
+library("Matrix")
+
+A <- as.matrix(readMM(paste(args[1], "A.mtx", sep="")))
+a <- as.numeric(readMM(paste(args[1], "a.mtx", sep="")))
+b <- as.numeric(readMM(paste(args[1], "b.mtx", sep="")))
+
+R <- (a-b)-A
+
+writeMM(as(R, "CsparseMatrix"), paste(args[2], "R", sep=""))

src/test/scripts/functions/rewrite/RewriteScalarMinusMatrixMinusScalar.dml

@@ -0,0 +1,28 @@
+#-------------------------------------------------------------
+#
+# 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.
+#
+#-------------------------------------------------------------
+A = read($1);
+a = read($2);
+b = read($3);
+
+R = a - A - b;
+
+write(R, $4);
+

src/test/scripts/functions/rewrite/RewriteScalarPlusMatrixMinusScalar.R

@@ -0,0 +1,30 @@
+#-------------------------------------------------------------
+#
+# 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.
+#
+#-------------------------------------------------------------
+args <- commandArgs(TRUE)
+library("Matrix")
+
+A <- as.matrix(readMM(paste(args[1], "A.mtx", sep="")))
+a <- as.numeric(readMM(paste(args[1], "a.mtx", sep="")))
+b <- as.numeric(readMM(paste(args[1], "b.mtx", sep="")))
+
+R <- (a-b)+A
+
+writeMM(as(R, "CsparseMatrix"), paste(args[2], "R", sep=""))

src/test/scripts/functions/rewrite/RewriteScalarPlusMatrixMinusScalar.dml

@@ -0,0 +1,28 @@
+#-------------------------------------------------------------
+#
+# 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.
+#
+#-------------------------------------------------------------
+A = read($1);
+a = as.scalar(read($2));
+b = as.scalar(read($3));
+
+# Original form: a + A - b
+R = a + A - b;
+
+write(R, $4);