[SYSTEMDS-3948] Row-wise Sparsity Estimator

src/main/java/org/apache/sysds/hops/estim/EstimatorRowWise.java

@@ -0,0 +1,356 @@
+/*
+ * 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.hops.estim;
+
+import org.apache.commons.lang3.ArrayUtils;
+import org.apache.commons.lang3.NotImplementedException;
+import org.apache.sysds.hops.OptimizerUtils;
+import org.apache.sysds.runtime.data.SparseRow;
+import org.apache.sysds.runtime.matrix.data.MatrixBlock;
+import org.apache.sysds.runtime.meta.DataCharacteristics;
+import org.apache.sysds.runtime.meta.MatrixCharacteristics;
+
+import java.util.stream.DoubleStream;
+import java.util.stream.IntStream;
+
+/**
+ * This estimator implements an approach based on row-wise sparsity estimation,
+ * introduced in
+ * Lin, Chunxu, Wensheng Luo, Yixiang Fang, Chenhao Ma, Xilin Liu and Yuchi Ma:
+ * On Efficient Large Sparse Matrix Chain Multiplication.
+ * Proceedings of the ACM on Management of Data 2 (2024): 1 - 27.
+ */
+public class EstimatorRowWise extends SparsityEstimator {
+	@Override
+	public DataCharacteristics estim(MMNode root) {
+		estimInternChain(root);
+		double sparsity = DoubleStream.of((double[])root.getSynopsis()).average().orElse(0);
+
+		DataCharacteristics outputCharacteristics = deriveOutputCharacteristics(root, sparsity);
+		return root.setDataCharacteristics(outputCharacteristics);
+	}
+
+	@Override
+	public double estim(MatrixBlock m1, MatrixBlock m2) {
+		return estim(m1, m2, OpCode.MM);
+	}
+
+	@Override
+	public double estim(MatrixBlock m1, MatrixBlock m2, OpCode op) {
+		if( isExactMetadataOp(op, m1.getNumColumns()) ) {
+			return estimExactMetaData(m1.getDataCharacteristics(),
+				m2.getDataCharacteristics(), op).getSparsity();
+		}
+
+		double[] rsOut = estimIntern(m1, m2, op);
+		return DoubleStream.of(rsOut).average().orElse(0);
+	}
+
+	@Override
+	public double estim(MatrixBlock m1, OpCode op) {
+		if( isExactMetadataOp(op, m1.getNumColumns()) )
+			return estimExactMetaData(m1.getDataCharacteristics(), null, op).getSparsity();
+
+		double[] rsOut = estimIntern(m1, op);
+		return DoubleStream.of(rsOut).average().orElse(0);
+	}
+
+	private double[] estimInternChain(MMNode node) {
+		return estimInternChain(node, null, null);
+	}
+
+	private double[] estimInternChain(MMNode node, double[] rsRightNeighbor, OpCode opRightNeighbor) {
+		double[] rsOut;
+		if(node.isLeaf()) {
+			MatrixBlock mb = node.getData();
+			if(rsRightNeighbor != null)
+				rsOut = estimIntern(mb, rsRightNeighbor, opRightNeighbor);
+			else
+				rsOut = getRowWiseSparsityVector(mb);
+		}
+		else {
+			MMNode nodeLeft = node.getLeft();
+			MMNode nodeRight = node.getRight();
+			switch(node.getOp()) {
+				case MM:
+					double[] rsRightMM = estimInternChain(nodeRight, rsRightNeighbor, opRightNeighbor);
+					rsOut = estimInternChain(nodeLeft, rsRightMM, node.getOp());
+					break;
+				case CBIND:
+					/**
+					 * NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into a cbind operation when having only row sparsity vectors
+					 */
+					double[] rsLeftCBind = estimInternChain(nodeLeft);
+					double[] rsRightCBind = estimInternChain(nodeRight);
+					double[] rsCBind = estimInternCBind(rsLeftCBind, rsRightCBind);
+					if(rsRightNeighbor != null) {
+						rsOut = estimInternMMFallback(rsCBind, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = rsCBind;
+					break;
+				case RBIND:
+					/**
+					 * NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into an rbind operation when having only row sparsity vectors
+					 */
+					double[] rsLeftRBind = estimInternChain(nodeLeft);
+					double[] rsRightRBind = estimInternChain(nodeRight);
+					double[] rsRBind = estimInternRBind(rsLeftRBind, rsRightRBind);
+					if(rsRightNeighbor != null) {
+						rsOut = estimInternMMFallback(rsRBind, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = rsRBind;
+					break;
+				case PLUS:
+					/**
+					 * NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into an element-wise operation when having only row sparsity vectors
+					 */
+					double[] rsLeftPlus = estimInternChain(nodeLeft);
+					double[] rsRightPlus = estimInternChain(nodeRight);
+					double[] rsPlus = estimInternPlus(rsLeftPlus, rsRightPlus);
+					if(rsRightNeighbor != null) {
+						rsOut = estimInternMMFallback(rsPlus, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = rsPlus;
+					break;
+				case MULT:
+					/**
+					 * NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into an element-wise operation when having only row sparsity vectors
+					 */
+					double[] rsLeftMult = estimInternChain(nodeLeft);
+					double[] rsRightMult = estimInternChain(nodeRight);
+					double[] rsMult = estimInternMult(rsLeftMult, rsRightMult);
+					if(rsRightNeighbor != null) {
+						rsOut = estimInternMMFallback(rsMult, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = rsMult;
+					break;
+				default:
+					throw new NotImplementedException("Chain estimation for operator " + node.getOp().toString() +
+					" is not supported yet.");
+			}
+		}
+		node.setSynopsis(rsOut);
+		node.setDataCharacteristics(deriveOutputCharacteristics(node, DoubleStream.of(rsOut).average().orElse(0)));
+		return rsOut;
+	}
+
+	private double[] estimIntern(MatrixBlock m1, MatrixBlock m2, OpCode op) {
+		double[] rsM2 = getRowWiseSparsityVector(m2);
+		return estimIntern(m1, rsM2, op);
+	}
+
+	private double[] estimIntern(MatrixBlock m1, double[] rsM2, OpCode op) {
+		switch(op) {
+			case MM:
+				return estimInternMM(m1, rsM2);
+			case CBIND:
+				return estimInternCBind(getRowWiseSparsityVector(m1), rsM2);
+			case RBIND:
+				return estimInternRBind(getRowWiseSparsityVector(m1), rsM2);
+			case PLUS:
+				return estimInternPlus(getRowWiseSparsityVector(m1), rsM2);
+			case MULT:
+				return estimInternMult(getRowWiseSparsityVector(m1), rsM2);
+			default:
+				throw new NotImplementedException("Sparsity estimation for operation " + op.toString() + " not supported yet.");
+		}
+	}
+
+	private double[] estimIntern(MatrixBlock mb, OpCode op) {
+		switch(op) {
+			case DIAG:
+				return estimInternDiag(mb);
+			default:
+				throw new NotImplementedException("Sparsity estimation for operation " + op.toString() + " not supported yet.");
+		}
+	}
+
+	/**
+	 * Corresponds to Algorithm 1 in the publication
+	 */
+	private double[] estimInternMM(MatrixBlock m1, double[] rsM2) {
+		double[] rsOut = new double[m1.getNumRows()];
+		for(int rIdx = 0; rIdx < m1.getNumRows(); rIdx++) {
+			double currentVal = 1;
+			for(int cIdx : getNonZeroColumnIndices(m1, rIdx)) {
+				currentVal *= 1.0 - rsM2[cIdx];
+			}
+			rsOut[rIdx] = 1 - currentVal;
+		}
+		return rsOut;
+	}
+
+	/**
+	 * NOTE: fallback estimate using the uniform estimator (aka average-case estimator, Naive Bayes estimator) for
+	 * the case when we are limited to the row sparsity vectors of both inputs
+	 * NOTE: Considering the average of the second matrix would probably not be far off while saving computing time
+	 */
+	private double[] estimInternMMFallback(double[] rsM1, double[] rsM2) {
+		double[] rsOut = new double[rsM1.length];
+		for(int i = 0; i < rsM1.length; i++) {
+			double rsM1i = rsM1[i];
+			if(rsM1i == 0) {
+				rsOut[i] = 0;
+			}
+			else {
+				double currentVal = 1;
+				for(int j = 0; j < rsM2.length; j++) {
+					currentVal *= 1.0 - (rsM1i * rsM2[j]);
+				}
+				rsOut[i] = 1.0 - currentVal;
+			}
+		}
+		return rsOut;
+	}
+
+	private double[] estimInternCBind(double[] rsM1, double[] rsM2) {
+		// FIXME: this estimate assumes that the number of columns is equivalent for both inputs
+		double[] rsOut = new double[rsM1.length];
+		for(int idx = 0; idx < rsM1.length; idx++) {
+			rsOut[idx] = (rsM1[idx] + rsM2[idx]) / 2.0;
+		}
+		return rsOut;
+	}
+
+	private double[] estimInternRBind(double[] rsM1, double[] rsM2) {
+		return ArrayUtils.addAll(rsM1, rsM2);
+	}
+
+	private double[] estimInternPlus(double[] rsM1, double[] rsM2) {
+		// row-wise average case estimates
+		// rsM1 + rsM2 - (rsM1 * rsM2)
+		double[] rsOut = new double[rsM1.length];
+		for(int idx = 0; idx < rsM1.length; idx++) {
+			rsOut[idx] = rsM1[idx] + rsM2[idx] - (rsM1[idx] * rsM2[idx]);
+		}
+		return rsOut;
+	}
+
+	private double[] estimInternMult(double[] rsM1, double[] rsM2) {
+		// row-wise average case estimates
+		// rsM1 * rsM2
+		double[] rsOut = new double[rsM1.length];
+		for(int idx = 0; idx < rsM1.length; idx++) {
+			rsOut[idx] = rsM1[idx] * rsM2[idx];
+		}
+		return rsOut;
+	}
+
+	private double[] estimInternDiag(MatrixBlock mb) {
+		double[] rsOut = new double[mb.getNumRows()];
+		for(int rIdx = 0; rIdx < mb.getNumRows(); rIdx++) {
+			rsOut[rIdx] = (mb.get(rIdx, rIdx) == 0) ? 0 : 1;
+		}
+		return rsOut;
+	}
+
+	private double[] getRowWiseSparsityVector(MatrixBlock mb) {
+		int numRows = mb.getNumRows();
+		double[] rsOut = new double[numRows];
+		if(mb.isInSparseFormat()) {
+			for(int rIdx = 0; rIdx < numRows; rIdx++) {
+				SparseRow sparseRow = mb.getSparseBlock().get(rIdx);
+				rsOut[rIdx] = (sparseRow == null) ? 0 : (double) sparseRow.size() / mb.getNumColumns();
+			}
+		}
+		else {
+			for(int rIdx = 0; rIdx < numRows; rIdx++) {
+				rsOut[rIdx] = (double) mb.getDenseBlock().countNonZeros(rIdx) / mb.getNumColumns();
+			}
+		}
+		return rsOut;
+	}
+
+	private int[] getNonZeroColumnIndices(MatrixBlock mb, final int rIdx) {
+		int[] nonZeroCols;
+		if(mb.isInSparseFormat()) {
+			SparseRow sparseRow = mb.getSparseBlock().get(rIdx);
+			nonZeroCols = (sparseRow == null) ? new int[0] : sparseRow.indexes();
+		}
+		else {
+			nonZeroCols = IntStream.range(0, mb.getNumColumns())
+				.filter(cIdx -> mb.get(rIdx, cIdx) != 0).toArray();
+		}
+		return nonZeroCols;
+	}
+
+	public static DataCharacteristics deriveOutputCharacteristics(MMNode node, double spOut) {
+		if(node.isLeaf() ||
+			(node.getDataCharacteristics() != null && node.getDataCharacteristics().getNonZeros() != -1)) {
+			return node.getDataCharacteristics();
+		}
+
+		MMNode nodeLeft = node.getLeft();
+		MMNode nodeRight = node.getRight();
+		int leftNRow = nodeLeft.getRows();
+		int leftNCol = nodeLeft.getCols();
+		int rightNRow = nodeRight.getRows();
+		int rightNCol = nodeRight.getCols();
+		switch(node.getOp()) {
+			case MM:
+				return new MatrixCharacteristics(leftNRow, rightNCol,
+					OptimizerUtils.getNnz(leftNRow, rightNCol, spOut));
+			case MULT:
+			case PLUS:
+			case NEQZERO:
+			case EQZERO:
+				return new MatrixCharacteristics(leftNRow, leftNCol,
+					OptimizerUtils.getNnz(leftNRow, leftNCol, spOut));
+			case RBIND:
+				return new MatrixCharacteristics(leftNRow+rightNRow, leftNCol,
+					OptimizerUtils.getNnz(leftNRow+rightNRow, leftNCol, spOut));
+			case CBIND:
+				return new MatrixCharacteristics(leftNRow, leftNCol+rightNCol,
+					OptimizerUtils.getNnz(leftNRow, leftNCol+rightNCol, spOut));
+			case DIAG:
+				int ncol = (leftNCol == 1) ? leftNRow : 1;
+				return new MatrixCharacteristics(leftNRow, ncol,
+					OptimizerUtils.getNnz(leftNRow, ncol, spOut));
+			case TRANS:
+				return new MatrixCharacteristics(leftNCol, leftNRow,
+					OptimizerUtils.getNnz(leftNCol, leftNRow, spOut));
+			case RESHAPE:
+				throw new NotImplementedException("Characteristics derivation for " + node.getOp() +" has not been " +
+					"implemented yet, but could be implemented similar to EstimatorMatrixHistogram.java");
+			default:
+				throw new NotImplementedException();
+		}
+	}
+};