Github user mengxr commented on a diff in the pull request: https://github.com/apache/spark/pull/3200#discussion_r23582386 --- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/BlockMatrix.scala --- @@ -0,0 +1,242 @@ +/* + * 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.spark.mllib.linalg.distributed + +import breeze.linalg.{DenseMatrix => BDM} + +import org.apache.spark.{Logging, Partitioner} +import org.apache.spark.mllib.linalg._ +import org.apache.spark.mllib.rdd.RDDFunctions._ +import org.apache.spark.rdd.RDD +import org.apache.spark.storage.StorageLevel + +/** + * A grid partitioner, which stores every block in a separate partition. + * + * @param numRowBlocks Number of blocks that form the rows of the matrix. + * @param numColBlocks Number of blocks that form the columns of the matrix. + */ +private[mllib] class GridPartitioner( + val numRowBlocks: Int, + val numColBlocks: Int, + val numParts: Int) extends Partitioner { + // Having the number of partitions greater than the number of sub matrices does not help + override val numPartitions = math.min(numParts, numRowBlocks * numColBlocks) + + /** + * Returns the index of the partition the SubMatrix belongs to. Tries to achieve block wise + * partitioning. + * + * @param key The key for the SubMatrix. Can be its position in the grid (its column major index) + * or a tuple of three integers that are the final row index after the multiplication, + * the index of the block to multiply with, and the final column index after the + * multiplication. + * @return The index of the partition, which the SubMatrix belongs to. + */ + override def getPartition(key: Any): Int = { + key match { + case (blockRowIndex: Int, blockColIndex: Int) => + getBlockId(blockRowIndex, blockColIndex) + case (blockRowIndex: Int, innerIndex: Int, blockColIndex: Int) => + getBlockId(blockRowIndex, blockColIndex) + case _ => + throw new IllegalArgumentException(s"Unrecognized key. key: $key") + } + } + + /** Partitions sub-matrices as blocks with neighboring sub-matrices. */ + private def getBlockId(blockRowIndex: Int, blockColIndex: Int): Int = { + val totalBlocks = numRowBlocks * numColBlocks + // Gives the number of blocks that need to be in each partition + val partitionRatio = math.ceil(totalBlocks * 1.0 / numPartitions).toInt + // Number of neighboring blocks to take in each row + val subBlocksPerRow = math.ceil(numRowBlocks * 1.0 / partitionRatio).toInt + // Number of neighboring blocks to take in each column + val subBlocksPerCol = math.ceil(numColBlocks * 1.0 / partitionRatio).toInt + // Coordinates of the block + val i = blockRowIndex / subBlocksPerRow + val j = blockColIndex / subBlocksPerCol + val blocksPerRow = math.ceil(numRowBlocks * 1.0 / subBlocksPerRow).toInt + j * blocksPerRow + i + } + + /** Checks whether the partitioners have the same characteristics */ + override def equals(obj: Any): Boolean = { + obj match { + case r: GridPartitioner => + (this.numRowBlocks == r.numRowBlocks) && (this.numColBlocks == r.numColBlocks) && + (this.numPartitions == r.numPartitions) + case _ => + false + } + } +} + +/** + * Represents a distributed matrix in blocks of local matrices. + * + * @param rdd The RDD of SubMatrices (local matrices) that form this matrix + * @param nRows Number of rows of this matrix + * @param nCols Number of columns of this matrix + * @param numRowBlocks Number of blocks that form the rows of this matrix + * @param numColBlocks Number of blocks that form the columns of this matrix + * @param rowsPerBlock Number of rows that make up each block. The blocks forming the final + * rows are not required to have the given number of rows + * @param colsPerBlock Number of columns that make up each block. The blocks forming the final + * columns are not required to have the given number of columns + */ +class BlockMatrix( + val rdd: RDD[((Int, Int), Matrix)], + private var nRows: Long, + private var nCols: Long, + val numRowBlocks: Int, + val numColBlocks: Int, + val rowsPerBlock: Int, + val colsPerBlock: Int) extends DistributedMatrix with Logging { + + private type SubMatrix = ((Int, Int), Matrix) // ((blockRowIndex, blockColIndex), matrix) + + /** + * Alternate constructor for BlockMatrix without the input of the number of rows and columns. + * + * @param rdd The RDD of SubMatrices (local matrices) that form this matrix + * @param numRowBlocks Number of blocks that form the rows of this matrix + * @param numColBlocks Number of blocks that form the columns of this matrix + * @param rowsPerBlock Number of rows that make up each block. The blocks forming the final + * rows are not required to have the given number of rows + * @param colsPerBlock Number of columns that make up each block. The blocks forming the final + * columns are not required to have the given number of columns + */ + def this( + rdd: RDD[((Int, Int), Matrix)], + numRowBlocks: Int, + numColBlocks: Int, + rowsPerBlock: Int, + colsPerBlock: Int) = { + this(rdd, 0L, 0L, numRowBlocks, numColBlocks, rowsPerBlock, colsPerBlock) + } + + private[mllib] var partitioner: GridPartitioner = + new GridPartitioner(numRowBlocks, numColBlocks, rdd.partitions.length) + + private lazy val dims: (Long, Long) = getDim + + override def numRows(): Long = { + if (nRows <= 0L) nRows = dims._1 + nRows + } + + override def numCols(): Long = { + if (nCols <= 0L) nCols = dims._2 + nCols + } + + /** Returns the dimensions of the matrix. */ + private def getDim: (Long, Long) = { + case class MatrixMetaData(var rowIndex: Int, var colIndex: Int, + var numRows: Int, var numCols: Int) + // picks the sizes of the matrix with the maximum indices + def pickSizeByGreaterIndex(example: MatrixMetaData, base: MatrixMetaData): MatrixMetaData = { + if (example.rowIndex > base.rowIndex) { + base.rowIndex = example.rowIndex + base.numRows = example.numRows + } + if (example.colIndex > base.colIndex) { + base.colIndex = example.colIndex + base.numCols = example.numCols + } + base + } + + // Aggregate will return an error if the rdd is empty + val lastRowCol = rdd.treeAggregate(new MatrixMetaData(0, 0, 0, 0))( + seqOp = (c, v) => (c, v) match { case (base, ((blockXInd, blockYInd), mat)) => + pickSizeByGreaterIndex( + new MatrixMetaData(blockXInd, blockYInd, mat.numRows, mat.numCols), base) + }, + combOp = (c1, c2) => (c1, c2) match { + case (res1, res2) => + pickSizeByGreaterIndex(res1, res2) + }) + // We add the size of the edge matrices, because they can be less than the specified + // rowsPerBlock or colsPerBlock. + (lastRowCol.rowIndex.toLong * rowsPerBlock + lastRowCol.numRows, + lastRowCol.colIndex.toLong * colsPerBlock + lastRowCol.numCols) + } + + /** Returns the Frobenius Norm of the matrix */ + def normFro(): Double = { + math.sqrt(rdd.map { mat => mat._2 match { + case sparse: SparseMatrix => + sparse.values.map(x => math.pow(x, 2)).sum + case dense: DenseMatrix => + dense.values.map(x => math.pow(x, 2)).sum + } + }.reduce(_ + _)) + } + + /** Cache the underlying RDD. */ + def cache(): BlockMatrix = { + rdd.cache() + this + } + + /** Set the storage level for the underlying RDD. */ + def persist(storageLevel: StorageLevel): BlockMatrix = { + rdd.persist(storageLevel) + this + } + + /** Collect the distributed matrix on the driver as a `DenseMatrix`. */ + def toLocalMatrix(): Matrix = { + require(numRows() < Int.MaxValue, "The number of rows of this matrix should be less than " + + s"Int.MaxValue. Currently numRows: ${numRows()}") + require(numCols() < Int.MaxValue, "The number of columns of this matrix should be less than " + + s"Int.MaxValue. Currently numCols: ${numCols()}") + val nRows = numRows().toInt + val nCols = numCols().toInt + val mem = nRows * nCols * 8 / 1000000 --- End diff -- This may overflow. See https://github.com/apache/spark/pull/4069.
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