019x_008_BlockMatrix(Scala)

Import Notebook

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

BlockMatrix in Scala

A BlockMatrix is a distributed matrix backed by an RDD of MatrixBlocks, where a MatrixBlock is a tuple of ((Int, Int), Matrix), where the (Int, Int) is the index of the block, and Matrix is the sub-matrix at the given index with size rowsPerBlock x colsPerBlock. BlockMatrix supports methods such as add and multiply with another BlockMatrix. BlockMatrix also has a helper function validate which can be used to check whether the BlockMatrix is set up properly.

A BlockMatrix can be most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix. toBlockMatrix creates blocks of size 1024 x 1024 by default. Users may change the block size by supplying the values through toBlockMatrix(rowsPerBlock, colsPerBlock).

Refer to the BlockMatrix Scala docs for details on the API.

//import org.apache.spark.mllib.linalg.{Matrix, Matrices}
import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry} 
val entries: RDD[MatrixEntry] = sc.parallelize(Array(MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7))) // an RDD of matrix entries
entries: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.distributed.MatrixEntry] = ParallelCollectionRDD[3746] at parallelize at command-2972105651607062:1 
// Create a CoordinateMatrix from an RDD[MatrixEntry].
val coordMat: CoordinateMatrix = new CoordinateMatrix(entries)
coordMat: org.apache.spark.mllib.linalg.distributed.CoordinateMatrix = org.apache.spark.mllib.linalg.distributed.CoordinateMatrix@161a1942 
// Transform the CoordinateMatrix to a BlockMatrix
val matA: BlockMatrix = coordMat.toBlockMatrix().cache()
matA: org.apache.spark.mllib.linalg.distributed.BlockMatrix = org.apache.spark.mllib.linalg.distributed.BlockMatrix@1ddf85ce 
// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
// Nothing happens if it is valid.
matA.validate()
// Calculate A^T A.
val ata = matA.transpose.multiply(matA)
ata: org.apache.spark.mllib.linalg.distributed.BlockMatrix = org.apache.spark.mllib.linalg.distributed.BlockMatrix@18c0eeca 
ata.blocks.collect()
res1: Array[((Int, Int), org.apache.spark.mllib.linalg.Matrix)] = Array(((0,0),5.85 0.0 0.0 13.690000000000001 )) 
ata.toLocalMatrix()
res2: org.apache.spark.mllib.linalg.Matrix = 5.85 0.0 0.0 13.690000000000001

BlockMatrix in Scala

A BlockMatrix can be created from an RDD of sub-matrix blocks, where a sub-matrix block is a ((blockRowIndex, blockColIndex), sub-matrix) tuple.

Refer to the BlockMatrix Python docs for more details on the API.

%py
from pyspark.mllib.linalg import Matrices
from pyspark.mllib.linalg.distributed import BlockMatrix
 
# Create an RDD of sub-matrix blocks.
blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
                         ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
 
# Create a BlockMatrix from an RDD of sub-matrix blocks.
mat = BlockMatrix(blocks, 3, 2)
 
# Get its size.
m = mat.numRows() # 6
n = mat.numCols() # 2
print (m,n)
 
# Get the blocks as an RDD of sub-matrix blocks.
blocksRDD = mat.blocks
 
# Convert to a LocalMatrix.
localMat = mat.toLocalMatrix()
 
# Convert to an IndexedRowMatrix.
indexedRowMat = mat.toIndexedRowMatrix()
 
# Convert to a CoordinateMatrix.
coordinateMat = mat.toCoordinateMatrix()
6 2