SystemML Engine Developer Guide

Building SystemML

SystemML is built using Apache Maven. SystemML will build on Linux, MacOS, or Windows, and requires Maven 3 and Java 7 (or higher). To build SystemML, run:

mvn clean package

To build the SystemML distributions, run:

mvn clean package -P distribution

Testing SystemML

SystemML features a comprehensive set of integration tests. To perform these tests, run:

mvn verify

Note: these tests require R to be installed and available as part of the PATH variable on the machine on which you are running these tests.

If required, please install the following packages in R:

install.packages(c("batch", "bitops", "boot", "caTools", "data.table", "doMC", "doSNOW", "ggplot2", "glmnet", "lda", "Matrix", "matrixStats", "moments", "plotrix", "psych", "reshape", "topicmodels", "wordcloud"), dependencies=TRUE)

Development Environment

SystemML itself is written in Java and is managed using Maven. As a result, SystemML can readily be imported into a standard development environment such as Eclipse and IntelliJ IDEA. The DMLScript class serves as the main entrypoint to SystemML. Executing DMLScript with no arguments displays usage information. A script file can be specified using the -f argument.

In Eclipse, a Debug Configuration can be created with DMLScript as the Main class and any arguments specified as Program arguments. A PyDML script requires the addition of a -python switch.

Suppose that we have a hello.dml script containing the following:

print('hello ' + $1)

This SystemML script can be debugged in Eclipse using a Debug Configuration such as the following:

Eclipse Debug Configuration - Main

Eclipse Debug Configuration - Arguments

Matrix Multiplication Operators

In the following, we give an overview of backend-specific physical matrix multiplication operators in SystemML as well as their internally used matrix multiplication block operations.

Basic Matrix Multiplication Operators

An AggBinaryOp hop can be compiled into the following physical operators.

1. Physical Operators in CP (single node, control program)

Name Description Operation
MM basic matrix multiplication mm
MMChain matrix multiplication chain mmchain
TSMM transpose-self matrix multiplication tsmm
PMM permutation matrix multiplication pmm

2. Physical Operator in MR (distributed, mapreduce)

Name Description Operation
MapMM map-side matrix multiplication, w/ or w/o agg mm
MapMMChain map-side matrix chain multiplication mmchain
TSMM map-side transpose-self matrix multiplication tsmm
PMM map-side permutation matrix multiplication pmm
CPMM cross-product matrix multiplication, 2 jobs mm
RMM replication-based matrix multiplication, 1 job mm

3. Physical Operators in SPARK (distributed, spark)

Name Description Operation
MapMM see MR, flatmap/mappartitions/maptopair + reduce/reducebykey/no_aggregation mm
MapMMChain see MR, mapvalues/maptopair + reduce mmchain
TSMM see MR, mapvalues + reduce tsmm
PMM see MR, flatmaptopair + reducebykey pmm
CPMM see MR, 2 x maptopair + join + maptopair + reduce/reducebykey mm
RMM see MR, 2 x flatmap + join + maptopair + reducebykey mm
ZIPMM partitioning-preserving 1-1 zipping mm, join + mapvalues + reduce mm

Complex Matrix Multiplication Operators

A QuaternaryOp hop can be compiled into the following physical operators. Note that wsloss, wsigmoid, wdivmm have different semantics though. The main goal of these operators is to prevent the creation of dense “outer” products via selective computation over a sparse driver (sparse matrix and sparse-safe operation).

1. Physical Operators in CP (single node, control program)

Name Description Operation
WSLoss weighted squared loss wsloss
WSigmoid weighted sigmoid wsigmoid
WDivMM weighted divide matrix multiplication wdivmm
WCeMM weighted cross entropy matrix multiplication wcemm
WuMM weighted unary op matrix multiplication wumm

2. Physical Operator in MR (distributed, mapreduce)

Name Description Operation
MapWSLoss map-side weighted squared loss wsloss
RedWSLoss reduce-side weighted squared loss wsloss
MapWSigmoid map-side weighted sigmoid wsigmoid
RedWSigmoid reduce-side weighted sigmoid wsigmoid
MapWDivMM map-side weighted divide matrix mult wdivmm
RedWDivMM reduce-side weighted divide matrix mult wdivmm
MapWCeMM map-side weighted cross entr. matrix mult wcemm
RedWCeMM reduce-side w. cross entr. matrix mult wcemm
MapWuMM map-side weighted unary op matrix mult wumm
RedWuMM reduce-side weighted unary op matrix mult wumm

3. Physical Operators in SPARK (distributed, spark)

Name Description Operation
MapWSLoss see MR, mappartitions + reduce wsloss
RedWSLoss see MR, 1/2x flatmaptopair + 1-3x join + maptopair + reduce wsloss
MapWSigmoid see MR, mappartitions wsigmoid
RedWSigmoid see MR, 1/2x flatmaptopair + 1/2x join + maptopair wsigmoid
MapWDivMM see MR, mappartitions + reducebykey wdivmm
RedWDivMM see MR, 1/2x flatmaptopair + 1/2x join + maptopair + reducebykey wdivmm
MapWCeMM see MR, mappartitions + reduce wcemm
RedWCeMM see MR, 1/2x flatmaptopair + 1/2x join + maptopair + reduce wcemm
MapWuMM see MR, mappartitions wumm
RedWuMM see MR, 1/2x flatmaptopair + 1/2x join + maptopair wumm

Core Matrix Multiplication Primitives

# Operation Equations Description
1 mm (a) A%*%B - sequential / multi-threaded (same block ops, par over rows in A)
- dense-dense, dense-sparse, sparse-dense, sparse-sparse, ultra-sparse
- ~20 special cases for matrix-vector, vector-vector, etc
2 mmchain (a) t(X)%*%(X%*%v)
(b) t(X)%*%(w*(X%*%v)) 		- sequential / multi-threaded (same block ops, par over rows in X)
- dense / sparse x 2 patterns
3 tsmm (a) t(X)%*%X
(b) X%*%t(X) 		- sequential / multi-threaded (same block ops, par over rows in R, 2x tasks)
- dense / sparse x 2 patterns; special cases for dot products
4 pmm (a) removeEmpty(diag(v),"rows")%*%X - sequential / multi-threaded (same block ops, par over rows in X)
- sparse-sparse, dense-dense, sparse-dense
5 wsloss (a) sum(W*(X-U%*%t(V))^2)
(b) sum((X-W*(U%*%t(V)))^2)
(c) sum((X-(U%*%t(V)))^2))
(d) sum(W*(U%*%t(V)-X)^2)
(e) sum((W*(U%*%t(V))-X)^2)
(f) sum(((U%*%t(V))-X)^2) 		- sequential / multi-threaded (same block ops, par over rows in W/X)
- all dense, sparse-dense factors, sparse/dense-* x 3 patterns
- special patterns for (a) and (d) if W is X!=0
6 wsigmoid (a) W*sigmoid(Y%*%t(X))
(b) W*sigmoid(-(Y%*%t(X)))
(c) W*log(sigmoid(Y%*%t(X)))
(d) W*log(sigmoid(-(Y%*%t(X)))) 		- sequential / multi-threaded (same block ops, par over rows in W)
- all dense, sparse-dense factors, sparse/dense-* x 4 patterns
7 wdivmm (a) t(t(U)%*%(W/(U%*%t(V))))
(b) (W/(U%*%t(V)))%*%V
(c) t(t(U)%*%(W*(U%*%t(V))))
(d) (W*(U%*%t(V)))%*%V
(e) W*(U%*%t(V))
(f) t(t(U)%*%((X!=0)*(U%*%t(V)-X)))
(g) (X!=0)*(U%*%t(V)-X)%*%V
(h) t(t(U)%*%(W*(U%*%t(V)-X)))
(i) (W*(U%*%t(V)-X))%*%V
(j) t(t(U)%*%(W/(U%*%t(V)+x)))
(k) (W/(U%*%t(V)+x))%*%V 		- sequential / multi-threaded (same block ops, par over rows in X)
- all dense, sparse-dense factors, sparse/dense-* x 9 patterns
8 wcemm (a) sum(X*log(U%*%t(V)))
(b) sum(X*log(U%*%t(V)+epsilon)) 		- sequential / multi-threaded (same block ops, par over rows in X)
- all dense, sparse-dense factors, sparse/dense-*, 1 pattern
9 wumm (a) X*uop(U%*%t(V))
(b) X/uop(U%*%t(V)) 		- any unary operator, e.g., X*exp(U%*%t(V)) or X*(U%*%t(V))^2
- sequential / multi-threaded (same block ops, par over rows in X)
- all dense, sparse-dense factors, sparse/dense-*, 2 pattern