Declarative Machine Learning (DML) Language Reference

Table of Contents

Introduction

SystemML compiles scripts written in Declarative Machine Learning (or DML for short) into mixed driver and distributed jobs. DML’s syntax closely follows R, thereby minimizing the learning curve to use SystemML. Before getting into detail, let’s start with a simple Hello World program in DML. Assuming that Spark is installed on your machine or cluster, place SystemML.jar into your directory. Now, create a text file hello.dml containing following code:

print("Hello World");

To run this program on your machine, use following command:

spark-submit SystemML.jar -f hello.dml

The option -f in the above command refers to the path to the DML script. A detailed list of the available options can be found running spark-submit SystemML.jar -help.

Variables

Identifier Names

Identifiers are case-sensitive (e.g., var1, Var1, and VAR1 are different identifier names), must start with either an upper-case or lower-case letter, and may contain any alphanumeric character including underscore after the first letter. The reserved keywords described later cannot be used as identifier names. Though it is allowed, but not recommended to use built-in functions as an identifier. The only exceptions to this rule are five built-in functions: ‘as.scalar’, ‘as.matrix’, ‘as.double’, ‘as.integer’ and ‘as.logical’.

Examples

A       # valid variable name
_A      # invalid variable name -- starts with underscore
1_A     # invalid variable name -- starts with number
A_1     # valid variable name
min = 10 # valid but deprecated

Before, proceeding ahead let’s run the Hello World program using variable:

helloStr = "Hello World"
print(helloStr)

As seen in above example, there is no formal declaration of a variable. A variable is created when first assigned a value, and its type is inferred.

Data Types

Three data types (frame, matrix and scalar) and four value types (double, integer, string, and boolean) are supported. Matrices are 2-dimensional, and support the double value type (i.e., the cells in a matrix are of type double). The frame data type denotes the tabular data, potentially containing columns of value type numeric, string, and boolean. Frame functions are described in Frames and Data Pre-Processing Built-In Functions. SystemML supports type polymorphism for both data type (primarily, matrix and scalar types) and value type during evaluation. For example:

# Spoiler alert: matrix() is a built-in function to
# create matrix, which will be discussed later
A = matrix(0, rows=10, cols=10)
B = 10
C = B + sum(A)
print( "B:" + B + ", C:" + C + ", A[1,1]:" + as.scalar(A[1,1]))

In the above script, we create three variables: A, B and C of type matrix, scalar integer and scalar double respectively. Since A is a matrix, it has to be converted to scalar using a built-in function as.scalar. In the above script the operator + used inside print() function, performs string concatenation. Hence, the output of above script is as follows:

B:10, C:10.0, A[1,1]:0.0

If instead of as.scalar(A[1,1]) we would have used A[1,1], then we will get an compilation error print statement can only print scalars.

Comments

Two forms of commenting are supported: line and block comments. A line comment is indicated using a hash (#), and everything to the right of the hash is commented out. A block comment is indicated using “/*” to start the comment block and “*/” to end it.

Examples

# this is an example of a line comment
/* this is an example of a
multi-line block comment
*/

Expressions

Now that we have familiarized ourselves with variables and data type, let’s understand how to use them in expressions.

Operators

SystemML follows same associativity and precedence order as R as described in below table. The dimensions of the input matrices need to match the operator semantics, otherwise an exception will be raised at compile time. When one of the operands is a matrix and the other operand is a scalar value, the operation is performed cell-wise on the matrix using the scalar operand.

Table 1: Operators

Operator Input Output Details
^ Matrix or Scalar Matrix or Scalar1, 2 Exponentiation (right associativity) – Highest precedence
- + Matrix or Scalar Matrix or Scalar1 Unary plus, minus
%*% Matrix Matrix Matrix multiplication
%/% %% Matrix or Scalar Matrix or Scalar1, 2 Integer division and Modulus operator
/ * Matrix or Scalar Matrix or Scalar1, 2 Multiplication and Division
+ - Matrix or Scalar Matrix or Scalar1, 2 Addition (or string concatenation) and Subtraction
< > == != <= >= Matrix or Scalar (any value type) Matrix or Scalar1, 2 (boolean type) Relational operators
& | ! Scalar Scalar Boolean operators (Note: operators && and || are not supported)
= - - Assignment (Lowest precendence). Note: associativity of assignment “a = b = 3” is not supported

1 If one of the operands is a matrix, output is matrix; otherwise it is scalar.

2 Support for Matrix-vector operations

Example

A = matrix(1, rows=2,cols=2)
B = matrix(3, rows=2,cols=2)
C = 10
D = A %*% B + C * 2.1
print( "D[1,1]:" + as.scalar(D[1,1]))

Since matrix multiplication has higher precedence than scalar multiplication, which in turns has higher precedence than addition, the first cell of matrix D is evaluated as ((1*3)+(1*3))+(10*2.1) = 27.0.

Matrix-Vector Operations

Arithmetic and relational operations described in above table support matrix-vector operations. This allows efficient cell-wise operations with either row or a column vector.

Syntax

Input_Matrix operation Input_Vector

Example

M + V or M > V, where M is a matrix and V is either row matrix or a column matrix.

Matrix-Vector operation avoids need for creating replicated matrix for certain subset of operations. For example: to compute class conditional probabilities in Naïve-Bayes, without support for matrix-vector operations, one might write below given inefficient script that creates unnecessary and possibly huge replicatedClassSums.

ones = matrix(1, rows=1, cols=numFeatures)
repClassSums = classSums %*% ones
class_conditionals = (classFeatureCounts + laplace_correction) / repClassSums

With support of matrix-vector operations, the above script becomes much more efficient as well as concise:

class_conditionals = (classFeatureCounts + laplace_correction) / classSums

Matrix Indexing

Each matrix has a specified number of rows and columns. A 1x1 matrix is not equivalent to a scalar double. The first index for both row and columns in a matrix is 1. For example, a matrix with 10 rows and 10 columns would have rows numbered 1 to 10, and columns numbered 1 to 10.

The elements of the matrix can be accessed by matrix indexing, with both row and column indices required. The indices must either be an expression evaluating to a positive numeric (integer or double) scalar value, or blank. To select the entire row or column of a matrix, leave the appropriate index blank. If a double value is used for indexing, the index value is implicitly cast to an integer with floor (value+eps) in order to account for double inaccuracy (see IEEE754, double precision, eps=pow(2,-53)).

Examples

X[1,4] # access cell in row 1, column 4 of matrix X
X[i,j] # access cell in row i, column j of X.
X[1,]  # access the 1st row of X 
X[,2]  # access the 2nd column of X
X[,]   # access all rows and columns of X

Range indexing is supported to access a contiguous block of rows and columns in the matrix. The grammar for range-based indexing is below. The constraint is that lower-row < upper-row, and lower-column < upper-column.

[Matrix name][lower-row : upper-row],[lower-column : upper-column]

Examples

X[1:4, 1:4] # access the 4 x 4 submatrix comprising columns 1 – 4 of rows 1 – 4 of X
X[1:4, ]    # select the first 4 rows of X
X[1:, ]     # incorrect format

Statements

A script is a sequence of statements with the default computation semantics being sequential evaluation of the individual statements. The use of a semi-colon at the end of a statement is optional. The types of statements supported are

Assignment Statement

An assignment statement consists of an expression, the result of which is assigned to a variable. The variable gets the appropriate data type (matrix or scalar) and value type (double, int, string, boolean) depending on the type of the variable output by the expression.

Examples

# max_iteration is of type integer
max_iteration = 3;
# V has data type matrix and value type double.
V = W %*% H;

Control Statements

While Statement

The syntax for a while statement is as follows:

while (predicate) {
    statement1
    statement2
    ...
}

The statements in the while statement body are evaluated repeatedly until the predicate evaluates to TRUE. The while statement body must be surrounded by braces, even if the body only has a single statement. The predicate in the while statement consist of operations on scalar variables and literals. The body of a while statement may contain any sequence of statements.

Example
while ((i < 20) & (!converge)) {
    H = H * (t(W) %*% V) / (t(W) %*% W %*% H);
    W = W * (V %*% t(H)) / (W %*% H %*% t(H));
    i = i + 1;
}

If Statement

The syntax for an if statement is as follows:

if (predicate1) {
    statement1
    statement2
    ...
} [ else if (predicate2) {
    statement1
    statement2
    ...
} ] [ else {
    statement1
    statement2
    ...
} ]

The If statement has three bodies: the if body (evaluated if predicate1 evaluates to TRUE), the optional else if body (evaluated if predicate2 evaluates to TRUE) and the optional else body (evaluated otherwise). There can be multiple else if bodies with different predicates but at most one else body. The bodies may contain any sequence of statements. If only a single statement is enclosed in a body, the braces surrounding the statement can be omitted.

Examples
# example of if statement
if (i < 20) {
    converge = FALSE;
} else {
    converge = TRUE;
}
# example of nested control structures
while (!converge) {
    H = H * (t(W) %*% V) / (t(W) %*% W %*% H);
    W = W * (V %*% t(H)) / (W %*% H %*% t(H));
    i = i + 1;
    zerror = sum(z - W %*% H);
    if (zerror < maxError) {
        converge = TRUE;
    } else {
        converge = FALSE;
    }
}

For Statement

The syntax for a for statement is as follows.

for (var in <for_predicate> ) {
    <statement>*
}
<for_predicate> ::= [lower]:[upper] | seq ([lower], [upper], [increment])

var is an integer scalar variable. lower, upper, and increment are integer expressions.

Similarly, seq([lower],[upper],[increment]) defines a sequence of numbers: {lower, lower + increment, lower + 2(increment), … }. For each element in the sequence, var is assigned the value, and statements in the for loop body are executed.

The for loop body may contain any sequence of statements. The statements in the for statement body must be surrounded by braces, even if the body only has a single statement.

Example
# example for statement
A = 5;
for (i in 1:20) {
    A = A + 1;
}

ParFor Statement

The syntax and semantics of a parfor (parallel for) statement are equivalent to a for statement except for the different keyword and a list of optional parameters.

parfor (var in <for_predicate> <parfor_paramslist> ) {
	<statement>*
}

<parfor_paramslist> ::= <,<parfor_parameter>>*
<parfor_parameter> ::
   = check = <dependency_analysis>
|| = par = <degree_of_parallelism>
|| = mode = <execution_mode>
|| = taskpartitioner = <task_partitioning_algorithm>
|| = tasksize = <task_size>
|| = datapartitioner = <data_partitioning_mode>
|| = resultmerge = <result_merge_mode>
|| = opt = <optimization_mode>
|| = log = <log_level>
|| = profile = <monitor>

<dependency_analysis>         0 1
<degree_of_parallelism>       arbitrary integer number
<execution_mode>              LOCAL REMOTE_MR REMOTE_MR_DP REMOTE_SPARK REMOTE_SPARK_DP
<task_partitioning_algorithm> FIXED NAIVE STATIC FACTORING FACTORING_CMIN FACTORING_CMAX
<task_size>                   arbitrary integer number
<data_partitioning_mode>      NONE LOCAL REMOTE_MR REMOTE_SPARK
<result_merge_mode>           LOCAL_MEM LOCAL_FILE LOCAL_AUTOMATIC REMOTE_MR REMOTE_SPARK
<optimization_mode>           NONE RULEBASED CONSTRAINED HEURISTIC GREEDY FULL_DP
<log_level>                   ALL TRACE DEBUG INFO WARN ERROR FATAL OFF
<monitor>                     0 1

If any of these parameters is not specified, the following respective defaults are used:

Table 2: Parfor default parameter values

Parameter Name Default Value
check 1
par [number of virtual processors on master node]
mode LOCAL
taskpartitioner FIXED
tasksize 1
datapartitioner NONE
resultmerge LOCAL_AUTOMATIC
opt RULEBASED
log INFO
profile 0

Of particular note is the check parameter. SystemML’s parfor statement by default (check = 1) performs dependency analysis in an attempt to guarantee result correctness for parallel execution. For example, the following parfor statement is incorrect because the iterations do not act independently, so they are not parallelizable. The iterations incorrectly try to increment the same sum variable.

sum = 0
parfor (i in 1:3) {
    sum = sum + i; # not parallelizable - generates error
}
print(sum)

SystemML’s parfor dependency analysis can occasionally result in false positives, as in the following example. This example creates a 2x30 matrix. It then utilizes a parfor loop to write 10 2x3 matrices into the 2x30 matrix. This parfor statement is parallelizable and correct, but the dependency analysis generates a false positive dependency error for the variable ms.

ms = matrix(0, rows=2, cols=3*10)
parfor (v in 1:10) { # parallelizable - false positive
    mv = matrix(v, rows=2, cols=3)
    ms[,(v-1)*3+1:v*3] = mv
}

If a false positive arises but you are certain that the parfor is parallelizable, the parfor dependency check can be disabled via the check = 0 option.

ms = matrix(0, rows=2, cols=3*10)
parfor (v in 1:10, check=0) { # parallelizable
    mv = matrix(v, rows=2, cols=3)
    ms[,(v-1)*3+1:v*3] = mv
}

While developing DML scripts or debugging, it can be useful to turn off parfor parallelization. This can be accomplished in the following three ways:

  1. Replace parfor() with for(). Since parfor is derived from for, you can always use for wherever you can use parfor.
  2. parfor(opt = NONE, par = 1, ...). This disables optimization, uses defaults, and overwrites the specified parameters.
  3. parfor(opt = CONSTRAINED, par = 1, ...). This optimizes using the specified parameters.

User-Defined Function (UDF)

The UDF function declaration statement provides the function signature, which defines the formal parameters used to call the function and return values for the function. The function definition specifies the function implementation, and can either be a sequence of statements or external packages / libraries. If the UDF is implemented in a SystemML script, then UDF declaration and definition occur together.

The syntax for the UDF function declaration is given as follows. The function definition is stored as a list of statements in the function body. The explanation of the parameters is given below. Any statement can be placed inside a UDF definition except UDF function declaration statements. The variables specified in the return clause will be returned, and no explicit return statement within the function body is required.

functionName = function([ <DataType>? <ValueType> <var>, ]* )
    return ([ <DataType>? <ValueType> <var>,]*) {
    # function body definition in DML
    statement1
    statement2
    ...
}

The syntax for the UDF function declaration for functions defined in external packages/ ibraries is given as follows. The parameters are explained below. The main difference is that a user must specify the appropriate collection of userParam=value pairs for the given external package. Also, one of the userParam should be ’classname’.

functionName = externalFunction(
    [<DataType>? <ValueType> <var>, ]* )
return ([<DataType>? <ValueType> <var>,]*)
implemented in ([userParam=value]*)

Table 3: Parameters for UDF Function Definition Statements

Parameter Name Description Optional Permissible Values
functionName Name of the function. No Any non-keyword string
DataType The data type of the identifier for a formal parameter or return value. If the value value is scalar or object, then DataType is optional matrix, scalar, object (capitalization does not matter)
ValueType The value type of the identifier for a formal parameter or return value. No. The value type object can only use used with data type object. double, integer, string, boolean, object
Var The identifier for a formal parameter or return value. No Any non-keyword sting
userParam=value User-defined parameter to invoke the package. Yes Any non-keyword string

Examples

# example of a UDF defined in DML
mean = function (matrix[double] A) return (double m) {
    m = sum(A)/nrow(A)
}

# example of a UDF defined in DML with multiple return values
minMax = function( matrix[double] M) return (double minVal, double maxVal) {
    minVal = min(M);
    maxVal = max(M);
}

# example of an external UDF
time = externalFunction(Integer i) return (Double B)
       implemented in (classname="org.apache.sysml.udf.lib.TimeWrapper", exectype="mem");
t = time(1);
print("Time: " + t);

A UDF invocation specifies the function identifier, variable identifiers for calling parameters, and the variables to be populated by the returned values from the function. The syntax for function calls is as follows.

returnVal = functionName(param1, param2, ...)
[returnVal1, returnVal2, ...] = functionName(param1, param2, ...)

Examples

# DML script with a function call
B = matrix(0, rows = 10,cols = 10);
C = matrix(0, rows = 100, cols = 100);
D = addEach(1, C);
index = 0;
while (index < 5) {
    [minD, maxD] = minMax(D);
    index = index + 1
}

Variable Scoping

DML supports following two types of scoping:

  1. Default: All the variables are bound to global unbounded scope.
  2. Function scope: Only the variables specified in the function declaration can be accessed inside function.

Note: The command-line parameters are treated as constants which are introduced during parse-time.

Example of Default Scope

if(1!=0) {
    A = 1;
}
print("A:" + A);

This will result in parser warning, but the program will run to completion. If the expression in the “if” predicate would have evaluated to FALSE, it would have resulted in runtime error. Also, functions need not be defined prior to its call. That is: following code will work without parser warning:

A = 2;
C = foo(1, A)
print("C:" + C);
foo = function(double A, double B) return (double C) {
    C = A + B;
}

Example of Function Scope

A = 2;
D = 1;
foo = function(double A, double B) return (double C) {
    A = 3.0; # value of global A won’t change since it is pass by value

    C = A + B # Note: C = A + D will result in compilation error
}
C = foo(A, 1)
print("C:" + C + " A:" + A);

The above code will output: C:4.0 A:2

Command-Line Arguments

Since most algorithms require arguments to be passed from command line, DML supports command-line arguments. The command line parameters are treated as constants (similar to arguments passed to main function of a java program). The command line parameters can be passed in two ways:

  1. As named arguments (recommended):

    -nvargs param1=7 param2="abc" param3=3.14

  2. As positional arguments (deprecated):

    -args 7 "abc" 3.14

The named arguments can be accessed by adding “\$” before the parameter name, i.e. \$param1. On the other hand, the positional parameter are accessible by adding “\$” before their positions (starting from index 1), i.e. \$1. A string parameter can be passed without quote. For example, param2=abc is valid argument, but it is not recommend.

Sometimes the user would want to support default values in case user does not explicitly pass the corresponding command line parameter (in below example: $nbrRows). To do so, we use the ifdef function which assigns either command line parameter or the default value to the local parameter.

local_variable = ifdef(command line variable, default value)

Example: Script in file test.dml

localVar_nbrRows=ifdef($nbrRows , 10)
M = rand (rows = localVar_nbrRows, cols = $nbrCols)
write (M, $fname, format="csv")
print("Done creating and writing random matrix in " + $fname)

In above script, ifdef(\$nbrRows, 10) function is a short-hand for “ifdef(\$nbrRows) then \$nbrRows else 10”.

Let’s assume that the above script is invoked using following the command line values:

spark-submit SystemML.jar -f test.dml -nvargs fname=test.mtx nbrRows=5 nbrCols=5

In this case, the script will create a random matrix M with 5 rows and 5 columns and write it to the file “text.mtx” in csv format. After that it will print the message “Done creating and writing random matrix in test.mtx” on the standard output.

If however, the above script is invoked from the command line using named arguments:

spark-submit SystemML.jar -f test.dml -nvargs fname=test.mtx nbrCols=5

Then, the script will instead create a random matrix M with 10 rows (i.e. default value provided in the script) and 5 columns.

It is important to note that the placeholder variables should be treated like constants that are initialized once, either via command line-arguments or via default values at the beginning of the script.

Each argValue passed from the command-line has a scalar data type, and the value type for argValue is inferred using the following logic:

if (argValue can be cast as Integer)
    Assign argValue integer value type
else if (argValue can be cast as Double)
    Assign argValue double value type
else if (argValue can be cast as Boolean)
    Assign argValue boolean value type
else
    Assign argValue string value type

In above example, the placeholder variable \$nbrCols will be treated as integer in the script. If however, the command line arguments were “nbrCols=5.0”, then it would be treated as a double.

NOTE: argName must be a valid identifier. NOTE: If argValue contains spaces, it must be enclosed in double-quotes. NOTE: The values passed from the command-line are passed as literal values which replace the placeholders in the DML script, and are not interpreted as DML.

Built-In Functions

Built-in functions are categorized in:

The tables below list the supported built-in functions. For example, consider the following expressions:

s = sum(A);
B = rowSums(A);
C = colSums(A);
D = rowSums(C);
diff = s – as.scalar(D);

The builtin function sum operates on a matrix (say A of dimensionality (m x n)) and returns a scalar value corresponding to the sum of all values in the matrix. The built-in functions rowSums and colSums, on the other hand, aggregate values on a per-row and per-column basis respectively. They output matrices of dimensionality (m x 1) and 1xn, respectively. Therefore, B is a m x 1 matrix and C is a 1 x n matrix. Applying rowSums on matrix C, we obtain matrix D as a 1 x 1 matrix. A 1 x 1 matrix is different from a scalar; to treat D as a scalar, an explicit as.scalar operation is invoked in the final statement. The difference between s and as.scalar(D) should be 0.

Matrix Construction, Manipulation, and Aggregation Built-In Functions

Table 4: Matrix Construction, Manipulation, and Aggregation Built-In Functions

Function Description Parameters Example
cbind() Column-wise matrix concatenation. Concatenates the second matrix as additional columns to the first matrix Input: (X <matrix>, Y <matrix>)
Output: <matrix>
X and Y are matrices, where the number of rows in X and the number of rows in Y are the same.
A = matrix(1, rows=2,cols=3)
B = matrix(2, rows=2,cols=3)
C = cbind(A,B)
print(“Dimensions of C: “ + nrow(C) + “ X “ + ncol(C))
Output:
Dimensions of C: 2 X 6
matrix() Matrix constructor (assigning all the cells to numeric literals). Input: (<init>, rows=<value>, cols=<value>)
init: numeric literal;
rows/cols: number of rows/cols (expression)
Output: matrix
# 10x10 matrix initialized to 0
A = matrix (0, rows=10, cols=10)
  Matrix constructor (reshaping an existing matrix). Input: (<existing matrix>, rows=<value>, cols=<value>, byrow=TRUE)
Output: matrix
A = matrix (0, rows=10, cols=10)
B = matrix (A, rows=100, cols=1)
  Matrix constructor (initializing using string). Input: (<initialization string>, rows=<value>, cols=<value>)
Output: matrix
A = matrix(“4 3 2 5 7 8”, rows=3, cols=2)
Creates a matrix: [ [4, 3], [2, 5], [7, 8] ]
min()
max()
Return the minimum/maximum cell value in matrix Input: matrix
Output: scalar
min(X)
max(Y)
min()
max()
Return the minimum/maximum cell values of two matrices, matrix and scalar, or scalar value of two scalars. Input: matrices or scalars
Output: matrix or scalar
With x,y, z as scalars, and X, Y, Z as matrices:
Z = min (X, Y)
Z = min (X, y)
z = min(x,y)
nrow(),
ncol(),
length()
Return the number of rows, number of columns, or number of cells in matrix or frame respectively. Input: matrix or frame
Output: scalar
nrow(X)
ncol(F)
length(X)
prod() Return the product of all cells in matrix Input: matrix
Output: scalarj
prod(X)
rand() Generates a random matrix Input: (rows=<value>, cols=<value>, min=<value>, max=<value>, sparsity=<value>, pdf=<string>, seed=<value>)
rows/cols: Number of rows/cols (expression)
min/max: Min/max value for cells (either constant value, or variable that evaluates to constant value)
sparsity: fraction of non-zero cells (constant value)
pdf: “uniform” (min, max) distribution, or “normal” (0,1) distribution; or “poisson” (lambda=1) distribution. string; default value is “uniform”. Note that, for the Poisson distribution, users can provide the mean/lambda parameter as follows:
rand(rows=1000,cols=1000, pdf=”poisson”, lambda=2.5).
The default value for lambda is 1.
seed: Every invocation of rand() internally generates a random seed with which the cell values are generated. One can optionally provide a seed when repeatability is desired.
Output: matrix
X = rand(rows=10, cols=20, min=0, max=1, pdf=”uniform”, sparsity=0.2)
The example generates a 10 x 20 matrix, with cell values uniformly chosen at random between 0 and 1, and approximately 20% of cells will have non-zero values.
rbind() Row-wise matrix concatenation. Concatenates the second matrix as additional rows to the first matrix Input: (X <matrix>, Y <matrix>)
Output: <matrix>
X and Y are matrices, where the number of columns in X and the number of columns in Y are the same.
A = matrix(1, rows=2,cols=3)
B = matrix(2, rows=2,cols=3)
C = rbind(A,B)
print(“Dimensions of C: “ + nrow(C) + “ X “ + ncol(C))
Output:
Dimensions of C: 4 X 3
removeEmpty() Removes all empty rows or columns from the input matrix target X according to the specified margin. The optional select vector F specifies selected rows or columns; if not provided, the semantics are F=(rowSums(X!=0)>0) and F=(colSums(X!=0)>0) for removeEmpty “rows” and “cols”, respectively. The optional empty.return flag indicates if a row or column of zeros should be returned for empty inputs. Input : (target= X <matrix>, margin=”…”[, select=F][, empty.return=TRUE])
Output : <matrix>
Valid values for margin are “rows” or “cols”.
A = removeEmpty(target=X, margin=”rows”, select=F)
replace() Creates a copy of input matrix X, where all values that are equal to the scalar pattern s1 are replaced with the scalar replacement s2. Input : (target= X <matrix>, pattern=<scalar>, replacement=<scalar>)
Output : <matrix>
If s1 is NaN, then all NaN values of X are treated as equal and hence replaced with s2. Positive and negative infinity are treated as different values.
A = replace(target=X, pattern=s1, replacement=s2)
rev() Reverses the rows in a matrix Input : (<matrix>)
Output : <matrix>
A = matrix(“1 2 3 4”, rows=2, cols=2)
B = matrix(“1 2 3 4”, rows=4, cols=1)
C = matrix(“1 2 3 4”, rows=1, cols=4)
revA = rev(A)
revB = rev(B)
revC = rev(C)
Matrix revA: [[3, 4], [1, 2]]
Matrix revB: [[4], [3], [2], [1]]
Matrix revC: [[1, 2, 3, 4]]
seq() Creates a single column vector with values starting from <from>, to <to>, in increments of <increment> Input: (<from>, <to>, <increment>)
Output: <matrix>
S = seq (10, 200, 10)
sum() Sum of all cells in matrix Input: matrix
Output: scalar
sum(X)

Matrix and/or Scalar Comparison Built-In Functions

Table 5: Matrix and/or Scalar Comparison Built-In Functions

Function Description Parameters Example
pmin()
pmax()
“parallel min/max”.
Return cell-wise minimum/maximum. If the second input is a scalar then it is compared against all cells in the first input.
Input: (<matrix>, <matrix>), or (<matrix>, <scalar>)
Output: matrix
pmin(X,Y)
pmax(X,y)
rowIndexMax() Row-wise computation – for each row, find the max value, and return its column index. Input: (matrix)
Output: (n x 1) matrix
rowIndexMax(X)
rowIndexMin() Row-wise computation – for each row, find the minimum value, and return its column index. Input: (matrix)
Output: (n x 1) matrix
rowIndexMin(X)
ppred() “parallel predicate”.
The relational operator specified in the third argument is cell-wise applied to input matrices. If the second argument is a scalar, then it is used against all cells in the first argument.
NOTE: ppred() has been replaced by the relational operators, so its use is discouraged.
Input: (<matrix>, <matrix>, <string with relational operator>), or
(<matrix>, <scalar>, <string with relational operator>)
Output: matrix
ppred(X,Y,”<”)
ppred(X,y,”<”)

Casting Built-In Functions

Table 6: Casting Built-In Functions

Function Description Parameters Example
as.scalar(),
as.matrix()
A 1x1 matrix is cast as scalar (value type preserving), and a scalar is cast as 1x1 matrix with value type double Input: (<matrix>), or (<scalar>)
Output: <scalar>, or <matrix>
as.scalar(X)
as.matrix(x)
as.double(),
as.integer(),
as.logical()
A variable is cast as the respective value type, data type preserving. as.integer() performs a safe cast. For numerical inputs, as.logical() returns FALSE if the input value is 0 or 0.0, and TRUE otherwise. Input: (<scalar>)
Output: <scalar>
as.double(X)
as.integer(x)
as.logical(y)

Statistical Built-In Functions

Table 7: Statistical Built-In Functions

Function Description Parameters Example
mean()
avg()
Return the mean value of all cells in matrix Input: matrix
Output: scalar
mean(X)
var()
sd()
Return the variance/stdDev value of all cells in matrix. Both use unbiased estimators with (n-1) denominator. Input: matrix
Output: scalar
var(X)
sd(X)
moment() Returns the kth central moment of values in a column matrix V, where k = 2, 3, or 4. It can be used to compute statistical measures like Variance, Kurtosis, and Skewness. This function also takes an optional weights parameter W. Input: (X <(n x 1) matrix>, [W <(n x 1) matrix>),] k <scalar>)
Output: <scalar>
A = rand(rows=100000,cols=1, pdf=”normal”)
print(“Variance from our (standard normal) random generator is approximately “ + moment(A,2))
colSums()
colMeans()
colVars()
colSds()
colMaxs()
colMins()
Column-wise computations – for each column, compute the sum/mean/variance/stdDev/max/min of cell values Input: matrix
Output: (1 x n) matrix
colSums(X)
colMeans(X)
colVars(X)
colSds(X)
colMaxs(X)
colMins(X)
cov() Returns the covariance between two 1-dimensional column matrices X and Y. The function takes an optional weights parameter W. All column matrices X, Y, and W (when specified) must have the exact same dimension. Input: (X <(n x 1) matrix>, Y <(n x 1) matrix> [, W <(n x 1) matrix>)])
Output: <scalar>
cov(X,Y)
cov(X,Y,W)
table() Returns the contingency table of two vectors A and B. The resulting table F consists of max(A) rows and max(B) columns.
More precisely, F[i,j] = |{ k | A[k] = i and B[k] = j, 1 ≤ k ≤ n }|, where A and B are two n-dimensional vectors.
This function supports multiple other variants, which can be found below, at the end of this Table 7.
Input: (<(n x 1) matrix>, <(n x 1) matrix>), [<(n x 1) matrix>])
Output: <matrix>
F = table(A, B)
F = table(A, B, C)
And, several other forms (see below Table 7.)
cdf()
pnorm()
pexp()
pchisq()
pf()
pt()
icdf()
qnorm()
qexp()
qchisq()
qf()
qt()
p=cdf(target=q, …) returns the cumulative probability P[X <= q].
q=icdf(target=p, …) returns the inverse cumulative probability i.e., it returns q such that the given target p = P[X<=q].
For more details, please see the section “Probability Distribution Functions” below Table 7.
Input: (target=<scalar>, dist=”…”, …)
Output: <scalar>
p = cdf(target=q, dist=”normal”, mean=1.5, sd=2); is same as p=pnorm(target=q, mean=1.5, sd=2);
q=icdf(target=p, dist=”normal”) is same as q=qnorm(target=p, mean=0,sd=1)
More examples can be found in the section “Probability Distribution Functions” below Table 7.
aggregate() Splits/groups the values from X according to the corresponding values from G, and then applies the function fn on each group.
The result F is a column matrix, in which each row contains the value computed from a distinct group in G. More specifically, F[k,1] = fn( {X[i,1] | 1<=i<=n and G[i,1] = k} ), where n = nrow(X) = nrow(G).
Note that the distinct values in G are used as row indexes in the result matrix F. Therefore, nrow(F) = max(G). It is thus recommended that the values in G are consecutive and start from 1.
This function supports multiple other variants, which can be found below, at the end of this Table 7.
Input:
(target = X <(n x 1) matrix, or matrix>,
   groups = G <(n x 1) matrix>,
   fn= “…”
   [,weights= W<(n x 1) matrix>]
   [,ngroups=N] )
Output: F <matrix>
Note: X is a (n x 1) matrix unless ngroups is specified with no weights, in which case X is a regular (n x m) matrix.
The parameter fn takes one of the following functions: “count”, “sum”, “mean”, “variance”, “centralmoment”. In the case of central moment, one must also provide the order of the moment that need to be computed (see example).
F = aggregate(target=X, groups=G, fn= “…” [,weights = W])
F = aggregate(target=X, groups=G1, fn= “sum”);
F = aggregate(target=Y, groups=G2, fn= “mean”, weights=W);
F = aggregate(target=Z, groups=G3, fn= “centralmoment”, order= “2”);
And, several other forms (see below Table 7.)
interQuartileMean() Returns the mean of all x in X such that x>quantile(X, 0.25) and x<=quantile(X, 0.75). X, W are column matrices (vectors) of the same size. W contains the weights for data in X. Input: (X <(n x 1) matrix> [, W <(n x 1) matrix>)])
Output: <scalar>
interQuartileMean(X)
interQuartileMean(X, W)
quantile () The p-quantile for a random variable X is the value x such that Pr[X<x] <= p and Pr[X<= x] >= p
let n=nrow(X), i=ceiling(p*n), quantile() will return X[i]. p is a scalar (0<p<1) that specifies the quantile to be computed. Optionally, a weight vector may be provided for X.
Input: (X <(n x 1) matrix>, [W <(n x 1) matrix>),] p <scalar>)
Output: <scalar>
quantile(X, p)
quantile(X, W, p)
quantile () Returns a column matrix with list of all quantiles requested in P. Input: (X <(n x 1) matrix>, [W <(n x 1) matrix>),] P <(q x 1) matrix>)
Output: matrix
quantile(X, P)
quantile(X, W, P)
median() Computes the median in a given column matrix of values Input: (X <(n x 1) matrix>, [W <(n x 1) matrix>),])
Output: <scalar>
median(X)
median(X,W)
rowSums()
rowMeans()
rowVars()
rowSds()
rowMaxs()
rowMins()
Row-wise computations – for each row, compute the sum/mean/variance/stdDev/max/min of cell value Input: matrix
Output: (n x 1) matrix
rowSums(X)
rowMeans(X)
rowVars(X)
rowSds(X)
rowMaxs(X)
rowMins(X)
cumsum() Column prefix-sum (For row-prefix sum, use cumsum(t(X)) Input: matrix
Output: matrix of the same dimensions
A = matrix(“1 2 3 4 5 6”, rows=3, cols=2)
B = cumsum(A)
The output matrix B = [[1, 2], [4, 6], [9, 12]]
cumprod() Column prefix-prod (For row-prefix prod, use cumprod(t(X)) Input: matrix
Output: matrix of the same dimensions
A = matrix(“1 2 3 4 5 6”, rows=3, cols=2)
B = cumprod(A)
The output matrix B = [[1, 2], [3, 8], [15, 48]]
cummin() Column prefix-min (For row-prefix min, use cummin(t(X)) Input: matrix
Output: matrix of the same dimensions
A = matrix(“3 4 1 6 5 2”, rows=3, cols=2)
B = cummin(A)
The output matrix B = [[3, 4], [1, 4], [1, 2]]
cummax() Column prefix-max (For row-prefix min, use cummax(t(X)) Input: matrix
Output: matrix of the same dimensions
A = matrix(“3 4 1 6 5 2”, rows=3, cols=2)
B = cummax(A)
The output matrix B = [[3, 4], [3, 6], [5, 6]]
sample(range, size, replacement, seed) Sample returns a column vector of length size, containing uniform random numbers from [1, range] Input:
range: integer
size: integer
replacement: boolean (Optional, default: FALSE)
seed: integer (Optional)
Output: Matrix dimensions are size x 1
sample(100, 5)
sample(100, 5, TRUE)
sample(100, 120, TRUE)
sample(100, 5, 1234) # 1234 is the seed
sample(100, 5, TRUE, 1234)
outer(vector1, vector2, “op”) Applies element wise binary operation “op” (for example: “<”, “==”, “>=”, “”, “min”) on the all combination of vector.
Note: Using “
”, we get outer product of two vectors.
Input: vectors of same size d, string
Output: matrix of size d X d
A = matrix(“1 4”, rows = 2, cols = 1)
B = matrix(“3 6”, rows = 1, cols = 2)
C = outer(A, B, “<”)
D = outer(A, B, “*”)
The output matrix C = [[1, 1], [0, 1]]
The output matrix D = [[3, 6], [12, 24]]

Alternative forms of table()

The built-in function table() supports different types of input parameters. These variations are described below:

Alternative forms of aggregate()

The built-in function aggregate() supports different types of input parameters. These variations are described below:

Probability Distribution Functions

p = cdf(target=q, dist=fn, ..., lower.tail=TRUE)

This computes the cumulative probability at the given quantile i.e., P[X<=q], where X is random variable whose distribution is specified via string argument fn.

q = icdf(target=p, dist=fn, ...)

This computes the inverse cumulative probability i.e., it computes a quantile q such that the given probability p = P[X<=q], where X is random variable whose distribution is specified via string argument fn.

Alternative to cdf() and icdf(), users can also use distribution-specific functions. The functions pnorm(), pf(), pt(), pchisq(), and pexp() computes the cumulative probabilities for Normal, F, t, Chi Squared, and Exponential distributions, respectively. Appropriate distribution parameters must be provided for each function. Similarly, qnorm(), qf(), qt(), qchisq(), and qexp() compute the inverse cumulative probabilities for Normal, F, t, Chi Squared, and Exponential distributions.

Following pairs of DML statements are equivalent.

p = cdf(target=q, dist="normal", mean=1.5, sd=2); is same as p=pnorm(target=q, mean=1.5, sd=2);

p = cdf(target=q, dist="exp", rate=5); is same as pexp(target=q,rate=5);

p = cdf(target=q, dist="chisq", df=100); is same as pchisq(target=q, df=100)

p = cdf(target=q, dist="f", df1=100, df2=200); is same as pf(target=q, df1=100, df2=200);

p = cdf(target=q, dist="t", df=100); is same as pt(target=q, df=100)

p = cdf(target=q, dist="normal", lower.tail=FALSE); is same as p=pnorm(target=q, lower.tail=FALSE); is same as p=pnorm(target=q, mean=0, sd=1.0, lower.tail=FALSE); is same as p=pnorm(target=q, sd=1.0, lower.tail=FALSE);

Examples of icdf():

q=icdf(target=p, dist="normal"); is same as q=qnorm(target=p, mean=0,sd=1);

q=icdf(target=p, dist="exp"); is same as q=qexp(target=p, rate=1);

q=icdf(target=p, dist="chisq", df=50); is same as qchisq(target=p, df=50);

q=icdf(target=p, dist="f", df1=50, df2=25); is same as qf(target=p, , df1=50, df2=25);

q=icdf(target=p, dist="t", df=50); is same as qt(target=p, df=50);

Mathematical and Trigonometric Built-In Functions

Table 8: Mathematical and Trigonometric Built-In Functions

Function Description Parameters Example
exp(), log(), abs(), sqrt(), round(), floor(), ceil(), ceiling() Apply mathematical function on input (cell wise if input is matrix) Input: (<matrix>), or (<scalar>)
Output: <matrix>, or <scalar>
sqrt(X)
log(X,y)
round(X)
floor(X)
ceil(X)
ceiling(X)
sin(), cos(), tan(), sinh(), cosh(), tanh(), asin(), acos(), atan() Apply trigonometric function on input (cell wise if input is matrix) Input: (<matrix>), or (<scalar>)
Output: <matrix>, or <scalar>
sin(X)
sign() Returns a matrix representing the signs of the input matrix elements, where 1 represents positive, 0 represents zero, and -1 represents negative Input : (A <matrix>)
Output : <matrix>
A = matrix(“-5 0 3 -3”, rows=2, cols=2)
signA = sign(A)
Matrix signA: [[-1, 0], [1, -1]]

Linear Algebra Built-In Functions

Table 9: Linear Algebra Built-In Functions

Function Description Parameters Example
cholesky() Computes the Cholesky decomposition of symmetric input matrix A Input: (A <matrix>)
Output: <matrix>
A = matrix(“4 12 -16 12 37 -43 -16 -43 98”, rows=3, cols=3)
B = cholesky(A)
Matrix B: [[2, 0, 0], [6, 1, 0], [-8, 5, 3]]
diag() Create diagonal matrix from (n x 1) matrix, or take diagonal from square matrix Input: (n x 1) matrix, or (n x n) matrix
Output: (n x n) matrix, or (n x 1) matrix
D = diag(matrix(1.0, rows=3, cols=1))
E = diag(matrix(1.0, rows=3, cols=3))
eigen() Computes Eigen decomposition of input matrix A. The Eigen decomposition consists of two matrices V and w such that A = V %*% diag(w) %*% t(V). The columns of V are the eigenvectors of the original matrix A. And, the eigen values are given by w.
It is important to note that this function can operate only on small-to-medium sized input matrix that can fit in the main memory. For larger matrices, an out-of-memory exception is raised.
Input : (A <matrix>)
Output : [w <(m x 1) matrix>, V <matrix>]
A is a square symmetric matrix with dimensions (m x m). This function returns two matrices w and V, where w is (m x 1) and V is of size (m x m).
[w, V] = eigen(A)
lu() Computes Pivoted LU decomposition of input matrix A. The LU decomposition consists of three matrices P, L, and U such that P %*% A = L %*% U, where P is a permutation matrix that is used to rearrange the rows in A before the decomposition can be computed. L is a lower-triangular matrix whereas U is an upper-triangular matrix.
It is important to note that this function can operate only on small-to-medium sized input matrix that can fit in the main memory. For larger matrices, an out-of-memory exception is raised.
Input : (A <matrix>)
Output : [<matrix>, <matrix>, <matrix>]
A is a square matrix with dimensions m x m. This function returns three matrices P, L, and U, all of which are of size m x m.
[P, L, U] = lu(A)
qr() Computes QR decomposition of input matrix A using Householder reflectors. The QR decomposition of A consists of two matrices Q and R such that A = Q%*%R where Q is an orthogonal matrix (i.e., Q%*%t(Q) = t(Q)%*%Q = I, identity matrix) and R is an upper triangular matrix. For efficiency purposes, this function returns the matrix of Householder reflector vectors H instead of Q (which is a large m x m potentially dense matrix). The Q matrix can be explicitly computed from H, if needed. In most applications of QR, one is interested in calculating Q %*% B or t(Q) %*% B – and, both can be computed directly using H instead of explicitly constructing the large Q matrix.
It is important to note that this function can operate only on small-to-medium sized input matrix that can fit in the main memory. For larger matrices, an out-of-memory exception is raised.
Input : (A <matrix>)
Output : [<matrix>, <matrix>]
A is a (m x n) matrix, which can either be a square matrix (m=n) or a rectangular matrix (m != n). This function returns two matrices H and R of size (m x n) i.e., same size as of the input matrix A.
[H, R] = qr(A)
solve() Computes the least squares solution for system of linear equations A %*% x = b i.e., it finds x such that ||A%*%x – b|| is minimized. The solution vector x is computed using a QR decomposition of A.
It is important to note that this function can operate only on small-to-medium sized input matrix that can fit in the main memory. For larger matrices, an out-of-memory exception is raised.
Input : (A <(m x n) matrix>, b <(m x 1) matrix>)
Output : <matrix>
A is a matrix of size (m x n) and b is a 1D matrix of size m x 1. This function returns a 1D matrix x of size n x 1.
x = solve(A,b)
svd() Singular Value Decomposition of a matrix A (of size m x m), which decomposes into three matrices U, V, and S as A = U %% S %% t(V), where U is an m x m unitary matrix (i.e., orthogonal), V is an n x n unitary matrix (also orthogonal), and S is an m x n matrix with non-negative real numbers on the diagonal. Input: matrix A <(m x n)>
Output: matrices U <(m x m)>, S <(m x n)>, and V <(n x n)>
[U, S, V] = svd(A)
t() Transpose matrix Input: matrix
Output: matrix
t(X)
trace() Return the sum of the cells of the main diagonal square matrix Input: matrix
Output: scalar
trace(X)

Read/Write Built-In Functions

The read and write functions support the reading and writing of matrices and scalars from/to the file system (local or HDFS). Typically, associated with each data file is a JSON-formatted metadata file (MTD) that stores metadata information about the content of the data file, such as the number of rows and columns. For data files written by SystemML, an MTD file will automatically be generated. The name of the MTD file associated with <filename> must be <filename.mtd>. In general, it is highly recommended that users provide MTD files for their own data as well.

Note: Metadata can also be passed as parameters to read and write function calls.

File formats and MTD files

SystemML supports 4 file formats:

The CSV format is a standard text-based format where columns are separated by delimiter characters, typically commas, and rows are represented on separate lines.

SystemML supports the Matrix Market coordinate format, which is a text-based, space-separated format used to represent sparse matrices. Additional information about the Matrix Market format can be found at http://math.nist.gov/MatrixMarket/formats.html#MMformat. SystemML does not currently support the Matrix Market array format for dense matrices. In the Matrix Market coordinate format, metadata (the number of rows, the number of columns, and the number of non-zero values) are included in the data file. Rows and columns index from 1. Matrix Market data must be in a single file, whereas the (i,j,v) text format can span multiple part files on HDFS. Therefore, for scalability reasons, the use of the (i,j,v) text and binary formats is encouraged when scaling to big data.

The (i,j,v) format is a text-based sparse format in which the cell values of a matrix are serialized in space-separated triplets of rowId, columnId, and cellValue, with the rowId and columnId indices being 1-based. This is similar to the Matrix Market coordinate format, except metadata is stored in a separate file rather than in the data file itself, and the (i,j,v) text format can span multiple part files.

The binary format can only be read and written by SystemML.

Let’s look at a matrix and examples of its data represented in the supported formats with corresponding metadata. In the table below, we have a matrix consisting of 4 rows and 3 columns.

Table 10: Matrix

1.0 2.0 3.0
0 0 0
7.0 8.0 9.0
0 0 0

Below, we have examples of this matrix in the CSV, Matrix Market, IJV, and Binary formats, along with corresponding metadata.

1.0,2.0,3.0
0,0,0
7.0,8.0,9.0
0,0,0
{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 4,
    "cols": 3,
    "nnz": 6,
    "format": "csv",
    "header": false,
    "sep": ",",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}
%%MatrixMarket matrix coordinate real general
4 3 6
1 1 1.0
1 2 2.0
1 3 3.0
3 1 7.0
3 2 8.0
3 3 9.0
1 1 1.0
1 2 2.0
1 3 3.0
3 1 7.0
3 2 8.0
3 3 9.0
{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 4,
    "cols": 3,
    "nnz": 6,
    "format": "text",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}
Binary is not a text-based format.
{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 4,
    "cols": 3,
    "rows_in_block": 1000,
    "cols_in_block": 1000,
    "nnz": 6,
    "format": "binary",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}

As another example, here we see the content of the MTD file scalar.mtd associated with a scalar data file scalar that contains the scalar value 2.0.

{
    "data_type": "scalar",
    "value_type": "double",
    "format": "text",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}

Metadata is represented as an MTD file that contains a single JSON object with the attributes described below.

Table 11: MTD attributes

Parameter Name Description Optional Permissible values Data type valid for
data_type Indicates the data type of the data Yes. Default value is matrix if not specified matrix, scalar matrix, scalar
value_type Indicates the value type of the data Yes. Default value is double if not specified double, int, string, boolean. Must be double when data_type is matrix matrix, scalar
rows Number of rows in matrix Yes – only when format is csv any integer > 0 matrix
cols Number of columns in matrix Yes – only when format is csv any integer > 0 matrix
rows_in_block, cols_in_block Valid only for binary format. Indicates dimensions of blocks No. Only valid if matrix is in binary format any integer > 0 matrix in binary format. Valid only when binary format
nnz Number of non-zero values Yes any integer > 0 matrix
format Data file format Yes. Default value is text csv, mm, text, binary matrix, scalar. Formats csv and mm are applicable only to matrices
description Description of the data Yes Any valid JSON string or object matrix, scalar
author User that created the metadata file, defaults to SystemML N/A N/A N/A
created Date/time when metadata file was written N/A N/A N/A

In addition, when reading or writing CSV files, the metadata may contain one or more of the following five attributes. Note that this metadata can be specified as parameters to the read and write function calls.

Table 12: Additional MTD attributes when reading/writing CSV files

Parameter Name Description Optional Permissible values Data type valid for
header Specifies whether the data file has a header. If the header exists, it must be the first line in the file. Yes, default value is false. true/false (TRUE/FALSE in DML) matrix
sep Specifies the separator (delimiter) used in the data file. Note that using a delimiter composed of just numeric values or a period (decimal point) can be ambiguous and may lead to unexpected results. Yes, default value is “,” (comma) string matrix
fill Only valid when reading CSV files. It specifies whether or not to fill the empty fields in the input file. Empty fields are denoted by consecutive separators (delimiters). If fill is true then every empty field is filled with the value specified by the “default” attribute. An exception is raised if fill is false and the input file has one or more empty fields. Yes, default is true. true/false (TRUE/FALSE in DML) matrix
default Only valid when reading CSV files and fill is true. It specifies the special value with which all empty values are filled while reading the input matrix. Yes, default value is 0 any double matrix
sparse Only valid when writing CSV files. It specifies whether or not to explicitly output zero (0) values. Zero values are written out only when sparse=FALSE. Yes, default value is FALSE. TRUE/FALSE in DML matrix

Furthermore, the following additional notes apply when reading and writing CSV files.

Read Built-In Function

The syntax of the read statement is as follows:

read("inputfile", [additional parameters])

where "inputfile" (also known as iofilename) is the path to the data file in the file system. The list of parameters is the same as the metadata attributes provided in MTD files. For the "inputfile" parameter, the user can use constant string concatenation to give the full path of the file, where “+” is used as the concatenation operator. However, the file path must evaluate to a constant string at compile time. For example, "/my/dir" + "filename.mtx" is valid parameter but "/my/dir" + "filename" + i + ".mtx" is not (where i is a variable).

The user has the option of specifying each parameter value in the MTD file, the read function invocation, or in both locations. However, parameter values specified in both the read invocation and the MTD file must have the same value. Also, if a scalar value is being read, then format cannot be specified.

The read invocation in SystemML is parameterized as follows during compilation.

  1. Default values are assigned to parameters.
  2. Parameters provided in read() either fill in values or override defaults.
  3. SystemML will look for the MTD file at compile time in the specified location (at the same path as the data file, where the filename of the MTD file is the same name as the data file with the extension .mtd).
  4. If all non-optional parameters aren’t specified or conflicting values are detected, then an exception is thrown.
Examples
# Read a matrix with path "in/v.ijv".
# Defaults for data_type and value_type are used.
V = read("in/v.ijv", rows=10, cols=8, format="text");

# Read a matrix with path "in/v.ijv".
# The user specifies "in/" as the directory and "v" as
# the file name and uses constant string concatenation.
dir = "in/";
file = "v.ijv";
V = read(dir + file, rows=10, cols=8, format="text");

# Read a matrix data file with an MTD file available
# (MTD file path: in/data.ijv.mtd)
V = read("in/data.ijv");

# Read a csv matrix data file with no header, comma as
# separator, 3 rows, and 3 columns.
V = read("m.csv", format="csv", header=FALSE, sep=",", rows=3, cols=3);

# Read a csv matrix data file with an MTD file available
# (MTD file: m.csv.mtd)
V = read("m.csv");

# Read a scalar integer value from file "in/scalar"
V = read("in/scalar", data_type="scalar", value_type="int");

Additionally, readMM() and read.csv() are supported and can be used instead of specifying format="mm" or format="csv" in the read() function.

Write Built-In Function

The write method is used to persist scalar and matrix data to files in the local file system or HDFS. The syntax of write is shown below. The parameters are described in Table 13. Note that the set of supported parameters for write is NOT the same as for read. SystemML writes an MTD file for the written data.

write(identifier, "outputfile", [additional parameters])

The user can use constant string concatenation in the "outputfile" parameter to give the full path of the file, where + is used as the concatenation operator.

Table 13: Parameters for write() method

Parameter Name Description Optional Permissible Values
identifier Variable whose data is to be written to a file. Data can be matrix or scalar. No Any variable name
"outputfile" The path to the data file in the file system No Any valid filename
[additional parameters] See Tables 11 and 12    
Examples

Write V matrix to file out/file.ijv in the default text format. This also creates the metadata file out/file.ijv.mtd.

write(V, "out/file.ijv");

Example content of out/file.ijv.mtd:

{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 10,
    "cols": 8,
    "nnz": 4,
    "format": "text",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}

Write V to out/file in binary format:

write(V, "out/file", format="binary");

Example content of out/file.mtd:

{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 10,
    "cols": 8,
    "nnz": 4,
    "rows_in_block": 1000,
    "cols_in_block": 1000,
    "format": "binary",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}

Write V to n.csv in csv format with column headers, ";" as delimiter, and zero values are not written.

write(V, "n.csv", format="csv", header=TRUE, sep=";", sparse=TRUE);

Example content of n.csv.mtd:

{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 3,
    "cols": 3,
    "nnz": 9,
    "format": "csv",
    "header": true,
    "sep": ";",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}

Write x integer value to file out/scalar_i

write(x, "out/scalar_i");

Example content of out/scalar_i.mtd:

{
    "data_type": "scalar",
    "value_type": "int",
    "format": "text",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}

Unlike read, the write function does not need a constant string expression, so the following example will work:

A = rand(rows=10, cols=2);
dir = "tmp/";
i = 1;
file = "A" + i + ".mtx";
write(A, dir + file, format="csv");

The description parameter can be used to attach a description to the metadata:

A = matrix("1 2 3 4", rows=2, cols=2)
write(A, "mymatrix.csv", format="csv", description="my matrix")

This will generate the following mymatrix.csv.mtd metadata file:

{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 2,
    "cols": 2,
    "nnz": 4,
    "format": "csv",
    "header": false,
    "sep": ",",
    "description": "my matrix",
    "author": "SystemML",
    "created": "2017-01-01 00:00:01 PST"
}

Data Pre-Processing Built-In Functions

The data pre-processing built-in transform() function is used to transform a given tabular input data set (with data type frame) in CSV format into a matrix. The transform() function supports the following six column-level data transformations:

The transformations are specified to operate on individual columns. The set of all required transformations across all the columns in the input data must be provided via a specification file in JSON format. Furthermore, the notation indicating missing values must be specified using the na.strings property in the mtd file associated with the input CSV data, along with other properties such as header and sep (the delimiter). Note that the delimiter cannot be part of any value. For example, if a “,” (comma) is part of any value, then it cannot be used a delimiter. Users must choose a different sep value (e.g., a tab “\t”).

The following table indicates which transformations can be used simultaneously on a single column.

Table 14: Data transformations that can be used simultaneously.

  OMIT MVI RCD BIN DCD SCL
OMIT - x * * * *
MVI x - * * * *
RCD * * - x * x
BIN * * x - * x
DCD * * * * - x
SCL * * x x x -
Key Meaning
OMITMissing value handling by omitting
MVIMissing value handling by imputation
RCDRecoding
BINBinning
DCDDummycoding
SCLScaling
Key Meaning
*Combination is allowed
xCombination is invalid
-Combination is not applicable



The transform() function signature is shown here:

output = transform(target = input,
                   transformSpec = "/path/to/transformation/specification",
                   transformPath = "/path/to/transformation/metadata",
                   applyTransformPath = "/path/to/transformation/metadata")

The target parameter points to the input tabular data that needs to be transformed, the transformSpec parameter refers to the transformation specification JSON file indicating the list of transformations that must be performed, and transformPath denotes the output directory at which all the resulting metadata constructed during the transformation process is stored. Examples of such metadata include the number of distinct values in a categorical column, the list of distinct values and associated recoded IDs, the bin definitions (number of bins, bin widths), etc. This metadata can subsequently be utilized to transform new incoming data, for example, the test set in a predictive modeling exercise. The parameter applyTransformPath refers to existing transformation metadata which was generated by some earlier invocation of the transform() function. Therefore, in any invocation of transform(), only transformSpec or applyTransformPath can be specified. The transformation metadata is generated when transformSpec is specified, and it is used and applied when applyTransformPath is specified. On the other hand, the transformPath always refers to a location where the resulting transformation metadata is stored.

The transform() function returns the actual transformed data in the form of a matrix, containing only numeric values.

As an example of the transform() function, consider the following data.csv file that represents a sample of homes data.

Table 15: The data.csv homes data set

zipcode district sqft numbedrooms numbathrooms floors view saleprice askingprice
95141 south 3002 6 3 2 FALSE 929 934
NA west 1373   1 3 FALSE 695 698
91312 south NA 6 2 2 FALSE 902  
94555 NA 1835 3   3   888 892
95141 west 2770 5 2.5   TRUE 812 816
95141 east 2833 6 2.5 2 TRUE 927  
96334 NA 1339 6 3 1 FALSE 672 675
96334 south 2742 6 2.5 2 FALSE 872 876
96334 north 2195 5 2.5 2 FALSE 799 803


Note that the missing values are denoted either by an empty value or as a String “NA”. This information must be captured via the na.strings property in the metadata file associated with the input data. In this example, the data is stored in CSV format with “,” as the delimiter (the sep property). Recall that the delimiter cannot be part of any value. The metadata file data.csv.mtd looks as follows:

{
    "data_type": "frame",
    "format": "csv",
    "sep": ",",
    "header": true,
    "na.strings": [ "NA", "" ]
}

An example transformation specification file data.spec.json is given below:

{
    "omit": [ "zipcode" ]
   ,"impute":
    [ { "name": "district"    , "method": "constant", "value": "south" }
     ,{ "name": "numbedrooms" , "method": "constant", "value": 2 }
     ,{ "name": "numbathrooms", "method": "constant", "value": 1 }
     ,{ "name": "floors"      , "method": "constant", "value": 1 }
     ,{ "name": "view"        , "method": "global_mode" }
     ,{ "name": "askingprice" , "method": "global_mean" }
     ,{ "name": "sqft"        , "method": "global_mean" }
    ]

    ,"recode":
    [ "zipcode", "district", "numbedrooms", "numbathrooms", "floors", "view" ]

    ,"bin":
    [ { "name": "saleprice"  , "method": "equi-width", "numbins": 3 }
     ,{ "name": "sqft"       , "method": "equi-width", "numbins": 4 }
    ]

    ,"dummycode":
    [ "district", "numbathrooms", "floors", "view", "saleprice", "sqft" ]

}

The following DML utilizes the transform() function.

D = read("/user/ml/data.csv");
tfD = transform(target=D,
                transformSpec="/user/ml/data.spec.json",
                transformPath="/user/ml/data-transformation");
s = sum(tfD);
print("Sum = " + s);

The transformation specification file can also utilize column numbers rather than than column names by setting the ids property to true. The following data.spec2.json specification file is the equivalent of the aforementioned data.spec.json file but with column numbers rather than column names.

{
    "ids": true
    ,"omit" : [ 1 ]
    ,"impute":
    [ { "id": 2, "method": "constant", "value": "south" }
     ,{ "id": 4, "method": "constant", "value": 2 }
     ,{ "id": 5, "method": "constant", "value": 1 }
     ,{ "id": 6, "method": "constant", "value": 1 }
     ,{ "id": 7, "method": "global_mode" }
     ,{ "id": 9, "method": "global_mean" }
     ,{ "id": 3, "method": "global_mean" }
    ]

    ,"recode": [ 1, 2, 4, 5, 6, 7 ]

    ,"bin":
    [ { "id": 8, "method": "equi-width", "numbins": 3 }
     ,{ "id": 3, "method": "equi-width", "numbins": 4 }
    ]

    ,"dummycode": [ 2, 5, 6, 7, 8, 3 ]

}

As a further JSON transformation specification example, the following data.spec3.json file specifies scaling transformations on three columns.

{
    "omit": [ "zipcode" ]
   ,"impute":
    [ { "name": "district"    , "method": "constant", "value": "south" }
     ,{ "name": "numbedrooms" , "method": "constant", "value": 2 }
     ,{ "name": "numbathrooms", "method": "constant", "value": 1 }
     ,{ "name": "floors"      , "method": "constant", "value": 1 }
     ,{ "name": "view"        , "method": "global_mode" }
     ,{ "name": "askingprice" , "method": "global_mean" }
     ,{ "name": "sqft"        , "method": "global_mean" }
    ]

    ,"recode":
    [ "zipcode", "district", "numbedrooms", "numbathrooms", "floors", "view" ]

    ,"dummycode":
    [ "district", "numbathrooms", "floors", "view" ]

    ,"scale":
    [ { "name": "sqft", "method": "mean-subtraction" }
     ,{ "name": "saleprice", "method": "z-score" }
     ,{ "name": "askingprice", "method": "z-score" }
    ]
}

The following code snippet shows an example scenario of transforming a training data set and subsequently testing the data set.

Training Phase

Train = read("/user/ml/trainset.csv");
trainD = transform(target=Train,
                   transformSpec="/user/ml/tf.spec.json",
                   transformPath="/user/ml/train_tf_metadata");
# Build a predictive model using trainD
...

Testing Phase

Test = read("/user/ml/testset.csv");
testD = transform(target=Test,
                  transformPath="/user/ml/test_tf_metadata",
                  applyTransformPath="/user/ml/train_tf_metdata");
# Test the model using testD
...

Note that the metadata generated during the training phase (located at /user/ml/train_tf_metadata) is used to apply the list of transformations (that were carried out on training data set) on the test data set. Since the second invocation of transform() does not really generate any new metadata data, the given metadata (/user/ml/train_tf_metdata) is copied to the target location (/user/ml/test_tf_metdata). Even though such a behavior creates redundant copies of transformation metadata, it is preferred as it allows the association of every data set with the corresponding transformation metadata.

Deep Learning Built-In Functions

SystemML represent a tensor as a matrix stored in a row-major format, where first dimension of tensor and matrix are exactly the same. For example, a tensor (with all zeros) of shape [3, 2, 4, 5] can be instantiated by following DML statement:

A = matrix(0, rows=3, cols=2*4*5) 

The images are assumed to be stored NCHW format, where N = batch size, C = #channels, H = height of image and W = width of image. Hence, the images are internally represented as a matrix with dimension (N, C * H * W).

Function name Input matrices Dimension of first input matrix Dimension of second input matrix (if applicable) Dimension of output matrix Input Parameters Notes
conv2d input, filter [batch_size X num_channels* height_image* width_image] [num_filters X num_channels* height_filter* width_filter] [batch_size X num_channels_out* height_out* width_out] stride=[stride_h, stride_w], padding=[pad_h, pad_w], input_shape=[batch_size, num_channels, height_image, width_image], filter_shape=[num_filters, num_channels, height_filter, width_filter] Performs 2D convolution operation
conv2d_backward_filter input, dout [batch_size X num_channels* height_image* width_image] [batch_size X num_channels_out* height_out* width_out] [num_filters X num_channels* height_filter* width_filter] stride=[stride_h, stride_w], padding=[pad_h, pad_w], input_shape=[batch_size, num_channels, height_image, width_image], filter_shape=[num_filters, num_channels, height_filter, width_filter] Computes the gradients wrt filter of 2D convolution
conv2d_backward_data filter, dout [num_filters X num_channels* height_filter* width_filter] [batch_size X num_channels_out* height_out* width_out] [batch_size X num_channels* height_image* width_image] stride=[stride_h, stride_w], padding=[pad_h, pad_w], input_shape=[batch_size, num_channels, height_image, width_image], filter_shape=[num_filters, num_channels, height_filter, width_filter] Computes the gradients wrt input of 2D convolution
max_pool, avg_pool input [batch_size X num_channels* height_image* width_image]   [batch_size X num_channels* height_out* width_out] stride=[stride_h, stride_w], padding=[pad_h, pad_w], input_shape=[batch_size, num_channels, height_image, width_image], pool_size=[height_pool, width_pool] Performs max/average pooling operation
max_pool_backward, avg_pool_backward input, dout [batch_size X num_channels* height_image* width_image] [batch_size X num_channels* height_out* width_out] [batch_size X num_channels* height_image* width_image] stride=[stride_h, stride_w], padding=[pad_h, pad_w], input_shape=[batch_size, num_channels, height_image, width_image], pool_size=[height_pool, width_pool] Computes the gradients wrt input of 2D max pooling, average pooling
bias_add input, bias [batch_size X num_channels* height_image* width_image] [num_channels X 1] [batch_size X num_channels* height_image* width_image]   Adds the bias (row vector of size num_channels) to input with the given num_channels
bias_multiply input, bias [batch_size X num_channels* height_image* width_image] [num_channels X 1] [batch_size X num_channels* height_image* width_image]   Multiplies the bias (row vector of size num_channels) to input with the given num_channels

Examples:

Function Parameters Visualization / Equivalent DML
conv2d stride=[1,1] conv2d with stride 1
conv2d stride=[2,2] conv2d with stride 2
conv2d_backward_data stride=[1,1] conv2d_backward_data with stride 1
conv2d_backward_data stride=[2,2] conv2d_backward_data with stride 2
conv2d_backward_data stride=[2,2] and 2x2 filter conv2d_backward_data with stride 2 2x2 filter
bias_add   ones = matrix(1, rows=1, cols=height*width); output = input + matrix(bias %*% ones, rows=1, cols=numChannels*height*width)
bias_multiply   ones = matrix(1, rows=1, cols=height*width); output = input * matrix(bias %*% ones, rows=1, cols=numChannels*height*width)

Other Built-In Functions

Table 16: Other Built-In Functions

Function Description Parameters Example
append() Append a string to another string separated by “\n”
Limitation: The string may grow up to 1 MByte.
Input: (<string>, <string>)
Output: <string>
s = “iter=” + i
i = i + 1
s = append(s, “iter=” + i)
write(s, “s.out”)
toString() Formats a Matrix or Frame object into a string.
“rows” & “cols” : number of rows and columns to print
“decimal” : number of digits after the decimal
“sparse” : set to TRUE to print Matrix object in sparse format, i.e. RowIndex ColIndex Value
“sep” and “linesep” : inter-element separator and the line separator strings
Input : (<matrix> or <frame>,
  rows=100,
  cols=100,
  decimal=3,
  sparse=FALSE,
  sep=” “,
  linesep=”\n”)
Output: <string>
X = matrix(seq(1, 9), rows=3, cols=3)
str = toString(X, sep=” | “)

F = as.frame(X)
print(toString(F, rows=2, cols=2))
print() Prints a scalar variable. The print() function allows printf-style formatting by optionally allowing multiple arguments, where the first argument is the string that specifies the formatting and the additional arguments are the arguments to format. Input: <scalar>
or
<string, args…>
print(“hello”)
print(“hello” + “world”)
print(“value of x is “ + x )

a=’hello’;
b=3;
c=4.5;
d=TRUE;
print(‘%s %d %f %b’, a, b, c, d);

a=’hello’;
b=’goodbye’;
c=4;
d=3;
e=3.0;
f=5.0;
g=FALSE;
print(‘%s %d %f %b’, (a+b), (c-d), (e*f), !g);
stop() Halts the execution of DML program by printing the message that is passed in as the argument.
Note that the use of stop() is not allowed inside a parfor loop.
Input: (<scalar>) stop(“Inputs to DML program are invalid”)
stop(“Class labels must be either -1 or +1”)
assert() Halts the execution of DML program if the boolean argument doesnot evaluate to TRUE.
Note that the use of assert() is not allowed inside a parfor loop.
Input: (<scalar of type boolean>) assert(1 != 2)
order() Sort a column of the matrix X in decreasing/increasing order and return either index (index.return=TRUE) or data (index.return=FALSE). Input: (target=X, by=column, decreasing, index.return) order(X, by=1, decreasing=FALSE, index.return=FALSE)

Frames

The frame data type represents tabular data. In contrast to a matrix, whose element values are of type double, a frame can be associated with a schema to specify additional value types. Frames can be read from and written to files and support both left and right indexing. Built-in functions are provided to convert between frames and matrices. Advanced transform operations can also be applied. Note that frames are only supported for standalone and spark modes.

Creating Frames

To create a frame, specify data_type="frame" when reading data from a file. Input formats csv, text, and binary are supported.

A = read("fileA", data_type="frame", rows=10, cols=8);
B = read("dataB", data_type="frame", rows=3, cols=3, format="csv");

A schema can be specified when creating a frame where the schema is a string containing a value type per column. The supported value types for a schema are string, double, int, boolean. Note schema="" resolves to a string schema and if no schema is specified, the default is "".

This example shows creating a frame with schema="string,double,int,boolean" since the data has four columns (one of each supported value type).

tableSchema = "string,double,int,boolean";
C = read("tableC", data_type="frame", schema=tableSchema, rows=1600, cols=4, format="csv");

Note: the header line in frame CSV files is sensitive to white spaces.
For example, CSV1 with header ID,FirstName,LastName results in three columns with tokens between separators. In contrast, CSV2 with header ID, FirstName,LastName also results in three columns but the second column has a space preceding FirstName. This extra space is significant when referencing the second column by name in transform specifications as described in Transforming Frames.

ID,FirstName,LastName
1,FirstName1,LastName1
2,FirstName2,LastName2
ID, FirstName,LastName
1,FirstName1,LastName1
2,FirstName2,LastName2
{
    "data_type": "frame",
    "format": "csv",
    "header": true
}

Appending Frames

Built-In functions cbind() and rbind() are supported for frames to add columns or rows to an existing frame.

Table F1: Frame Append Built-In Functions

Function Description Parameters Example
cbind() Column-wise frame concatenation. Concatenates the second frame as additional columns to the first frame. Input: (X <frame>, Y <frame>)
Output: <frame>
X and Y are frames, where the number of rows in X and the number of rows in Y are the same.
A = read(“file1”, data_type=”frame”, rows=2, cols=3, format=”binary”)
B = read(“file2”, data_type=”frame”, rows=2, cols=3, format=”binary”)
C = cbind(A, B)
# Dimensions of C: 2 X 6
rbind() Row-wise frame concatenation. Concatenates the second frame as additional rows to the first frame. Input: (X <fame>, Y <frame>)
Output: <frame>
X and Y are frames, where the number of columns in X and the number of columns in Y are the same.
A = read(“file1”, data_type=”frame”, rows=2, cols=3, format=”binary”)
B = read(“file2”, data_type=”frame”, rows=2, cols=3, format=”binary”)
C = rbind(A, B)
# Dimensions of C: 4 X 3

Indexing Frames

Similar to matrices, frames support both right and left indexing. Note for left indexing, the right hand side frame size and selected left hand side frame slice must match.

# = [right indexing]
A = read("inputA", data_type="frame", rows=10, cols=10, format="binary")
B = A[4:5, 6:7]
C = A[1, ]
D = A[, 3]
E = A[, 1:2]

# [left indexing] =
F = read("inputF", data_type="frame", rows=10, cols=10, format="binary")
F[4:5, 6:7] = B
F[1, ] = C
F[, 3] = D
F[, 1:2] = E

Casting Frames

Frames support converting between matrices and scalars using as.frame(), as.matrix() and as.scalar(). Casting a frame to a matrix is a best effort operation, which tries to parse doubles. If there are strings that cannot be parsed, the as.frame() operation produces errors. For example, a java.lang.NumberFormatException may occur for invalid data since Java’s Double.parseDouble() is used internally for parsing.

Table F2: Casting Built-In Functions

Function Description Parameters Example
as.frame(<matrix>) Matrix is cast to frame. Input: (<matrix>)
Output: <frame>
A = read(“inputMatrixDataFile”)
B = as.frame(A)
write(B, “outputFrameDataFile”, format=”binary”)
as.frame(<scalar>) Scalar is cast to 1x1 frame. Input: (<scalar>)
Output: <frame>
A = read(“inputScalarData”, data_type=”scalar”, value_type=”string”)
B = as.frame(A)
write(B, “outputFrameData”)
as.matrix(<frame>) Frame is cast to matrix. Input: (<frame>)
Output: <matrix>
B = read(“inputFrameDataFile”)
C = as.matrix(B)
write(C, “outputMatrixDataFile”, format=”binary”)
as.scalar(<frame>) 1x1 Frame is cast to scalar. Input: (<frame>)
Output: <scalar>
B = read(“inputFrameData”, data_type=”frame”, schema=”string”, rows=1, cols=1)
C = as.scalar(B)
write(C, “outputScalarData”)

Note: as.frame(matrix) produces a double schema, and as.scalar(frame) produces of scalar of value type given by the frame schema.

Transforming Frames

Frames support additional Data Pre-Processing Built-In Functions as shown below.

Function Description Parameters Example
transformencode() Transforms a frame into a matrix using specification.
Builds and applies frame metadata.
Input:
target = <frame>
spec = <json specification>
Outputs: <matrix>, <frame>
transformencode
transformdecode() Transforms a matrix into a frame using specification.
Valid only for specific transformation types.
Input:
target = <matrix>
spec = <json specification>
meta = <frame>
Output: <frame>
transformdecode
transformapply() Transforms a frame into a matrix using specification.
Applies existing frame metadata.
Input:
target = <frame>
spec = <json specification>
meta = <frame>
Output: <matrix>
transformapply
transformcolmap() Obtains the column mapping of a transformed frame using the given specification. The input frame is assumed to be the meta data frame returned from a transformencode call.
The output has a row per encoded input attribute, indicating the source column position, as well as the start and end positions in the encode output.
Input:
target = <frame>
spec = <json specification>
Output: <matrix>
transformcolmap

The following table summarizes the supported transformations for transformencode(), transformdecode(), transformapply(). Note only recoding, dummy coding and pass-through are reversible, i.e., subject to transformdecode(), whereas binning, missing value imputation, and omit are not.

Table F3: Frame data transformation types.

  encode decode apply
RCD * * *
DCD * * *
BIN * x *
MVI * x *
OMIT * x *
Key Meaning
RCDRecoding
DCDDummycoding
BINBinning
MVIMissing value handling by imputation
OMITMissing value handling by omitting
Key Meaning
*Supported
xNot supported



The following examples use homes.csv data set.

Table F4: The homes.csv data set

zipcode district sqft numbedrooms numbathrooms floors view saleprice askingprice
95141 west 1373 7 1 3 FALSE 695 698
91312 south 3261 6 2 2 FALSE 902 906
94555 north 1835 3 3 3 TRUE 888 892
95141 east 2833 6 2.5 2 TRUE 927 932
96334 south 2742 6 2.5 2 FALSE 872 876
96334 north 2195 5 2.5 2 FALSE 799 803
98755 north 3469 7 2.5 2 FALSE 958 963
96334 west 1685 7 1.5 2 TRUE 757 760
95141 west 2238 4 3 3 FALSE 894 899
91312 west 1245 4 1 1 FALSE 547 549
98755 south 3702 7 3 1 FALSE 959 964
98755 north 1865 7 1 2 TRUE 742 745
94555 north 3837 3 1 1 FALSE 839 842
91312 west 2139 3 1 3 TRUE 820 824
95141 north 3824 4 3 1 FALSE 954 958
98755 east 2858 5 1.5 1 FALSE 759 762
91312 south 1827 7 3 1 FALSE 735 738
91312 south 3557 2 2.5 1 FALSE 888 892
91312 south 2553 2 2.5 2 TRUE 884 889
96334 west 1682 3 1.5 1 FALSE 625 628

The metadata file homes.csv.mtd looks as follows:

{
    "data_type": "frame",
    "format": "csv",
    "header": true,
}

transformencode

The transformencode() function takes a frame and outputs a matrix based on defined transformation specification. In addition, the corresponding metadata is output as a frame.

Note: the metadata output is simply a frame so all frame operations (including read/write) can also be applied to the metadata.

This example replaces values in specific columns to create a recoded matrix with associated frame identifying the mapping between original and substituted values. An example transformation specification file homes.tfspec_recode2.json is given below:

{
     "recode": [ "zipcode", "district", "view" ]
}

The following DML utilizes the transformencode() function.

F1 = read("/user/ml/homes.csv", data_type="frame", format="csv");
jspec = read("/user/ml/homes.tfspec_recode2.json", data_type="scalar", value_type="string");
[X, M] = transformencode(target=F1, spec=jspec);
print(toString(X));
while(FALSE){}
print(toString(M));

The transformed matrix X and output M are as follows.

1.000 1.000 1373.000 7.000 1.000 3.000 1.000 695.000 698.000
2.000 2.000 3261.000 6.000 2.000 2.000 1.000 902.000 906.000
3.000 3.000 1835.000 3.000 3.000 3.000 2.000 888.000 892.000
1.000 4.000 2833.000 6.000 2.500 2.000 2.000 927.000 932.000
4.000 2.000 2742.000 6.000 2.500 2.000 1.000 872.000 876.000
4.000 3.000 2195.000 5.000 2.500 2.000 1.000 799.000 803.000
5.000 3.000 3469.000 7.000 2.500 2.000 1.000 958.000 963.000
4.000 1.000 1685.000 7.000 1.500 2.000 2.000 757.000 760.000
1.000 1.000 2238.000 4.000 3.000 3.000 1.000 894.000 899.000
2.000 1.000 1245.000 4.000 1.000 1.000 1.000 547.000 549.000
5.000 2.000 3702.000 7.000 3.000 1.000 1.000 959.000 964.000
5.000 3.000 1865.000 7.000 1.000 2.000 2.000 742.000 745.000
3.000 3.000 3837.000 3.000 1.000 1.000 1.000 839.000 842.000
2.000 1.000 2139.000 3.000 1.000 3.000 2.000 820.000 824.000
1.000 3.000 3824.000 4.000 3.000 1.000 1.000 954.000 958.000
5.000 4.000 2858.000 5.000 1.500 1.000 1.000 759.000 762.000
2.000 2.000 1827.000 7.000 3.000 1.000 1.000 735.000 738.000
2.000 2.000 3557.000 2.000 2.500 1.000 1.000 888.000 892.000
2.000 2.000 2553.000 2.000 2.500 2.000 2.000 884.000 889.000
4.000 1.000 1682.000 3.000 1.500 1.000 1.000 625.000 628.000


# FRAME: nrow = 5, ncol = 9
# zipcode district sqft numbedrooms numbathrooms floors view saleprice askingprice
# STRING STRING STRING STRING STRING STRING STRING STRING STRING
96334·4 south·2 FALSE·1
95141·1 east·4 TRUE·2
98755·5 north·3
94555·3 west·1
91312·2


As mentioned in Creating Frames, the header line in frame CSV files is sensitive to white space. The tabs below show compatible transform specifications for the given CSV header. Note the extra (possibly inadvertent) space before the district column in CSV2 impacts the transform specification. More specifically, transform spec1 does not match the header in CSV2. To match, either remove the extra space before district in CSV2 or use spec2 which quotes the district token name to include the extra space.

zipcode,district,sqft,numbedrooms,numbathrooms,floors,view,saleprice,askingprice
95141,west,1373,7,1,3,FALSE,695,698
91312,south,3261,6,2,2,FALSE,902,906
zipcode, district,sqft,numbedrooms,numbathrooms,floors,view,saleprice,askingprice
95141,west,1373,7,1,3,FALSE,695,698
91312,south,3261,6,2,2,FALSE,902,906
{
     ids:false, recode: [ zipcode, district, view ]
}
{
     ids:false, recode: [ zipcode, " district", view ]
}
{
    "data_type": "frame",
    "format": "csv",
    "header": true
}


transformdecode

The transformdecode() function can be used to transform a matrix back into a frame. Only recoding, dummy coding and pass-through transformations are reversible and can be used with transformdecode(). The transformations binning, missing value imputation, and omit are not reversible and cannot be used with transformdecode().

The next example takes the outputs from the transformencode example and reconstructs the original data using the same transformation specification.

F1 = read("/user/ml/homes.csv", data_type="frame", format="csv");
jspec = read("/user/ml/homes.tfspec_recode2.json", data_type="scalar", value_type="string");
[X, M] = transformencode(target=F1, spec=jspec);
F2 = transformdecode(target=X, spec=jspec, meta=M);
print(toString(F2));

# FRAME: nrow = 20, ncol = 9
# C1 C2 C3 C4 C5 C6 C7 C8 C9
# STRING STRING DOUBLE DOUBLE DOUBLE DOUBLE STRING DOUBLE DOUBLE
95141 west  1373.000 7.000 1.000 3.000 FALSE 695.000 698.000
91312 south 3261.000 6.000 2.000 2.000 FALSE 902.000 906.000
94555 north 1835.000 3.000 3.000 3.000 TRUE  888.000 892.000
95141 east  2833.000 6.000 2.500 2.000 TRUE  927.000 932.000
96334 south 2742.000 6.000 2.500 2.000 FALSE 872.000 876.000
96334 north 2195.000 5.000 2.500 2.000 FALSE 799.000 803.000
98755 north 3469.000 7.000 2.500 2.000 FALSE 958.000 963.000
96334 west  1685.000 7.000 1.500 2.000 TRUE  757.000 760.000
95141 west  2238.000 4.000 3.000 3.000 FALSE 894.000 899.000
91312 west  1245.000 4.000 1.000 1.000 FALSE 547.000 549.000
98755 south 3702.000 7.000 3.000 1.000 FALSE 959.000 964.000
98755 north 1865.000 7.000 1.000 2.000 TRUE  742.000 745.000
94555 north 3837.000 3.000 1.000 1.000 FALSE 839.000 842.000
91312 west  2139.000 3.000 1.000 3.000 TRUE  820.000 824.000
95141 north 3824.000 4.000 3.000 1.000 FALSE 954.000 958.000
98755 east  2858.000 5.000 1.500 1.000 FALSE 759.000 762.000
91312 south 1827.000 7.000 3.000 1.000 FALSE 735.000 738.000
91312 south 3557.000 2.000 2.500 1.000 FALSE 888.000 892.000
91312 south 2553.000 2.000 2.500 2.000 TRUE  884.000 889.000
96334 west  1682.000 3.000 1.500 1.000 FALSE 625.000 628.000

transformapply

In contrast to transformencode(), which creates and applies frame metadata (transformencode := build+apply), transformapply() applies existing metadata (transformapply := apply).

The following example uses transformapply() with the input matrix and second output (i.e., existing frame metadata built with transformencode()) from the transformencode example for the homes.tfspec_bin2.json transformation specification.

{
 "recode": [ zipcode, "district", "view" ], "bin": [
 { "name": "saleprice"  , "method": "equi-width", "numbins": 3 }
 ,{ "name": "sqft", "method": "equi-width", "numbins": 4 }]
}

F1 = read("/user/ml/homes.csv", data_type="frame", format="csv");
jspec = read("/user/ml/homes.tfspec_bin2.json", data_type="scalar", value_type="string");
[X, M] = transformencode(target=F1, spec=jspec);
X2 = transformapply(target=F1, spec=jspec, meta=M);
print(toString(X2));

1.000 1.000 1.000 7.000 1.000 3.000 1.000 1.000 698.000
2.000 2.000 1.000 6.000 2.000 2.000 1.000 1.000 906.000
3.000 3.000 1.000 3.000 3.000 3.000 2.000 1.000 892.000
1.000 4.000 1.000 6.000 2.500 2.000 2.000 1.000 932.000
4.000 2.000 1.000 6.000 2.500 2.000 1.000 1.000 876.000
4.000 3.000 1.000 5.000 2.500 2.000 1.000 1.000 803.000
5.000 3.000 1.000 7.000 2.500 2.000 1.000 1.000 963.000
4.000 1.000 1.000 7.000 1.500 2.000 2.000 1.000 760.000
1.000 1.000 1.000 4.000 3.000 3.000 1.000 1.000 899.000
2.000 1.000 1.000 4.000 1.000 1.000 1.000 1.000 549.000
5.000 2.000 1.000 7.000 3.000 1.000 1.000 1.000 964.000
5.000 3.000 1.000 7.000 1.000 2.000 2.000 1.000 745.000
3.000 3.000 1.000 3.000 1.000 1.000 1.000 1.000 842.000
2.000 1.000 1.000 3.000 1.000 3.000 2.000 1.000 824.000
1.000 3.000 1.000 4.000 3.000 1.000 1.000 1.000 958.000
5.000 4.000 1.000 5.000 1.500 1.000 1.000 1.000 762.000
2.000 2.000 1.000 7.000 3.000 1.000 1.000 1.000 738.000
2.000 2.000 1.000 2.000 2.500 1.000 1.000 1.000 892.000
2.000 2.000 1.000 2.000 2.500 2.000 2.000 1.000 889.000
4.000 1.000 1.000 3.000 1.500 1.000 1.000 1.000 628.000

Modules

A module is a collection of UDF declarations. For calling a module, source(…) and setwd(…) are used to read and use a source file.

Syntax

setwd(<file-path>);
source(<DML-filename>) as <namespace-name>;

It is important to note that:

  1. setwd(…) and source(…) do not support $-parameters. 
  2. Nested namespaces are not supported.
  3. Namespace are required for source(…).
  4. Only UDFs are imported, not the statements.
  5. Path for input/output files is not affected by setwd.
  6. setwd is applicable only for local filesystem not HDFS.
  7. Spaces are not allowed between namespace and function name during call. For example: ns1::foo(…) is correct way to call the function.
  8. Like R, the path of source() is relative to where the calling java program is running.

Example

Assume the file a.dml contains:

#source("/home/ml/spark_test/b.dml") as ns1 # will work
#source("b.dml") as ns1 # will work
#source("./b.dml") as ns1 # will work
source("hdfs:/user/ml/nike/b.dml") as ns1
f1 = function() {
    print("From a.dml's function()");
}
setwd("dir1")
source("c.dml") as ns2
tmp = ns2::f();
tmp1 = ns1::f();
tmp = f1();

The file b.dml contains:

f = function() {
    print("From b.dml's function()");
}

The file c.dml contains:

f = function() {
    print("From c.dml's function()");
}

The output after running a.dml is as follows:

From c.dml's function()
From b.dml's function()
From a.dml's function()

Reserved Keywords

Reserved keywords cannot be used as variable names.

All reserved keywords are case-sensitive.

as
boolean
Boolean
double
Double
else
externalFunction
for
function
FALSE
if
ifdef
implemented
in
int
integer
Int
Integer
parfor
return
setwd
source
string
String
TRUE
while