DML Language Reference

Table of Contents

• Introduction
• Variables
  • Identifier Names
  • Data Types
  • Comments
• Expressions
  • Operators
  • Matrix-Vector Operations
  • Matrix Indexing
• Statements
  • Assignment Statement
  • Control Statements
    • While Statement
    • If Statement
    • For Statement
    • ParFor Statement
  • User-Defined Function (UDF)
• Variable Scoping
• Command-Line Arguments
• Built-in Functions
  • Matrix Construction, Manipulation, and Aggregation Built-In Functions
  • Matrix and/or Scalar Comparison Built-In Functions
  • Casting Built-In Functions
  • Statistical Built-In Functions
  • Mathematical and Trigonometric Built-In Functions
  • Linear Algebra Built-In Functions
  • Read/Write Built-In Functions
  • Data Pre-Processing Built-In Functions
  • Deep Learning Built-In Functions
  • Parameter Server Built-In Function
  • Other Built-In Functions
• Frames
  • Creating Frames
  • Appending Frames
  • Indexing Frames
  • Casting Frames
  • Transforming Frames
  • Processing Frames
• Modules
• Reserved Keywords

Introduction

SystemDS 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 SystemDS. 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 SystemDS.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 SystemDS.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 SystemDS.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. SystemDS 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

SystemDS 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

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,
• control structures (while, if, for), and
• user-defined function declaration.

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_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_SPARK
<result_merge_mode>           LOCAL_MEM LOCAL_FILE LOCAL_AUTOMATIC 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

Of particular note is the check parameter. SystemDS’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)

SystemDS’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 SystemDS 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

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.sysds.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 SystemDS.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 SystemDS.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:

• Matrix Construction, Manipulation, and Aggregation Built-In Functions
• Matrix and/or Scalar Comparison Built-In Functions
• Casting Built-In Functions
• Statistical Built-In Functions
• Mathematical and Trigonometric Built-In Functions
• Linear Algebra Built-In Functions
• Other Built-In Functions

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

Matrix and/or Scalar Comparison Built-In Functions

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

Casting Built-In Functions

Table 6: Casting Built-In Functions

Statistical Built-In Functions

Table 7: Statistical Built-In Functions

Alternative forms of table()

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

• Basic form: F=table(A,B) As described above in Table 7.
• Weighted form: F=table(A,B,W) Users can provide an optional third parameter C with the same dimensions as of A and B. In this case, the output F[i,j] = ∑kC[k], where A[k] = i and B[k] = j (1 ≤ k ≤ n).
• Scalar form In basic and weighted forms, both B and W are one dimensional matrices with same number of rows/columns as in A. Instead, one can also pass-in scalar values in the place of B and W. For example, F=table(A,1) is same as the basic form where B is a matrix with all 1’s. Similarly, F=table(A,B,3) is identical to the following two DML statements.
  m3 = matrix(3,rows=nrow(A),cols=1);
F = table(A,B,m3);
• Specified Output Size In the above forms, the dimensions of the matrix produced this function is known only after its execution is complete. Users can precisely control the size of the output matrix via two additional arguments, odim1 and odim2, as shown below:
  F = table(A,B,odim1,odim2);
  The output F will have exactly odim1 rows and odim2 columns. F may be a truncated or padded (with zeros) version of the output produced by table(A,B) – depending on the values of max(A) and max(B). For example, if max(A) < odim1 then the last (odim1-max(A)) rows will have zeros.

Alternative forms of aggregate()

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

• Basic form: F=aggregate(target=X, groups=G, fn="sum") As described above in Table 7.
• Weighted form: F=aggregate(target=X, groups=G, weights=W, fn="sum") Users can provide an optional parameter W with the same dimensions as of A and B. In this case, fn computes the weighted statistics over values from X, which are grouped by values from G.
• Specified Output Size As noted in Table 7, the number of rows in the output matrix F is equal to the maximum value in the grouping matrix G. Therefore, the dimensions of F are known only after its execution is complete. When needed, users can precisely control the size of the output matrix via an additional argument, ngroups, as shown below:
  F = aggregate(target=X, groups=G, fn="sum", ngroups=10);
  The output F will have exactly 10 rows and 1 column. F may be a truncated or padded (with zeros) version of the output produced by aggregate(target=X, groups=G, fn="sum") – depending on the values of ngroups and max(G). For example, if max(G) < ngroups then the last (ngroups-max(G)) rows will have zeros.

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.

• target: input quantile at which cumulative probability P[X<=q] is computed, where X is random variable whose distribution is specified via string argument fn. This is a mandatory argument.
• dist: name of the distribution specified as a string. Valid values are “normal” (for Normal or Gaussian distribution), “f” (for F distribution), “t” (for Student t-distribution), “chisq” (for Chi Squared distribution), and “exp” (for Exponential distribution). This is a mandatory argument.
• ...: parameters of the distribution
  • For dist="normal", valid parameters are mean and sd that specify the mean and standard deviation of the normal distribution. The default values for mean and sd are 0.0 and 1.0, respectively.
  • For dist="f", valid parameters are df1 and df2 that specify two degrees of freedom. Both these parameters are mandatory.
  • For dist="t", and dist=”chisq”, valid parameter is df that specifies the degrees of freedom. This parameter is mandatory.
  • For dist="exp", valid parameter is rate that specifies the rate at which events occur. Note that the mean of exponential distribution is 1.0/rate. The default value is 1.0.
• Lower.tail: a Boolean value with default set to TRUE. cdf() computes P[X<=q] when lower.tail=TRUE and it computes P[X>q] when lower.tail=FALSE. In other words, a complement of the cumulative distribution is computed when lower.tail=FALSE.

`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.

• target: a mandatory argument that specifies the input probability.
• dist: name of the distribution specified as a string. Same as that in cdf().
• ...: parameters of the distribution. Same as those in cdf().

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

Linear Algebra Built-In Functions

Table 9: Linear Algebra Built-In Functions

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 SystemDS, 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

SystemDS supports 4 file formats:

• CSV (delimited)
• Matrix Market (coordinate)
• Text (i,j,v)
• Binary
• HDF5

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.

SystemDS 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. SystemDS 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 SystemDS.

Hierarchical Data Format (HDF) is a file format designed to store and organize large amounts of data. SystemDS supports some features of the HDF5 like two dimension data (Matrix), matrix with FP64 (double) data type, single dataset, single group, and contiguous dataset.

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

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": "SystemDS",
    "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": "SystemDS",
    "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": "SystemDS",
    "created": "2017-01-01 00:00:01 PST"
}

HDF5 is not a text-based format.

{
    "data_type": "matrix",
    "value_type": "double",
    "rows": 4,
    "cols": 3,
    "nnz": 6,
    "dataset": "systemds",
    "format": "hdf5",
    "author": "SystemDS",
    "created": "2021-06-11 13:36:15 CET"
}

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": "SystemDS",
    "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

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

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

• Every line in the input file must have the same number of fields or values.
• The input file can only contain numeric values separated by the delimiter (as specified by sep).
• While writing CSV files, if header=TRUE is specified as a parameter to the write function, then the header line is formed as a concatenated string of column names separated by delimiters. Columns are of the form C<column_id>. For a matrix with 5 columns, the header line would look like: C1,C2,C3,C4,C5 (assuming sep=",").

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 SystemDS 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. SystemDS 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. SystemDS 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

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": "SystemDS",
    "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": "SystemDS",
    "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": "SystemDS",
    "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": "SystemDS",
    "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": "SystemDS",
    "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:

• Omitting: Given a list of columns, this transformation removes all rows which contain missing values for at least one of the specified columns.
• Missing Value Imputation: This replaces missing data in individual columns with valid values, depending on the specific imputation method. There are three supported imputation methods – global_mean that replaces a missing value in a numeric/scale column with the mean of all non-missing entries in the column; global_mode that replaces a missing value in a categorical column with the mode of all non-missing entries in the column; and constant that replaces missing values in a scale/categorical column with the specified constant.
• Recoding: This is applicable for categorical columns. It maps all distinct categories (potentially, strings and booleans) in the column into consecutive numbers, starting from 1. For example, a direction column with four distinct values (east, west, north, south) into a column with four numeric values 1.0, 2.0, 3.0, and 4.0.
• Binning: This procedure is used to group a number of continuous values (i.e., discretize) into a small number of bins. For example, a column with age values can be discretized into a small number of age intervals. The only method that is currently supported is equi-width binning.
• Dummycoding: This procedure transforms a categorical column into multiple columns of zeros and ones, which collectively capture the full information about the categorical variable. The number of resulting columns is equal to the number of distinct values in the input column. In the example of the direction variable mentioned above, this procedure replaces the original column with four new columns with zeros and ones – direction_east, direction_west, direction_north, and direction_south.
• Scaling: This centers and/or scales the values in a given numeric/continuous column. The two supported methods are mean-subtraction that centers each value by subtracting the mean, and z-score that scales mean subtracted values by dividing them with the respective column-wise standard deviation.

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.

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

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

SystemDS 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).

Note: the builtin functions batch_norm2d and batch_norm2d_backward are deprecated and will be removed in the next release. The lstm builtin function is in experimental phase and is only supported for the GPU backend.

Examples:

Function	Parameters	Visualization / Equivalent DML
conv2d	stride=[1,1]
conv2d	stride=[2,2]
conv2d_backward_data	stride=[1,1]
conv2d_backward_data	stride=[2,2]
conv2d_backward_data	stride=[2,2] and 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)

Parameter Server Built-in Function

Apart from data-parallel operations and task-parallel parfor loops, SystemDS also supports a data-parallel Parameter Server via a built-in function paramserv. Currently both local multi-threaded and spark distributed backend are supported to execute the paramserv function. So far we only support a single parameter server with N workers as well as synchronous and asynchronous model updates per batch or epoch. For example, in order to train a model in local backend with update strategy BSP, 10 epochs, 64 batchsize, 10 workers, paramserv function should look like this:

resultModel=paramserv(model=initModel, features=X, labels=Y, 
                      upd="fun1", agg="fun2", epochs=10, k=10, hyperparams=hParams)

Table: Inputs of paramserv function

Table: Output of paramserv function

Update function:

The update function calculates the gradients for a single mini-batch and the given model (e.g., via a forward and backward pass through a neural network). The implementation of this function should be based on a function signature like this: (i.e., the input parameter including both type and name should be exactly the same as the below, except that the output name could be different)

gradients = function(list[unknown] model, list[unknown] hyperparams,
                     matrix[double] features, matrix[double] labels)
          return (list[unknown] gradients)
          # the output name can be something else than "gradients" but should always return a list

Aggregate function:

The aggregate function then takes the computed or accrued gradients and updates the model via some optimizer such as Adagrad or Adam. The implementation of this function should be based on a function signature like this: (i.e., the input parameter including both type and name should be exactly the same as the below, except that the output name could be different)

aggregation = function(list[unknown] model, list[unknown] hyperparams,
                       list[unknown] gradients)
         return (list[unknown] modelResult)
         # the output name can be something else than "modelResult" but should always return a list

Update strategy:

Currently, two types of update strategy, ASP and BSP, are supported. ASP, a.k.a. Asynchronous Parallel, means that the model updates will be completed in an asynchronous manner. The parameter server updates the model and broadcasts the updated model immediately with the fresh gradients pushed by the worker and then the worker is able to pull the new updated model. This push-and-pull process is done asynchronously across workers. While BSP, a.k.a. Bulk Synchronous Parallel, the server will update the global model until having received all the gradients sent by workers in one iteration and then workers could move into the next iteration. Hence, the overall performance is affected by stragglers (i.e., the slowest worker).

Update frequency:

When pushing the gradients from workers to server for updating the model, we could determine how often this push-and-pull process will be done. Currently, two types of update frequency, EPOCH and BATCH are supported. When setting to EPOCH, the generated gradients of each mini-batch are accumulated locally in each worker. The accrued gradients are then pushed to the server whenever a worker finished an epoch. While setting to BATCH, the generated gradients of each mini-batch are pushed to server immediately to launch the push-and-pull process.

Data partition schemes:

Before launching the data-parallel parameter server, the original data will be partitioned across workers according to some schemes. Currently, four types of schemes are supported, Disjoint_Contigous, Disjoint_Round_Robin, Disjoint_Random, Overlap_Reshuffle.

Other Built-In Functions

Table 16: Other Built-In Functions

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

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

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.

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.

The following examples use homes.csv data set.

Table F4: The homes.csv data set

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

Processing Frames

Table F5: Frame processing built-in functions

map

The built-in function map() provides support for the lambda expressions.

Simple example

X = read("file1", data_type="frame", rows=2, cols=3, format="binary") <br/> y = "lambda expression" <br/> Z = map(X, y) <br/> # Dimensions of Z = Dimensions of X; <br/> example: <br/> <code> Z = map(X, "x -> x.charAt(2)")     </code>

Example with data let X =

# FRAME: nrow = 10, ncol = 1
# C1 
# STRING 
  west
  south
  north
  east
  south
  north
  north
  west
  west
  east

Z = map(X, "x -> x.toUpperCase()")
print(toString(Z))

# FRAME: nrow = 10, ncol = 1 
# C1 
# STRING 
  WEST
  SOUTH
  NORTH
  EAST
  SOUTH
  NORTH
  NORTH
  WEST
  WEST
  EAST

It is also possible to compute Jaccard similarity matrix of rows of a vector. dist = map(Xi, "(x, y) -> UtilFunctions.jaccardSim(x, y)")
print(toString(dist))

# FRAME: nrow = 10, ncol = 10 
# DOUBLE 
# 0,000 0,286 0,125 0,600 0,286 0,125 0,125 1,000 1,000 0,600 
  0,286 0,000 0,429 0,286 1,000 0,429 0,429 0,286 0,286 0,286 
  0,125 0,429 0,000 0,125 0,429 1,000 1,000 0,125 0,125 0,125 
  0,600 0,286 0,125 0,000 0,286 0,125 0,125 0,600 0,600 1,000 
  0,286 1,000 0,429 0,286 0,000 0,429 0,429 0,286 0,286 0,286 
  0,125 0,429 1,000 0,125 0,429 0,000 1,000 0,125 0,125 0,125 
  0,125 0,429 1,000 0,125 0,429 1,000 0,000 0,125 0,125 0,125 
  1,000 0,286 0,125 0,600 0,286 0,125 0,125 0,000 1,000 0,600 
  1,000 0,286 0,125 0,600 0,286 0,125 0,125 1,000 0,000 0,600 
  0,600 0,286 0,125 1,000 0,286 0,125 0,125 0,600 0,600 0,000
#

tokenize

Simple example

X = read(“file1”, data_type=”frame”, rows=3, cols=2, format=”binary”);
spec = "{\"algo\": \"whitespace\",\"out\": \"count\",\"id_cols\": [1],\"tokenize_col\": 2}";
Y = tokenize(target=X, spec=jspec, max_tokens=1000);
write(Y, "file2");

Example spec

{
  "algo": "split",
  "out": "count",
  "id_cols": [1],
  "tokenize_col": 2
}

The frame is tokenized along the tokenize_col and replicates the id_cols.

The output frame can be converted into a matrix with the transform functions. For instance, using transformencode with recode, followed by table. Alternatively, for certain algorithms by specifying "format_wide": true expands the tokens in the columns instead of creating new rows.

Table F6: Tokenizer Algorithms for algo field

Table F7: Output Representations of Tokens for out field

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