SystemML compiles scripts written in Declarative Machine Learning (or DML for short) into MapReduce 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 Hadoop is installed on your machine or cluster, place SystemML.jar and SystemML-config.xml 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:
hadoop jar SystemML.jar –f hello.dml
The option -f in the above command refers to the path to the DML script. The detailed list of the options is given in the section “Invocation of SystemML”.
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’.
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.
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, This data type currently supports a single operation, transform(), which transforms the given tabular data with arbitrary value types into a matrix of doubles. 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.
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.
# this is an example of a line comment /* this is an example of a multi-line block comment */
Now that we have familiarized ourselves with variables and data type, let’s understand how to use them in expressions.
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) | Scalar2 (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
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.
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.
Input_Matrix operation Input_Vector
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
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)).
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]
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
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
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.
# max_iteration is of type integer max_iteration = 3; # V has data type matrix and value type double. V = W %*% H;
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.
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;
}
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.
# 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;
}
}
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.
[lower]:[upper] defines a sequence of numbers with increment 1: {lower, lower + 1, lower + 2, …, upper – 1, upper}.
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 for statement
A = 5;
for (i in 1:20) {
A = A + 1;
}
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>
<dependency_analysis> is one of the following tokens: 0 1
<degree_of_parallelism> is an arbitrary integer number
<execution_mode> is one of the following tokens: LOCAL REMOTE_MR
<task_partitioning_algorithm> is one of the following tokens: FIXED NAIVE STATIC FACTORING FACTORING_CMIN FACTORING_CMAX
<task_size> is an arbitrary integer number
<data_partitioning_mode> is one of the following tokens: NONE LOCAL REMOTE_MR
<result_merge_mode> is one of the following tokens: LOCAL_MEM LOCAL_FILE LOCAL_AUTOMATIC REMOTE_MR
<optimization_mode> is one of the following tokens: NONE CONSTRAINED RULEBASED HEURISTIC GREEDY FULL_DP
If any of these parameters is not specified, the following respective defaults are used: check = 1, par = [number of virtual processors on master node], mode = LOCAL, taskpartitioner = FIXED, tasksize = 1, datapartitioner = NONE, resultmerge = LOCAL_AUTOMATIC, opt = RULEBASED.
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 parallizable. The iterations incorrectly try to increment the same sum variable.
sum = 0
parfor(i in 1:3) {
sum = sum + i; # not parallizable - 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 parallizable 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) { # parallizable - 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 parallizable, 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) { # parallizable
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:
parfor() with for(). Since parfor is derived from for, you can always use for wherever you can use parfor.parfor(opt = NONE, par = 1, ...). This disables optimization, uses defaults, and overwrites the specified parameters.parfor(opt = CONSTRAINED, par = 1, ...). This optimizes using the specified parameters.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 2: 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 |
# 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
eigen = externalFunction(matrix[double] A)
return (matrix[double] evec, matrix[double] eval)
implemented in (classname="org.apache.sysml.packagesupport.JLapackEigenWrapper")
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, ….)
# 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
}
DML supports following two types of scoping:
Note: The command-line parameters are treated as constants which are introduced during parse-time.
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;
}
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
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:
As named arguments (recommended):
-nvargs param1=7 param2="abc" param3=3.14
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: $nbrRows). To do so, we use the ifdef function which assigns either command line parameter or the default value to the local parameter.
local_variable = ifdef(command line variable, default value)
localVar_nbrRows=ifdef($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:
hadoop jar 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:
hadoop jar 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 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.
Table 3: Matrix Construction, Manipulation, and Aggregation Built-In Functions
| Function | Description | Parameters | Example |
|---|---|---|---|
| append() | Adds the second argument as additional columns to the first argument (note that the first argument is not over-written). Append is meant to be used in situations where one cannot use left-indexing. NOTE: append() has been replaced by cbind(), so its use is discouraged. | Input: (X <matrix>, Y <matrix>) Output: <matrix> X and Y are matrices (with possibly multiple columns), where the number of rows in X and Y must be the same. Output is a matrix with exactly the same number of rows as X and Y. Let n1 and n2 denote the number of columns of matrix X and Y, respectively. The returned matrix has n1+n2 columns, where the first n1 columns contain X and the last n2 columns contain Y. | A = matrix(1, rows=2,cols=5) B = matrix(1, rows=2,cols=3) C = append(A,B) print("Dimensions of C: " + nrow(C) + " X " + ncol(C)) The output of above example is: Dimensions of C: 2 X 8 |
| 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 respectively. | Input: matrix Output: scalar | nrow(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. | Input : (target= X <matrix>, margin=“...”) Output : <matrix> Valid values for margin are “rows” or “cols”. | A = removeEmpty(target=X, margin=“rows”) |
| 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) |
Table 4: 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. | Input: (<matrix>, <matrix>, <string with relational operator>), or (<matrix>, <scalar>, <string with relational operator>) Output: matrix | ppred(X,Y,“<”) ppred(X,y,“<”) |
Table 5: 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) |
Table 6: 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 | 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 6. | 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 6.) |
| 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 6. | 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 6. |
| 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 6. | 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 6.) |
| 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]] |
The built-in function table() supports different types of input parameters. These variations are described below:
F=table(A,B) As described above in Table 6.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).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);F = table(A,B,odim1,odim2); 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.The built-in function aggregate() supports different types of input parameters. These variations are described below:
F=aggregate(target=X, groups=G, fn="sum") As described above in Table 6.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.ngroups, as shown below: F = aggregate(target=X, groups=G, fn="sum", ngroups=10); 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.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 distributiondist="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.dist="f", valid parameters are df1 and df2 that specify two degrees of freedom. Both these parameters are mandatory.dist="t", and dist=“chisq”, valid parameter is df that specifies the degrees of freedom. This parameter is mandatory.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);
Table 7: Mathematical and Trigonometric Built-In Functions
| Function | Description | Parameters | Example |
|---|---|---|---|
| exp(), log(), abs(), sqrt(), round(), floor(), ceil() | 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) |
| sin(), cos(), tan(), 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]] |
Table 8: 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) or (1 x n) matrix, or take diagonal from square matrix | Input: (n x 1) or (1 x n) matrix, or (n x n) matrix Output: (n x n) matrix, or (n x 1) matrix | diag(X) |
| 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) |
| 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) |
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.
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 Table 9, we have a matrix consisting of 4 rows and 3 columns.
Table 9: Matrix
Below, we have examples of this matrix in the CSV, Matrix Market, IJV, and Binary formats, along with corresponding metadata.
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",
"description": { "author": "SystemML" }
}
Metadata is represented as an MTD file that contains a single JSON object with the attributes described below.
Table 10: 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 |
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 11: 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.
sep).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=",").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.
read() either fill in values or override defaults..mtd).# 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.
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 12. 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 12: 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 10 and 11 |
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",
"description": { "author": "SystemML" }
}
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",
"description": { "author": "SystemML" }
}
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": ";",
"description": { "author": "SystemML" }
}
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",
"description": { "author": "SystemML" }
}
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 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:
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.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.age values can be discretized into a small number of age intervals. The only method that is currently supported is equi-width binning.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.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 13**: 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 14: 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.
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
...
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.
Table 15: 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 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 in sparse format, i.e. RowIndex ColIndex Value “sep” and “linesep” : inter-element separator and the line separator strings | Input : (<matrix>, 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=" | ") |
| print() | Prints the value of a scalar variable x. This built-in takes an optional string parameter. | Input: (<scalar>) | print(“hello”) print(“hello” + “world”) print("value of x is " + x ) |
| 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”) |
| 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) |
A module is a collection of UDF declarations. For calling a module, source(...) and setwd(...) are used to read and use a source file.
setwd(<file-path>); source(<DML-filename>) as <namespace-name>;
It is important to note that:
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 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
To execute a DML script, SystemML is invoked as follows:
hadoop jar SystemML.jar [-? | -help | -f] <filename> (-config=<config_filename>)? (-args | -nvargs)? <args-list>?
Where
-f <filename>: will be interpreted as a path to file with DML script. <filename> prefixed with hdfs or gpfs is assumed path in DFS, otherwise <filename> treated as path on local file system
-debug: (optional) run in debug mode
-config=<config_filename>: (optional) use config file located at specified path <config_filename>. <config_filename> prefixed with hdfs or gpfs is assumed path in DFS, otherwise <config_filename> treated as path on local file system (default value for <config_filename> is ./SystemML-config.xml)
-args <args-list>: (optional) parameterize DML script with contents of <args-list>, which is ALL args after -args flag. Each argument must be an unnamed-argument, where 1st value after -args will replace \$1 in DML script, 2nd value will replace \$2 in DML script, and so on.
-nvargs <args-list>: (optional) parameterize DML script with contents of <args-list>, which is ALL args after -nvargs flag. Each argument must be named-argument of form name=value, where value will replace \$name in DML script.
-?, or -help: show this help.
NOTE: Please refer to section on Command-line Arguments for more details and restrictions on usage of command-line arguments to DML script using –args <args-list> and –nvargs <args-list>.
Run a script in local file foo.dml:
hadoop jar SystemML.jar -f foo.dml
An example debug session:
First, you need to call SystemML using –debug flag.
hadoop jar SystemML.jar -f test.dml –debug
You can see the line numbers in your DML script by “list” (or simply “l”) command:
(SystemMLdb) l
line 1: A = matrix("1 2 3 4 5 6", rows=3, cols=2)
line 2:
line 3: B = cumsum(A)
line 4: #print(B)
line 5: print(sum(B))
The next step is usually to set a breakpoint where we need to analyze the state of our variables:
(SystemMLdb) b 5
Breakpoint added at .defaultNS::main, line 5.
Now, that we have set a breakpoint, we can start running our DML script:
(SystemMLdb) r Breakpoint reached at .defaultNS::main instID 15: (line 5). (SystemMLdb) p B 1.0000 2.0000 4.0000 6.0000 9.0000 12.0000
The MLContext API allows users to pass RDDs as input/output to SystemML through Java, Scala, or Python.
Typical usage for MLContext using Spark's Scala Shell is as follows:
scala> import org.apache.sysml.api.MLContext
Create input DataFrame from CSV file and potentially perform some feature transformation
scala> val W = sqlContext.load(...)
scala> val H = sc.textFile("V.csv")
scala> val V = sc.textFile("V.text")
Create MLContext
scala> val ml = new MLContext(sc)
Register input and output DataFrame/RDD
Supported formats are:
Also overloaded to support metadata information such as format, rlen, clen, etc.
Please note the variable names given below in quotes correspond to the variables in DML script.
These variables need to have corresponding read/write associated in DML script.
Currently, only matrix variables are supported through registerInput/registerOutput interface.
To pass scalar variables, use named/positional arguments (described later) or wrap them into matrix variable.
scala> ml.registerInput("V", V)
scala> ml.registerInput("W", W, "csv")
scala> ml.registerInput("H", H, "text", 50, 1500)
scala> ml.registerOutput("H")
scala> ml.registerOutput("W")
As DataFrame is internally converted to CSV format, one can skip providing dimensions.
Call script with default arguments:
scala> val outputs = ml.execute("GNMF.dml")
MLContext also supports calling script with positional arguments (args) and named arguments (nargs):
scala> val args = Array("V.mtx", "W.mtx", "H.mtx", "2000", "1500", "50", "1", "WOut.mtx", "HOut.mtx")
scala> val nargs = Map("maxIter"->"1")
scala> val outputs = ml.execute("GNMF.dml", args) # or ml.execute("GNMF.dml", nargs)
We can then fetch the output RDDs in SystemML’s binary blocked format or as DataFrame.
scala> val HOut = outputs.getDF(sqlContext, "H") scala> val WOut = outputs. getBinaryBlockedRDD(sqlContext, "W")
To register new input/outputs and to re-execute the script, it is recommended that you first reset MLContext
scala> ml.reset()
scala> ml.registerInput("V", newV)
Though it is possible to re-run the script using different (or even same arguments), but using same registered input/outputs without reset, it is discouraged. This is because the symbol table entries would have been updated since last invocation:
scala> val new_outputs = ml.execute("GNMF.dml", new_args)
The Python MLContext API is similar to Scala/Java MLContext API. Here is an example:
>>> from pyspark.sql import SQLContext
>>> from SystemML import MLContext
>>> sqlContext = SQLContext(sc)
>>> H = sqlContext.jsonFile("H.json")
>>> V = sqlContext.jsonFile("V.json")
>>> W = sqlContext.jsonFile("W.json")
>>> ml = MLContext(sc)
>>> ml.registerInput("V", V)
>>> ml.registerInput("W", W)
>>> ml.registerInput("H", H)
>>> ml.registerOutput("H")
>>> ml.registerOutput("W")
>>> outputs = ml.execute("GNMF.dml")
Note: