Higher-Order Functions

Introduction

A template is a built-in higher order function, which can extend or enhance a function or an operator. A template takes a function and some objects as input. It works like a pipe between the function and its input data. In general, the input data is dissembled into multiple pieces (which may or may not overlap) in a preset way at first; then the individual pieces of data are applied to the given function to produce results one at a time; finally all individual results are assembled into one object to return. The input data for a template can be vectors, matrices or tables, with the occasional use of scalars and dictionaries. With a template, complicated analytical tasks can be accomplished very efficiently with only a few lines of statements.

Syntax

Templates are always used together with operators, user-defined functions, or system functions. All template symbols start with the symbol colon “:” followed by an upper-case single character.

templateFunctionName (<functionName>, functionParameter1, …functionParameterN)

or

<functionName> :<template symbol> functionParameter

or

functionParameter1 <functionName> :<template symbol> functionParameter2

In DolphinDB, the first parameter of all templates must be a function name. It cannot be a function name array. If we would like to run a template over multiple functions, we need to use the template call inside the template. Please refer to the section about the template call.

Template Summary

The summary table below shows template names and applications.

Symbol	Name	Applications	Examples
:E	each	unary operators, binary operators, function calls
	peach	parallel version of each
:R	eachRight	binary operators
:L	eachLeft	binary operators
:P	eachPre	binary operators, function calls
:O	eachPost	binary operators, function calls
	pivot	function calls	Transpose rows and columns of raw data or grouped aggregation results
:A	accumulate	binary operators, function calls
:T	reduce	binary operators, function calls
:G	groupby	binary operators, function calls
:C	cross	binary operators, function calls
	pcross	parallel version of cross
:M	moving	binary operators, function calls (aggregate function)
	loop	unary operators, binary operators, function calls, mixed return types
	ploop	parallel version of loop
	all	binary operators, function calls
	any	binary operators, function calls
	call	function calls	Usually used with function each to simultaneously call a batch of functions
	pcall	parallel version of call
:X	contextby	binary operators, function calls	Perform specified calculations in groups
	segmentby	binary operators, function calls
	rolling	binary operators, function calls	Calculate the beta value of APPL on the market (SPY)
	withNullFill	binary operators	Replace the Null value with a specific value in the calculation
	byRow	function calls	Calculate data in each row of a matrix

The adverbs listed above can be used iteratively.

The operations of each adverb are conducted in left-to-right order. Take X <operator> :E:L Y for example, the leftmost adverb :E is first applied to each element in X and Y (X(i) and Y(i)), and then the next adverb :L is used to apply the operator for each X(i). The result is returned after all adverbs are applied.

$ a=1 2 3
$ b=4 5 6
$ c=(a,b)
$ re=c +:E:L c
$ re
(1 2 3
- - -
2 3 4
3 4 5
4 5 6
,4  5  6
-- -- --
8  9  10
9  10 11
10 11 12
)

Rules to Dissemble and Assemble

In general, a vector is dissembled into scalars, a matrix into columns (vectors), a tuple into multiple elements (of different data forms), and a table into rows (represented by dictionaries).

In the assembly phase, the results of scalar type are merged to form a vector, vectors to a matrix, dictionaries to a table, and other data forms (which are inconsistent) into a tuple.

A template function iterates over a vector/tuple by elements, a matrix by columns, and a table by rows.