# Set, aggregte and loop operations

This chapter lists code examples of handling sets, aggregate operations and loop operation, including Judge if it is an interger sequence, Judge if it is an ascending integer sequence, Judge if it is a member or a subset of an integer sequence, Judge if members from two sequences are equal, Perform union, intersection and difference on sorted sequences by merge function, Calculate quadratic sum and variance, Calculate weighted average, Calculate average of an integer sequence after removing the max and the min, Calculate link relative ratio over adjacent rows, Calculate moving average over adjacent sets, Aggregate loop, Union record sequences with different data structures, Set operations, Get topN, Synced segmentation where max/mix value in a segment is used to represent a value, Caculate product of three sets’ Catesian products, and Get Fibonacci sequence.

## Judge if it is an integer sequence

 A 1 [1,2,3,4] 2 =A1.pselect(~!=int(~))==null Check if any member is not integer

## Judge if it is an ascending integer sequence

 A 1 [1,2,3,4,5] 2 =A1.pselect(~!=int(~) || ~<=~[-1] )==null

## Judge if it is a member or a subset of an integer sequence

 A 1 [1,2,3,4,5,6,7] 2 =A1.pos(2)!=null true for member 3 =A1.pos@c([2,3])!=null true for continuous subset 4 =A1.pos@c([3,2])!=null false 5 =A1.pos@c([2,5])!=null false 6 =A1.pos@i([2,3])!=null true for subset 7 =A1.pos@i([3,2])!=null false 8 =A1.pos@i([2,5])!=null true

## Judge if members from two sequences are equal

 A 1 [1,2,3] 2 [3,2,1] 3 =A1.eq(A2) true

## Perform union, intersection, and difference on sorted sequences by merge function

 A 1 =demo.query("select CLASS,STUDENTID, SUBJECT, SCORE from SCORES where CLASS=? and SUBJECT=? and STUDENTID?","Class two", "Math",5) 3 =A1.sort(STUDENTID) 4 =A2.sort(STUDENTID) 5 =[A3:A4].merge(STUDENTID) Concatenation 6 =[A3:A4].merge@u(STUDENTID) Union 7 =[A3:A4].merge@i(STUDENTID) Intersection 8 =[A3:A4].merge@d(STUDENTID) Difference

## Calculate quadratic sum and variance

 A 1 [1,2,3,4,5,6,7,8] 2 =A1.sum(~*~) Quadratic sum 3 =A1.variance() Variance 4 =demo.query("select NAME,EVENT,SCORE from GYMSCORE") 5 =A4.variance(SCORE)

## Calculate weighted average

 A 1 [9,9.1,8.5,9.8,9.4] 2 [0.9,0.8,1.0,0.95,1.0] 3 =(A1**A2).sum()/A2.sum()

## Calculate average of an integer sequence after removing the max and the min

 A 1 [99,98,95,93,87,89,90,96,94] 2 =(A1.sum()-A1.max()-A1.min())/(A1.len()-2) 3 =(A1\A1.min()\A1.max()).avg()

 A 1 [1,2,3,4,5,6] 2 =A1.(~/~[-1]-1) 3 =demo.query("select DATE,sum(CLOSING) AMOUNT from STOCKRECORDS GROUP BY DATE") 4 =A3.derive(AMOUNT/AMOUNT[-1]-1: Period-over-period)

## Calculate moving average over adjacent sets

 A 1 [1,2,3,4,5,6] 2 =A1.(~[-1,1].avg()) 3 =demo.query("select STOCKID, DATE,CLOSING from STOCKRECORDS where STOCKID=?","000062") 4 =A3.(CLOSING[-3,3].avg())

## Aggregate loop

 A 1 [1,2,3,4,5,6,7] 2 =A1.iterate(~*~~;1) Return the product

## Union record sequences with different data structures

 A 1 =demo.query("select * from STUDENTS") 2 =demo.query("select * from EMPLOYEE ").derive(interval@y(BIRTHDAY,now()):AGE) 3 =A1|A2 4 =A3.select(GENDER:"F").avg(AGE)

## Set operations

 A B 1 [1,1,2,3,5,8] 2 [1,2,3,4,5,6] 3 =[A1,A2].isect() =A1^A2 Intersection 4 =[A1,A2].diff() =A1\A2 Difference 5 =[A1,A2].union() =A1&A2 Union 6 =[A1,A2].conj() =A1|A2 Concatenation 7 =[A1,A2].xunion() Retain unique members of every sequence 8 =demo.query("select * from EMPLOYEE") 9 =A8.select(GENDER:"F") 10 =A8.select(DEPT:"Sales") 11 =A8.select(age(BIRTHDAY)>=40) Perform set operations on table sequences 12 =[A9,A10,A11].isect() =A9^A10^A11 13 =[A9,A10,A11].diff() =A9\A10\A11 14 =[A9,A10,A11].union() =A9&A10&A11 15 =[A9,A10,A11].conj() =A9|A10|A11 16 =[A9,A10,A11].xunion()

## Get topN

 A 1 =100.(rand(100)) 2 =A1.top(5,~) Get topN in ascending order 3 =A1.top(-5,~) Get topN in descending order 4 =demo.query("select * from EMPLOYEE ") 5 =A4.top(5,SALARY) Get 5 lowest SALARY values 6 =A4.top(-5;SALARY) Get records holding 5 highest SALARY values

## Alignment arithmetic operations

 A 1 [1,2,3] 2 [5,6,7] 3 =A1++A2 alignment addition 4 =A1--A2 alignment subtraction 5 =A1**A2 alignment multiplication 6 =A1//A2 alignment division 7 =A1%%A2 mod operation

## Synced segmentation where max/mix value is used to represent a value

 A 1 =to(100).sort(rand()) 2 =A1.median(:4)|A1.max() Define the number of segments 3 =A1.((n=~,A2.pseg@r(n))) Find which segment each value belongs to 4 =A3.(A2(~+1)) Represent the value with max value in its segment 5 =A1.min()|A1.median(:4) Define the number of segments 6 =A1.((n=~,A5.segp(n))) Represent the value with min value in its segment

## Get product of three sets’ Cartesian products

 A 1 [1,2,3] 2 [2,3,4] 3 [3,4,5] 4 =A1.((x=~,A2.((y=~,A3.(x*y*~))))) Calculate Cartesian products in a triplevel loop

## Calculate Fibonacci sequence

 A 1 =10.iterate([~~(2),~~(1)+~~(2)],[1,1])