Chapter 10 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.

10.1 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

 

10.2 Judge if it is an ascending integer sequence

 

A

 

1

[1,2,3,4,5]

 

2

=A1.pselect(~!=int(~) || ~<=~[-1] )==null

 

 

10.3 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

 

10.4 Judge if members from two sequences are equal

 

A

 

1

[1,2,3]

 

2

[3,2,1]

 

3

=A1.eq(A2)

true

10.5 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 one", "Math",10)

 

2

=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

 

10.6 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)

 

 

10.7 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()

 

 

10.8 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()

 

 

10.9 Calculate link relative ratio over adjacent rows

 

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)

 

 

10.10 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())

 

 

10.11 Aggregate loop

 

A

 

1

[1,2,3,4,5,6,7]

 

2

=A1.iterate(~*~~;1)

Return the product

 

10.12 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)

 

 

10.13 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()

 

 

 

10.14 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

 

10.15 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

 

10.16 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

 

10.17 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

 

10.18 Calculate Fibonacci sequence

 

A

 

1

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