集合、聚合与循环
本章主要展示关于集合、聚合与循环的代码参考，比如判断是否是数列、判断是否递增数列、判断是否成员或子集、判断两个序列的成员是否相同、对有序序列用归并法快速做并交差、计算平方和方差、计算加权平均、去掉最大值和最小值的平均、取相邻行计算比上期、取相邻集合计算移动平均、汇总循环、不同数据结构的排列作并集、集合运算、TOPN问题、等频分段，用分段最大值或最小值表示该值、三个集合的笛卡尔积乘积、菲波那切数列等。
判断是否是数列
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A |
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1 |
[1,2,3,4] |
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2 |
=A1.pselect(~!=int(~))==null |
检查是否有不是整数的成员 |
判断是否递增数列
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A |
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[1,2,3,4,5] |
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2 |
=A1.pselect(~!=int(~) || ~<=~[-1] )==null |
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判断是否成员或子集
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A |
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1 |
[1,2,3,4,5,6,7] |
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2 |
=A1.pos(2)!=null |
true，成员 |
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3 |
=A1.pos@c([2,3])!=null |
true ，连续子集 |
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4 |
=A1.pos@c([3,2])!=null |
false |
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5 |
=A1.pos@c([2,5])!=null |
false |
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6 |
=A1.pos@i([2,3])!=null |
true，子集判断 |
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7 |
=A1.pos@i([3,2])!=null |
false |
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=A1.pos@i([2,5])!=null |
true |
判断两个序列的成员是否相同
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A |
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1 |
[1,2,3] |
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2 |
[3,2,1] |
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3 |
=A1.eq(A2) |
true |
对有序序列用归并法快速做并、交、差
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A |
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=demo.query("select CLASS,STUDENTID, SUBJECT, SCORE from SCORES where CLASS=? and SUBJECT=? and STUDENTID<?","Class one", "Math",10) |
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=demo.query("select CLASS,STUDENTID, SUBJECT,SCORE from SCORES where CLASS=? and SUBJECT=? and STUDENTID>?","Class two", "Math",5) |
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=A1.sort(STUDENTID) |
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=A2.sort(STUDENTID) |
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=[A3:A4].merge(STUDENTID) |
和 |
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=[A3:A4].merge@u(STUDENTID) |
并 |
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=[A3:A4].merge@i(STUDENTID) |
交 |
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=[A3:A4].merge@d(STUDENTID) |
差 |
计算平方和、方差
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A |
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1 |
[1,2,3,4,5,6,7,8] |
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=A1.sum(~*~) |
平方和 |
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=var(A1) |
方差 |
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=demo.query("select NAME,EVENT,SCORE from GYMSCORE") |
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=var(A4.(SCORE)) |
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计算加权平均
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A |
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1 |
[9,9.1,8.5,9.8,9.4] |
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2 |
[0.9,0.8,1.0,0.95,1.0] |
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3 |
=(A1**A2).sum()/A2.sum() |
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去掉最大值和最小值的平均
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A |
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[99,98,95,93,87,89,90,96,94] |
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=(A1.sum()-A1.max()-A1.min())/(A1.len()-2) |
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=(A1\A1.min()\A1.max()).avg() |
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取相邻行计算比上期
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A |
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[1,2,3,4,5,6] |
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=A1.(~/~[-1]-1) |
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=demo.query("select DATE,sum(CLOSING) AMOUNT from STOCKRECORDS GROUP BY DATE") |
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=A3.derive(AMOUNT/AMOUNT[-1]-1: Period-over-period) |
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取相邻集合计算移动平均
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A |
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[1,2,3,4,5,6] |
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=A1.(~[-1,1].avg()) |
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=demo.query("select STOCKID, DATE,CLOSING from STOCKRECORDS where STOCKID=?","000062") |
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=A3.(CLOSING[-3,3].avg()) |
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汇总循环
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A |
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1 |
[1,2,3,4,5,6,7] |
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2 |
=A1.iterate(~*~~;1) |
返回连乘最终结果 |
不同数据结构的排列作并集
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A |
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=demo.query("select * from STUDENTS") |
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=demo.query("select * from EMPLOYEE ").derive(interval@y(BIRTHDAY,now()):AGE) |
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=A1|A2 |
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=A3.select(GENDER:"F").avg(AGE) |
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集合运算
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A |
B |
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1 |
[1,1,2,3,5,8] |
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2 |
[1,2,3,4,5,6] |
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=[A1,A2].isect() |
=A1^A2 |
交 |
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=[A1,A2].diff() |
=A1\A2 |
差 |
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=[A1,A2].union() |
=A1&A2 |
并 |
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=[A1,A2].conj() |
=A1|A2 |
和 |
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7 |
=[A1,A2].xunion() |
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保留各序列不重复成员 |
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=demo.query("select * from EMPLOYEE") |
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=A8.select(GENDER:"F") |
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10 |
=A8.select(DEPT:"Sales") |
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=A8.select(age(BIRTHDAY)>=40) |
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序表同样可以进行集合运算 |
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=[A9,A10,A11].isect() |
=A9^A10^A11 |
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13 |
=[A9,A10,A11].diff() |
=A9\A10\A11 |
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=[A9,A10,A11].union() |
=A9&A10&A11 |
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=[A9,A10,A11].conj() |
=A9|A10|A11 |
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16 |
=[A9,A10,A11].xunion() |
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TOPN 问题
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A |
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1 |
=100.(rand(100)) |
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2 |
=A1.top(5,~) |
最小的5个 |
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3 |
=A1.top(-5,~) |
最大的5个 |
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=demo.query("select * from EMPLOYEE ") |
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=A4.top(5,SALARY) |
最小的5个SALARY |
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=A4.top(-5;SALARY) |
SALARY最大的5条记录 |
对位运算
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A |
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1 |
[1,2,3] |
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2 |
[5,6,7] |
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3 |
=A1++A2 |
对位加 |
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4 |
=A1--A2 |
对位减 |
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5 |
=A1**A2 |
对位乘 |
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=A1//A2 |
对位除 |
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7 |
=A1%%A2 |
对位取余 |
等频分段，用分段最大值或最小值表示该值
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A |
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1 |
=to(100).sort(rand()) |
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2 |
=A1.median(:4)|A1.max() |
确定分段 |
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3 |
=A1.((n=~,A2.pseg@r(n))) |
循环每个值属于哪段 |
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4 |
=A3.(A2(~+1)) |
用各段最大值代表该值 |
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=A1.min()|A1.median(:4) |
确定分段 |
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6 |
=A1.((n=~,A5.segp(n))) |
用各段最小值代表该值 |
三个集合的笛卡尔积乘积
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A |
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1 |
[1,2,3] |
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2 |
[2,3,4] |
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3 |
[3,4,5] |
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=A1.((x=~,A2.((y=~,A3.(x*y*~))))) |
三层循环计算笛卡尔积 |
菲波那切数列
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A |
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1 |
=10.iterate([~~(2),~~(1)+~~(2)],[1,1]) |
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