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Published on 05 September 14

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A sequence is an ordered set consisting of some data, which are called members of the sequence. A sequence is similar to an array in high-level language, but the data type of its members not have to be the same. The following will explain its basic computation through creation, access, operators and functions.

Creation

A5=[15.2,"b",1] /Members of a sequence can be float, string and integer

B5=[A1:C3] /Members are cell area, i.e.

C5=[3,A5,B4] /A member of a sequence can also be a sequence,i.e.

A6=[1,2,3,3] /Members can be repeated

B6=[] / A empty sequence

C6=[[]] /A non-empty sequence that its member is an empty sequence

to(2,6) / Numbers of the integer sequence are [2,3,4,5,6]. A integer sequence beginning with 1 can be expressed with to(6)

"1,a,b,c".array() /Split a character string into a sequence [1,a,b,c], a reversed joint can be expressed with [1,a,b,c].string()

periods@y("2012-08-10 12:00:00",now(),1) /Create a integer sequence for a period of time by dividing it into smaller time periods whose starting and ending points are in adjacent years, sequential value is ["2012-08-10 12:00:00","2013-01-01 00:00:00","2014-01-01 00:00:00","2014-07-01 10:10:41"]

file("e:/sales.txt").import@t() /Import records from structured text files to form a sequence, sequential value is:

A sequence whose members are records is table sequence, which is often used to make computations of structured data. Itâs not the focus in this article, for more information please refer to âBasic Computation of esProc Table Sequence and Record Sequenceâ.

Description: read the text file sales.txt into table sequence A1, fetch column Client to create sequence A2; group the records according to Client to create sequence A3.

Codeï¼

A1=file("e:/sales.txt").import@t()

A2=A1.(Client)

A3=A1.group(Client)

2. Value of sequence A3ï¼

We can see that members of sequence A3 are a number of sequences whose members are records.

A1=[a,b,c,d,e,f,g] /Sequence A1

A1(2) /Fetch the second member whose value is string âbâ, which equals to A1.m(2)

A1([2,3,4]) /Fetch members from the second to the fourth, whose value is expressed by the sequence [b,c,d]. Note that [2,3,4] is also a sequence(integer sequence). Intervals can be used to rewritten the expression as A1(to(2,4)).

A1.m(-1) /Fetch the last member. Note that m function must be used when fetching members backwards, the expression cannot be abbreviated to A1(-1).

A1(2)=r /Modify the second member to r, now value of sequence A1 is [a,r,c,d,e,f,g]

A1([2,4])=["r","s"] /Modify the second and the fourth member. A1=[a,r,c,s,d,e,f,g]

A1.Modify(2,["r","s"]) /Modify in turn from the second member, expression A1= [a,r,s,d,e,f,g] equals to A1([2,3])=["r","s"]

A1.Insert(0,"r") Add members at the end of the sequence, A1=[a,b,c,d,e,f,g,r]

A1.Insert(2,["r","s","t"]) /Insert three members consecutively before the second member, A1=[ a,r,s,t,b,c,d,e,f,g,r]

A1.Delete(2) /Delete the second member

A1.Delete([2,4]) /Delete the second and the fourth member

Sets computation include ^ intersection, & union, \complement, and |concatenate, etc. For example:

A1=["a","b",1,2,3,4] /Sequence A1

B1= ["d","b",10,12,3,4] /Sequence A2

A1^B1 /Intersection, return the sequence made up of members of both thetwo sequences, value is ["a","b",3,4]

A1\B1 /Complement, a new sequence created by successively removing from A1 the members of B1, value is ["a",1,2]

A1&B1 /Union, value is["a","b",1,2,3,4,"d",10,12]

A1|B1 /Concatenate, value is ["a","b",1,2,3,4,"d","b",10,12,3,4]

Two sequences of the same length can make alignment operation according to members and return the sequence. The operation includes ++ (add), -- (subtract), ** (multiply), // (divide) and %% (complementation). For example:

A1=[1,2,3,4] /Sequence A1

B1= [10,12,3,4] /Sequence A2

A1++B1 /Counterpoint addition, value is [11,14,16,18]

Two sequences can compare in alignment, the result is a Boolean type.

[1,2,3]==[1,2,3] /Comparative result is true

[1,B,3]<=[1,b,4] /Comparative result is true, because B is less than b

[1,2,3]<[1,3,4] /Result is true, because the second member of [1,2,3] is â2â , which is smaller than the second member â3â of [1,3,4]

Functions for sequences include sum, avg, max, variance,etc. For example:

A1=[2,4,6] /Sequence

A1.sum() /Summation, result is 12

A1.sum(~*~) /Quadratic sum, which equals to 2*2+4*4+6*6, result is 56. ~ represents each member of a sequence.

Loop function can make computation aiming at every member of a sequence, and express complex loop statement with simple functions, including loop computation, filter, locate, look up, rank, sort, etc.

A1=[2,4,-6] /Construct sequence A1

A1=(~+1) /Add 1 to every member, result is [3,5,-5]

A1.select(~>1) /Filter out members that are greater than 1, result is [2,4]

A1.pselect@a(~>1) /Locate serial numbers of members that are greater than 1, result is [1,2]

A1.pos([-6,2]) /Look up serial numbers of members -6 and 2 in A1, result is [3,1]

A1.rank() /Rank of members of the sequence, result is [2,1,3]

A1.sort() /Sort in ascending order, result is [-6,2,4]; [2,4,-6].sort(~:-1) is the expression when sorting in descending order

A sequence is an ordered set consisting of some data, which are called members of the sequence. A sequence is similar to an array in high-level language, but the data type of its members not have to be the same. The following will explain its basic computation through creation, access, operators and functions.

Creation

**1. Create with Constant **

Bracketing members with â[]â represents sequence constant, e.g.

A5=[15.2,"b",1] /Members of a sequence can be float, string and integer

B5=[A1:C3] /Members are cell area, i.e.

C5=[3,A5,B4] /A member of a sequence can also be a sequence,i.e.

A6=[1,2,3,3] /Members can be repeated

B6=[] / A empty sequence

C6=[[]] /A non-empty sequence that its member is an empty sequence

**Note:** Members of a sequence can be any data types, including atom type, another sequences, records, etc. A sequence that all its members are integers is called an integer sequence.

**2. Create with functions**

to(2,6) / Numbers of the integer sequence are [2,3,4,5,6]. A integer sequence beginning with 1 can be expressed with to(6)

"1,a,b,c".array() /Split a character string into a sequence [1,a,b,c], a reversed joint can be expressed with [1,a,b,c].string()

periods@y("2012-08-10 12:00:00",now(),1) /Create a integer sequence for a period of time by dividing it into smaller time periods whose starting and ending points are in adjacent years, sequential value is ["2012-08-10 12:00:00","2013-01-01 00:00:00","2014-01-01 00:00:00","2014-07-01 10:10:41"]

file("e:/sales.txt").import@t() /Import records from structured text files to form a sequence, sequential value is:

A sequence whose members are records is table sequence, which is often used to make computations of structured data. Itâs not the focus in this article, for more information please refer to âBasic Computation of esProc Table Sequence and Record Sequenceâ.

**3. Create by computing**

Description: read the text file sales.txt into table sequence A1, fetch column Client to create sequence A2; group the records according to Client to create sequence A3.

Codeï¼

A1=file("e:/sales.txt").import@t()

A2=A1.(Client)

A3=A1.group(Client)

**Noteï¼**

1. Value of sequence A2ï¼

2. Value of sequence A3ï¼

We can see that members of sequence A3 are a number of sequences whose members are records.

**Accessing**

**4.Access members according to serial numbers**

A1=[a,b,c,d,e,f,g] /Sequence A1

A1(2) /Fetch the second member whose value is string âbâ, which equals to A1.m(2)

A1([2,3,4]) /Fetch members from the second to the fourth, whose value is expressed by the sequence [b,c,d]. Note that [2,3,4] is also a sequence(integer sequence). Intervals can be used to rewritten the expression as A1(to(2,4)).

A1.m(-1) /Fetch the last member. Note that m function must be used when fetching members backwards, the expression cannot be abbreviated to A1(-1).

**5. Assignment and modification**

A1(2)=r /Modify the second member to r, now value of sequence A1 is [a,r,c,d,e,f,g]

A1([2,4])=["r","s"] /Modify the second and the fourth member. A1=[a,r,c,s,d,e,f,g]

A1.Modify(2,["r","s"]) /Modify in turn from the second member, expression A1= [a,r,s,d,e,f,g] equals to A1([2,3])=["r","s"]

**6. Add members**

A1.Insert(0,"r") Add members at the end of the sequence, A1=[a,b,c,d,e,f,g,r]

A1.Insert(2,["r","s","t"]) /Insert three members consecutively before the second member, A1=[ a,r,s,t,b,c,d,e,f,g,r]

**7. Delete members**

A1.Delete(2) /Delete the second member

A1.Delete([2,4]) /Delete the second and the fourth member

**Operators**

**8. Sets computation**

Sets computation include ^ intersection, & union, \complement, and |concatenate, etc. For example:

A1=["a","b",1,2,3,4] /Sequence A1

B1= ["d","b",10,12,3,4] /Sequence A2

A1^B1 /Intersection, return the sequence made up of members of both thetwo sequences, value is ["a","b",3,4]

A1\B1 /Complement, a new sequence created by successively removing from A1 the members of B1, value is ["a",1,2]

A1&B1 /Union, value is["a","b",1,2,3,4,"d",10,12]

A1|B1 /Concatenate, value is ["a","b",1,2,3,4,"d","b",10,12,3,4]

**Note: **Both union and concatenate are created by combining members of two sequences in order. Common members only appear once in union while, in concatenate, all of them will appear.

**9. Alignment arithmetic operation**

Two sequences of the same length can make alignment operation according to members and return the sequence. The operation includes ++ (add), -- (subtract), ** (multiply), // (divide) and %% (complementation). For example:

A1=[1,2,3,4] /Sequence A1

B1= [10,12,3,4] /Sequence A2

A1++B1 /Counterpoint addition, value is [11,14,16,18]

**10. Boolean operation**

Two sequences can compare in alignment, the result is a Boolean type.

[1,2,3]==[1,2,3] /Comparative result is true

[1,B,3] /Comparative result is true, because B is less than b

[1,2,3] /Result is true, because the second member of [1,2,3] is â2â , which is smaller than the second member â3â of [1,3,4]

**Note**: âinâ function is used to judge the inclusion relation between sequences.

**Functions**

**11. Aggregate function**

Functions for sequences include sum, avg, max, variance,etc. For example:

A1=[2,4,6] /Sequence

A1.sum() /Summation, result is 12

A1.sum(~*~) /Quadratic sum, which equals to 2*2+4*4+6*6, result is 56. ~ represents each member of a sequence.

**12. Loop function**

Loop function can make computation aiming at every member of a sequence, and express complex loop statement with simple functions, including loop computation, filter, locate, look up, rank, sort, etc.

A1=[2,4,-6] /Construct sequence A1

A1=(~+1) /Add 1 to every member, result is [3,5,-5]

A1.select(~>1) /Filter out members that are greater than 1, result is [2,4]

A1.pselect@a(~>1) /Locate serial numbers of members that are greater than 1, result is [1,2]

A1.pos([-6,2]) /Look up serial numbers of members -6 and 2 in A1, result is [3,1]

A1.rank() /Rank of members of the sequence, result is [2,1,3]

A1.sort() /Sort in ascending order, result is [-6,2,4]; [2,4,-6].sort(~:-1) is the expression when sorting in descending order

Creation

Bracketing members with â[]â represents sequence constant, e.g.

A5=[15.2,"b",1] /Members of a sequence can be float, string and integer

B5=[A1:C3] /Members are cell area, i.e.

C5=[3,A5,B4] /A member of a sequence can also be a sequence,i.e.

A6=[1,2,3,3] /Members can be repeated

B6=[] / A empty sequence

C6=[[]] /A non-empty sequence that its member is an empty sequence

to(2,6) / Numbers of the integer sequence are [2,3,4,5,6]. A integer sequence beginning with 1 can be expressed with to(6)

"1,a,b,c".array() /Split a character string into a sequence [1,a,b,c], a reversed joint can be expressed with [1,a,b,c].string()

periods@y("2012-08-10 12:00:00",now(),1) /Create a integer sequence for a period of time by dividing it into smaller time periods whose starting and ending points are in adjacent years, sequential value is ["2012-08-10 12:00:00","2013-01-01 00:00:00","2014-01-01 00:00:00","2014-07-01 10:10:41"]

file("e:/sales.txt").import@t() /Import records from structured text files to form a sequence, sequential value is:

A sequence whose members are records is table sequence, which is often used to make computations of structured data. Itâs not the focus in this article, for more information please refer to âBasic Computation of esProc Table Sequence and Record Sequenceâ.

Description: read the text file sales.txt into table sequence A1, fetch column Client to create sequence A2; group the records according to Client to create sequence A3.

Codeï¼

A1=file("e:/sales.txt").import@t()

A2=A1.(Client)

A3=A1.group(Client)

1. Value of sequence A2ï¼

2. Value of sequence A3ï¼

We can see that members of sequence A3 are a number of sequences whose members are records.

A1=[a,b,c,d,e,f,g] /Sequence A1

A1(2) /Fetch the second member whose value is string âbâ, which equals to A1.m(2)

A1([2,3,4]) /Fetch members from the second to the fourth, whose value is expressed by the sequence [b,c,d]. Note that [2,3,4] is also a sequence(integer sequence). Intervals can be used to rewritten the expression as A1(to(2,4)).

A1.m(-1) /Fetch the last member. Note that m function must be used when fetching members backwards, the expression cannot be abbreviated to A1(-1).

A1(2)=r /Modify the second member to r, now value of sequence A1 is [a,r,c,d,e,f,g]

A1([2,4])=["r","s"] /Modify the second and the fourth member. A1=[a,r,c,s,d,e,f,g]

A1.Modify(2,["r","s"]) /Modify in turn from the second member, expression A1= [a,r,s,d,e,f,g] equals to A1([2,3])=["r","s"]

A1.Insert(0,"r") Add members at the end of the sequence, A1=[a,b,c,d,e,f,g,r]

A1.Insert(2,["r","s","t"]) /Insert three members consecutively before the second member, A1=[ a,r,s,t,b,c,d,e,f,g,r]

A1.Delete(2) /Delete the second member

A1.Delete([2,4]) /Delete the second and the fourth member

Sets computation include ^ intersection, & union, \complement, and |concatenate, etc. For example:

A1=["a","b",1,2,3,4] /Sequence A1

B1= ["d","b",10,12,3,4] /Sequence A2

A1^B1 /Intersection, return the sequence made up of members of both thetwo sequences, value is ["a","b",3,4]

A1\B1 /Complement, a new sequence created by successively removing from A1 the members of B1, value is ["a",1,2]

A1&B1 /Union, value is["a","b",1,2,3,4,"d",10,12]

A1|B1 /Concatenate, value is ["a","b",1,2,3,4,"d","b",10,12,3,4]

Two sequences of the same length can make alignment operation according to members and return the sequence. The operation includes ++ (add), -- (subtract), ** (multiply), // (divide) and %% (complementation). For example:

A1=[1,2,3,4] /Sequence A1

B1= [10,12,3,4] /Sequence A2

A1++B1 /Counterpoint addition, value is [11,14,16,18]

Two sequences can compare in alignment, the result is a Boolean type.

[1,2,3]==[1,2,3] /Comparative result is true

[1,B,3] /Comparative result is true, because B is less than b

[1,2,3] /Result is true, because the second member of [1,2,3] is â2â , which is smaller than the second member â3â of [1,3,4]

Functions for sequences include sum, avg, max, variance,etc. For example:

A1=[2,4,6] /Sequence

A1.sum() /Summation, result is 12

A1.sum(~*~) /Quadratic sum, which equals to 2*2+4*4+6*6, result is 56. ~ represents each member of a sequence.

Loop function can make computation aiming at every member of a sequence, and express complex loop statement with simple functions, including loop computation, filter, locate, look up, rank, sort, etc.

A1=[2,4,-6] /Construct sequence A1

A1=(~+1) /Add 1 to every member, result is [3,5,-5]

A1.select(~>1) /Filter out members that are greater than 1, result is [2,4]

A1.pselect@a(~>1) /Locate serial numbers of members that are greater than 1, result is [1,2]

A1.pos([-6,2]) /Look up serial numbers of members -6 and 2 in A1, result is [3,1]

A1.rank() /Rank of members of the sequence, result is [2,1,3]

A1.sort() /Sort in ascending order, result is [-6,2,4]; [2,4,-6].sort(~:-1) is the expression when sorting in descending order

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