是否有一种算法可以对数据使用不同的约束进行平均？

Question

Month	Product	Product	Product	Current
1	Y		A	17
2	Y		A	22
3	Y		A	21
4	Y	S	Q	44
5	Y	S	Q	32
6	Y	S	Q	23
7	Y	S	B	56
8	Y	S	B	73
9	Y	S	B	12
10	Y		C	26
11	Y		C	45
12	Y		C	37

As seen in table above I have some data, elements of which form part of different products. For example, 4th element in above table (highlighted row) ie, 44 is part of product Q , S and Y . Each product has an average as below :

average of Product A=(17+22+21)/3=20
average of Product Q=(44+32+23)/3=33
average of Product S=(44+32+23+56+73+12)/6=40
average of Product Y=(17+22+21+44+32+23+56+73+12+26+45+37)/12=34

Now I want to manipulate the data such that new averages are:

Average of product A=   25
Average of product Q =  35
Average of Product S=   32
Average of product Y=   39

and shape of months within a product should be maintained.

So result should be (example calculation):

new Month 1= (new average - current average) +current month 1 value
new Month 1= (25 - 20) + 17 = 22

new Month 2= (new average - current average) +current month 2 value
new month 2 = (25 - 20 ) + 22 = 27

new Month 3= (new average - current average) +current month 3 value
new months 3 =(25-20)+ 21= 26

monthly shape difference example

month	month 1	month 2	month 3
current	17	22	21
current monthly difference		22-17= 5	21-22= -1
New	22	27	26
New monthly difference		27-22= 5	26-27= -1

It can see that month 2 - month1 for both current and new data is 5 and month 3- month 2 is -1 for both current and new data. Hence, monthly shape for product A is maintained.

Month	Product	Product	Product	New
1	Y		A	22
2	Y		A	27
3	Y		A	26
4	Y	S	Q	46
5	Y	S	Q	34
6	Y	S	Q	25
7	Y	S	B	38
8	Y	S	B	55
9	Y	S	B	-6
10	Y		C	57
11	Y		C	76
12	Y		C	68

Currently I have a VBA code that loops over each element multiple times to calculate difference between current and new averages and apply this difference to elements. Is there any matrix algorithm I can use that would make the same calculations instead of using iterative loops ? Algorithm code will be implemented in Matlab, C++ or Python or VBA. Currently I have been exploring MATLAB function lsqlin but cannot get it to do what I want.

Could you please help?

Answer 1

The method :

1. Ignore individual month value, view it as a sum (that relates to its shape). [ mth1-mth12 >> ad ]
2. Write all needed relation. [ avg_X <--> a,b,c,d ]
3. Using the relation & new known value, solve for the sum [ a,b,c,d ]

Implementation :

Step1 : line 1-4 | Step2 : line 5-8

Defining :

Value & relation	"Current" case	"new" case
a = sum(mth1,mth2,mth3)	60	?
b = sum(mth4,mth5,mth6)	99	?
c = sum(mth7,mth8,mth9)	141	?
d = sum(mth10,mth11,mth12)	108	?
avg_A = a/3	20	25
avg_Q = b/3	33	35
avg_S = (b+c)/6	40	32
avg_Y = (a+b+c+d)/12	34	39

In "Current" case : all variable above have defined values.

In "new" case (Step3) :

 avg_A = a/3 = 25 >> a = 25*3 = 75
 avg_Q = b/3 = 35 >> b = 35*3 = 105
 avg_S = (b+c)/6 = ((105)+c)/6 = 32 >> c = 32*6-105 = 87
 avg_Y = (a+b+c+d)/12 = ((75)+(105)+(87)+d)/12 = 39 >> d = 201

Fill in mth1-12 with any value that can produce a,b,c,d value above.

Done.

p/s: since OP only share 1 new "case", Step2 detail may varies. However, at least for this "shapes", this works.

_{My comment earlier actually in point to a statement "since the (observed relation is not really linear, a matrix cannot be built on the original table". Nevertheless, if you can figure out how to solve/put the Step2 relations in matrix form, step3 should be easier/automated.}