Oblique results can be achieved by using rotate. The performance is quite
different. In a test example,
if
rotate =. 0 [ oblique =. 0 1
then
ts 'rotate test 55'
0.194581 9.71479e7
ts 'oblique test 55'
0.870818 6.29288e7
For example, one can project the population of a given population by sex age
and service. The estimation of the aging of a particular population and its
consequences can then be estimated. The technique requires multiplication
along a 3d diagonal.
test=: 3 : 0
NB. x: 0 for projection, 1 for rotation
NB. y: number of age and service
:
POP=:((>:/)~i.y)*"2 (1000*i.2)+/(100*i.y)+/1+i.y NB. SERVICE AGE
QR=: ((>:/)~i.y)*"2 (0.0001* (1000*i.2)+/(100*i.-y)+/1+i.-y) NB. SERVICE
AGE
NV=: (2, y+4,0) $,10000+(100*i.y+4)+/i.y NB. ANS AGE
projrotate`[email protected] POP;NV;QR
)
ProjRotate=: 3 : 0
NB. Population projection using rotation
NB. result by sex year age service will allow us to determine the probable
aging of our population.
NB. pop: number of active employees by sex(2), age(55=16 to 70), service(55
= 0 to 54)
NB. new: number of new employees by sex(2), year of employment(50=years of
projection), age(55)
NB. srv: probability of survival (not dying,quitting or retiring) by
sex(2),age(55),service(55)
'pop new srv'=.y
p=. pop,"2 3 (new,"1 (0)),"0 1"1 2 (0,"2 srv) NB. setup a matrix :
sex,year of projection, age,service
'a n'=. (1 0)+ 1}.$new
r=. (,.)~i.a NB. to shift each slice to the left and to the top
by 1 for each year of projection
t=.-(0,0,a,a)+$p NB. to make space for our rotation
f=.2,a,1+n,n NB. to return to the original size
(-f){.(-r)|.!.0"1 2"2 3 */\"3 r |.!.1"1 2"2 3 t{.!.1 p
)
ProjOblique=: 3 : 0
'pop new srv'=.y
p=. pop,"2 3 (new,"1 (0)),"0 1"1 2 (0,"2 srv)
'a n'=. (1 0)+ 1}.$new
r=. |."1|."2*//./.\"3|."2|."1 p NB. this is the 3d oblique
cumulative product, by year of projection
b=. (1+i.a)|."0 1 ((a,n)#0 1) NB. eliminate the unused rows of
the oblique
s=.|:n-(i.n)<./i.a NB. a rotation will position the
required results
n{."1 s|."0 1 " 2 3 b#"1 2"2 3 r NB. we retain the correct number of
columns
)
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