| endpointCoordinates {compositions} | R Documentation |
Computes the convex combination of amounts given by endpoints
to explain X as good as possible.
endpointCoordinates(X,...)
endpointCoordinatesInv(K,endpoints,...)
## Default S3 method:
endpointCoordinates(X,endpoints=diag(gsi.getD(X)), ...)
## S3 method for class 'acomp':
endpointCoordinates(X,endpoints=clr.inv(diag(gsi.getD(X))),...)
## S3 method for class 'aplus':
endpointCoordinates(X,endpoints,...)
## S3 method for class 'rplus':
endpointCoordinates(X,endpoints,...)
## S3 method for class 'rmult':
endpointCoordinatesInv(K,endpoints,...)
## S3 method for class 'acomp':
endpointCoordinatesInv(K,endpoints,...)
## S3 method for class 'rcomp':
endpointCoordinatesInv(K,endpoints,...)
## S3 method for class 'aplus':
endpointCoordinatesInv(K,endpoints,...)
## S3 method for class 'rplus':
endpointCoordinatesInv(K,endpoints,...)
X |
a dataset of amounts or compositions, to be represented in as convex combination of the endpoints in the given geometry |
K |
Konvex combination weights to the endpoints |
endpoints |
a dataset of extremal compositions from the same space as X. The number of endpoints given must not exceed the dimension of the space plus one. |
... |
currently unused |
The convex combination is performed in the respective geometry. This
means that for rcomp positivity of the result is only guaranteed with
extermal endmembers and that in acomp-geometry it is not possible to
give extremal endmembers.
The main idea behind this functions is that the actually observed
composition came from a convex combination of some extremal
compositions specified by endpoints. Strictly speaking this is
meaningfull in strictly this sense only in rplus-geometry and under
some special circumstances in rcomp geometry. It is not
meaningfull in terms of mass conservation in acomp- and aplus-geometry
due to the non mass-balancing
character of the geometry. In rcomp-geometry it dependent on unit of
measurements and different for volume and mass % and only valid if
the whole composition is observed.
The endpointCoordinates functions give a "rmult"-dataset
giving the convex weights, which allow to combine X from
endpoints as good as possible. The result is an "rmult"
since there is guarantee that the resulting weights are positive.
The endpointCoordinates functions reconstruct the convex
combination from coordinates K and the given
endpoints. The class of endpoints determines the
geometry chosen and the class of the result.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de, Raimon Tolosana-Delgado
Shurtz, Robert F., 2003. Compositional geometry and mass conservation. Mathematical Geology 35~(8), 972–937.
data(SimulatedAmounts) ep <- aplus(rbind(c(2,1,2),c(2,2,1),c(1,2,2))) dat <- endpointCoordinatesInv(acomp(sa.lognormals),acomp(ep)) plot(dat) plot( acomp(endpointCoordinates(dat,acomp(ep)))) dat <- endpointCoordinatesInv(rcomp(sa.lognormals),rcomp(ep)) plot(dat) plot( rcomp(endpointCoordinates(dat,rcomp(ep)))) dat <- endpointCoordinatesInv(aplus(sa.lognormals),aplus(ep)) plot(dat) plot( endpointCoordinates(dat,aplus(ep))) dat <- endpointCoordinatesInv(rplus(sa.lognormals),rplus(ep)) plot(dat) plot(endpointCoordinates(rplus(dat),rplus(ep)))