zonoseg-invert {zonohedra}

invert points in a zonoseg

Description

For points in a zonoseg, find points in the unit cube that map to those points.

Usage

## S3 method for class 'zonoseg'
invert( x, z, tol=0, ... )

Arguments

x

a zonoseg object as returned by the constructor zonoseg()

z

a numeric M-vector

tol

points that are within tol of a boundary point are taken to be that point

...

not used

Details

For a point in the interior of the zonoseg, there are infinitely many points in the cube that map to it. This function tries to find one with the fewest number of non-zero components.

Value

invert.zonoseg() returns a data.frame with M rows and these columns:

z

the given point

pcube

a point in the unit cube that maps to z. For the 2 boundary points, pcube is a vertex. If z is outside the zonoseg, pcube is all NA, and a warning message is printed

If the names of z are unique, they are copied to the row names of the output. The column names are copied from the ground set of the associated matroid.

In case of error, the function returns NULL.

See Also

zonoseg()

Examples

zono1 = zonoseg( c(1,-2,3,0,-3,-4) )
zono1
# generators:        6 -- 3 negative, 2 positive, and 1 loops.
# 
# segment:                   [-9,4]
#      value pcube.1 pcube.2 pcube.3 pcube.4 pcube.5 pcube.6
# zmin    -9       0       1       0       0       1       1
# zmax     4       1       0       1       0       0       0
# 
# 2-transition subsegment:   [-8,3]
#             value source.1 source.2 source.3 source.4 source.5 source.6
# tmin-2trans    -8        1        1        0        0        1        1
# tmax-2trans     3        0        0        1        1        0        0


z = c( 0, -3*pi, pi, 2*pi, getsegment(zono1) )

invert( zono1, z )
#           z   pcube.1   pcube.2   pcube.3   pcube.4   pcube.5   pcube.6
# 1  0.000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
# 2 -9.424778        NA        NA        NA        NA        NA        NA
# 3  3.141593 1.0000000 0.0000000 0.7138642 0.0000000 0.0000000 0.0000000
# 4  6.283185        NA        NA        NA        NA        NA        NA
# 5 -9.000000 0.0000000 1.0000000 0.0000000 0.0000000 1.0000000 1.0000000
# 6  4.000000 1.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000