Linear Transformation of a Generalized Ellipsoid

Linear transformation of a generalized ellipsoid, including projections to subspaces.

Usage

gmult(A, G, epsfac = 2)

Arguments

A

A matrix describing a linear transformation, conforming to the U component of G for matrix multiplication.

G

A gell object

epsfac

Factor of .Machine$double.eps used to distinguish zero vs. positive singular values

Value

gell object

Details

The matrix A can be non-singular, for a standard linear transformation, or singular, for a projection to a subspace.

Note

This implementation should be changed so that it provides an S3 method for class "gell" objects for which it was intended.

See also

gell, dual, signature

Author

Georges Monette

Examples

(zplane <- gell(span = diag(3)[,1:2]))  # a plane
#> $center
#> [1] 0 0 0
#> 
#> $u
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    1    0
#> [3,]    0    0    1
#> 
#> $d
#> [1] Inf Inf   0
#> 
#> attr(,"class")
#> [1] "gell"

dual(zplane)  # orthogonal line
#> $center
#> [1] 0 0 0
#> 
#> $u
#>      [,1] [,2] [,3]
#> [1,]    0    0    1
#> [2,]    0    1    0
#> [3,]    1    0    0
#> 
#> $d
#> [1] Inf   0   0
#> 
#> attr(,"class")
#> [1] "gell"
(zplane2 <- gmult( cbind( c(1,1,1), c(1,-1,0), c(1,0,-1)), zplane))
#> $center
#> [1] 0 0 0
#> 
#> $u
#>            [,1]       [,2]       [,3]
#> [1,] -0.8040001  0.4323391 -0.4082483
#> [2,] -0.2628040 -0.8742239 -0.4082483
#> [3,] -0.5334021 -0.2209424  0.8164966
#> 
#> $d
#> [1] Inf Inf   0
#> 
#> attr(,"class")
#> [1] "gell"

# correctly wipes out one dimension
(zplane3 <- gmult( cbind( c(1,0,0), c(1,0,0), c(0,0,1)), zplane)) 
#> $center
#> [1] 0 0 0
#> 
#> $u
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    1    0
#> [3,]    0    0    1
#> 
#> $d
#> [1] Inf   0   0
#> 
#> attr(,"class")
#> [1] "gell"