Complex function

Complex functionality for onions

Functionality in the Complex group.

The norm Norm(O) of onion $O$ is the product of $O$ with its conjugate: $|O|=OO^*$ but a more efficient numerical method is used (see dotprod()).

The Mod Mod(O) of onion $O$ is the square root of its norm.

The sign of onion $O$ is the onion with the same direction as $O$ but with unit Norm: sign(O)=O/Mod(O).

Function Im() sets the real component of its argument to zero and returns that; Conj() flips the sign of its argument's non-real components. Function Re() returns the real component (first row) of its argument as a numeric vector. If x is an onion, then x == Re(x) + Im(x).

## S4 method for signature 'onion'
Re(z)
## S4 method for signature 'onion'
Im(z)
Re(z) <- value
Im(x) <- value
## S4 method for signature 'onion'
Conj(z)
## S4 method for signature 'onion'
Mod(z)
onion_abs(x)
onion_conjugate(z)
## S4 method for signature 'onion'
sign(x)

Arguments

• x,z: Object of class onion or glub
• value: replacement value

Returns

All functions documented here return a numeric vector or matrix of the same dimensions as their argument, apart from functions Im()

and Conj(), which return an object of the same class as its argument.

Author(s)

Robin K. S. Hankin

Note

If x is a numeric vector and y an onion, one might expect typing x[1] <- y to result in x being a onion. This is impossible, according to John Chambers.

Extract and set methods for components such as i,j,k are documented at Extract.Rd

Compare clifford::Conj(), which is more complicated.

See Also

Extract

Examples

a <- rquat()
Re(a)
Re(a) <- j(a)

Im(a)

b <- romat()

A <- romat()
Im(A) <- Im(A)*10