Complex Vectors

Description

Basic functions which support complex arithmetic in R.

Usage

complex(length.out = 0, real = numeric(), imaginary = numeric(),
        modulus = 1, argument = 0)
as.complex(x, ...)
is.complex(x)

Re(z)
Im(z)
Mod(z)
Arg(z)
Conj(z)

Arguments

Details

Complex vectors can be created with complex. The vector can be specified either by giving its length, its real and imaginary parts, or modulus and argument. (Giving just the length generates a vector of complex zeroes.)

as.complex attempts to coerce its argument to be of complex type: like as.vector it strips attributes including names. All forms of NA and NaN are coerced to a complex NA, for which both the real and imaginary parts are NA.

Note that is.complex and is.numeric are never both TRUE.

The functions Re, Im, Mod, Arg and Conj have their usual interpretation as returning the real part, imaginary part, modulus, argument and complex conjugate for complex values. The modulus and argument are also called the polar coordinates. If z = x + i y with real x and y, for r = Mod(z) = √(x^2 + y^2), and φ = Arg(z), x = r*cos(φ) and y = r*sin(φ). They are all internal generic primitive functions: methods can be defined for them individually or via the Complex group generic.

In addition, the elementary trigonometric, logarithmic, exponential, square root and hyperbolic functions are implemented for complex values.

Internally, complex numbers are stored as a pair of double precision numbers, either or both of which can be NaN or plus or minus infinity.

S4 methods

as.complex is primitive and can have S4 methods set.

Re, Im, Mod, Arg and Conj constitute the S4 group generic Complex and so S4 methods can be set for them individually or via the group generic.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Examples

require(graphics)

0i ^ (-3:3)

matrix(1i^ (-6:5), nrow=4) #- all columns are the same
0 ^ 1i # a complex NaN

## create a complex normal vector
z <- complex(real = stats::rnorm(100), imaginary = stats::rnorm(100))
## or also (less efficiently):
z2 <- 1:2 + 1i*(8:9)

## The Arg(.) is an angle:
zz <- (rep(1:4,len=9) + 1i*(9:1))/10
zz.shift <- complex(modulus = Mod(zz), argument= Arg(zz) + pi)
plot(zz, xlim=c(-1,1), ylim=c(-1,1), col="red", asp = 1,
     main = expression(paste("Rotation by "," ", pi == 180^o)))
abline(h=0,v=0, col="blue", lty=3)
points(zz.shift, col="orange")