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(x)
Im(x)
Mod(x)
Arg(x)
Conj(x)

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.

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. Modulus and argument are also called the polar coordinates. If z = x + i y with real x and y, Mod(z) = \sqrt{x^2 + y^2}, and for \phi= Arg(z), x = \cos(\phi) and y = \sin(\phi). They are all generic functions: methods can be defined for them individually or via the Complex group generic.

In addition, the elementary trigonometric, logarithmic and exponential functions are available for complex values.

is.complex is generic: you can write methods to handle specific classes of objects, see InternalMethods.

References

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

Examples

0i ^ (-3:3)

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

## create a complex normal vector
z <- complex(real = rnorm(100), imag = 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")