complex {base}

R Documentation

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

length.out	numeric. Desired length of the output vector, inputs being recycled as needed.
real	numeric vector.
imaginary	numeric vector.
modulus	numeric vector.
argument	numeric vector.
x	an object, probably of mode complex.
...	further arguments passed to or from other methods.

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.)

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).

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

Examples

( z <- 0i ^ (-3:3) )
stopifnot(Re(z) == 0 ^ (-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)

all(Mod ( 1 -  sin(z) / ( (exp(1i*z)-exp(-1i*z))/(2*1i) ))
    < 100*.Machine$double.eps)
## 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")

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