| complex {base} | R Documentation |
Basic functions which support complex arithmetic in R.
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)
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 |
z |
an object of mode |
... |
further arguments passed to or from other methods. |
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.
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.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
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")