| 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 complex. |
z |
an object of mode complex, or one of a class for which
a methods has been defined. |
... |
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. Modulus and argument are also called the polar
coordinates. If z = x + i y with real x and y,
for r = Mod(z) = sqrt{x^2 + y^2}, and
phi = Arg(z), x = r*cos(phi) and
y = r*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.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
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")