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(x) Im(x) Mod(x) Arg(x) Conj(x)
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. |
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.
is.complex
is generic: you can write methods to handle
of specific classes of objects, see InternalMethods.
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")