RTMB (version 1.7)

ADcomplex: AD complex numbers

Description

A limited set of complex number operations can be used when constructing AD tapes. The available methods are listed in this help page.

Usage

adcomplex(real, imag = rep(advector(0), length(real)))
# S3 method for adcomplex
Re(z)
# S3 method for adcomplex
Im(z)
# S4 method for adcomplex
show(object)
# S3 method for adcomplex
dim(x)
# S3 method for adcomplex
dim(x) <- value
# S3 method for adcomplex
[(x, ...)
# S3 method for adcomplex
[(x, ...) <- value
# S3 method for adcomplex
t(x)
# S3 method for adcomplex
length(x)
# S3 method for adcomplex
Conj(z)
# S3 method for adcomplex
Mod(z)
# S3 method for adcomplex
Arg(z)
# S3 method for adcomplex
+(x, y)
# S3 method for adcomplex
-(x, y)
# S3 method for adcomplex
*(x, y)
# S3 method for adcomplex
/(x, y)
# S3 method for adcomplex
exp(x)
# S3 method for adcomplex
log(x, base)
# S3 method for adcomplex
sqrt(x)
# S4 method for adcomplex
fft(z, inverse = FALSE)
# S4 method for advector
fft(z, inverse = FALSE)
# S3 method for adcomplex
rep(x, ...)
# S3 method for adcomplex
as.vector(x, mode = "any")
# S3 method for adcomplex
is.matrix(x)
# S3 method for adcomplex
as.matrix(x, ...)
# S4 method for adcomplex,ANY
%*%(x, y)
# S4 method for adcomplex,ANY
solve(a, b)
# S4 method for adcomplex
colSums(x)
# S4 method for adcomplex
rowSums(x)
# S4 method for adcomplex,ANY,ANY
diag(x)
# S4 method for advector,adcomplex
Ops(e1, e2)
# S4 method for adcomplex,advector
Ops(e1, e2)

Value

Object of class "adcomplex".

Arguments

real

Real part

imag

Imaginary part

z

An object of class 'adcomplex'

object

An object of class 'adcomplex'

x

An object of class 'adcomplex'

value

Replacement value

...

As [

y

An object of class 'adcomplex'

base

Not implemented

inverse

As fft

mode

As as.vector

a

matrix

b

matrix, vector or missing

e1

Left operand

e2

Right operand

Functions

• adcomplex(): Construct adcomplex vector

• Re(adcomplex): As complex

• Im(adcomplex): As complex

• show(adcomplex): Print method

• dim(adcomplex): As dim

• dim(adcomplex) <- value: As dim

• [: As [

• `[`(adcomplex) <- value: As [<-

• t(adcomplex): As t

• length(adcomplex): As length

• Conj(adcomplex): As complex

• Mod(adcomplex): As complex

• Arg(adcomplex): As complex

• + : As complex

• - : As complex

• * : As complex

• / : As complex

• exp(adcomplex): As complex

• log(adcomplex): As complex

• sqrt(adcomplex): As complex

• fft(adcomplex): Fast Fourier Transform equivalent to fft. Notably this is the multivariate transform when x is an array.

• fft(advector): If real input is supplied it is first converted to complex.

• rep(adcomplex): As rep

• as.vector(adcomplex): Apply for each of real/imag

• is.matrix(adcomplex): Apply for real

• as.matrix(adcomplex): Apply for each of real/imag

• x %*% y: Complex matrix multiply

• solve(a = adcomplex, b = ANY): Complex matrix inversion and solve

• colSums(adcomplex): Apply for each of real/imag

• rowSums(adcomplex): Apply for each of real/imag

• diag(x = adcomplex, nrow = ANY, ncol = ANY): Apply for each of real/imag

• Ops(e1 = advector, e2 = adcomplex): Mixed real/complex arithmetic

• Ops(e1 = adcomplex, e2 = advector): Mixed real/complex arithmetic

Examples

## Tape using complex operations
F <- MakeTape(function(x) {
  x <- as.complex(x)
  y <- exp( x * ( 1 + 2i ) )
  c(Re(y), Im(y))
}, numeric(1))
F
F(1)
## Complex FFT on the tape
G <- MakeTape(function(x) sum(Re(fft(x))), numeric(3))
G$simplify()
G$print()