ADcomplex: AD complex numbers

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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 class 'adcomplex'
Re(z)

## S3 method for class 'adcomplex'
Im(z)

## S4 method for signature 'adcomplex'
show(object)

## S3 method for class 'adcomplex'
dim(x)

## S3 replacement method for class 'adcomplex'
dim(x) <- value

## S3 method for class 'adcomplex'
x[...]

## S3 replacement method for class 'adcomplex'
x[...] <- value

## S3 method for class 'adcomplex'
t(x)

## S3 method for class 'adcomplex'
length(x)

## S3 method for class 'adcomplex'
Conj(z)

## S3 method for class 'adcomplex'
Mod(z)

## S3 method for class 'adcomplex'
Arg(z)

## S3 method for class 'adcomplex'
x + y

## S3 method for class 'adcomplex'
x - y

## S3 method for class 'adcomplex'
x * y

## S3 method for class 'adcomplex'
x / y

## S3 method for class 'adcomplex'
exp(x)

## S3 method for class 'adcomplex'
log(x, base)

## S3 method for class 'adcomplex'
sqrt(x)

## S4 method for signature 'adcomplex'
fft(z, inverse = FALSE)

## S4 method for signature 'advector'
fft(z, inverse = FALSE)

## S3 method for class 'adcomplex'
rep(x, ...)

## S3 method for class 'adcomplex'
as.vector(x, mode = "any")

## S3 method for class 'adcomplex'
is.matrix(x)

## S3 method for class 'adcomplex'
as.matrix(x, ...)

## S4 method for signature 'adcomplex,ANY'
x %*% y

## S4 method for signature 'adcomplex,ANY'
solve(a, b)

## S4 method for signature 'adcomplex'
colSums(x)

## S4 method for signature 'adcomplex'
rowSums(x)

## S4 method for signature 'adcomplex,ANY,ANY'
diag(x)

## S4 method for signature 'advector,adcomplex'
Ops(e1, e2)

## S4 method for signature 'adcomplex,advector'
Ops(e1, e2)

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

Value

Object of class "adcomplex".

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()

RTMB documentation built on Sept. 12, 2024, 6:45 a.m.