Arithmetic Operators

Description

Arithmetic operators for objects of class 'dual'

Usage

## S4 method for signature 'dual,dual'
e1 + e2

## S4 method for signature 'dual,numericOrArray'
e1 + e2

## S4 method for signature 'numericOrArray,dual'
e1 + e2

## S4 method for signature 'dual,missing'
e1 + e2

## S4 method for signature 'dual,dual'
e1 - e2

## S4 method for signature 'dual,missing'
e1 - e2

## S4 method for signature 'dual,numericOrArray'
e1 - e2

## S4 method for signature 'numericOrArray,dual'
e1 - e2

## S4 method for signature 'dual,dual'
e1 * e2

## S4 method for signature 'dual,numeric'
e1 * e2

## S4 method for signature 'numeric,dual'
e1 * e2

## S4 method for signature 'dual,numeric'
e1 / e2

## S4 method for signature 'numeric,dual'
e1 / e2

## S4 method for signature 'dual,dual'
e1 / e2

## S4 method for signature 'dual,numeric'
e1 ^ e2

## S4 method for signature 'numeric,dual'
e1 ^ e2

## S4 method for signature 'dual,dual'
e1 ^ e2

Arguments

Details

The usual operations are performed, with appropriate propagation of the derivatives

Value

An object of class 'dual'.

Examples

x <- dual( c(1,2) )
a <- 2 * x + 3
a
d(a)
b <- x[1] + 3*x[2]
b
d(b)

Comparison Operators

Description

Comparison operators for objects of class 'dual'

Usage

## S4 method for signature 'dual,ANY'
Compare(e1, e2)

Arguments

Details

usual comparison operators, ignoring derivatives valuesa

Value

a logical vector

Extract or replace parts of an object

Description

Methods for extraction or replacements of parts of dual objects.

Usage

## S4 replacement method for signature 'dual,index,index,dual'
x[i, j, ...] <- value

## S4 replacement method for signature 'dual,missing,index,dual'
x[i, j, ...] <- value

## S4 replacement method for signature 'dual,index,missing,dual'
x[i, j, ...] <- value

## S4 replacement method for signature 'dual,missing,missing,dual'
x[i, j, ...] <- value

## S4 replacement method for signature 'dual,index,index,logicalOrNumericOrArray'
x[i, j, ...] <- value

## S4 replacement method for signature 'dual,missing,index,logicalOrNumericOrArray'
x[i, j, ...] <- value

## S4 replacement method for signature 'dual,index,missing,logicalOrNumericOrArray'
x[i, j, ...] <- value

## S4 replacement method for signature 'dual,missing,missing,logicalOrNumericOrArray'
x[i, j, ...] <- value

## S4 method for signature 'dual,index,index'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'dual,missing,index'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'dual,index,missing'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'dual,missing,missing'
x[i, j, ..., drop = TRUE]

Arguments

Value

returns a dual object (the semantic is the same as base extraction and replacement methods).

Examples

x <- c(1, 2, 3)
x[2] <- dual(4)
x
d(x)

Mathematical functions

Description

various mathematical functions and methods

Usage

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

## S3 method for class 'dual'
expm1(x)

logNeper(x)

## S3 method for class 'dual'
log(x, base = exp(1))

## S3 method for class 'dual'
log10(x)

## S3 method for class 'dual'
log2(x)

## S3 method for class 'dual'
log1p(x)

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

## S3 method for class 'dual'
cos(x)

## S3 method for class 'dual'
sin(x)

## S3 method for class 'dual'
tan(x)

## S3 method for class 'dual'
cospi(x)

## S3 method for class 'dual'
sinpi(x)

## S3 method for class 'dual'
tanpi(x)

## S3 method for class 'dual'
acos(x)

## S3 method for class 'dual'
asin(x)

## S3 method for class 'dual'
atan(x)

## S4 method for signature 'dual,dual'
atan2(y, x)

## S4 method for signature 'dual,numericOrArray'
atan2(y, x)

## S4 method for signature 'numericOrArray,dual'
atan2(y, x)

## S3 method for class 'dual'
cosh(x)

## S3 method for class 'dual'
sinh(x)

## S3 method for class 'dual'
tanh(x)

## S3 method for class 'dual'
acosh(x)

## S3 method for class 'dual'
asinh(x)

## S3 method for class 'dual'
atanh(x)

## S3 method for class 'dual'
abs(x)

## S3 method for class 'dual'
sign(x)

## S3 method for class 'dual'
ceiling(x)

## S3 method for class 'dual'
floor(x)

## S3 method for class 'dual'
trunc(x, ...)

## S3 method for class 'dual'
gamma(x)

## S3 method for class 'dual'
lgamma(x)

## S3 method for class 'dual'
digamma(x)

## S3 method for class 'dual'
trigamma(x)

psigamma.dual(x, deriv = 0)

## S4 method for signature 'dual'
psigamma(x, deriv = 0)

## S4 method for signature 'dual,dual'
beta(a, b)

## S4 method for signature 'dual,numericOrArray'
beta(a, b)

## S4 method for signature 'numericOrArray,dual'
beta(a, b)

## S4 method for signature 'dual,dual'
lbeta(a, b)

## S4 method for signature 'dual,numericOrArray'
lbeta(a, b)

## S4 method for signature 'numericOrArray,dual'
lbeta(a, b)

factorial.dual(x)

lfactorial.dual(x)

## S4 method for signature 'dual,numeric'
choose(n, k)

## S4 method for signature 'dual,numeric'
lchoose(n, k)

Arguments

Details

The derivative of 'abs' is set to be the function 'sign', so its derivative in 0 is considered as null. You may want to redefine 'abs' using 'dualFun1' to get an undefined derivative.

Value

All functions return dual objects.

Examples

x <- dual(1)
y <- log(x)
y
d(y)

Summary methods for objects of class dual

Description

Methods extending to dual objects the corresponding methods for numeric objects.

Usage

## S3 method for class 'dual'
sum(x, ..., na.rm = FALSE)

## S4 method for signature 'numericOrArray'
sum(x, ..., na.rm = FALSE)

## S3 method for class 'dual'
prod(x, ..., na.rm = FALSE)

## S4 method for signature 'numericOrArray'
prod(x, ..., na.rm = FALSE)

## S3 method for class 'dual'
max(x, ..., na.rm = TRUE)

## S4 method for signature 'numericOrArray'
max(x, ..., na.rm = TRUE)

## S3 method for class 'dual'
min(x, ..., na.rm = TRUE)

## S4 method for signature 'numericOrArray'
min(x, ..., na.rm = TRUE)

## S3 method for class 'dual'
range(x, ..., na.rm = TRUE)

## S4 method for signature 'numericOrArray'
range(x, ..., na.rm = TRUE)

## S4 method for signature 'dual'
which.min(x)

## S4 method for signature 'dual'
which.max(x)

Arguments

Details

For 'max' and 'min', the derivative is equal to the derivative of maximum element as identified by 'which.max' and 'which.min'. This is unfortunately problematic in presence of ties. If this is an issue, you may redefine this function (at the expense of speed).

Value

'which.min' and 'which.max' return an integer, the other methods return a dual object.

Examples

x <- dual( c(1,2,4) )
sum(x)
d(sum(x), "x1")

Apply functions over array margins of dual objects

Description

This method generalizes 'base::apply' to dual objects.

Usage

## S4 method for signature 'dual'
apply(X, MARGIN, FUN, ..., simplify = TRUE)

Arguments

Value

The returned value depends on the values returned by 'FUN', similarly to 'base::apply'

See Also

apply

Examples

A <- matrix( c(1,2,3,4), 2, 2)
x <- dual(A)
cs <- apply(x, 2, sum)
cs
d(cs)
# prefered method for summing over the columns
colSums(x) 

Binding methods for dual objects

Description

Methods allowing to use 'cbind' and 'rbind' with dual objects.

Usage

## S4 method for signature 'dual,dual'
rbind2(x,y,...)

## S4 method for signature 'dual,numericOrArray'
rbind2(x,y,...)

## S4 method for signature 'numericOrArray,dual'
rbind2(x,y,...)

## S4 method for signature 'dual,missing'
rbind2(x,y,...)

## S4 method for signature 'dual,dual'
cbind2(x,y,...)

## S4 method for signature 'dual,numericOrArray'
cbind2(x,y,...)

## S4 method for signature 'numericOrArray,dual'
cbind2(x,y,...)

## S4 method for signature 'dual,missing'
cbind2(x,y,...)

Arguments

Value

A dual matrix combining the arguments.

Examples

x <- dual( c(1, 3) )
y <- cbind(x, 2*x+1, 3*x+2, c(0,1))
y
d(y, "x1")

Concatenation methods

Description

Methods have been defined in order to allow the concatenation of 'dual' objects together and with constant objects.

Usage

## S4 method for signature 'numericOrArray'
c(x, ...)

Arguments

Value

an object of class dual.

Examples

x <- dual( 1 )
# concatenation with a constant
x <- c(x, 2)
x
d(x)
# concatenation of dual objects
x1 <- sum(x)
x2 <- sum(x**2)
y <- c(a = x1, b = x2)  # you can use named arguments
y
d(y)

Row and column sums and means

Description

Method extending to dual matrices the corresponding methods for dual matrices.

Usage

rowSums.dual(x, na.rm = FALSE, dims = 1, ...)

## S4 method for signature 'dual'
rowSums(x, na.rm = FALSE, dims = 1, ...)

colSums.dual(x, na.rm = FALSE, dims = 1, ...)

## S4 method for signature 'dual'
colSums(x, na.rm = FALSE, dims = 1, ...)

rowMeans.dual(x, na.rm = FALSE, dims = 1, ...)

## S4 method for signature 'dual'
rowMeans(x, na.rm = FALSE, dims = 1, ...)

colMeans.dual(x, na.rm = FALSE, dims = 1, ...)

## S4 method for signature 'dual'
colMeans(x, na.rm = FALSE, dims = 1, ...)

Arguments

Value

a dual object (usually a dual vector).

Examples

x <- dual( c(1,2) )
x <- cbind(x, 2*x+1)
rowSums(x)
d(rowSums(x), "x1")

get list of derivatives

Description

Get value, differential of a dual object, and the names of associated variables.

Usage

d(x, varnames)

value(x)

## S3 method for class 'dual'
value(x)

## S3 method for class 'numeric'
value(x)

varnames(x)

## S3 method for class 'dual'
varnames(x)

## S3 method for class 'numeric'
varnames(x)

Arguments

Details

If 'varnames' is provided to the function 'd', a list of derivatives along the given variables will be sent back. In general, it sends back the derivatives along all associated variables.

The 'varnames' function sends back the names of all variables for which a derivative is defined.

Value

A named list of derivatives.

Examples

x <- dual(c(3,2))
varnames(x^2)
x**2
value(x**2)
d(x**2)
d(x**2, "x1")
# you can use these methods with a numerical constant
value(1)
varnames(1)
d(1, "x1")

Matrix diagonals

Description

Methods extending to dual objects the corresponding methods for numeric objects.

Usage

diag.dual(x, nrow, ncol, names = TRUE)

## S4 method for signature 'dual'
diag(x = 1, nrow, ncol, names = TRUE)

## S4 replacement method for signature 'dual,dual'
diag(x) <- value

## S4 replacement method for signature 'dual,numericOrArray'
diag(x) <- value

Arguments

Value

A dual object, similarly to 'base::diag'

Examples

x <- dual( c(1,2) )
diag(x)
d(diag(x), "x1")
y <- matrix(x, 2, 2)
diag(y) <- 2*diag(y)
y
d(y)
diag(y)

Normal distribution

Description

Density for the normal distribution, accepting objects of class 'dual'

Usage

dnorm(x, mean = 0, sd = 1, log = FALSE)

dnorm.dual(x, mean = 0, sd = 1, log = FALSE)

Arguments

Details

'dnorm.dual' will make straightfoward a computation (in R), that works both with numeric or dual objects. 'dnorm' will call 'dnorm.dual' if any of the objects is of class dual, or 'stats::dnorm' is all objects are of class numeric. As 'stats::dnorm' is in written in C it is factor.

If you care for performance, use 'stats::dnorm' directly for non dual numbers, and 'dnorm.dual' for dual numbers.

Value

a dual object.

Examples

x <- dual(0)
dnx <- dnorm(x)
dnx
d(dnx)

Dual objects

Description

Create a dual object

Usage

dual(x, varnames, dx, constant = FALSE)

Arguments

Details

The basic usage is dual(x) which will create an object of class 'dual' with unit derivatives in each of its components. The variable names will be derived from the names of x, or generated in the form x1, x2, etc.

Another possible usage is dual(x, varnames = c('x1', 'x2'), constant = TRUE) which returns an object with null derivatives in x1 and x2.

Finally, a list of derivatives can be defined using option dx.

Value

an object of class 'dual'

Examples

# simple usage
x <- dual( c(1,2) )
x
d(x)
x <- dual(matrix(c(1,2,3,4), 2, 2))
x
d(x, "x1.1")

# using an object with names
x <- dual( c(a = 1, b = 2) )
x
d(x)

# generate a constant 
x <- dual(1, varnames = c("x1", "x2"), constant = TRUE)

# specify dx
x <- dual(c(1,2), dx = list(x1 = c(1,1)))
x
d(x)
# this is equivalent to :
x <- dual(1)
x <- c(x, x + 1)
x
d(x)

dual class

Description

An S4 class for forward differentiation of vector and matrix computations.

Details

A dual object can be either a vector or a matrix. It can contain derivatives with respect to several variables. The derivatives will have the same shape as the value.

The shape of an object can be changed using 'dim<-'. Note that by default 'as.matrix' and 'as.vector' will send back a regular vector/matrix object, dropping the derivatives. See 'salad' to change this behaviour if needed (this is not the recommended solution).

Many methods and functions have been redefined in the package, in order to allow to apply existing code to 'dual' objects, with no or little change.

Slots

x

the value of the object. Use the function 'value' to access this slot.

d

a (named) list of derivatives. Use the function 'd' to access this slot.

See Also

value, d, dual, salad.

Examples

# creating a vector of length 4
x <- dual( c(1,2,1,0) )
x
d(x)
# turning x into a matrix
dim(x) <- c(2,2)
x
d(x)
# and back into a vector
dim(x) <- NULL
x
# weighted sum of the elements of x
S <- sum(1:4 * x)
S
d(S)

Defining in-house derivatives

Description

Defining the differential of a univariate function

Usage

dualFun1(f, df)

Arguments

Details

This function returns a new function that can be applied to a dual object. This allows to extend the package by defining functions it is currenlty unable to derive. It can also gain some time for intensively used functions (see examples below).

Value

Returns a function.

Examples

# using salad do compute the differential of a quadratic function
f <- function(x) x**2 + x + 1
x <- dual(4)
f(x)
d(f(x))

# using `dualFun1` to define the differential of f saves time
f1 <- dualFun1(f, \(x) 2*x + 1)
f1(x)
d(f1(x))
system.time( for(i in 1:500) f(x) )
system.time( for(i in 1:500) f1(x) )

Gradient descent

Description

A simple implementation of the gradient descent algorithm

Usage

gradient.descent(
  par,
  fn,
  ...,
  step = 0.1,
  maxit = 100,
  reltol = sqrt(.Machine$double.eps),
  trace = FALSE
)

Arguments

Details

First note that this is not an efficient optimisation method. It is included in the package as a demonstration only.

The function iterates x_{n+1} = x_{n} - step \times grad f(x_n) until convergence. The gradient is computed using automatic differentiation.

The convergence criterion is as in optim \frac{ |f(x_{n+1}) - f(x_n)| }{ |f(x[n])| + reltol } < reltol .

Value

a list with components: 'par' is the final value of the parameter, 'value' is the value of 'f' at 'par', 'counts' is the number of iterations performed, 'convergence' is '0' is the convergence criterion was met. If 'trace' is 'TRUE', an extra component 'trace' is included, which is a matrix giving the successive values of x_n.

Examples

f <- function(x) (x[1] - x[2])**4 + (x[1] + 2*x[2])**2 + x[1] + x[2]

X <- seq(-1, .5, by = 0.01)
Y <- seq(-0.5, 0.5, by = 0.01)
Z <- matrix(NA_real_, nrow = length(X), ncol = length(Y))
for(i in seq_along(X)) for(j in seq_along(Y)) Z[i,j] <- f(c(X[i],Y[j]))

par(mfrow = c(2,2), mai = c(1,1,1,1)/3)
contour(X,Y,Z, levels = c(-0.2, 0, 0.3, 2**(0:6)), main = "step = 0.01")
gd1 <- gradient.descent(c(0,0), f, step = 0.01, trace = TRUE)
lines(t(gd1$trace), type = "o", col = "red")

contour(X,Y,Z, levels = c(-0.2, 0, 0.3, 2**(0:6)))
gd2 <- gradient.descent(c(0,0), f, step = 0.1, trace = TRUE)
lines(t(gd2$trace), type = "o", col = "red")

contour(X,Y,Z, levels = c(-0.2, 0, 0.3, 2**(0:6)))
gd3 <- gradient.descent(c(0,0), f, step = 0.18, trace = TRUE)
lines(t(gd3$trace), type = "o", col = "red")

contour(X,Y,Z, levels = c(-0.2, 0, 0.3, 2**(0:6)))
gd4 <- gradient.descent(c(0,0), f, step = 0.2, trace = TRUE)
lines(t(gd4$trace), type = "o", col = "red")

Conditionnal Element Selection

Description

‘ifelse' methods extend 'base::ifelse' to allow using dual objects for ’yes' or 'no' arguments.

Usage

ifelse(test, yes, no)

Arguments

Value

A dual object (dual vector).

Examples

x <- dual(c(1,2,4,6))
y <- ifelse(x > 2, x, x/2)
y
d(y)

Determinant and matrix inversion for dual matrices

Description

Methods extending to dual matrices the corresponding methods for numeric matrices.

Usage

det.dual(x, ...)

## S4 method for signature 'dual'
det(x, ...)

## S3 method for class 'dual'
determinant(x, logarithm = TRUE, ...)

## S4 method for signature 'dual,dual'
solve(a, b, ...)

## S4 method for signature 'dual,missing'
solve(a, b, ...)

## S4 method for signature 'numericOrArray,dual'
solve(a, b, ...)

## S4 method for signature 'dual,numericOrArray'
solve(a, b, ...)

Arguments

Value

'det' returns a dual scalar, 'determinant' a list with components 'modulus' (which is a dual object) and 'sign', and 'solve' returns a dual object (vector or matrix).

Examples

x <- dual( matrix(c(1,2,1,3), 2, 2) )
det(x)
d(det(x), "x1.1")
solve(x)
d(solve(x), "x1.1")

Matrix Arithmetic

Description

Methods and functions for dual matrix arithmetic

Usage

matrixprod_dn(x, y)

matrixprod_nd(x, y)

matrixprod_dd(x, y)

## S4 method for signature 'dual,numericOrArray'
x %*% y

## S4 method for signature 'numericOrArray,dual'
x %*% y

## S4 method for signature 'dual,dual'
x %*% y

## S4 method for signature 'dual,dual'
crossprod(x, y)

## S4 method for signature 'dual,numericOrArray'
crossprod(x, y)

## S4 method for signature 'numericOrArray,dual'
crossprod(x, y)

## S4 method for signature 'dual,missing'
crossprod(x, y)

## S4 method for signature 'dual,dual'
tcrossprod(x, y)

## S4 method for signature 'dual,numericOrArray'
tcrossprod(x, y)

## S4 method for signature 'numericOrArray,dual'
tcrossprod(x, y)

## S4 method for signature 'dual,missing'
tcrossprod(x, y)

Arguments

Details

All methods are the analog of the corresponding methods for matrices. The functions 'matrixprod_dd', 'matrixprod_nd' and 'matrixprod_dn' are for multiplication of two dual objects, of a numeric and a dual object, or of a dual and a numeric object, respectively. You may use these functions to save the method dispatching time.

Value

A dual object.

Examples

x <- dual( matrix(c(0,1,3,1), 2, 2) )
y <- x %*% c(2,-2)
d(y, "x1.1")

Methods for 'matrix', 'array', 'as.matrix' and 'as.vector'

Description

Methods for 'matrix', 'array', 'as.matrix' and 'as.vector'

Usage

## S4 method for signature 'dual'
matrix(data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL)

## S4 method for signature 'dual'
array(data = NA, dim = length(data), dimnames = NULL)

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

## S4 method for signature 'dual'
as.matrix(x, ...)

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

## S4 method for signature 'dual'
as.vector(x, mode = "any")

Arguments

Details

The default behaviour for 'as.matrix' dans 'as.vector' is to drop the derivatives. This can be modified using 'salad' (to use with care). The prefered method to change the shape is to use 'dim<-'.

Value

A dual object for 'matrix' and 'array', a base object for 'as.matrix' and 'as.vector'.

See Also

shape, salad, dual-class

Examples

x <- dual(c(1,2,0,4))
y <- matrix(x, 2, 2)
y
as.matrix(y)
dim(x) <- c(2,2)
x

Wrapper for optimisation with automatically computed gradient

Description

Wrapper for calling stats::optim with a gradient computed by automatic differentiation

Usage

optiWrap(
  par,
  fn,
  ...,
  method = c("BFGS", "L-BFGS-B", "CG"),
  lower = -Inf,
  upper = Inf,
  control = list(),
  hessian = FALSE,
  trace = FALSE
)

Arguments

Details

The gradient of fn is computed using unlist(d(fn(x))). It is computed at the same time as fn(x)' and stored for when optim calls the gradient. In most cases this should be more efficient than defining gr = \(x) unlist(d(f(dual(x)))).

Parameters 'method' 'lower' 'upper' 'control' and 'hessian' are passed directly to optim.

See Also

optim

Examples

f <- function(x) (x[1] - x[2])**4 + (x[1] + 2*x[2])**2 + x[1] + x[2]

X <- seq(-1, 0.5, by = 0.01)
Y <- seq(-1, 0.5, by = 0.01)
Z <- matrix(NA_real_, nrow = length(X), ncol = length(Y))
for(i in seq_along(X)) for(j in seq_along(Y)) Z[i,j] <- f(c(X[i],Y[j]))

contour(X,Y,Z, levels = c(-0.2, 0, 0.3, 2**(0:6)), main = "BFGS")
opt <- optiWrap(c(0,0), f, method = "BFGS", trace = TRUE)
lines(t(opt$trace), type = "o", col = "red")

Outer product for dual objects

Description

Method extending to dual object the usual method method

Usage

outer.dual(X, Y, FUN = "*", ...)

## S4 method for signature 'dual,dual'
outer(X, Y, FUN = "*", ...)

## S4 method for signature 'numericOrArray,dual'
outer(X, Y, FUN = "*", ...)

## S4 method for signature 'dual,numericOrArray'
outer(X, Y, FUN = "*", ...)

## S4 method for signature 'dual,dual'
X %o% Y

## S4 method for signature 'numericOrArray,dual'
X %o% Y

## S4 method for signature 'dual,numericOrArray'
X %o% Y

Arguments

Details

Methods extending 'outer' and '

Value

A dual matrix.

Examples

x <- dual(1:3)
outer(x, x)
d(outer(x,x), "x2")

Replicate elements of a dual vector

Description

A method extending 'rep' to dual objects

Usage

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

Arguments

Value

A dual object.

Examples

x <- rep( dual(1:2), each = 4 )
x
d(x)

Salad options

Description

Set or get options values for package 'salad'

Usage

salad(...)

Arguments

Details

Currently, only one option can be defined, drop.derivatives, which modifies the bevahiour of S3 methods as.vector and as.matrix and corresponding S4 methods. The default value is set to 'TRUE', which means that as.vector and as.matrix will return a 'base' objects, without derivatives. Setting drop.derivatives = FALSE will make these functions return an object of class dual. This might be useful to re-use exiting code, but may cause some functions to break, and should be use with care.

Use salad() to get the current value of all options, or salad(name) to get the current value of a given option.

Value

A list with the defined options, or a single element when salad(name) is used.

Examples

salad("drop.derivatives")
x <- dual(matrix(c(1,2,3,4), 2, 2))
salad(drop.derivatives = FALSE)
as.vector(x)
salad(drop.derivatives = TRUE)
as.vector(x)

Dual objects length, dim, names and dimnames

Description

S3 methods for length, dim, names and dimnames

Usage

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

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

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

## S3 method for class 'dual'
dimnames(x)

## S3 replacement method for class 'dual'
dimnames(x) <- value

## S3 method for class 'dual'
names(x)

## S3 replacement method for class 'dual'
names(x) <- value

Arguments

Details

As the methods 'dimnames' and 'dimnanes<-.dual' have been defined, you can use 'rownames' and 'colnames' as with numeric matrices (see examples).

Value

Return values are similar to the base methods.

Examples

x <- dual( matrix(c(1,0,2,3,2,4), 2, 3) )
dim(x)
length(x)
rownames(x) <- c("L1", "L2")
x
d(x, "x1.1")

# modifying dim is the recommended way to change dual object shape
dim(x) <- NULL
x

# back to matrix shape
dim(x) <- c(2, 3)
x

Transposition of matrices and arrays

Description

Transposition of matrices and arrays

Usage

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

## S3 method for class 'dual'
aperm(a, perm = NULL, resize = TRUE, ...)

Arguments

Value

A dual matrix or array.

Examples

x <- dual( matrix(c(1,2,0,3), 2, 2) )
t(x)

# creation of an array using dim<-
y <- dual( c(1,-1) ) + 1:12
dim(y) <- c(2,3,2)
z <- aperm(y, c(2,3,1))
z
d(z, "x1")