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ADtools (version 0.5.4)

Automatic Differentiation Toolbox

Description

Implements the forward-mode automatic differentiation for multivariate functions using the matrix-calculus notation from Magnus and Neudecker (2019) . Two key features of the package are: (i) it incorporates various optimisation strategies to improve performance; this includes applying memoisation to cut down object construction time, using sparse matrix representation to speed up derivative calculation, and creating specialised matrix operations to reduce computation time; (ii) it supports differentiating random variates with respect to their parameters, targeting Markov chain Monte Carlo (MCMC) and general simulation-based applications.

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Install

install.packages('ADtools')

Monthly Downloads

10

Version

0.5.4

License

MIT + file LICENSE

Issues

Pull Requests

Stars

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Repository

https://github.com/kcf-jackson/ADtools

Maintainer

Chun Fung Kwok

Last Published

November 9th, 2020

Functions in ADtools (0.5.4)

Diagonal matrix

Compute (I %x% C) D

The density of the Wishart distribution

-,dual,missing-method

Subtraction of 'dual'-class objects (unary dual)

The density of the multivariate normal distribution

crossprod,dual,missing-method

Crossproduct of 'dual'-class objects

-,dual,dual-method

Subtraction of 'dual'-class objects (dual-dual)

The density of the multivariate t distribution

Compute A (I %x% C)

%*%,dual,dual-method

Matrix multiplication of 'dual'-class objects (dual-dual)

Return the First or Last Part of an Object

Diagonal matrix (memoised)

%*%,ANY,dual-method

Matrix multiplication of 'dual'-class objects (ANY-dual)

log,dual-method

Element-wise logarithm of a dual object

add_vector_to_matrix_row

Add a column vector to each row of a matrix

The density of the gamma distribution

add_vector_to_matrix_column

Add a column vector to each column of a matrix

-,ANY,dual-method

Subtraction of 'dual'-class objects (dual-ANY)

nrow,dual-method

kronecker,ANY,dual-method

Kronecker multiplication of 'dual'-class objects (ANY-dual)

inverse_transform

Simulation by inverse transform

^,dual,dual-method

Powers of 'dual'-class objects (dual-dual)

colSums,dual-method

Column sum of a matrix.

Simulate multivariate normal random variates

^,dual,ANY-method

Powers of 'dual'-class objects (dual-ANY)

rchisq0,numeric,dual-method

Simulate Chi-square random variates

Coerce the first component of the dual object into a matrix.

Cholesky decomposition

colMeans,dual-method

Column mean of a matrix.

as.vector,dual-method

Coerce the first component of the dual object into a vector.

mcm_optimal_order

Find the optimal order of multiplying a matrix chain

Diagonal matrix

rowSums,dual-method

Row sum of a matrix.

Simulate Chi-square random variates

/,dual,dual-method

(Element-wise) Division of 'dual'-class objects (dual-dual)

solve,dual,missing-method

Inverse of 'dual'-class objects

Automatic differentiation

/,dual,ANY-method

(Element-wise) Division of 'dual'-class objects (dual-ANY)

commutation_matrix

Commutation matrix

Determinant of a 'dual'-class object

rbind2,dual,dual-method

Combine 'dual'-class objects by Rows (dual-dual)

sqrt,dual-method

Element-wise square-root of a dual object

%*%,dual,ANY-method

Matrix multiplication of 'dual'-class objects (dual-ANY)

Simulate gamma random variates

The density of the exponential distribution

cbind2,dual,ANY-method

Combine 'dual'-class objects by Columns (dual-ANY)

Pre-multiplying a kronecker product

The density of the normal distribution

sum,dual-method

Sum of matrix elements

det,dual-method

Determinant of a 'dual'-class object

Converting a list of parameters into a list of dual numbers

cbind2,dual,dual-method

Combine 'dual'-class objects by Columns (dual-dual)

commutation_matrix0

Commutation matrix (memoised)

Simulate univariate normal random variates

chol,dual-method

Cholesky decomposition of 'dual'-class objects

Simulate multivariate normal random variates

Coerce the first component of the dual object into a matrix.

cos,dual-method

Element-wise cosine of a dual object

dim,dual-method

Dimension of an Object

The density of the chi-squared distribution

Half-vectorisation

rWishart0,dual,dual-method

Simulating from Wishart distribution using Bartlett decomposition

The density of the student-t distribution

Dual number constructor

Transpose of 'dual'-class objects

Interface for optimal matrix chain multiplication

length,dual-method

Length of an Object

matrix_determinant

Determinant of a matrix

chol0,dual-method

Cholesky decomposition of 'dual'-class objects

Finite difference method

exp,dual-method

Element-wise exponential of a dual object

Simulate Wishart random variates

Simulate random variates from the student-t distribution

Matrix of zeroes

^,ANY,dual-method

Powers of 'dual'-class objects (ANY-dual)

+,dual,dual-method

Addition of 'dual'-class objects (dual-dual)

Generate a matrix randomly from a normal distribution

tan,dual-method

Element-wise tangent of a dual object

gamma,dual-method

Element-wise gamma of a dual object

elimination_matrix

Elimination matrix

Generate a matrix randomly from a uniform distribution

S4 class "dual"

The density of the inverse Wishart distribution

upper_tri_matrix

Construct an upper triangular matrix from a vector

Initialise the dual component

Matrix of zeroes (memoised)

round,dual,integer-method

Rounding of Numbers

tcrossprod,dual,ANY-method

Crossproduct of 'dual'-class objects

rexp0,numeric,dual-method

Simulate exponential random variates

-,dual,ANY-method

Subtraction of 'dual'-class objects (dual-ANY)

Extract parts of an object

elimination_matrix0

Elimination matrix (memoised)

Simulate exponential random variates

lower_tri_matrix

Construct a lower triangular matrix from a vector

mean,dual-method

Mean of vector or matrix elements

ncol,dual-method

Number of columns

rbind2,ANY,dual-method

Combine 'dual'-class objects by Rows (ANY-dual)

*,dual,ANY-method

(Element-wise) Multiplication of 'dual'-class objects (dual-ANY)

+,ANY,dual-method

Addition of 'dual'-class objects (ANY-dual)

rgamma0,numeric,dual,dual-method

Simulate gamma random variates

vec,dual-method

kronecker,dual,ANY-method

Kronecker multiplication of 'dual'-class objects (dual-ANY)

/,ANY,dual-method

(Element-wise) Division of 'dual'-class objects (ANY-dual)

*,dual,dual-method

(Element-wise) Multiplication of 'dual'-class objects (dual-dual)

Matrix of ones (memoised)

kronecker,dual,dual-method

Kronecker product of 'dual'-class objects (dual-dual)

rbind2,dual,ANY-method

Combine 'dual'-class objects by Rows (dual-ANY)

+,dual,ANY-method

Addition of 'dual'-class objects (dual-ANY)

rt0,numeric,dual-method

Simulate random variates from the student-t distribution

Executing the matrix multiplication given the optimal order

Simulate random variates from the multivariate t distribution

rowMeans,dual-method

Row mean of a matrix.

Rounding of Numbers

Add rownames and colnames to the dual component

sin,dual-method

Element-wise sine of a dual object

Trace of a matrix

Return the First or Last Part of an Object

*,ANY,dual-method

(Element-wise) Multiplication of 'dual'-class objects (ANY-dual)

Trace of a matrix

vech,dual-method

Half-vectorisation

Compute A (B %x% I)

Compute (B %x% I) D

Post-multiplying a kronecker product

ADtools-package

ADtools: Automatic Differentiation

Band matrix (memoised)

cbind2,ANY,dual-method

Combine 'dual'-class objects by Columns (ANY-dual)