Package: nabla 0.7.1

nabla: Exact Derivatives via Automatic Differentiation

Exact automatic differentiation for R functions. Provides a composable derivative operator D that computes gradients, Hessians, Jacobians, and arbitrary-order derivative tensors at machine precision. D(D(f)) gives Hessians, D(D(D(f))) gives third-order tensors for skewness of maximum likelihood estimators, and so on to any order. Works through any R code including loops, branches, and control flow.

Authors:Alexander Towell [aut, cre]

nabla_0.7.1.tar.gz
nabla_0.7.1.zip(r-4.7)nabla_0.7.1.zip(r-4.6)nabla_0.7.1.zip(r-4.5)
nabla_0.7.1.tgz(r-4.6-any)nabla_0.7.1.tgz(r-4.5-any)
nabla_0.7.1.tar.gz(r-4.7-any)nabla_0.7.1.tar.gz(r-4.6-any)
nabla_0.7.1.tgz(r-4.6-emscripten)
manual.pdf |manual.html✨
DESCRIPTION |NEWS
card.svg |card.png
nabla/json (API)

# Install 'nabla' in R:
install.packages('nabla', repos = c('https://queelius.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/queelius/nabla/issues

On CRAN:

Conda:

automatic-differentiationderivative-operatorgradienthessianhigher-order-derivativesjacobianmle

4.88 score 8 scripts 185 downloads 26 exports 0 dependencies

Last updated from:0e1ef3ca94. Checks:9 OK. Indexed: yes.

TargetResultTimeFilesSyslog
linux-devel-x86_64OK145
source / vignettesOK192
linux-release-x86_64OK144
macos-release-arm64OK94
macos-oldrel-arm64OK124
windows-develOK104
windows-releaseOK103
windows-oldrelOK108
wasm-releaseOK84

Exports:atan2betaDderivderiv_ndifferentiate_ndualdual_constantdual_constant_ndual_variabledual_variable_ndual_vectorerferfcgradienthessianis_dualjacobianlbetaMathMath2OpspsigammashowSummaryvalue

Dependencies:

Gradient and Hessian Computation with nabla
Helper: finite difference utilities | Normal log-likelihood: known sigma, unknown mu | Normal log-likelihood: unknown mu and sigma | Poisson log-likelihood: unknown lambda | Visualizing the gradient | Gamma log-likelihood: unknown shape, known rate | Logistic regression: 2 predictors | Newton-Raphson optimizer | Contour plot: Normal(mu, sigma) log-likelihood surface | Newton-Raphson convergence path | jacobian(): differentiating a vector-valued function | Summary
Rendered frommle-workflow.Rmdusingknitr::rmarkdown

Last update: 2026-02-07
Started: 2026-01-31

Higher-Order Derivatives
The D operator | Curvature analysis | Visualizing curvature along sin(x) | Taylor expansion | Connection to MLE: exact Hessians for standard errors | How it works: nested duals | Summary
Rendered fromhigher-order.Rmdusingknitr::rmarkdown

Last update: 2026-02-07
Started: 2026-01-31

Higher-Order MLE Analysis
Motivation | The Gamma model | Finding the MLE | Score and observed information | Third-order derivative tensor | Asymptotic skewness of the MLE | Monte Carlo validation | Visualizing MLE asymmetry | Summary
Rendered frommle-skewness.Rmdusingknitr::rmarkdown

Last update: 2026-02-07
Started: 2026-02-02

Introduction to nabla
What is nabla? | Quick start | Works through any R code | Multi-parameter functions | Quick comparison: three ways to differentiate | Why exact derivatives matter | How it works: dual numbers | What's next?
Rendered fromintroduction.Rmdusingknitr::rmarkdown

Last update: 2026-02-07
Started: 2026-01-31

Optimizer Integration
Introduction | optim() with AD gradients | nlminb() with AD gradient + Hessian | Logistic regression example | Standard errors from the Hessian | Convergence comparison | Summary
Rendered fromoptimizer-integration.Rmdusingknitr::rmarkdown

Last update: 2026-02-07
Started: 2026-01-31

Readme and manuals

Help Manual

Help pageTopics
nabla: Exact Derivatives via Automatic Differentiationnabla-package nabla
Beta function for dual numbersbeta beta,ANY,ANY-method beta,numeric,numeric-method
Composable total derivative operatorD
Extract the derivative (tangent) part of a dual numberderiv deriv,dualr-method deriv,numeric-method
Extract the k-th derivative from a nested dual resultderiv_n
Compute a function value and all derivatives up to order ndifferentiate_n
Create a dual numberdual
Create a dual constant (derivative seed = 0)dual_constant
Create a constant dual for n-th order differentiationdual_constant_n
Create a dual variable (derivative seed = 1)dual_variable
Create a dual seeded for n-th order differentiationdual_variable_n
Create a vector of dual numbersdual_vector
Indexing and length for dual_vectordual_vector-access length,dual_vector-method [,dual_vector,numeric-method
Dual Number Vectordual_vector-class
Arithmetic and comparison operators for dual numbers!,dualr-method *,dualr,dualr-method *,dualr,numeric-method *,numeric,dualr-method +,dualr,dualr-method +,dualr,missing-method +,dualr,numeric-method +,numeric,dualr-method -,dualr,dualr-method -,dualr,missing-method -,dualr,numeric-method -,numeric,dualr-method /,dualr,dualr-method /,dualr,numeric-method /,numeric,dualr-method dual-arithmetic Ops,dualr,dualr-method Ops,dualr,numeric-method Ops,numeric,dualr-method ^,dualr,dualr-method ^,dualr,numeric-method ^,numeric,dualr-method
Two-argument arctangent for dual numbersatan2,dualr,dualr-method atan2,dualr,numeric-method atan2,numeric,dualr-method dual-atan2
Coerce dual to numericas.numeric,dualr-method dual-coerce
Combine dual numbers into a dual_vectorc,dualr-method dual-combine
Check if a dual number is numericdual-is-numeric is.numeric,dualr-method
Logarithm with optional base for dual numbersdual-log log,dualr-method
Math group generic for dual numbersdual-math exp,dualr-method Math,dualr-method sqrt,dualr-method
Math2 group generic for dual numbersdual-math2 Math2,dualr-method
Piecewise max and min for dual numbersdual-maxmin max,dualr-method min,dualr-method
Display a dual numberdual-show show,dualr-method show,dual_vector-method
Summary group generic for dual numbersdual-summary Summary,dualr-method
Dual Number Class for Automatic Differentiationdualr-class
Error functionerf erf,dualr-method erf,numeric-method
Complementary error functionerfc erfc,dualr-method erfc,numeric-method
Compute the gradient of a scalar-valued functiongradient
Compute the Hessian of a scalar-valued functionhessian
Test whether an object is a dual numberis_dual
Compute the Jacobian of a vector-valued functionjacobian
Log-beta function for dual numberslbeta lbeta,dualr,dualr-method lbeta,dualr,numeric-method lbeta,numeric,dualr-method lbeta,numeric,numeric-method
Polygamma function for dual numberspsigamma psigamma,dualr-method psigamma,numeric-method
Extract the value (primal) part of a dual numbervalue value,dualr-method value,numeric-method