pnd 0.dev roadmap (2024-XX-XX)

• BUG: Check the example with neural networks where gr does not accept the arguments of f
• BUG: Matching in the Hessian is too slow – de-duplicate first
• BUG: 1x1 Hessians?
• BUG: arguments are sometimes not passed to FUN; example: AE98 simulation
• UX: make the warnings once-per-sessionl; print the first error in runParallel in Grad
• FEATURE: make all helper generators use runParallel instead of the long if-else
• FEATURE: add an algorithm where the two lines intersect; should fix sin'(pi/2) with two branches
• FEATURE: Implement de-duplication in the grid of points; reuse f0 and other precomputed values
• FEATURE: If h is a character in Grad, extract the gradient directly if the order is 2
• FEATURE: disable parallelisation if f(x) takes less than 0.002 s
• FEATURE: SW algorithm for arbitrary derivative and accuracy orders
• FEATURE: if any algorithm returns a step size larger than 0.5*|x|, throw a warning
• FEATURE: update the rounding error as the estimated sum of differences and evaluations of f
• FEATURE: Handle NA in step size selection
• FEATURE: Auto-shrink the step size at the beginning of all procedures if FUN(x) is not finite
• FEATURE: Add absolute or relative step size
• FEATURE: add diagnostics to return an attribute of grad containing original f evaluations
• FEATURE: Add a vector of step sizes for different arguments
• FEATURE: Pass arguments from Grad to fdCoef, e.g. allow stencils in Grad or stencil matrices like in the presentation
• FEATURE: Create control or method.args for Grad with automatic step selection
• FEATURE: Hessian via direct 4-term difference for a faster evaluation
• FEATURE: Functions for fast and reliable Hessian computation based on parallel gradient evaluation
• FEATURE: Return attribute of the estimated absolute error
• FEATURE: Arbitrary mixed orders
• DOCUMENTATION: Compare with stats::numericDeriv
• MISC: Write the list of controls on the help page of gradstep() explicitly!
• MISC: Check which packages depend on numDeriv and check compatibility with 10 top!
• MISC: Add links to documentation and tutorials onto the GitHub page.
• MISC: Detailed vignette explaining the mathematics behind the functions with full transparency about the choice of parameters
• DEV: add examples for large matrices (200 x 200)
• DEV: ensure that Grad takes all the arguments of GenD and Jacobian, and vice versa
• DEV: Ensure unit-test coverage >90%
• DEV: Check the compatibility between the function and its documentation
• DEV: Check the release with todor::todor_package(), lintr::lint_package(), R CMD check --as-cran, and goodpractice::gp(checks = all_checks()[!grepl("^lintr", all_checks())])

pnd 0.0.7 (2025-XX-XX)

pnd 0.0.6 (2025-01-25)

• Fix: Derivatives of vectorised functions are working. Example: Grad(sin, 1:4)
• Feature: Auto-detecting the number of cores available on multi-core machines to speed up computations
• Feature: Added plug-in step size selection with an estimated f''' with a rule of thumb
• Feature: Auto-detection of parallel type
• Feature: Added zero tolerance to the default step for a fixed step

pnd 0.0.5 (2025-01-14)

• Feature: Extended the step-selection routines to gradients (vector input x)
• Feature: Parallelisation of step selection in all algorithms
• Feature: Mathur’s AutoDX algorithm for step size selection step.M()
• Feature: Added Hessian() that supports central differences (for the moment) and arbitrary accuracy
• Feature: Separate Grad() and Jacobian() that call the workhorse, GenD(), for compatibility with numDeriv

pnd 0.0.4 (2024-06-10)

• Feature: Stepleman–Winarsky algorithm for step size selection step.SW()
• Feature: Automated wrapper for step size selection gradstep()
• Improvement: Safe handling of function errors and non-finite returns in step-size selection procedures
• Improvement: Finite-difference coefficients gained attributes: Taylor expansion, coefficient on the largest truncated term, and effective accuracy (useful for custom stencils)
• Improvement: added unit tests for core features

pnd 0.0.3 (2024-06-01)

• Feature: solveVandermonde() to solve ill-conditioned problems that arise in weight calculation
• Feature: Dumontet–Vignes algorithm for step size selection step.DV()
• Feature: Curtis–Reid algorithm for step size selection step.CR() and its modification
• Feature: Different step sizes for the gradient
• Fix: If the user supplies a short custom stencil and requests a high accuracy order, it will provide the best available order and produce a warning
• Fix: The output of Grad() preserves the names of x and FUN(x), which prevents errors in cases where names are required

pnd 0.0.2 (2023-12-06)

• Fix: bug in stencil calculation

pnd 0.0.1 (2023-09-01)

• Initial release
• Computing finite-difference coefficients on arbitrary stencils
• Computing numerical gradients with reasonable default step sizes
• Numerical Jacobians
• Support for mclapply() on *nix systems only