| Type: | Package |
| Title: | 'Rcpp' Bindings to 'FastAD' Auto-Differentiation |
| Version: | 0.0.4 |
| Date: | 2024-09-24 |
| Description: | The header-only 'C++' template library 'FastAD' for automatic differentiation https://github.com/JamesYang007/FastAD is provided by this package, along with a few illustrative examples that can all be called from R. |
| URL: | https://github.com/eddelbuettel/rcppfastad |
| BugReports: | https://github.com/eddelbuettel/rcppfastad/issues |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Suggests: | tinytest |
| Encoding: | UTF-8 |
| RoxygenNote: | 6.0.1 |
| Imports: | Rcpp |
| LinkingTo: | Rcpp, RcppEigen |
| NeedsCompilation: | yes |
| Packaged: | 2024-09-24 12:26:58 UTC; edd |
| Author: | Dirk Eddelbuettel 
[aut, cre],
James Yang [aut] |
| Maintainer: | Dirk Eddelbuettel <edd@debian.org> |
| Repository: | CRAN |
| Date/Publication: | 2024-09-24 12:50:06 UTC |
'Rcpp' Bindings to 'FastAD' Auto-Differentiation
Description
The header-only 'C++' template library 'FastAD' for automatic differentiation <https://github.com/JamesYang007/FastAD> is provided by this package, along with a few illustrative examples that can all be called from R.
Package Content
Index of help topics:
RcppFastAD-package 'Rcpp' Bindings to 'FastAD'
Auto-Differentiation
black_scholes Black-Scholes valuation and first derivatives
via Automatic Differentiation
linear_regression Evaluate a squared-loss linear regression at a
given parameter value
quadratic_expression Compute the value and derivate of a quadratic
expression X' * Sigma * X
Maintainer
Dirk Eddelbuettel <edd@debian.org>
Author(s)
Dirk Eddelbuettel [aut, cre] (<https://orcid.org/0000-0001-6419-907X>), James Yang [aut] (<https://orcid.org/0000-0002-0015-7812>)
Black-Scholes valuation and first derivatives via Automatic Differentiation
Description
This example illustrate how to use automatic differentiation to calculate the delte of a Black-Scholes call and put. It is based on the same example in the FastAD sources.
Usage
black_scholes(spot = 105, strike = 100, vol = 5, r = 1.25/100,
tau = 30/365)
Arguments
spot |
A double with the spot price, default is 105 as in Boost example |
strike |
A double with the strike price, default is 100 as in Boost example |
vol |
A double with the (annualized) volatility (in percent), default is 5 (for 500 per cent) as in Boost example |
r |
A double with the short-term risk-free rate, default is 0.0125 as in Boost example |
tau |
A double with the time to expiration (in fractional years), default is 30/365 as in Boost example |
Value
A matrix with rows for the call and put variant, and columns for option value, delta and vega
Examples
black_scholes()
Evaluate a squared-loss linear regression at a given parameter value
Description
Not that this function does not actually fit the model. Rather it evaluates the squared sum of residuals and ‘gradient’ of parameters.
Usage
linear_regression(X, y, theta_hat, initial_lr = 1e-04, max_iter = 100L,
tol = 1e-07)
Arguments
X |
Matrix with independent explanatory variables |
y |
Vector with dependent variable |
theta_hat |
Vector with initial ‘guess’ of parameter values |
initial_lr |
[Optional] Scalar with initial step-size value, default is 1e-4 |
max_iter |
[Optional] Scalar with maximum number of iterations, default is 100 |
tol |
[Optional] Scalar with convergence tolerance, default is 1e-7 |
Value
A list object with the ‘loss’, ‘theta’ (parameters), ‘gradient’ and ‘iter’ for iterations
Examples
data(trees) # also used in help(lm)
X <- as.matrix(cbind(const=1, trees[, c("Girth", "Height")]))
y <- trees$Volume
linear_regression(X, y, rep(0, 3), tol=1e-12)
coef(lm(y ~ X - 1)) # for comparison
Compute the value and derivate of a quadratic expression X' * Sigma * X
Description
Compute the value and derivate of a quadratic expression X' * Sigma * X
Usage
quadratic_expression(X, Sigma)
Arguments
X |
A 2 element vector |
Sigma |
A 2 x 2 matrix |
Value
A list with two elements for the expression evaluated for X and Sigma as well as
Examples
X <- c(0.5, 0.6)
S <- matrix(c(2, 3, 3, 6), 2, 2)
quadratic_expression(X, S)