Package 'RcppFastAD'

'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 <[email protected]>

Author(s)

Dirk Eddelbuettel [aut, cre] (<https://orcid.org/0000-0001-6419-907X>), James Yang [aut] (<https://orcid.org/0000-0002-0015-7812>)

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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()

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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

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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)

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