deriv: Differentiation of `mvp` objects

Description

Differentiation of mvp objects

Usage

# S3 method for mvp
deriv(expr, v, ...)
# S3 method for mvp
aderiv(expr, ...)

Arguments

expr: Object of class mvp
v: Character vector. Elements denote variables to differentiate with respect to
...: Further arguments. In deriv(), a non-negative integer argument specifies the order of the differential, and in aderiv() the argument names specify the differentials and their values their respective orders

Author

Robin K. S. Hankin

Details

deriv(S,v) returns \(\frac{\partial^r S}{\partial v_1\partial v_2\ldots\partial v_r}\). Here, v is a (character) vector of symbols.

deriv(S,v,n) returns the n-th derivative of S with respect to symbol v, \(\frac{\partial^n S}{\partial v^n}\).

aderiv() uses the ellipsis construction with the names of the argument being the variable to be differentiated with respect to. Thus aderiv(S,x=1,y=2) returns \(\frac{\partial^3 S}{\partial x\partial y^2}\).

Examples

Run this code


(p <- rmvp(10,4,15,5))
deriv(p,"a")
deriv(p,"a",3)
deriv(p,letters[1:3])
deriv(p,rev(letters[1:3]))  # should be the same

aderiv(p,a=1,b=2,c=1)

## verify the chain rule:
x <- rmvp(7,symbols=6)
v <- allvars(x)[1]
s <- as.mvp("1  +  y  -  y^2 zz  +  y^3 z^2")
LHS <- subsmvp(deriv(x,v)*deriv(s,"y"),v,s)   # dx/ds*ds/dy
RHS <- deriv(subsmvp(x,v,s),"y")              # dx/dy

LHS - RHS # should be zero