Differentiation of mvp objects

Differentiation of mvp objects

Usage

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

See also

taylor

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

(p <- rmvp(10,4,15,5))
#> mvp object algebraically equal to
#> 13 + 7 a b^3 c^4 e + 6 a^3 b^7 c e^4 + 5 a^3 c^2 d^2 e^4 + 5 a^3 d e^5 + 10 a^4
#> b^4 e + 3 a^5 b^4 c d^3 + 6 b c
deriv(p,"a")
#> mvp object algebraically equal to
#> 18 a^2 b^7 c e^4 + 15 a^2 c^2 d^2 e^4 + 15 a^2 d e^5 + 40 a^3 b^4 e + 15 a^4
#> b^4 c d^3 + 7 b^3 c^4 e
deriv(p,"a",3)
#> mvp object algebraically equal to
#> 240 a b^4 e + 180 a^2 b^4 c d^3 + 36 b^7 c e^4 + 30 c^2 d^2 e^4 + 30 d e^5
deriv(p,letters[1:3])
#> mvp object algebraically equal to
#> 126 a^2 b^6 e^4 + 60 a^4 b^3 d^3 + 84 b^2 c^3 e
deriv(p,rev(letters[1:3]))  # should be the same
#> mvp object algebraically equal to
#> 126 a^2 b^6 e^4 + 60 a^4 b^3 d^3 + 84 b^2 c^3 e

aderiv(p,a=1,b=2,c=1)
#> mvp object algebraically equal to
#> 756 a^2 b^5 e^4 + 180 a^4 b^2 d^3 + 168 b c^3 e

## 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
#> mvp object algebraically equal to
#> 0