deriv {spray} | R Documentation |
Partial differentiation of spray objects
Description
Partial differentiation of spray objects interpreted as multivariate polynomials
Usage
## S3 method for class 'spray'
deriv(expr, i , derivative = 1, ...)
aderiv(S,orders)
Arguments
expr |
A spray object, interpreted as a multivariate polynomial |
i |
Dimension to differentiate with respect to |
derivative |
How many times to differentiate |
... |
Further arguments, currently ignored |
S |
spray object |
orders |
The orders of the differentials |
Details
Function deriv.spray()
is the method for generic spray()
;
if S
is a spray object, then spray(S,i,n)
returns
\(\partial^n S/\partial x_i^n =
S^{\left(x_i,\ldots,x_i\right)}\).
Function aderiv()
is the generalized derivative; if S
is a
spray of arity 3, then aderiv(S,c(i,j,k))
returns
\(\frac{\partial^{i+j+k} S}{\partial x_1^i\partial x_2^j\partial
x_3^k}\).
Value
Both functions return a spray object.
Author(s)
Robin K. S. Hankin
See Also
Examples
(S <- spray(matrix(sample(-2:2,15,replace=TRUE),ncol=3),addrepeats=TRUE))
deriv(S,1)
deriv(S,2,2)
# differentiation is invariant under order:
aderiv(S,1:3) == deriv(deriv(deriv(S,1,1),2,2),3,3)
# Leibniz's rule:
S1 <- spray(matrix(sample(0:3,replace=TRUE,21),ncol=3),sample(7),addrepeats=TRUE)
S2 <- spray(matrix(sample(0:3,replace=TRUE,15),ncol=3),sample(5),addrepeats=TRUE)
S1*deriv(S2,1) + deriv(S1,1)*S2 == deriv(S1*S2,1)
# Generalized Leibniz:
aderiv(S1*S2,c(1,1,0)) == (
aderiv(S1,c(0,0,0))*aderiv(S2,c(1,1,0)) +
aderiv(S1,c(0,1,0))*aderiv(S2,c(1,0,0)) +
aderiv(S1,c(1,0,0))*aderiv(S2,c(0,1,0)) +
aderiv(S1,c(1,1,0))*aderiv(S2,c(0,0,0))
)
[Package spray version 1.0-25 Index]