numerical first derivative of a function

Description

numerical first derivative of a function

Usage

gradmn(expr, ..., values = NULL, sym = 0, ntogoback = 1, print = 0, debug = 0)

Arguments

Examples

## Not run: 
# functions to be differentiated
func1="tr(A%*%X)"

# numerical values of the variables
Xn=demomat(3,2)
An=demomat(2,3)

Gradmn1 <- gradmn( func1, X=Xn, A=An, print=1, debug=0 )
Gradma1 <- gradma( func1, X=Xn, A=An, print=1, debug=0 )
printm(Gradmn1,Gradma1, fmt="9.5")
printm(max(abs(Gradmn1-Gradma1)))

# symmetric X
Xn=demomat(3,3, shape="sym")
An=demomat(3,3)
Gradmn1s <- gradmn( func1, X=Xn, A=An, sym=1, print=1, debug=0 )
Gradma1s <- gradma( func1, X=Xn, A=An, sym=1, print=1, debug=0 )
printm(Gradmn1s,Gradma1s, fmt="9.5")
printm(max(abs(Gradmn1s-Gradma1s)))


# functions to be differentiated
func5="tr(A%*%t(X)%*%B%*%X%*%C)"

# analytic derivative w.r.t. X
dexpr5="B%*%X%*%C%*%A+t(B)%*%X%*%t(A)%*%t(C)"

# numerical values of the variables
set.seed(1701)
Xn=matrix(rnorm(3*2),3,2)
An=matrix(rnorm(3*2),3,2)
Bn=matrix(rnorm(3*3),3,3)
Cn=matrix(rnorm(3*2),2,3)

Gradmn5 <- gradmn( func5, X=Xn, A=An, B=Bn, C=Cn, print=1, debug=0 )
Gradma5 <- gradma( func5, dexpr=dexpr5, X=Xn, A=An, B=Bn, C=Cn
                   , print=1, debug=0 )
printm(Gradmn5,Gradma5, fmt="9.5")
printm(max(abs(Gradmn5-Gradma5)))

# symmetric X
# numerical values of the variables
set.seed(1701)
Xn=matrix(rnorm(3*3),3,3)
Xn=Xn+t(Xn)
An=matrix(rnorm(3*3),3,3)
Bn=matrix(rnorm(3*3),3,3)
Cn=matrix(rnorm(3*3),3,3)

Gradmn5s <- gradmn( func5, X=Xn, A=An, B=Bn, C=Cn, sym=1, print=1, debug=0 )
Gradma5s <- gradma( func5, dexpr=dexpr5, X=Xn, A=An, B=Bn, C=Cn, sym=1
                   , print=1, debug=0 )
printm(Gradmn5s,Gradma5s, fmt="9.5")
printm(max(abs(Gradmn5s-Gradma5s)))

## End(Not run)