Numerical Differentiation Toolbox

Functions to evaluate derivatives, partial derivatives, gradients, directional derivatives, Jacobians, and Hessians.

Numerical Differentiation Toolbox

This toolbox supplies functions to evaluate derivatives, partial derivatives, gradients, directional derivatives, Jacobians, and Hessians using the forward difference, central difference, and complex-step approximations of a derivative.

Documentation

Toolbox Documentation
Technical Documentation

To open the home page of the toolbox documentation in MATLAB, type

doc_NDT

in the Command Window. To open the documentation of a specific function with name function_name from the Command Window, type

doc_NDT function_name

To open the PDF file with the technical documentation (Numerical_Differentiation_using_Finite_Difference_and_Complex_Step_Approximations.pdf) from the Command Window, type

doc_NDT tech

Complex-Step Differentiation Functions

df = iderivative(f,x0)
pf = ipartial(f,x0,k)
g = igradient(f,x0)
Dv = idirectional(f,x0,v)
J = ijacobian(f,x0)
H = ihessian(f,x0)

"Complexified" Functions

y = iabs(x)
z = iatan2(y,x)
z = iatan2d(y,x)
z = idot(x,y)
m = imax(x1,x2)
m = imin(x1,x2)
r = imod(a,n)
y = inorm(x)

Central Difference Differentiation Functions

df = cderivative(f,x0)
pf = cpartial(f,x0,k)
g = cgradient(f,x0)
Dv = cdirectional(f,x0,v)
J = cjacobian(f,x0)
H = chessian(f,x0)

Forward Difference Differentiation Functions

df = fderivative(f,x0)
pf = fpartial(f,x0,k)
g = fgradient(f,x0)
Dv = fdirectional(f,x0,v)
J = fjacobian(f,x0)
H = fhessian(f,x0)