Constructs the numerical derivatives of mathematical expressions
a mathematical expression (see examples and
additional parameters, typically default values for mathematical parameters
numerical finite-difference step (default is 1e-6 or 1e-4 for first and second-order derivatives, respectively)
arranges the returned function to have a
Uses a simple finite-difference scheme to evaluate the derivative. The function created
will not contain a formula for the derivative. Instead, the original function is stored
at the time the derivative is constructed and that original function is re-evaluated at the
finitely-spaced points of an interval. If you redefine the original function, that won't affect
any derivatives that were already defined from it.
Numerical derivatives, particularly high-order ones, are unstable. The finite-difference parameter
.hstep is set, by default, to give reasonable results for first- and second-order derivatives.
It's tweaked a bit so that taking a second derivative by differentiating a first derivative
will give reasonably accurate results. But,
if taking a second derivative, much better to do it in one step to preserve numerical accuracy.
a function implementing the derivative as a finite-difference approximation
WARNING: In the expressions, do not use variable names beginning with a dot, particularly
Daniel Kaplan (firstname.lastname@example.org)
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g = numD( a*x^2 + x*y ~ x, a=1) g(x=2,y=10) gg = numD( a*x^2 + x*y ~ x&x, a=1) gg(x=2,y=10) ggg = numD( a*x^2 + x*y ~ x&y, a=1) ggg(x=2,y=10) h = numD( g(x=x,y=y,a=a) ~ y, a=1) h(x=2,y=10) f = numD( sin(x)~x, add.h.control=TRUE) # plotFun( f(3,.hstep=h)~h, hlim=range(.00000001,.000001)) # ladd( panel.abline(cos(3),0))
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