public class Function.Cts2Cts.Derivative extends Function.Cts2Cts
f
'
uses finite-differences – see apply_x(x)
and
apply_xx(δ,x)
.
A Derivative is essentialy a Cts2Cts
with
an extra apply_xx(δ,x)
(for
finite-differences).
Also see Cts2Cts.d_dx()
and
Cts2Cts.make_d_dx()
.Function.Cts2Cts.Derivative, Function.Cts2Cts.Integral, Function.Cts2Cts.WithInverse
Function.Cts2Cts, Function.Cts2Cts2Cts, Function.CtsD2CtsD, Function.HasInverse, Function.Native, Function.Native2, Function.Native3
Value.Atomic, Value.Bool, Value.Char, Value.Chars, Value.Cts, Value.Defer, Value.Discrete, Value.Enum, Value.Inc_Or, Value.Int, Value.Lambda, Value.List, Value.Maybe, Value.Option, Value.Real, Value.Scannable, Value.Structured, Value.Triv, Value.Tuple
Modifier and Type | Field and Description |
---|---|
Function.Cts2Cts |
f
"f" is a synonym for Cts2Cts.this, the Cts2Cts of
which "this" is the Derivative, f'.
|
Constructor and Description |
---|
Derivative()
Construct the Derivative of the Cts2Cts, '
f '. |
Modifier and Type | Method and Description |
---|---|
double |
apply_x(double x)
Calls
apply_xx(δ,x) for
some "small" finite-difference δ. |
double |
apply_xx(double delta,
double x)
Compute the Derivative of
f by finite-difference,
δ. |
protected Function.Cts2Cts |
make_d_dx()
The Derivative of 'this' derivative is the second
Derivative of
f , by finite differences. |
protected Function.Cts2Cts2Cts |
make_integral()
|
apply, d_dx, d2_dx2, exactIntegral, fromFunction, integral, NewtonRaphson, root, turning, uOp
public final Function.Cts2Cts f
public Derivative()
f
'.public double apply_x(double x)
apply_xx(δ,x)
for
some "small" finite-difference δ. If you do not want to
take your chances with δ being chosen for you, set your
own with apply_xx(δ,x)
;
also see make_d_dx()
.apply_x
in class Function.Cts2Cts
public double apply_xx(double delta, double x)
f
by finite-difference,
δ. Called by apply_x(x)
.
Return (f(x+δ/2)−f(x-δ/2)/δ.
Override it if there is something better (a closed form).protected Function.Cts2Cts make_d_dx()
f
, by finite differences.make_d_dx
in class Function.Cts2Cts
protected Function.Cts2Cts2Cts make_integral()
make_integral
in class Function.Cts2Cts