[Dhbnumerics-discussion] Code for spline differentiation

[d p. <mr....@gm...>]

!DhbNumericalMethodsTestCase methodsFor: 'functionEvaluation' !
 
testSplineDifferentiation
"
self debug: #testSplineDifferentiation
"
	| interval testInterval interpolator |
	interval := 0.0 to: 10.0 by: 0.1.
	testInterval := 1.0 to: 9.0 by: 0.05.
	interpolator := DhbSplineInterpolator new.
	interval do: [:x | interpolator add: x @ x sin].
	testInterval do: [:x | self assert: (x cos - (interpolator
valueDerivative: x)) abs < 1.0e-6]! !



!DhbSplineInterpolator methodsFor: 'information' !
  
valueDerivative: aNumber 
"needs a trivial refactoring with #value to remove identical code"
	| answer n1 n2 n step a b  constantTerm aTerm bTerm |
	coefficients isNil ifTrue: [self computeSecondDerivatives].
	n2 := pointCollection size.
	n1 := 1.
	[n2 - n1 > 1] whileTrue: 
			[n := (n1 + n2) // 2.
			(self xPointAt: n) > aNumber ifTrue: [n2 := n] ifFalse: [n1 := n]].
	step := (self xPointAt: n2) - (self xPointAt: n1).
	a := ((self xPointAt: n2) - aNumber) / step.
	b := (aNumber - (self xPointAt: n1)) / step.
	constantTerm := ((self yPointAt: n2)  - (self yPointAt: n1)) / step. 
	aTerm := (coefficients at: n1) * (1 - (3 * a squared)) * step / 6 .
	bTerm := (coefficients at: n2) * (1 - (3 * b squared)) * step / 6 . 
	^ constantTerm + aTerm - bTerm. 
	! !