Numerical integration/Adaptive Simpson's method: Difference between revisions
Numerical integration/Adaptive Simpson's method (view source)
Revision as of 16:59, 10 April 2024
, 2 months agoAdded FreeBASIC
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Such a bit of executable code on the stack often is not allowed on systems hardened against hackers. Otherwise you probably needn't be concerned, even though warnings are being generated both by the compiler ''and'' the linker. :)
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<syntaxhighlight lang="vbnet">Type QuadSimpsonMem
As Double m, fm, simp
End Type
Function quadSimpsonMem(f As Function(As Double) As Double, a As Double, fa As Double, b As Double, fb As Double) As QuadSimpsonMem
Dim As QuadSimpsonMem r
r.m = (a + b) / 2
r.fm = f(r.m)
r.simp = Abs(b - a) / 6 * (fa + 4 * r.fm + fb)
Return r
End Function
Function quadAsrRec(f As Function(As Double) As Double, a As Double, fa As Double, b As Double, fb As Double, eps As Double, whole As Double, m As Double, fm As Double) As Double
Dim As QuadSimpsonMem r1 = quadSimpsonMem(f, a, fa, m, fm)
Dim As QuadSimpsonMem r2 = quadSimpsonMem(f, m, fm, b, fb)
Dim As Double delta = r1.simp + r2.simp - whole
If Abs(delta) < eps * 15 Then Return r1.simp + r2.simp + delta / 15
Return quadAsrRec(f, a, fa, m, fm, eps / 2, r1.simp, r1.m, r1.fm) + quadAsrRec(f, m, fm, b, fb, eps / 2, r2.simp, r2.m, r2.fm)
End Function
Function quadAsr(f As Function(As Double) As Double, a As Double, b As Double, eps As Double) As Double
Dim As Double fa = f(a), fb = f(b)
Dim As QuadSimpsonMem r = quadSimpsonMem(f, a, fa, b, fb)
Return quadAsrRec(f, a, fa, b, fb, eps, r.simp, r.m, r.fm)
End Function
Function sinx(x As Double) As Double
Return Sin(x)
End Function
Dim As Double a = 0, b = 1
Dim As Double result = quadAsr(@sinx, a, b, 1e-09)
Print "Simpson's integration of sine from"; a; " to"; b; " ="; result
Sleep</syntaxhighlight>
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<pre>Simpson's integration of sine from 0 to 1 = 0.4596976941317858</pre>
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<syntaxhighlight lang="
/* "structured" adaptive version, translated from Racket */
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