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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Numerical-integration/PureBasic/numerical-integration.basic Normal file
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Prototype.d TestFunction(Arg.d)
Procedure.d LeftIntegral(Start, Stop, Steps, *func.TestFunction)
Protected.d n=(Stop-Start)/Steps, sum, x=Start
While x <= Stop-n
sum + n * *func(x)
x + n
Wend
ProcedureReturn sum
EndProcedure
Procedure.d MidIntegral(Start, Stop, Steps, *func.TestFunction)
Protected.d n=(Stop-Start)/Steps, sum, x=Start
While x <= Stop-n
sum + n * *func(x+n/2)
x + n
Wend
ProcedureReturn sum
EndProcedure
Procedure.d RightIntegral(Start, Stop, Steps, *func.TestFunction)
Protected.d n=(Stop-Start)/Steps, sum, x=Start
While x < Stop
x + n
sum + n * *func(x)
Wend
ProcedureReturn sum
EndProcedure
Procedure.d Trapezium(Start, Stop, Steps, *func.TestFunction)
Protected.d n=(Stop-Start)/Steps, sum, x=Start
While x<=Stop
sum + n * (*func(x) + *func(x+n))/2
x+n
Wend
ProcedureReturn sum
EndProcedure
Procedure.d Simpson(Start, Stop, Steps, *func.TestFunction)
Protected.d n=(Stop-Start)/Steps, sum1, sum2, x=Start
Protected i
For i=0 To steps-1
sum1+ *func(Start+n*i+n/2)
Next
For i=1 To Steps-1
sum2+ *func(Start+n*i)
Next
ProcedureReturn n * (*func(Start)+ *func(Stop)+4*sum1+2*sum2) / 6
EndProcedure
;- Set up functions to integrate
Procedure.d Test1(n.d)
ProcedureReturn n*n*n
EndProcedure
Procedure.d Test2(n.d)
ProcedureReturn 1/n
EndProcedure
; This function should be integrated as a integer function, but for
; comparably this will stay as a float.
Procedure.d Test3(n.d)
ProcedureReturn n
EndProcedure
;- Test the code & present the results
CompilerIf #PB_Compiler_Debugger
MessageRequester("Notice!","Running this program in Debug-mode will be slow")
CompilerEndIf
; = 0.25
Define Answer$
Answer$="Left ="+StrD(LeftIntegral (0,1,100,@Test1()))+#CRLF$
Answer$+"Mid ="+StrD(MidIntegral (0,1,100,@Test1()))+#CRLF$
Answer$+"Right ="+StrD(RightIntegral(0,1,100,@Test1()))+#CRLF$
Answer$+"Trapezium="+StrD(Trapezium (0,1,100,@Test1()))+#CRLF$
Answer$+"Simpson ="+StrD(Simpson (0,1,100,@Test1()))
MessageRequester("Answer should be 1/4",Answer$)
; = Ln(100) e.g. ~4.60517019...
Answer$="Left ="+StrD(LeftIntegral (1,100,1000,@Test2()))+#CRLF$
Answer$+"Mid ="+StrD(MidIntegral (1,100,1000,@Test2()))+#CRLF$
Answer$+"Right ="+StrD(RightIntegral (1,100,1000,@Test2()))+#CRLF$
Answer$+"Trapezium="+StrD(Trapezium (1,100,1000,@Test2()))+#CRLF$
Answer$+"Simpson ="+StrD(Simpson (1,100,1000,@Test2()))
MessageRequester("Answer should be Ln(100), e.g. ~4.60517019",Answer$)
; 12,500,000
Answer$="Left ="+StrD(LeftIntegral (0,5000,5000000,@Test3()))+#CRLF$
Answer$+"Mid ="+StrD(MidIntegral (0,5000,5000000,@Test3()))+#CRLF$
Answer$+"Right ="+StrD(RightIntegral (0,5000,5000000,@Test3()))+#CRLF$
Answer$+"Trapezium="+StrD(Trapezium (0,5000,5000000,@Test3()))+#CRLF$
Answer$+"Simpson ="+StrD(Simpson (0,5000,5000000,@Test3()))
MessageRequester("Answer should be 12,500,000",Answer$)
; 18,000,000
Answer$="Left ="+StrD(LeftIntegral (0,6000,6000000,@Test3()))+#CRLF$
Answer$+"Mid ="+StrD(MidIntegral (0,6000,6000000,@Test3()))+#CRLF$
Answer$+"Right ="+StrD(RightIntegral (0,6000,6000000,@Test3()))+#CRLF$
Answer$+"Trapezium="+StrD(Trapezium (0,6000,6000000,@Test3()))+#CRLF$
Answer$+"Simpson ="+StrD(Simpson (0,6000,6000000,@Test3()))
MessageRequester("Answer should be 18,000,000",Answer$)