XProfan

English

p.specht

Interessanter point is not always integrally simply, for defined Funktionskurven whom rose at a place X To detect. if the namely at all meaningfully is, remaining sometimes nevertheless nothing other over as mere numerische modes To use. These having but too your Tücken, z.B. with Nullstellen or (+/-Infinity)-Polstellen. hereinafter get The worst entrapments abgefangen, but warranty is the still always no, that the with others Funktionstypen too works. means is it testing, checken, try - for what the nachstehende Progi helpful his could.

Compile Mark Separation

Window Title "Test: Numerische Differentiation (rose "+\
"in x to the Differenzenmethode)"
' *************************************************
' (CL) CopyLeft 2013-09 by P. woodpecker, Wien
' without jedwede Gewähr!
' *************************************************

proc FNY : parameters x!

    return -1*10^-35' here comment, function hereinafter program:
    return sin(x!)

endproc

' *************************************************
' *** Differenzenmethode, here optimiert for    ***
' *** Winkelfunktionen in the area sew (+1..-1) ***
' *************************************************

proc Ableitung :parameters x!

    var nenn!=x!*(1.000005-0.999995)
    case nenn!=0:return 0
    return (fny(x!*1.000005)-fny(x!*0.999995))/nenn!

endproc

Window Style 24:font 2:randomize
Window 0,0-%maxx,%maxy-40
var xh&=width(%hwnd)\2:var yh&=height(%hwnd)\2

if fny(1)=-1*10^-35

    print "\n Abzuleitende function Please in Proc FNY(x) einprogrammieren!"
    sound 770,100:sound 440,300
    waitinput 10000
    end

endif

declare xa!,xm!,xe!,xd!,y$,x!,y!
declare xl&,yl&,xn&,yn&
declare xo&,yo&,xm&,ym&
declare xp&,yp&,xq&,yq&
Print "\n     present ex X-Start = ";:input xa!
print "                 To X-End = ";:input xe!

if xe!=0:xe!=8:xa!=-8:endif'== pure Laziness ====

    print "  Fehlerfunktion present? ";:input y$
    case y$="":y$="Ja"
    y$=upper$(left$(y$,1)):case y$="Y":y$="J"
    'only Schleppwerte the unterschiedlichen Line-command:
    xl&=0:yl&=yh& : xo&=0:yo&=yh& : xq&=0:yq&=yh&
    x!=xa!
    xd!=(xe!-xa!)/(2*xh&)
    case xd!=0:xd!=1*10^-35

    repeat

        usepen 0,2,rgb(255,0,0)
        y!=fny(x!)
        xn&=(x!-xa!)/xd!
        yn&=yh&-100*y!
        line xl&,yl& - xn&,yn&
        xl&=xn&:yl&=yn&
        usepen 0,1,rgb(0,0,155)
        y!=Ableitung(x!)
        xm&=(x!-xa!)/xd!
        ym&=yh& - 100*y!
        line xo&,yo& - xm&,ym&
        xo&=xm&:yo&=ym&

        if y$="J"

            usepen 0,1,rgb(0,255,0)
            y!=Ableitung(x!)-cos(x!)
            xq&=(x!-xa!)/xd!
            yq&=yh& - 10^12*y!
            line xp&,yp& - xq&,yq&
            xp&=xq&:yp&=yq&

        endif

        x!=x!+xd!' STEP

    until x!>xe!

    waitinput
    end

P.s.: on the most dangerous attend Divisionen through zero, same behind it are negatives Wurzelargumente one beliebter Exception- or quite Aufhängegrund. negatives Logarithmen make The thing too tensive, solid followed of To high greifenden Potenzfunktionen..

XProfan 11
Computer: Gerät, daß es in Mikrosekunden erlaubt, 50.000 Fehler zu machen, zB 'daß' statt 'das'...

05/10/21 ▲

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