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@@ -496,501 +496,3 @@ begin
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Showresults;
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Showresults;
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end;
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end;
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end.
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end.
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-program intge1te;
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-
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-uses
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- typ,
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- spe,
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- int;
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-
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-const
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- e = 2.71828182845905;
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- fnames = 'KI A0 A1 A2 A3 A4 SS SL SE V1 V2 ';
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- ogs: array[1..11] of ArbFloat = (0, 0, 1, e, 0, 1, 0, 1, 1, 1, 1);
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- integraaltekst: array[1..11, 1..5] of string[60] =
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- ((' ì ',
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- ' ô -àcosh(x) ',
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- {k0} ' ³ e dx = k0(à), mits à > 0. ',
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- ' õ ',
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- '0 '),
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- (' ì ',
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- ' ô sin x àcos x ',
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- {a0} ' ³ ------- + ---------- dx = 1, mits à>0 ',
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- ' õ (x+1)à (x+1)(à+1) ',
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- '0 '),
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- (' ì ',
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- ' ô 1 ',
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- {a1} ' ³ ---- dx = 1/(à-1), mits à>1 ',
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- ' õ xà ',
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- '1 '),
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- (' ì ',
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- ' ô dx ',
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- {a2} ' ³ --------- = 1/(à-1), mits à>1 ',
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- ' õ x.ln(x)à ',
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- 'e '),
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- (' ì ',
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- ' ô Ú àùxàùsin(xà) cos(xà)¿ ',
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- {a3} ' ³ ³ -------------- + ---------³ dx = 1, mits à>0 ',
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- ' õ À x(x+1) (x+1)ý Ù ',
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- '0 '),
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- (' ì ',
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- ' ô Ú 2sin(«ãùxà) xàùcos(«ãùxà) ¿ ',
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- {a4} ' ³ ³-------------- + ãà-----------------³ dx = 1, mits àò0',
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- ' õ À (x+1)ý x(x+1) Ù ',
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- '1 '),
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- (' ss(n)=2*(n+1)(à-1)/n (n=1,2,3...), àò0 ',
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- {ss} ' ss(x)=0 als min(|n-x|) ò 0.5/(n+1)à ',
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- ' ss lineair interpoleren als min(|n-x|) ó 0.5/(n+1)à ',
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- ' int. 0:ì = ä [1:ì] 1/(n(n+1)) = 1 ',
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- ' '),
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- (' ì ',
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- ' ô sin(ln(x)) 1 ',
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- {sl} ' ³ --------- dx = ---------, mits à>1 ',
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- ' õ xà (à-1)ý+1 ',
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- '1 '),
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- (' ì ',
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- ' ô sin(xà)-à.x(à-1).cos(xà) sin(1) ',
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- {se} ' ³ --------------------------- dx = ------ ',
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- ' õ ex e ',
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- '1 '),
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- (' ì ',
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- ' ô à.|x|(à-1) ',
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- {v1} ' ³ ---------------- dx = 1, mits à > 0 ',
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- ' õ ã.(|x|(2à) + 1) ',
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- '-ì '),
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- (' ì 0 ì ',
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- ' ô ô àx ô -x/à ',
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- {v2} ' ³ v2(x)dx = ³ e dx + ³ e dx = à + 1/à, mits à > 0',
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- ' õ õ õ ',
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- '-ì -ì 0 '));
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-
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-var
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- alfa, ond, inte, int1: ArbFloat;
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- u, i: ArbInt;
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- s: string;
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- q: char;
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- f: rfunc1r;
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- scale: boolean;
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-
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- function Ki(x: ArbFloat): ArbFloat;
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- var
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- kk: ArbFloat;
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- begin
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- if abs(x) < ln(100 / alfa) then
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- kk := Exp(-alfa * Specoh(x))
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- else
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- kk := 0;
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- if scale then
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- ki := kk / int1
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- else
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- ki := kk;
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- end;
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-
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- function uki(u: ArbFloat): ArbFloat; {u=1/(x+1), of x=1/u-1}
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- begin
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- if u > 0 then
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- uki := ki((1 - u) / u) / sqr(u)
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- else
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- uki := 0;
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- end;
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-
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- function a0(x: ArbFloat): ArbFloat;
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- begin
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- a0 := ((x + 1) * sin(x) + alfa * cos(x)) * spepow(x + 1, -alfa - 1);
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- end;
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-
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- function ua0(u: ArbFloat): ArbFloat; {u=1/(x+1), of x=1/u-1}
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- begin
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- if u > 0 then
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- ua0 := a0((1 - u) / u) / sqr(u)
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- else
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- ua0 := 0;
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- end;
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-
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- function a1(x: ArbFloat): ArbFloat;
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- var
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- a: ArbFloat;
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- begin
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- a := spepow(x, -alfa);
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- if scale then
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- a1 := (alfa - 1) * a
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- else
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- a1 := a;
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- end;
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-
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- function ua1(u: ArbFloat): ArbFloat; {u=ond/x of x=ond/u}
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- begin
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- if u > 0 then
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- ua1 := a1(ond / u) * ond / sqr(u)
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- else
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- ua1 := 0;
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- end;
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-
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- function a2(x: ArbFloat): ArbFloat;
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- var
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- a: ArbFloat;
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- begin
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- a := spepow(ln(x), -alfa) / x;
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- if scale then
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- a2 := (alfa - 1) * a
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- else
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- a2 := a;
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- end;
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-
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- function ua2(u: ArbFloat): ArbFloat; {u=ond/x of x=ond/u}
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- begin
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- if u > 0 then
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- ua2 := a2(ond / u) * ond / sqr(u)
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- else
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- ua2 := 0;
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- end;
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-
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- function a3(x: ArbFloat): ArbFloat;
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- var
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- y: ArbFloat;
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- begin
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- if x = 0 then
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- a3 := 0
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- else
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- begin
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- y := spepow(x, alfa);
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- a3 := alfa * y * sin(y) / (x * (x + 1)) + cos(y) / sqr(x + 1);
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- end;
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- end;
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-
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- function ua3(u: ArbFloat): ArbFloat; {u=1/(x+1), of x=1/u-1}
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- begin
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- if u > 0 then
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- ua3 := a3((1 - u) / u) / sqr(u)
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- else
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- ua3 := 0;
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- end;
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-
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- function a4(x: ArbFloat): ArbFloat;
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- var
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- y, z: ArbFloat;
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- begin
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- y := spepow(x, alfa);
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- z := y * pi / 2;
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- a4 := 2 * sin(z) / sqr(x + 1) - pi * alfa * y * cos(z) / (x * (x + 1));
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- end;
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-
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- function ua4(u: ArbFloat): ArbFloat; {u=ond/x of x=ond/u}
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- begin
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- if u > 0 then
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- ua4 := a4(ond / u) * ond / sqr(u)
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- else
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- ua4 := 0;
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- end;
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-
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- function ss(x: ArbFloat): ArbFloat;
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- var
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- d, eps, r: ArbFloat;
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- begin
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- if x > 0.5 then
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- begin
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- d := frac(x);
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- r := x - d;
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- if d > 0.5 then
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- begin
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- d := 1 - d;
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- r := r + 1;
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- end;
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- eps := 0.5 / spepow(r + 1, alfa);
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- if d > eps then
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- ss := 0
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- else
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- ss := (1 - d / eps) / (r * (r + 1) * eps);
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- end
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- else
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- ss := 0;
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- end;
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-
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- function uss(u: ArbFloat): ArbFloat; {u=ond/x of x=ond/u}
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- begin
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- if u > 0 then
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- uss := ss(ond / u) * ond / sqr(u)
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- else
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- uss := 0;
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- end;
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-
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- function sl(x: ArbFloat): ArbFloat;
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- var
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- sl1: ArbFloat;
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- begin
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- sl1 := sin(ln(x)) * spepow(x, -alfa);
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- if scale then
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- sl := sl1 / int1
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- else
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- sl := sl1;
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- end;
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-
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- function usl(u: ArbFloat): ArbFloat; {u=ond/x of x=ond/u}
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- begin
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- if u > 0 then
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- usl := sl(ond / u) * ond / sqr(u)
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- else
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- usl := 0;
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- end;
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-
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- function se(x: ArbFloat): ArbFloat;
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- var
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- y, se1: ArbFloat;
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- begin
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- y := spepow(x, alfa);
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- se1 := (sin(y) - alfa * (y / x) * cos(y)) * exp(-x);
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- if scale then
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- se := se1 / int1
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- else
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- se := se1;
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- end;
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-
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- function use(u: ArbFloat): ArbFloat; {u=ond/x of x=ond/u}
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- begin
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- if u > 0 then
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- use := se(ond / u) * ond / sqr(u)
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- else
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- use := 0;
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- end;
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-
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- function v1(x: ArbFloat): ArbFloat;
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- var
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- a, y: ArbFloat;
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- begin
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- x := abs(x);
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- alfa := abs(alfa);
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- if x = 0 then
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- begin
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- if alfa = 1 then
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- v1 := alfa / pi
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- else
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- v1 := 0;
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- end
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- else
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- begin
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- if x > 1 then
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- a := -alfa - 1
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- else
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- a := alfa - 1;
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- y := spepow(x, a);
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- v1 := alfa * y / (pi * (sqr(x * y) + 1));
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- end;
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- end;
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-
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- function uv1(u: ArbFloat): ArbFloat; { u=«((2/ã)arctan(x)+1) of x=tan(«ã(2u-1)) }
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- var
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- y: ArbFloat; { 0 ó u ó 1 }
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- begin
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- if (u = 0) or (u = 1) then
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- uv1 := 0
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- else
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- begin
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- y := 1 / sqr(cos(pi * (u - 0.5)));
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- uv1 := pi * v1(sqrt(y - 1)) * y;
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- end;
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- end;
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-
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- function v2(x: ArbFloat): ArbFloat;
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- var
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- v: ArbFloat;
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- begin
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- alfa := abs(alfa);
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- if x > 0 then
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- v := exp(-x / alfa)
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- else
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- if x < 0 then
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- v := exp(x * alfa)
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- else
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- v := 1;
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- if scale then
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- v2 := v / (alfa + 1 / alfa)
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- else
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- v2 := v;
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- end;
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-
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- function uv2(u: ArbFloat): ArbFloat; { u=«((2/ã)arctan(x)+1) of x=tan(«ã(2u-1)) }
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- var
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- y: ArbFloat; { 0 ó u ó 1 }
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- begin
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- if (u = 0) or (u = 1) then
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- uv2 := 0
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- else
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- begin
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- y := 1 / sqr(cos(pi * (u - 0.5)));
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- if u > 0.5 then
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- uv2 := pi * v2(sqrt(y - 1)) * y
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- else
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- uv2 := pi * v2(-sqrt(y - 1)) * y;
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- end;
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- end;
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-
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-var
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- integral, ae, err: ArbFloat;
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- term, num2: ArbInt;
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- intex, First: boolean;
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-
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- procedure Header;
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- var
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- i: ArbInt;
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- begin
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- for i := 1 to 5 do
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- if i = 3 then
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- writeln(s: 3, ': ', Integraaltekst[u, i])
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- else
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- writeln('': 5, Integraaltekst[u, i]);
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- end;
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-
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- procedure ShowResults;
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- var
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- f: ArbFloat;
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- begin
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- if First then
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- writeln('alfa': num2, '': numdig - num2, 'ae': 7, ' ': 4, 'int': num2,
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- '': numdig - num2, ' ', 'err': 7, ' ': 4, 'f': 6);
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- First := False;
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- if intex then
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- f := inte - integral;
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- case term of
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- 1:
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- begin
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- Write(alfa: numdig, ae: 10, integral: numdig, ' ', err: 10, ' ');
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- if intex then
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|
|
|
- writeln(f: 10)
|
|
|
|
- else
|
|
|
|
- writeln;
|
|
|
|
- end;
|
|
|
|
- 2:
|
|
|
|
- begin
|
|
|
|
- Write(alfa: numdig, ae: 10, integral: numdig, ' ', err: 10, ' ');
|
|
|
|
- if intex then
|
|
|
|
- writeln(f: 10)
|
|
|
|
- else
|
|
|
|
- writeln;
|
|
|
|
- Writeln(' process afgebroken, te hoge nauwkeurigheid?');
|
|
|
|
- end;
|
|
|
|
- 3: Writeln('Verkeerde waarde ae (<=0) bij aanroep: ', ae: 8);
|
|
|
|
- 4:
|
|
|
|
- begin
|
|
|
|
- Write(alfa: numdig, ae: 10, integral: numdig, ' ', err: 10, ' ');
|
|
|
|
- if intex then
|
|
|
|
- writeln(f: 10)
|
|
|
|
- else
|
|
|
|
- writeln;
|
|
|
|
- writeln(' process afgebroken, moeilijk, mogelijk divergent?');
|
|
|
|
- end;
|
|
|
|
- end;
|
|
|
|
- end;
|
|
|
|
-
|
|
|
|
-const
|
|
|
|
- fint: array[boolean, 1..11] of rfunc1r =
|
|
|
|
- ((@ki, @a0, @a1, @a2, @a3, @a4, @ss, @sl, @se, @v1, @v2),
|
|
|
|
- (@uki, @ua0, @ua1, @ua2, @ua3, @ua4, @uss, @usl, @use, @uv1, @uv2));
|
|
|
|
-begin
|
|
|
|
- s := ParamStr(1);
|
|
|
|
- if s = '' then
|
|
|
|
- begin
|
|
|
|
- writeln(' Vergeten functienaam mee te geven!');
|
|
|
|
- writeln(' Kies uit: ', fnames);
|
|
|
|
- halt;
|
|
|
|
- end;
|
|
|
|
- for i := 1 to length(s) do
|
|
|
|
- s[i] := Upcase(s[i]);
|
|
|
|
- u := (Pos(s, fnames) + 2) div 3;
|
|
|
|
- if u = 0 then
|
|
|
|
- begin
|
|
|
|
- writeln(' Commandlineparameter ', s, ' bestaat niet');
|
|
|
|
- writeln(' Kies uit: ', fnames);
|
|
|
|
- halt;
|
|
|
|
- end;
|
|
|
|
-
|
|
|
|
- Write('program results int1fr function ' + s);
|
|
|
|
- case SizeOf(ArbFloat) of
|
|
|
|
- 4: writeln('(single)');
|
|
|
|
- 8: writeln('(double)');
|
|
|
|
- 6: writeln('(real)');
|
|
|
|
- end;
|
|
|
|
- num2 := numdig div 2;
|
|
|
|
- if Pos(s, 'a0 a4 a3 ss v1') > 0 then
|
|
|
|
- scale := True
|
|
|
|
- else
|
|
|
|
- begin
|
|
|
|
- Write(' scale ? (y or n)');
|
|
|
|
- readln(q);
|
|
|
|
- scale := Upcase(q) = 'Y';
|
|
|
|
- end;
|
|
|
|
- Write('Transformatie naar 0 => 1 ? (y or n)');
|
|
|
|
- readln(q);
|
|
|
|
- ond := ogs[u];
|
|
|
|
- f := fint[Upcase(q) = 'Y'][u];
|
|
|
|
- Header;
|
|
|
|
- Writeln('à en ae: ');
|
|
|
|
- First := True;
|
|
|
|
- while not eoln do
|
|
|
|
- begin
|
|
|
|
- Read(alfa, ae);
|
|
|
|
- intex := True;
|
|
|
|
- case u of
|
|
|
|
- 1: int1 := spebk0(alfa);
|
|
|
|
- 2:
|
|
|
|
- begin
|
|
|
|
- int1 := 1;
|
|
|
|
- intex := alfa > 0;
|
|
|
|
- end;
|
|
|
|
- 3:
|
|
|
|
- begin
|
|
|
|
- if alfa > 1 then
|
|
|
|
- int1 := 1 / (alfa - 1);
|
|
|
|
- intex := alfa > 1;
|
|
|
|
- end;
|
|
|
|
- 4:
|
|
|
|
- begin
|
|
|
|
- if alfa > 1 then
|
|
|
|
- int1 := 1 / (alfa - 1);
|
|
|
|
- intex := alfa > 1;
|
|
|
|
- end;
|
|
|
|
- 5:
|
|
|
|
- begin
|
|
|
|
- if alfa > 0 then
|
|
|
|
- int1 := 1
|
|
|
|
- else
|
|
|
|
- int1 := cos(1);
|
|
|
|
- intex := alfa > 0;
|
|
|
|
- end;
|
|
|
|
- 6:
|
|
|
|
- begin
|
|
|
|
- int1 := 1;
|
|
|
|
- intex := alfa > 0;
|
|
|
|
- end;
|
|
|
|
- 7: int1 := 1;
|
|
|
|
- 8:
|
|
|
|
- begin
|
|
|
|
- if alfa > 1 then
|
|
|
|
- int1 := 1 / (sqr(alfa - 1) + 1);
|
|
|
|
- intex := alfa > 1;
|
|
|
|
- end;
|
|
|
|
- 9: int1 := sin(1) / e;
|
|
|
|
- 10:
|
|
|
|
- begin
|
|
|
|
- int1 := 1;
|
|
|
|
- intex := alfa <> 0;
|
|
|
|
- end;
|
|
|
|
- 11:
|
|
|
|
- begin
|
|
|
|
- if alfa <> 0 then
|
|
|
|
- int1 := abs(alfa) + 1 / abs(alfa);
|
|
|
|
- intex := alfa <> 0;
|
|
|
|
- end;
|
|
|
|
- end;
|
|
|
|
- if scale then
|
|
|
|
- inte := 1
|
|
|
|
- else
|
|
|
|
- inte := int1;
|
|
|
|
- if Upcase(q) = 'Y' then
|
|
|
|
- int1fr(f, 0, 1, ae, integral, err, term)
|
|
|
|
- else if u < 10 then
|
|
|
|
- int1fr(f, ond, infinity, ae, integral, err, term)
|
|
|
|
- else
|
|
|
|
- int1fr(f, -infinity, infinity, ae, integral, err, term);
|
|
|
|
- Showresults;
|
|
|
|
- end;
|
|
|
|
-end.
|
|
|