/usr/share/openturns/validation/Cas6.txt is in openturns-validation 1.5-7build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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> Digits:=20:
> G1:=2-x2+exp(-0.1*x1^2)+(0.2*x1)^4:
> G2:=4.5-x1*x2;
> G:=max(G1,G2);
> with(plots):
> p1:=implicitplot(G1,x1=-5..5,x2=-5..5,grid=[101,101]):
> p2:=implicitplot(G2,x1=-5..5,x2=-5..5,grid=[101,101],color=blue):
> p3:=implicitplot(G=0,x1=-5..5,x2=-5..5,grid=[101,101],color=green,thic
> kness=4):
> with(plottools):
> c := circle([0,0], 3, color=magenta):
> display([p1,p2,p3,c]);
> evalf(subs(x1=0,x2=0,G));
G2 := 4.5 - x1 x2
2 4
G := max(4.5 - x1 x2, 2 - x2 + exp(-0.1 x1 ) + 0.0016 x1 )
Warning, the name changecoords has been redefined
Warning, the name arrow has been redefined
4.5
> y1:=solve(G1,x2);
> y2:=solve(G2,x2);
> xL:=fsolve(y1=y2,x1);
2
y1 := 2. + exp(-0.10000000000000000000 x1 )
4
+ 0.0016000000000000000000 x1
4.5000000000000000000
y2 := ---------------------
x1
xL := 1.6183841765382898291
> Pdef:=(Int(Int(1/(2*Pi)*exp(-(x1^2+x2^2)/2),x2=-infinity..y2),x1=-infi
> nity..0))+(Int(Int(1/(2*Pi)*exp(-(x1^2+x2^2)/2),x2=y1..infinity),x1=-i
> nfinity..xL))+(Int(Int(1/(2*Pi)*exp(-(x1^2+x2^2)/2),x2=y2..infinity),x
> 1=xL..infinity));
0
/
|
Pdef := |
|
|
/
-infinity
4.5000000000000000000
--------------------- 2 2
x1 x1 x2
/ exp(- --- - ---)
| 2 2
| 1/2 ---------------- dx2 dx1 +
| Pi
|
/
-infinity
1.6183841765382898291 2 2
/ x1 x2
| exp(- --- - ---)
| 2 2
| Int(1/2 ----------------, x2 = 2.
| Pi
|
/
-infinity
2
+ exp(-0.10000000000000000000 x1 )
4
+ 0.0016000000000000000000 x1 .. infinity) dx1 +
infinity
/
|
|
|
|
/
1.6183841765382898291
2 2
infinity x1 x2
/ exp(- --- - ---)
| 2 2
| 1/2 ---------------- dx2 dx1
| Pi
|
/
4.5000000000000000000
---------------------
x1
> Pdef_num:=evalf(Pdef);
Pdef_num := 0.0034789463209310872097
> PHI:=proc(x)
> int(1/sqrt(2*Pi)*exp(-t^2/2),t=-infinity..x)
> end:
> -fsolve(PHI(x)=Pdef_num,x);
2.6988528870368598063
>
> 1-7.1529e-3/9.81929e-3;
0.27154610974927922487
> Digits:=20:evalf(sqrt(1/2));
0.70710678118654752440
> evalf(subs(x1=xL,y1));
2.7805511603712427742
> evalf(subs(x1=xL,x2=evalf(subs(x1=xL,y1)),G));
-19
-0.4 10
> evalf(3*sqrt(3));
5.1961524227066318805
>
|