/usr/share/openturns/validation/ValidCovarianceGauss.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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | > restart:
> f:=(exp(alpha*(x-mu))-exp(-beta*(x-mu)))/(exp(alpha*(x-mu))+exp(-beta*
> (x-mu)));
exp(alpha (x - mu)) - exp(-beta (x - mu))
f := -----------------------------------------
exp(alpha (x - mu)) + exp(-beta (x - mu))
> with(plots):
> for i from 0 to 6 do
> p[i]:=plot(subs(alpha=3,beta=i,mu=1,f),x=-5..5);
>
> q[i]:=plot(subs(alpha=i,beta=3,mu=1,f),x=-5..5,color="green",style="po
> int",symbol="circle");
> od:
> display(seq(p[i],i=0..5),seq(q[i],i=0..5));
>
> plot(subs(mu=1,alpha=2,beta=0.3,factor(diff(f,x))),x=-5..5);
> F:=exp(-alpha*exp(-(x-mu)/beta));
x - mu
F := exp(-alpha exp(- ------))
beta
> for i from 1 to 6 do
> p[i]:=plot(subs(alpha=1,beta=i,mu=1,F),x=-5..5);
> od:
> display(seq(p[i],i=0..5));
>
> phi:=tanh((x-mu)/alpha);
x - mu
phi := tanh(------)
alpha
> phi := tanh((x-mu)/alpha);
x - mu
phi := tanh(------)
alpha
> restart:
> phi := tanh((x-mu)/alpha);
> assume(q>-1,q<1);
> sys:=subs(x=x1,phi)=0,subs(x=x2,phi)=q;
x - mu
phi := tanh(------)
alpha
x1 - mu x2 - mu
sys := tanh(-------) = 0, tanh(-------) = q~
alpha alpha
> sol:=allvalues(solve({sys},{mu,alpha}));
2 (-x2 + x1)
sol := {mu = x1, alpha = -------------},
-1 + q~
ln(- -------)
1 + q~
-x2 + x1
{mu = x1, alpha = -------------------}
/ -1 + q~\1/2
ln(-|- -------| )
\ 1 + q~ /
> phiinv:=subs(sol[1],convert(solve(phi=y,x),ln));
2 (1/2 ln(y + 1) - 1/2 ln(1 - y)) (-x2 + x1)
phiinv := x1 + --------------------------------------------
-1 + q~
ln(- -------)
1 + q~
> J:=convert(subs(sol[1],x=phiinv,diff(phi,x)),exp);
2 -1 + q~
(1 - y ) ln(- -------)
1 + q~
J := 1/2 ----------------------
-x2 + x1
> simplify(subs(x=solve(phi=q,x),diff(phi,x)));
2
-1 + q~
- --------
alpha
> ff:=collect(factor(convert(solve(phi=q,x),ln)),ln);
ff := mu + 1/2 alpha ln(1 + q~) - 1/2 alpha ln(1 - q~)
> subs(q=0,ff);
> evalf[25](simplify(solve(subs(q=3/4,ff)-subs(q=1/4,ff)=m3-m1,alpha)));
mu
1.393646133559127220494626 m3 - 1.393646133559127220494626 m1
>
-1.386294361
>
|