/usr/share/openturns/validation/ValidQuadraticTaylor.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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> with(LinearAlgebra):
> Point:=<1,2>:
> center:=Vector(Point):
> "center",evalf(center);
> f:=<x1*sin(x2),cos(x1+x2),(x2+1)*exp(x1-2*x2)>:
> const:=subs(x1=Point[1],x2=Point[2],f):
> "const",evalf(const);
> Df:=<map(_x->diff(_x,x1),f)|map(_x->diff(_x,x2),f)>:
> Linear:=Transpose(subs(x1=Point[1],x2=Point[2],Df)):
> "linear",evalf(Linear);
> Quadratic:=array(1..3):
> Quadratic[1]:=subs(x1=Point[1],x2=Point[2],<<diff(diff(f[1],x1),x1),di
> ff(diff(f[1],x1),x2)>|<diff(diff(f[1],x2),x1),diff(diff(f[1],x2),x2)>>
> ):
> Quadratic[2]:=subs(x1=Point[1],x2=Point[2],<<diff(diff(f[2],x1),x1),di
> ff(diff(f[2],x1),x2)>|<diff(diff(f[2],x2),x1),diff(diff(f[2],x2),x2)>>
> ):
> Quadratic[3]:=subs(x1=Point[1],x2=Point[2],<<diff(diff(f[3],x1),x1),di
> ff(diff(f[3],x1),x2)>|<diff(diff(f[3],x2),x1),diff(diff(f[3],x2),x2)>>
> ):
> "quadratic",map(evalf,Quadratic);
> res:=const+Transpose(Linear).(Point-center)+1/2*<Transpose(Point-cente
> r).Quadratic[1].(Point-center),Transpose(Point-center).Quadratic[2].(P
> oint-center),Transpose(Point-center).Quadratic[3].(Point-center)>:
> evalf(res);
> Point[1]:=Point[1]+0.4:
> Point[2]:=Point[2]-0.4/2:
> evalf(Point);
> res:=const+Transpose(Linear).(Point-center)+1/2*<Transpose(Point-cente
> r).Quadratic[1].(Point-center),Transpose(Point-center).Quadratic[2].(P
> oint-center),Transpose(Point-center).Quadratic[3].(Point-center)>:
> evalf(res);
[1.]
"center", [ ]
[2.]
[0.9092974268 ]
[ ]
"const", [-0.9899924966]
[ ]
[0.1493612051 ]
[0.9092974268 -0.1411200081 0.1493612051 ]
"linear", [ ]
[-0.4161468365 -0.1411200081 -0.2489353418]
[[ 0. -0.4161468365]
"quadratic", [[ ],
[[-0.4161468365 -0.9092974268]
[0.9899924966 0.9899924966]
[ ],
[0.9899924966 0.9899924966]
[0.1493612051 -0.2489353418]]
[ ]]
[-0.2489353418 0.3982965470 ]]
[0.9092974268 ]
[ ]
[-0.9899924966]
[ ]
[0.1493612051 ]
[ 1.4 ]
[ ]
[1.800000000]
[ 1.371351563 ]
[ ]
[-0.9984166483]
[ ]
[0.2987224102 ]
>
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