validation/src/Sensibilite_ref2.mws

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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 262 "restart:\ng:=S+x1^2
-x2:\nT1:=(x1-mu1)/sigma1:\nT2:=(x2-mu2)/sigma2:\ng_tilde:=subs(x1=sol
ve(T1=u1,x1), x2=solve(T2=u2,x2),g);\ndgtilde_u1:=diff(g_tilde,u1);\nd
gtilde_u2:=diff(g_tilde,u2);\neq_u1:=u1=lambda*dgtilde_u1;\neq_u2:=u2=
lambda*dgtilde_u2;\neq_lambda:=g_tilde=0;\n" }}{PARA 11 "" 1 ""
{XPPMATH 20 "6#>%(g_tildeG,*%\"SG\"\"\"*$),&%$mu1GF'*&%#u1GF'%'sigma1G
F'F'\"\"#F'F'%$mu2G!\"\"*&%#u2GF'%'sigma2GF'F1" }}{PARA 11 "" 1 ""
{XPPMATH 20 "6#>%+dgtilde_u1G,$*(\"\"#\"\"\",&%$mu1GF(*&%#u1GF(%'sigma
1GF(F(F(F-F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+dgtilde_u2G,$%'si
gma2G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&eq_u1G/%#u1G,$**\"\"#
\"\"\"%'lambdaGF*,&%$mu1GF**&F&F*%'sigma1GF*F*F*F/F*F*" }}{PARA 11 ""
1 "" {XPPMATH 20 "6#>%&eq_u2G/%#u2G,$*&%'lambdaG\"\"\"%'sigma2GF*!\"\"
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*eq_lambdaG/,*%\"SG\"\"\"*$),&%$
mu1GF(*&%#u1GF(%'sigma1GF(F(\"\"#F(F(%$mu2G!\"\"*&%#u2GF(%'sigma2GF(F2
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ve(\{eq_u1,eq_u2,eq_lambda\},\{u1,u2,lambda\})):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 485 "valnum:=mu1=1,sigma1=0.2,mu2=2,sigma2=5,S=5:
\nnsol:=1:\nwith(plots):\ngtildeNum:=subs(valnum,g_tilde):\np1:=implic
itplot(gtildeNum,u1=-3..3,u2=-3..5,grid=[81,81]):\np2:=plot([[0,0],sub
s(sol[nsol],valnum,[u1,u2])],color=blue):\ndisplay(\{p1,p2\},scaling=c
onstrained);\nexpre:=subs(sol[nsol],[u1,u2,lambda]):\nd_mu1:=evalf(sub
s(valnum,diff(expre,mu1))):\nd_mu2:=evalf(subs(valnum,diff(expre,mu2))
):\nd_sigma1:=evalf(subs(valnum,diff(expre,sigma1))):\nd_sigma2:=evalf
(subs(valnum,diff(expre,sigma2))):" }}{PARA 13 "" 1 "" {GLPLOT2D 484
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3>++++]CH5F*F_gn7$Fegn7$$\"3GrxnT%ePP#F*$\"3^T'HWu))\\.\"F*7$7$$\"3o,+
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$\"3P++++]g$3\"F*Fj[o7$F`\\o7$$\"3B*G9dGUiy#F*$\"3/'G9dG5]3\"F*7$7$$\"
3v-+++++]GF*$\"3G+++++)H4\"F*Ff\\o7$F\\]o7$$\"3p!>Vlv4[&GF*$\"3w]dF\"*
pe$4\"F*7$7$$\"36(H\"\\!*fi0HF*$\"3k,++++++6F*Fb]o7$Fh]o7$$\"3xWf,2[KB
HF*$\"3:7ak!fLA5\"F*7$7$$\"3$H+++++]#HF*$\"3M++++]W-6F*F^^o7$Fd^o7$$\"
3WQ&*>[\\y\"*HF*$\"38@1S-M&46\"F*7$7$$\"37.++++++IF*$\"3K++++++76F*Fj^
o-%'COLOURG6&%$RGBG\"\"\"\"\"!Fj_o-F$6$7$7$$Fj_oFj_oF_`o7$$!3+%pkQIu,G
'Fb[m$\"31'\\[a8u+&zF--Ff_o6&Fh_oF_`oF_`o$\"*++++\"!\")-%(SCALINGG6#%,
CONSTRAINEDG-%+AXESLABELSG6%%#u1G%#u2G-%%FONTG6#%(DEFAULTG-%%VIEWG6$Ff
aoFfao" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 46.000000 0 0 "Curve
 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 779 "DthetaU_r
ef:=<<d_mu1[1..2]>|<d_sigma1[1..2]>|<d_mu2[1..2]>|<d_sigma2[1..2]>>;\n
DthetaLambda_ref:=<<d_mu1[3]>|<d_sigma1[3]>|<d_mu2[3]>|<d_sigma2[3]>>;
\nG_:=<dgtilde_u1,dgtilde_u2>;\nG_num:=evalf(subs(sol[nsol],valnum,G_)
);\ndgtilde_mu1:=diff(g_tilde,mu1); \ndgtilde_mu2:=diff(g_tilde,mu2);
\ndgtilde_sigma1:=diff(g_tilde,sigma1);\ndgtilde_sigma2:=diff(g_tilde,
sigma2);\nK_:=<dgtilde_mu1,dgtilde_sigma1,dgtilde_mu2,dgtilde_sigma2>;
\nK_num:=evalf(subs(sol[nsol],valnum,K_));\nE_:=<<diff(G_[1],u1),diff(
G_[2],u1)> | <diff(G_[1],u2),diff(G_[2],u2)>>;\nE_num:=evalf(subs(sol[
nsol],valnum,E_));\nF_:=< <diff(G_[1],mu1),diff(G_[2],mu1)> | <diff(G_
[1],sigma1),diff(G_[2],sigma1)> | <diff(G_[1],mu2),diff(G_[2],mu2)> | \+
<diff(G_[1],sigma2),diff(G_[2],sigma2)> >;\nF_num:=evalf(subs(sol[nsol
],valnum,F_));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,DthetaU_refG-%'RT
ABLEG6%\"*[I2Q\"-%'MATRIXG6#7$7&$!)ax.$*!\"*$!)$HK-$!\")$\"+6`]]:!#6$
\")mKlCF07&$\"+xKEwQ!#5$!+n?so[F6$!+d<v()>F<$!+R*R0d\"F<%'MatrixG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%1DthetaLambda_refG-%'RTABLEG6%\"*We2
Q\"-%'MATRIXG6#7#7&$!+bl__x!#6$\"+MqWP(*!#7$\"+8N]vRF0$\"+S&46K'F0%'Ma
trixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#G_G-%'RTABLEG6%\"*_&e!Q\"-
%'MATRIXG6#7$7#,$*(\"\"#\"\"\",&%$mu1GF1*&%#u1GF1%'sigma1GF1F1F1F6F1F1
7#,$%'sigma2G!\"\"&%'VectorG6#%'columnG" }}{PARA 11 "" 1 "" {XPPMATH
20 "6#>%&G_numG-%'RTABLEG6%\"*#fe!Q\"-%'MATRIXG6#7$7#$\"*he(\\R!\"*7#$
!\"&\"\"!&%'VectorG6#%'columnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,d
gtilde_mu1G,&*&\"\"#\"\"\"%$mu1GF(F(*(F'F(%#u1GF(%'sigma1GF(F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,dgtilde_mu2G!\"\"" }}{PARA 11 "" 1
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