In[]:=
data={{-633.`,4.`},{-633.`,5.`},{-690.`,​​6.`},{-821.`,7.`},{-897.`,8.`},{-991.`,9.`},{-1094.`,​​10.`},{-1217.`,11.`},{629.`,4.`},{629.`,5.`},{704.`,​​6.`},{818.`,7.`},{912.`,8.`},{1006.`,9.`},{1107.`,​​10.`},{1214.`,11.`}}​​ClearAll[Phiu,Hu,H1,Ms,H0,Phi,PhiH];​​data={{-633.`,4.`},{-633.`,5.`},{-690.`,6.`},{-821.`,​​7.`},{-897.`,8.`},{-991.`,9.`},{-1094.`,10.`},{-1217.`,​​11.`},{629.`,4.`},{629.`,5.`},{704.`,6.`},{818.`,​​7.`},{912.`,8.`},{1006.`,9.`},{1107.`,10.`},{1214.`,11.`}}​​ClearAll[Phiu,Hu,H1,Ms,H0,Phi,PhiH];​​Phiua=45;​​Print[Phiua];​​PhiH=135;​​gamma=28.02*10^-4;​​g[H0_,H1_,Ms_,Phi_,Hu_,Phiu_]:=​​Piecewise[{{gamma*(Abs[H0]Cos[Pi/180*(Phi-PhiH)]+4PiMs+​​1/2H1*(3+Cos[Pi/180*4Phi])-​​2Hu(Cos[Pi/180*(Phi-Phiu)])^2)^0.5*(Abs[H0]Cos[​​Pi/180*(Phi-PhiH)]+2H1Cos[Pi/180*4Phi]-​​2HuCos[Pi/180*2*(Phi-Phiu)])^0.5,​​H0≥0},{gamma*(Abs[H0]Cos[Pi/180*(Phi-PhiH)]+4PiMs+​​1/2H1*(3+Cos[Pi/180*4Phi])-​​2Hu(Cos[Pi/180*(Phi-Phiu)])^2)^0.5*(Abs[H0]Cos[​​Pi/180*(Phi-PhiH)]+2H1Cos[Pi/180*4Phi]-​​2HuCos[Pi/180*2*(Phi-Phiu)])^0.5,H0<0}},True];​​nlmd=Assuming[{Phi,Ms}∈PositiveReals,​​NonlinearModelFit[data,​​g[H0,H1,Ms,Phi,Hu,​​Phiu],{{H1,200.},{Ms,1600.},{Phi,135.},{Hu,270},{Phiu,​​Phiua}},H0,​​Method{"Newton","StepControl""TrustRegion"},​​MaxIterationsInfinity]];​​Print[nlmd["ParameterTable"]];
Out[]=
{{-633.,4.},{-633.,5.},{-690.,6.},{-821.,7.},{-897.,8.},{-991.,9.},{-1094.,10.},{-1217.,11.},{629.,4.},{629.,5.},{704.,6.},{818.,7.},{912.,8.},{1006.,9.},{1107.,10.},{1214.,11.}}
Out[]=
{{-633.,4.},{-633.,5.},{-690.,6.},{-821.,7.},{-897.,8.},{-991.,9.},{-1094.,10.},{-1217.,11.},{629.,4.},{629.,5.},{704.,6.},{818.,7.},{912.,8.},{1006.,9.},{1107.,10.},{1214.,11.}}
45
Dot
:Tensors -0.0000195688,-4.45678×
-6
10
,-4.53388×
-19
10
,0.0000192142,-2.17677×
-20
10
,1,{1},{24,3,-23},-2.17677×
-20
10
,-4.95757×
-21
10
,0.0048863,-4.21189×
-20
10
,-0.0048863,15 and {7.27296,6.27296,5.69708,5.62556,5.13887,4.75183,4.39907,4.14298,19,6.24268,5.79925,5.60494,5.23824,4.8476,4.47912,4.12518} have incompatible shapes.
NonlinearModelFit
:The Hessian is not a matrix of real numbers at {H1,Ms,Phi,Hu,Phiu} = {200.,1600.,135.,270.,45.}.
Estimate
Standard Error
t-Statistic
P-Value
H1
200.
422.656
0.473198
0.645323
Ms
1600.
2237.79
0.714992
0.489511
Phi
135.
7.46789×
-13
10
1.80774×
14
10
1.86445×
-152
10
Hu
270.
248.148
1.08806
0.299834
Phiu
45.
1.02849×
-13
10
4.37535×
14
10
1.11662×
-156
10