hessian using symbolic variables

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sensation
sensation 2018-5-7
评论: sensation 2018-5-22
Hi there,
I am struggling with obtaining the Hessian of my function. In the first case it works fine but in the second case I can not get it (still symbolic variables X are presented in H). So my question is why this happen? This is small portion of the code where I want to find hessian of my Rtot function with X being x1,x2,x3,x4.
Rtot= -sum(Rsub(:,i));
H=hessian(Rtot,X);
H1 = 0.5.*double(H);
with Rtot:
(6234858085755363*x1*((17865509505801117*x1)/14411518807585587200000 + (17865509505801117*x3)/14411518807585587200000 - 16863388614392257743519/1441151880758558720000))/140737488355328000 + (6069173180546921*x2*((17865509505801117*x1)/7205759403792793600000 + (17865509505801117*x2)/14411518807585587200000 + (17865509505801117*x3)/7205759403792793600000 + (17865509505801117*x4)/14411518807585587200000 - 16867211833426499182557/1441151880758558720000))/140737488355328000
and H1:
1.0e-07 *
0.5492 0.5346 0.2746 0
0.5346 0.5346 0.5346 0.2673
0.2746 0.5346 0 0
0 0.2673 0 0
This is fine. But then when I want to find hessian of different data set i get this. Rtot:
- (2587079436111693477*x2*(665101922855875194446501149/3153075739026468800000 - (4398046511104*x2)/5912017010674629 - (4398046511104*x3)/5912017010674629 - (4398046511104*x4)/5912017010674629 - (4398046511104*x1)/5912017010674629)^(1/3))/28147497671065600000000 - (4554081285294461427*x1*(1299027180826527113674752/6158351052786071875 - (4398046511104*x3)/5912017010674629 - (4398046511104*x1)/5912017010674629)^(1/3))/56294995342131200000000
and H still have symbolic variables inside which does not allow me to calculate H1. Difference is in Rtot but I still can not find out why it does not work.
Thank you a lot!!!
  4 个评论
Torsten
Torsten 2018-5-7
if you want to use the Hessian in quadprog, use
func_H = matlabFunction(H)
Best wishes
Torsten.
sensation
sensation 2018-5-22
Hi Torsten, Thanks for the tip. I created my Hessian as:
%
hessObj = hessian(Rtot(:,i),X(:,i));
H=matlabFunction(hessObj);
However, when I use H in my quadprog, H is still not double type. Any clue?
Thanks and cheers

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回答(1 个)

Alan Weiss
Alan Weiss 2018-5-7
There are some examples in the documentation that show how to do this:
Alan Weiss
MATLAB mathematical toolbox documentation
  2 个评论
sensation
sensation 2018-5-8
Hi Alan, I had a view on this. My issue is following once I do:
%
gradf = jacobian(Rtot,X); % column gradf
hessf = jacobian(gradf,X);
qpoptions = optimset('Algorithm','interior-point-convex','Disp','iter');
tic
[x3(:,i),fval3(:,i)] = quadprog(hessf,f,A,b(:,i),Aeq,beq(:,i),LB(:,i),UB(:,i),[],qpoptions);
toc
hessf need to be of type H (double) but I can not convert it to double since there are still x unknowns in hessf. My hessf, instead of being a number able to be converted in double is:
(154325299586858956762382336*x2)/(13653103568166475135677228237359765625*(665101922855875194446501149/3153075739026468800000 - (4398046511104*x2)/5912017010674629 - (4398046511104*x3)/5912017010674629 - (4398046511104*x4)/5912017010674629 - (4398046511104*x1)/5912017010674629)^(5/3)) + (15092307240482528980631552*x1)/(1517011507574052792853025359706640625*(1299027180826527113674752/6158351052786071875 - (4398046511104*x3)/5912017010674629 - etc
thanks for any tip!
Alan Weiss
Alan Weiss 2018-5-8
Torsten gave you good advice: use matlabFunction exactly as he said.
Alan Weiss
MATLAB mathematical toolbox documentation

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