Hessian calculation
- To: mathgroup at smc.vnet.net
- Subject: [mg30924] Hessian calculation
- From: Jorge Luis LLanio Trujillo <jolla at taurus.ci.uc.pt>
- Date: Thu, 27 Sep 2001 02:16:41 -0400 (EDT)
- Organization: Universidade de Coimbra
- Sender: owner-wri-mathgroup at wolfram.com
I posted a similar question some days ago, but some people, in order to
help, asked more details. Here the full problem(i am completely new to
MATHEMATICA). Excuse-me!
I have:
______________________________
/ 2 2 2
R1= \/ (x4-x1) + (x5-x2) + (x6-x3) ;
______________________________
/ 2 2 2
R2= \/ (x7-x1) + (x8-x2) + (x9-x3) ;
_________________________________
/ 2 2 2
R3= \/ (x10-x1) + (x11-x2) + (x12-x3) ;
_______________________________
/ 2 2 2
R4= \/ (x7-x4) + (x8-x5) + (x9-x6) ;
________________________________
/ 2 2 2
R5= \/ (x10-x4) + (x11-x5) + (x12-x6) ;
________________________________
/ 2 2 2
R6= \/ (x10-x7) + (x11-x8) + (x12-x9) ;
Then
S1= 1/sqrt(6) (R1+R2+R3+R4+R5+R6) ;
S2= 1/sqrt(2) (R1-R4);
S3= 1/sqrt(2) (R2-R5);
S4= 1/sqrt(2) (R3-R6);
S5= 1/2 (R2-R3+R5-R6);
S6= 1/2sqrt(3) (2R1-R2-R3+2R4-R5-R6);
Then
Q1 = S1;
2
Q2 = S1 ;
2 2 2
Q3 = S2 + S3 + S4 ;
2 2
Q4= S5 + S6 ;
3
Q5 = S1 ;
2 2 2
Q6 = S1 ( S2 + S3 + S4 ) ;
2 2
Q7= S1 ( S5 + S6 ) ;
Q8= S2 S3 S4 ;
2 2
Q9= S6 -3 S6 S5 ;
2 2 2 2 2
Q10= S6 ( 2 S2 - S3 -S4 ) + sqrt(3) S5 ( S3 - S4 ) ;
And finally my function:
V = (Vo + C1 Q1 + C2 Q2 + C3 Q3 + C4 Q4 + C5 Q5 + C6 Q6 + C7 Q7 + C8 Q8 + C9 Q9 + C10 Q10) Exp[ -GANMA ( (R1-a)**2
+ (R2-b)**2 + (R3-c)**2 + (R4-d)**2 + (R5-e)**2 + (R6-f)**2 ]
Here,
Vo, C1, C2, ... C10 & GANMA are coefficients
I need to calculate the Hessian (all second partial derivatives) .
For example, the element (1,2) is the second partial derivative:
2
d V
----
dx1dx2
and so on and so for ..
Thanks for the help,
Jorge Luis