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)
• 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

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