Re: Hessian calculation

• To: mathgroup at smc.vnet.net
• Subject: [mg30951] Re: Hessian calculation
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Fri, 28 Sep 2001 03:54:59 -0400 (EDT)
• References: <9ougqi\$169\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Jorge,
I hope that the followint examples may help:

Outer[D,{x^3 y^3},{x,y},{x,y}]

{{{6*x*y^3, 9*x^2*y^2}, {9*x^2*y^2, 6*x^3*y}}}

Outer[D,{x^3 y^3 z^3},{x,y,z},{x,y,z}]

{{{6*x*y^3*z^3, 9*x^2*y^2*z^3, 9*x^2*y^3*z^2},
{9*x^2*y^2*z^3, 6*x^3*y*z^3, 9*x^3*y^2*z^2},
{9*x^2*y^3*z^2, 9*x^3*y^2*z^2, 6*x^3*y^3*z}}}

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Jorge Luis LLanio Trujillo" <jolla at taurus.ci.uc.pt> wrote in message
news:9ougqi\$169\$1 at smc.vnet.net...
>
>
> 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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```

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