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 > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >