Re: How can I get better solution for this...?

*To*: mathgroup at smc.vnet.net*Subject*: [mg120056] Re: How can I get better solution for this...?*From*: Siddharth Srivastava <siddys at gmail.com>*Date*: Thu, 7 Jul 2011 07:30:44 -0400 (EDT)*References*: <201107060939.FAA29377@smc.vnet.net>

Hi Bobby, The P matrix and D are constants, the values of which I will know at the time of the evaluation. Maybe the mistake I made was in not "somehow" specifying that the elements of P and D itself are constants? How is this fact specified in Mathematica? i.e, for a given P and D, solve for sx, sy, gx and gy..... In light of this, maybe, new information, would you be kind enough to re-evaluate the problem? Or if you can let me know, I can try it myself.... Thanks again for all your help, and time # On Wed, Jul 6, 2011 at 11:18 AM, DrMajorBob <btreat1 at austin.rr.com> wrote: > Someone else may have more insight into "the decomposition of an Affine > transformation matrix into scale (sx sy) and shear (gx gy) components", but > there IS no alternative way to solve that system of equations, nor any > system equivalent to it, with d and the p parameters variable. > > Bobby > > > On Wed, 06 Jul 2011 13:05:39 -0500, Siddharth Srivastava <siddys at gmail.com> > wrote: > > Hi Bobby, >> Thanks for the quick reply. What I am trying to do is to get an >> analytical form for >> the decomposition of an Affine transformation matrix into scale (sx sy) >> and >> shear >> (gx gy) components. Maybe if you have an alternative way to get this, that >> would >> be helpful too... >> Thanks, >> # >> >> On Wed, Jul 6, 2011 at 10:36 AM, DrMajorBob <btreat1 at austin.rr.com> >> wrote: >> >> Ah yes... I misread your post in the heat of the moment. >>> >>> The first three equations determine sy, gx, and gy in terms of p00, p01, >>> p11, and sx: >>> >>> soln = Quiet@ >>> >>> Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00, >>> sx sy gx (1 + gx gy) + sx sy gy == p01, >>> sy^2 (1 + gx^2) == p11}, {sx, sy, gx, gy}]; >>> soln[[All, All, 1]] >>> >>> {{sy, gx, gy}, {sy, gx, gy}, {sy, gx, gy}, {sy, gx, gy}} >>> >>> giving four solutions. If the fourth equation is also true, each of these >>> solutions determines a value for d: >>> >>> Solve[sx sy == d, d] /. soln >>> >>> (four solutions) >>> >>> Hence, your four equations have no solution with d free to vary. >>> >>> >>> Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00, >>> sx sy gx (1 + gx gy) + sx sy gy == p01, sy^2 (1 + gx^2) == p11, >>> sx sy == d}, {gx}] >>> >>> {} >>> >>> Bobby >>> >>> >>> On Wed, 06 Jul 2011 11:50:17 -0500, Siddharth Srivastava < >>> siddys at gmail.com> >>> wrote: >>> >>> Hi Bobby, >>> >>>> Thanks. I actually wanted sx, sy, gx and gy in terms of the P coeff. >>>> The >>>> solution >>>> you gave is just the equation that I wanted to solve! >>>> # >>>> >>>> On Wed, Jul 6, 2011 at 9:18 AM, DrMajorBob <btreat1 at austin.rr.com> >>>> wrote: >>>> >>>> Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00, >>>> >>>>> sx sy gx (1 + gx gy) + sx sy gy == p01, sy^2 (1 + gx^2) == p11, >>>>> sx sy == d}, {p00, p01, p11, d}] >>>>> >>>>> {{p00 -> sx^2 + 2 gx gy sx^2 + gy^2 sx^2 + gx^2 gy^2 sx^2, >>>>> p01 -> gx sx sy + gy sx sy + gx^2 gy sx sy, p11 -> (1 + gx^2) sy^2, >>>>> d -> sx sy}} >>>>> >>>>> Bobby >>>>> >>>>> On Wed, 06 Jul 2011 04:39:55 -0500, sid <siddys at gmail.com> wrote: >>>>> >>>>> Hi all, >>>>> >>>>> I am trying to solve the following for {sx,sy,gx,gy} >>>>>> >>>>>> sx^2 (1 + gx gy)^2 + sx^2 gy^2 = P00 ........(1) >>>>>> sx sy gx (1 + gx gy) + sx sy gy = P01 .......(2) >>>>>> sy^2 ( 1 + gx^2) = P11 ..............................******.(3) >>>>>> sx sy = D ..............................** >>>>>> ****..................(4) >>>>>> >>>>>> in terms of P00,P01,P11, and D. >>>>>> >>>>>> When I use Solve[] , I get a huge output containing the P terms up >>>>>> till the order of 16 (i.e P00^16 etc..), which >>>>>> I know is not correct. I do not think I am specifying the problem >>>>>> correctly, and being a non-expert in Mathematica, would appreciate >>>>>> some help. Specifically >>>>>> 1) should I specify the simultaneous equation using && operator? I >>>>>> have tried it, and I get different (but huge) output >>>>>> 2) can I break the problem into parts? how? >>>>>> Thanks, >>>>>> s. >>>>>> >>>>>> >>>>>> >>>>>> -- >>>>> DrMajorBob at yahoo.com >>>>> >>>>> >>>>> >>> -- >>> DrMajorBob at yahoo.com >>> >>> > > -- > DrMajorBob at yahoo.com >

**References**:**How can I get better solution for this...?***From:*sid <siddys@gmail.com>