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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
>



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