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Re: digit-precision for gaussian inputs converting cartesian matrix from

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  • Subject: [mg128945] Re: digit-precision for gaussian inputs converting cartesian matrix from
  • From: "locometro, INMETRO/UFRJ, Brasil - RJ" <decicco10 at gmail.com>
  • Date: Wed, 5 Dec 2012 03:12:18 -0500 (EST)
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Bill,

Thanks for the suggestions!


Em segunda-feira, 3 de dezembro de 2012 06h37min55s UTC-2, Bill Rowe  escreveu:
> On 11/30/12 at 5:59 AM, decicco10 at gmail.com (locometro, INMETRO/UFRJ,
> 
> Brasil - RJ) wrote:
> 
> 
> 
> >I have some issues to discuss here:
> 
> 
> 
> >My goal:  rotation,x-y plane, apllying over some cartesians vectors.
> 
> 
> 
> >(*step 1: I import a input.txt for Gaussian program like this:  *)
> 
> 
> 
> >%chk=campoX_1.chk %mem=2gb %nproc=4
> 
> >#p b3lyp/6-31+g(d,p) geom=connectivity field=x+1 pop=reg
> 
> >#int=ultrafine
> 
> 
> 
> >single point campo direcao X+01
> 
> 
> 
> >0 1
> 
> >C                  0.00000000    0.00000000    0.00000000
> 
> >C                  1.41786969    0.00000000    0.00000000
> 
> >C                 -0.68401407    1.24221249    0.00000000
> 
> >etc...(72lines).
> 
> 
> 
> >(*step 2: I extract the  data from input above, as below:*)
> 
> 
> 
> >data2 = Take[data1, {9, 56}, {2, 4}]] data3 = Flatten[Take[data1,
> 
> >{9, 56}, {1}]]; data4 = Drop[data1, {8, 56}, None];
> 
> 
> 
> >(*As I need the 1st(molecules symbol), 2nd (X) , 3rd (Y) and 4th(Z)
> 
> >columns, for my table and calculations*).
> 
> 
> 
> >(*step 3:  Rotation 45 degree, over plane x-y, using the exctracted
> 
> >columns*)
> 
> 
> 
> >rotZ = RotationMatrix[45 Degree, {0, 0, 1}]; datarotZ = (rotZ.#) &
> 
> >/@ data2 (*this promote the rotation matrice over  x-y-x*)
> 
> 
> 
> >output-> {{0., 0., 0.}, {1.00259, 1.00259, 0.}, {-1.36205, 0.394706,
> 
> >0.}, {-2.49436, 0.668808, 0.00086376}, {1.85795, 1.79358,
> 
> >-0.00004936}, {-3.36958, -5.96549, -0.00908542}, \
> 
> >{-2.95205, -7.30672, 0.00803008},...etc (* cartesians numbers
> 
> >already rotated 45 degrees*).
> 
> 
> 
> >BUT NOTICE that the numbers of digits has been modified!, I need the
> 
> >original 8 digits, including zeros, after the decimal point! I do
> 
> >not want mathematica aplying any aproximation or cuts.
> 
> 
> 
> There are a couple of issues here. First, any number entered
> 
> with a decimal point and not given an explicit precision is a
> 
> machine precision number in Mathematica. All machine precision
> 
> numbers are stored as binary data. In general, numbers you enter
> 
> as decimal numbers cannot be represented exactly in a finite
> 
> number of binary digits. So, the value Mathematica uses
> 
> typically is slightly different than the value you entered.
> 
> 
> 
> Once you start using machine precision values, by default
> 
> Mathematica will use machine precision for other parts of you
> 
> computation. These values also will be slightly different than
> 
> what you enter. As the computation proceeds these small
> 
> differences accumulate. The end result is reversing computations
> 
> often will not result in exactly the same decimal digits even
> 
> though the reverse computation would mathematically be an exact
> 
> inverse, resulting in an identity operation.
> 
> 
> 
> The only way around this issue is to either use exact values (no
> 
> decimal point, all fractions expressed as rationals) or to
> 
> increase the precision in the values you enter to make use of
> 
> Mathematica's arbitrary precision arithmetic. The cost is slower
> 
> execution of computations.
> 
> 
> 
> A second issue is by default Mathematica doesn't display
> 
> trailing zeros. You can change this by changing your display
> 
> options or by using functions like NumberForm to control how
> 
> Mathematica displays numbers.




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