Re: Export table problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg30938] Re: [mg30891] Export table problem*From*: Tomas Garza <tgarza01 at prodigy.net.mx>*Date*: Thu, 27 Sep 2001 02:17:00 -0400 (EDT)*References*: <OF544D7872.E7ECB40C-ONC1256AD2.00262E35@icos.be>*Sender*: owner-wri-mathgroup at wolfram.com

Maarten, You're quite right. I was too hasty in assuming that people only use Excel outside Mathematica! I guess the problem has to do with a very complicated subject, viz. the arithmetic used by Mathematica. After some thinking, I concluded that your numbers Round[100*Table[{i,i/5,i/3},{i,1,20}]]/100. must have different degrees of error when they are computed, so that when the error is "small" they are exported as they appear in the display, and otherwise they are exported with as many figures as the precision allows. This seems to be the case for i = 7, 14 and 19 above. I checked this in the AddOn NumericalMath`Microscope`, where I found the following illuminating text: "Numbers on a computer comprise a discrete set. There are gaps between the numbers and when you do arithmetic the result often is not representable. When the result falls between two representable numbers the best that can be done is to use the closest representable number as the result instead of the correct result. The set of numbers that can be represented on a computer in floating-point format are commonly referred to as the set of machine numbers." This led me to calculate the "MachineError" for your table In[1]:= <<NumericalMath`Microscope` In[2]:= Table[MachineError[Round[100*x/5]/100.,x\[Rule]j],{j,1,20}] Out[2]= {0.25 Ulps,0.25 Ulps,-0.3125 Ulps,0.25 Ulps,-0.1875 Ulps,-0.3125 Ulps, 0.46875 Ulps,0.25 Ulps,0.03125 Ulps,-0.1875 Ulps,0.296875 Ulps,-0.3125 Ulps, 0.078125 Ulps,0.46875 Ulps,-0.140625 Ulps,0.25 Ulps,-0.359375 Ulps, 0.03125 Ulps,0.421875 Ulps,-0.1875 Ulps} (the difference between two consecutive machine numbers is called an ulp - "unit in the last place"). Here you can see that the machine errors for j = 7, 14 and 19 are indeed the largest ones (0.46875, 0.46875 and 0.421875, respectively) in the list, and this is why (I venture to guess, since I am far from being a computer expert, let alone a Mathematica expert) those 3 particular numbers are exported with so many decimals. We should look forward to a good, informed explanation from the great gurus. Now, back to your original problem. The difficulty arises because you want to keep at most 2 decimal figures, and you want to force this using Round together with multiplication and division by 100 (this, by the way, is what I always do - but, then, I only use Excel if at all and this why I have never have experienced the situation). We see that Mathematica refuses to export the result with only 2 decimals because of the error problem mentioned above. One way out (not the only one, I'm sure, but this one seems to work) is to look at the real digits in the result, throw away all but the first two decimals, and reconstruct each quotient i/5 and i/3. I propose the following apparently messy procedure: the function red[r_] takes a number r, works with the string of its real digits, throws away all but the first two after rounding, and returns the new expression for r: red[r_]:=Module[{z=RealDigits[r]}, v={{z[[1,1]], If[z[[1,3]]>=5, z[[1,2]]+1,z[[1,2]]]}, z[[2]]}; y=ToString/@v[[1]]; ToExpression[ If[v[[2]]>0, ToString/@Take[y,v[[2]]][[1]]<>"."<> ToString/@Take[y,-(Length[y]-v[[2]])][[1]], "0"<>"."<>ToString/@v[[1]]]]] (it's just an exercise in list and string manipulation). I then calculate the following In[3]:= x=Table[{i,red[i/5.],red[i/3.]},{i,1,20}] Out[3]= {{1,0.2,0.33},{2,0.4,0.67},{3,0.6,1.},{4,0.8,1.3},{5,1.,1.7},{6,1.2,2.},{7, 1.4,2.3},{8,1.6,2.7},{9,1.8,3.},{10,2.,3.3},{11,2.2,3.7},{12,2.4,4.},{13, 2.6,4.3},{14,2.8,4.7},{15,3.,5.},{16,3.2,5.3},{17,3.4,5.7},{18,3.6, 6.},{19,3.8,6.3},{20,4.,6.7}} and then In[4]:= Export["table.txt",x,"Table"] Out[4]= table.txt Now I read in table.txt from Microsoft Word and it gives exactly what you wanted! Actually, you don't need the ToExpression part in the function red, since you are going to use a text editor, where there is no difference between strings and numbers. Regards, Tomas ----- Original Message ----- From: <maarten.vanderburgt at icos.be> To: mathgroup at smc.vnet.net Subject: [mg30938] Re: [mg30891] Export table problem > > Tomas, > > You should open it in a text editor. Depending on your settings, Excel > round or truncates when you open the txt file. > > BR > maarten >

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**Re: Export table problem**

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