Skip to main content

output formatting - export table with number written in scientific notation


I am trying to write on a file the table generated in this way:


error = ConstantArray[0, 3];
error[[1]] = ScientificForm[Sqrt[CovMat[[1, 1]] /. out[[2]]]];
error[[2]] = ScientificForm[Sqrt[CovMat[[2, 2]] /. out[[2]]]];
error[[3]] = ScientificForm[Sqrt[CovMat[[3, 3]] /. out[[2]]]];

Ris = out[[2]] /. Rule -> (#2 &);
par = out[[2]] /. Rule -> (#1 &);
Finale = MapThread[{#1, ScientificForm[#2], #3} &, {par, Ris, 
    error}] // TableForm

CovMat anf out are generated in a previoous part of the code (a NMinimize). Typing Finale on the notebook I find:


M   4.35203*10^(10) 4.2566*10^(9)
\[Delta]    4.10847*10^(5)  2.12356*10^(4)
L   1.01689*10^(9)  1.30717*10^(16)


The problem is that in the file I find:


"M  ScientificForm[1.7467449664329874*^11]  \
ScientificForm[4.784135569792907*^9]

[\Delta]    ScientificForm[606745.0359163599]   \
ScientificForm[10326.21966853348]

L   ScientificForm[2.788541796939519*^10]   \
ScientificForm[1.5410843643505646*^18]"


I used Export and


file = OpenAppend["out.txt"]

string = ExportString[Finale,"Table"];

WriteString[file, string]
WriteString[file, "\n"];

Close[file]


(I thought that ExportString read the values as they are) but I cannot get rid of that ScientificForm.


I suspect that I should use something like:


Export["file.dat", {elem1->expr1, elem2->expr2, ...}, "Rules"]

but I cannot find a way to express the rule.



Answer



Why your file looks like that


As we can read at the end of of "Details and Options" section of ScientificForm documentation:



ScientificForm acts as a "wrapper", which affects printing, but not evaluation.




So although


In[1]:=  ScientificForm[410846.99999999994`]

is outputted as


Out[1]//ScientificForm=
          4.10847 x 10^5

under the hood it is still number 410846.99999999994` wrapped with ScientificForm:


In[2]:=  ScientificForm[410846.99999999994`] // FullForm

Out[2]//FullForm=
          ScientificForm[410846.99999999994`]

This number wrapped with ScientificForm when exported to "Table" format is somehow converted to a string:


In[3]:=  ExportString[ScientificForm[410846.99999999994`],"Table"]
Out[3]:= ScientificForm[410846.99999999994]

From simple experiment:


In[4]:=  Block[{ToString = toString}, ExportString[{{a, b}, {c, d}}, "Table"]]
Out[4]:= toString[a, InputForm]    toString[b, InputForm]

          toString[c, InputForm]    toString[d, InputForm]

we see that ToString[#, InputForm]& is used and, as one would expect, in input form we have:


In[5]:=  ToString[ScientificForm[410846.99999999994`], InputForm]
Out[5]:= ScientificForm[410846.99999999994`]

This is the reason behind output you're getting.


How to get what you want


What you want is to convert numbers wrapped with ScientificForm to strings in OutputForm not in InputForm. Since OutputForm is default form of ToString we don't specify any form:


In[6]:=  ScientificForm[410846.99999999994`] // ToString

Out[6]:=              5
          4.10847 x 10

It's not exactly what we want, but since "ordinary" *.dat file has no support for superscripts we need to change our scientific form a bit, to take that into account. We can do that using NumberFormat option:


In[7]:=  ScientificForm[410846.99999999994`, NumberFormat -> (#1 <> "*10^(" <> #3 <> ")" &)] // ToString
Out[7]:= "4.10847*10^(5)"

That's of course just an example you can customize it to suit your needs.


Going back to your particular case. Start with your table containing "raw" numbers not wrapped with any formating function:


In[8]:=  data = {

             {M, 4.35203*10^(10), 4.2566*10^(9)},
             {δ, 4.10847*10^(5), 2.12356*10^(4)},
             {L, 1.01689*10^(9), 1.30717*10^(16)}
          };

and make appropriate conversion just before exporting:


In[9]:=  Export[
              "file.dat"
              ,
              data /. a_?NumberQ :> 

                  ToString@ScientificForm[a, NumberFormat -> (#1 <> "*10^(" <> #3 <> ")" &)]
          ]
Out[9]:= file.dat

this produces following file.dat file:


M   4.35203*10^(10)  4.2566*10^(9)
δ   4.10847*10^(5)   2.12356*10^(4)
L   1.01689*10^(9)   1.30717*10^(16)

Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more