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Get two columns of numerical data as output data format?

Lev Dorosinskiy

Lev Dorosinskiy, National Metrology Institute

Posted 6 years ago

Hi I am solving a system of two equations with two variables z and x repeatedly in a cycle. At each step the solution is output into a file using Write function. I've pasted a part of the file below. Apart from the numerical data, it contains also other things, like curly brackets, symbols like z-> . But I need to make a file that contains only two columns of numerical data, nothing else. How can I do that? {z -> -2.1337292689248377, x -> -1.0028011752012573} {z -> -1.5494511566425633, x -> -1.0015118850013995} {z -> 0.14651664469911463, x -> -622.9327284292021} {z -> 2.3907571924477877, x -> -1.0037755798274968} {z -> 3.928880270839741, x -> -52.74880957186027} {z -> 5.2048915646949965, x -> -1.017772661581148} {z -> 9.062107349506263, x -> -1.0515309552374674} {z -> 10.152134293099394, x -> -1.0641971180448309} {z -> 14.312077199555635, x -> -395.73358957571725}

I am solving a system of two equations with two variables z and x repeatedly in a cycle. At each step the solution is output into a file using Write function. I've pasted a part of the file below. Apart from the numerical data, it contains also other things, like curly brackets, symbols like z-> . But I need to make a file that contains only two columns of numerical data, nothing else. How can I do that?

{z -> -2.1337292689248377, x -> -1.0028011752012573}

{z -> -1.5494511566425633, x -> -1.0015118850013995}

{z -> 0.14651664469911463, x -> -622.9327284292021}

{z -> 2.3907571924477877, x -> -1.0037755798274968}

{z -> 3.928880270839741, x -> -52.74880957186027}

{z -> 5.2048915646949965, x -> -1.017772661581148}

{z -> 9.062107349506263, x -> -1.0515309552374674}

{z -> 10.152134293099394, x -> -1.0641971180448309}

{z -> 14.312077199555635, x -> -395.73358957571725}

POSTED BY: Lev Dorosinskiy

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Dima Panna

Dima Panna, Technion - Israel Institute of Technology

Posted 6 years ago

Hi Lev, The fact that you are using FindRoot instead of NSolve doesn't really matter, please see the following code: (Define File Path and File Name and Open it for writing appending \ new data to the end of the file ) MyPath = "C:\\MyPath\\Wolfram \ Mathematica\\"; MyFile = "MyFile.csv"; FileH = OpenAppend[(MyPath ~~ MyFile)]; sol[p1_, p2_, p3_, p4_, p5_] := {x, z} /. FindRoot[{Exp[p1 x] == p2 x, Exp[p3 z] == p4 z}, {{z, p5}, {x, p5}}] (* Solving Some Equation in the Loop) Do[ ({x,z}/. is used to remove rule sign "\[Rule]" ) Sol = {sol[1, 5, 1, 4, 0]}; (Write CSV formated String into the File ) WriteString[FileH, ExportString[Sol, "CSV", Alignment -> Left]] , {10}]; ( Close the file*) Close[FileH]; The output is : Please notice, that this is only needed when you HAVE TO update the file on-fly in the loop, as Gianluca Gorni mentioned you can do it much easier outside the loop using Export[] with Table attribute

Hi Lev, The fact that you are using FindRoot instead of NSolve doesn't really matter, please see the following code:

(*Define File Path and File Name and Open it for writing appending \
new data to the end of the file *)
MyPath = "C:\\MyPath\\Wolfram \
Mathematica\\";
MyFile = "MyFile.csv";
FileH = OpenAppend[(MyPath ~~ MyFile)];

sol[p1_, p2_, p3_, p4_, p5_] := {x, z} /. 
  FindRoot[{Exp[p1 x] == p2 x, Exp[p3 z] == p4 z}, {{z, p5}, {x, p5}}]

(* Solving Some Equation in the Loop*)
Do[
  (*{x,z}/. is used to remove rule sign "\[Rule]" *)
  Sol = {sol[1, 5, 1, 4, 0]};
  (*Write CSV formated String into the File *)
  WriteString[FileH, ExportString[Sol, "CSV", Alignment -> Left]]
  , {10}];

(* Close the file*)
Close[FileH];

The output is :

enter image description here

Please notice, that this is only needed when you HAVE TO update the file on-fly in the loop, as Gianluca Gorni mentioned you can do it much easier outside the loop using Export[] with Table attribute

POSTED BY: Dima Panna

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 6 years ago

Try something like this: sol[p1_?NumberQ, p2_?NumberQ, p3_?NumberQ, p4_?NumberQ, p5_?NumberQ] := {z, x} /. FindRoot[my equations, {{z, p5}, {x, 5}}]; Export[file, sol[p1, p2, p3, p4, p5], "Table"] Instead of writing the numbers separately into the file, you can do it at the end.

POSTED BY: Gianluca Gorni

Lev Dorosinskiy

Lev Dorosinskiy, National Metrology Institute

Posted 6 years ago

Thank you. My problem is somewhat different and I could not figure out how to apply your solutions to my case sol[p1_?NumberQ, p2_?NumberQ, p3_?NumberQ, p4_?NumberQ, p5_?NumberQ] := FindRoot[my equations, {{z, p5}, {x, 5}}]; And then in the cycle: Write[file, sol[p1, p2, p3, p4, p5]]; My equations are non-polynomial. Besides, they have 5 parameters p1 - p5 which are varied et each step of the cycle. That's why I use FIndRoot instead of NSolve and I define function sol[...] with parameters. In this case there is no expression like sol[...] = something. That's why I could not figure out where to insert `{x, z} /.`

POSTED BY: Lev Dorosinskiy

Dima Panna

Dima Panna, Technion - Israel Institute of Technology

Posted 6 years ago

Hi Lev, A possible solution is to export your data into CSV file: (NOTE: this is the way to do it on-fly in the loop, if you can wait till the loop terminates,then just use Export["MyFile.csv", Sol] ) (Define a File Path and a File Name and Open it for writing, appending \ a new data to the end of the file ) MyPath = "C:\MY_PATH\\Wolfram \\Mathematica\\"; MyFile = "MyFile.csv"; FileH = OpenAppend[(MyPath ~~ MyFile)]; (* Solving Some Equation 10 Times in a Loop) Do[ ( Solve a system of dummy equations. {x,z}/. is used to remove the rule sign "->" from the output) Sol = {x, z} /. NSolve[{x^2 + z^2 == RandomReal[1], z == x^2 + 0.001 RandomReal[1]}, {x, z} \[Element] Reals]; (Write CSV formated String into the File ) WriteString[FileH, ExportString[Sol, "CSV", Alignment -> Left]] , {10}]; ( Close the file*) Close[FileH]; The resulted file output looks like this: .

Hi Lev,

A possible solution is to export your data into CSV file: (NOTE: this is the way to do it on-fly in the loop, if you can wait till the loop terminates,then just use Export["MyFile.csv", Sol] )

(*Define a File Path and a File Name and Open it for writing, appending \
a new data to the end of the file *)
MyPath = "C:\MY_PATH\\Wolfram \\Mathematica\\";
MyFile = "MyFile.csv";
FileH = OpenAppend[(MyPath ~~ MyFile)];

(* Solving Some Equation 10 Times in a Loop*)
Do[
  (* Solve a system of dummy equations.
       {x,z}/. is used to remove the rule sign "->"  from the output*)
  Sol = {x, z} /.
    NSolve[{x^2 + z^2 == RandomReal[1], 
      z == x^2 + 0.001 RandomReal[1]}, {x, z} \[Element] Reals];
  (*Write CSV formated String into the File *)
  WriteString[FileH, ExportString[Sol, "CSV", Alignment -> Left]]
  , {10}];

(* Close the file*)
Close[FileH];

The resulted file output looks like this:

. enter image description here

POSTED BY: Dima Panna

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 6 years ago

You get rid of the variable names with the `{x,z}/.` syntax. Then you can export to `"Table"` format: sols = {x, z} /. NSolve[{x^2 + z^2 == 1, x == z}, {x, z}] Export["~/Desktop/file.txt", sols, "Table"]

POSTED BY: Gianluca Gorni

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