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Engineering Wolfram Language

How to use NumberForm for producing a Fortran-like EngineeringForm?

Werner Geiger

Posted 5 years ago

I want to produce a number-form like 1.23456x10^-2 => "+12.35e-3". I.e. something similar to EngineeringForm, but as a flat string in Fortran-Notation ("e" instead of "x10^") and with a mandatory sign. Clear[x2e31]; x2e31[x_, digs_Integer : 3, signs_ : True] := TextString[If[x != 0, NumberForm[x, digs, NumberFormat -> (Row[{#1, "e", #3}] &), ExponentFunction -> (3 Quotient[#, 3] &), NumberSigns -> If[signs, {"-", "+"}, {"-", ""}]] , If[signs, "+0", "0"]]]; x = 1.2345610^-2; {x, EngineeringForm[x, 4], x2e31[x, 4]} ==> {0.0123456, 12.35x10^-3, +12.3510^-3} I cannot succeed. Either the NumberForm-option NumberFormat is unevaluated as above or the mantissa does not have digs significant digits as below: Clear[x2e32]; x2e32[x_, digs_Integer : 3, signs_ : True] := TextString[If[x != 0, NumberForm[N[x, digs], NumberFormat -> (Row[{#1, "e", #3}] &), ExponentFunction -> (3 Quotient[#, 3] &), NumberSigns -> If[signs, {"-", "+"}, {"-", ""}]] , If[signs, "+0", "0"]]]; x = 1.23456*10^-2; {x, EngineeringForm[x, 4], x2e32[x, 4]} ==> {0.0123456, 12.35x10^-3, +12.3456e-3} The only difference between the two versions ist NumberForm[N[x, digs], ...] instead of NumberForm[x, digs, ...]. Can anybody explain and resolve that strange behavior of NumberForm?

I want to produce a number-form like 1.23456x10^-2 => "+12.35e-3". I.e. something similar to EngineeringForm, but as a flat string in Fortran-Notation ("e" instead of "x10^") and with a mandatory sign.

Clear[x2e31];
x2e31[x_, digs_Integer : 3, signs_ : True] :=
  TextString[If[x != 0,
    NumberForm[x, digs, NumberFormat -> (Row[{#1, "e", #3}] &), 
     ExponentFunction -> (3 Quotient[#, 3] &), 
     NumberSigns -> If[signs, {"-", "+"}, {"-", ""}]]
    , If[signs, "+0", "0"]]];

x = 1.23456*10^-2; {x, EngineeringForm[x, 4], x2e31[x, 4]}

==> {0.0123456, 12.35x10^-3, +12.35*10^-3}

I cannot succeed. Either the NumberForm-option NumberFormat is unevaluated as above or the mantissa does not have digs significant digits as below:

Clear[x2e32];
x2e32[x_, digs_Integer : 3, signs_ : True] :=
  TextString[If[x != 0,
    NumberForm[N[x, digs], NumberFormat -> (Row[{#1, "e", #3}] &), 
     ExponentFunction -> (3 Quotient[#, 3] &), 
     NumberSigns -> If[signs, {"-", "+"}, {"-", ""}]]
    , If[signs, "+0", "0"]]];

x = 1.23456*10^-2; {x, EngineeringForm[x, 4], x2e32[x, 4]}

==> {0.0123456, 12.35x10^-3, +12.3456e-3}

The only difference between the two versions ist NumberForm[N[x, digs], ...] instead of NumberForm[x, digs, ...].

Can anybody explain and resolve that strange behavior of NumberForm?

POSTED BY: Werner Geiger

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Werner Geiger

Posted 5 years ago

I found a solution now which does everything I need and gives a string. It seems to be similar to Neils suggestions in that it works with StringReplace: Clear[x2e3]; x2e3[x_, digs_Integer : 3, signs_ : True] := StringReplace[TextString[If[x != 0, EngineeringForm[x, digs, NumberSigns -> If[signs, {"-", "+"}, {"-", ""}]] , If[signs, "+0", "0"] ]], {".10^" -> "e", "10^" -> "e"}]; Note that I ommit a decimal point at the end of the mantissa. I.e x=0.123456 = 123.10^-3 => x2e[x] = "+123e-3". If[True, Block[{x, digs = 4}, Table[{i, x = If[NumericQ[i], If[OddQ[i], -1, 1]1.2345610^i, 0], N[x, digs], TextString[EngineeringForm[x, digs]] // InputForm, x2e3[x, digs, True] // InputForm, x2e3[x] // InputForm }, {i, Append[Range[-6, 6], "-"]} ] // TableForm ]] -6 1.2345610^-6 1.2345610^-6 "1.23510^-6" "+1.235e-6" "+1.23e-6" -5 -0.0000123456 -0.0000123456 "-12.3510^-6" "-12.35e-6" "-12.3e-6" -4 0.000123456 0.000123456 "123.510^-6" "+123.5e-6" "+123e-6" -3 -0.00123456 -0.00123456 "-1.23510^-3" "-1.235e-3" "-1.23e-3" -2 0.0123456 0.0123456 "12.3510^-3" "+12.35e-3" "+12.3e-3" -1 -0.123456 -0.123456 "-123.510^-3" "-123.5e-3" "-123e-3" 0 1.23456 1.23456 "1.235" "+1.235" "+1.23" 1 -12.3456 -12.3456 "-12.35" "-12.35" "-12.3" 2 123.456 123.456 "123.5" "+123.5" "+123." 3 -1234.56 -1234.56 "-1.23510^3" "-1.235e3" "-1.23e3" 4 12345.6 12345.6 "12.3510^3" "+12.35e3" "+12.3e3" 5 -123456. -123456. "-123.510^3" "-123.5e3" "-123e3" 6 1.2345610^6 1.2345610^6 "1.235*10^6" "+1.235e6" "+1.23e6" - 0 0 "0" "+0" "+0"

I found a solution now which does everything I need and gives a string. It seems to be similar to Neils suggestions in that it works with StringReplace:

Clear[x2e3];
x2e3[x_, digs_Integer : 3, signs_ : True] :=
  StringReplace[TextString[If[x != 0,
     EngineeringForm[x, digs, 
      NumberSigns -> If[signs, {"-", "+"}, {"-", ""}]]
     , If[signs, "+0", "0"]
     ]], {".*10^" -> "e", "*10^" -> "e"}];

Note that I ommit a decimal point at the end of the mantissa. I.e x=0.123456 = 123.*10^-3 => x2e[x] = "+123e-3".

If[True, Block[{x, digs = 4},
  Table[{i,
     x = If[NumericQ[i], If[OddQ[i], -1, 1]*1.23456*10^i, 0],
     N[x, digs],
     TextString[EngineeringForm[x, digs]] // InputForm,
     x2e3[x, digs, True] // InputForm,
     x2e3[x] // InputForm
     }, {i, Append[Range[-6, 6], "-"]}
    ] // TableForm
  ]]

-6  1.23456*10^-6      1.23456*10^-6 "1.235*10^-6"   "+1.235e-6"   "+1.23e-6"
-5  -0.0000123456     -0.0000123456      "-12.35*10^-6"   "-12.35e-6"   "-12.3e-6"
-4  0.000123456        0.000123456      "123.5*10^-6"    "+123.5e-6"    "+123e-6"
-3  -0.00123456    -0.00123456       "-1.235*10^-3"    "-1.235e-3"    "-1.23e-3"
-2  0.0123456          0.0123456        "12.35*10^-3"    "+12.35e-3"    "+12.3e-3"
-1  -0.123456         -0.123456         "-123.5*10^-3"   "-123.5e-3"   "-123e-3"
0   1.23456            1.23456          "1.235"           "+1.235"  "+1.23"
1   -12.3456         -12.3456         "-12.35"        "-12.35"   "-12.3"
2   123.456          123.456          "123.5"          "+123.5" "+123."
3   -1234.56      -1234.56         "-1.235*10^3"   "-1.235e3"    "-1.23e3"
4   12345.6         12345.6               "12.35*10^3"  "+12.35e3"   "+12.3e3"
5   -123456.      -123456.                "-123.5*10^3"  "-123.5e3"   "-123e3"
6   1.23456*10^6     1.23456*10^6       "1.235*10^6"  "+1.235e6"   "+1.23e6"
-   0                 0               "0"               "+0"      "+0"

POSTED BY: Werner Geiger

Neil Singer

Neil Singer, AC Kinetics, Inc.

Posted 5 years ago

Werner, Look at this thread. I show several ways to do the formatting. My last post in the thread is most relevant. Thread link here. For the most flexibility in getting exactly the format you want, I would use my SPrintf[] function. The Paddedform solution is not bad as well. Would either of these work for you? Regards, Neil

POSTED BY: Neil Singer

Werner Geiger

Posted 5 years ago

Yes, this works. Pretty strange, since TextString is evaluated after NumberForm. The reason might be that NumberForm is just an output-wrapper which does not affect evaluation. But why, in x2e31, digs is respected, but NumberFormat is not? And why does TextString[EngineeringForm[x,4] work? Anyway, omitting TextString is a bypass. Thank you! But until now I don't know how to use x2e31 then as a string concatenated with other strings.

POSTED BY: Werner Geiger

Rohit Namjoshi

Posted 5 years ago

Hi Werner, Looks like the problem is caused by `TextString`, `NumberForm` appears to be working fine. After removing `TextString` {x, EngineeringForm[x, 4], x2e31[x, 4]} (* {0.0123456, 12.3510^(-3), +12.35e-3} )

POSTED BY: Rohit Namjoshi

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