Isolating characters in a string

Question

I'm struggling to find the right function in mathematica to isolate specific characters in a string. I have got a formula as string (I imported it from an excelfile) like this:

y = 0.97*x1 + 0.521*x2 - 30.21 - 0.07431*x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6

Now I want to isolate the coefficients, e.g. 0.97,0.521 from the x's and maybe store it seperately, so that I know which coefficients were for which x. I thought this would be easily done and I browsed through the help of mathematica, but I couln't find any example which helps me so far. Maybe some of you can help me out which functions is best for this task?

Answer 1

Using the internal expression parser:

string = "y = 0.97*x1 + 0.521*x2 - 30.21 - 0.07431*x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6";

Cases[
  ToHeldExpression[string],
  s_Symbol * Except[_Symbol, n_?NumericQ] :> {HoldForm[s], n},
  {-2}
]

{{x1,0.97}, {x2,0.521}, {x3,-0.07431}, {x4,-0.126}, {x5,-0.1939}, {x6,-0.361}}

• Note use of HoldForm to keep Symbols unevaluated in case they have values assigned.

• In this simple case the rule s_Symbol * n_ :> {HoldForm[s], n} could be used but I believe the code above is more robust.

• ToHeldExpression is a deprecated function but still entirely usable, and more concise than ToExpression[string, InputForm, Hold].

Answer 2

This answer is just for exercise purposes, I would use Coefficient way.

string = "y = 0.97*x1 + 0.521*x2 - 30.21 - 0.07431*x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6";

StringCases[
  StringReplace[string, "- " -> "-"],
  c : NumberString ~~ _ ~~ x : ("x" ~~ DigitCharacter) :> {c, x}]

{{"0.97", "x1"}, {"0.521", "x2"}, {"-0.07431", "x3"}, {"-0.126", "x4"},
 {"-0.1939", "x5"}, {"-0.361", "x6"}}

When there are cases like "+ x2" we need one more replacement:

string = "y = 0.97*x1 + x2 - 30.21 - x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6";

StringCases[
 Fold[StringReplace, string, {s : ("+ " | "- ") ~~ "x" :> s <> "1.*x", "- " -> "-"}]
 ,
 c : NumberString ~~ _ ~~ x : ("x" ~~ DigitCharacter) :> {c, x}]

{{"0.97", "x1"}, {"1.", "x2"}, {"-1.", "x3"}, {"-0.126", "x4"}, 
 {"-0.1939", "x5"}, {"-0.361", "x6"}}

Answer 3

There are several ways it might be done. This is one example. Here is something like your string:

str = "y=0.97*x1+0.52*x2-30.21-0.07*x3";

I do not take the full version, since you did not give it in M form, which normally you should have done. Now, let us make a list out of it:

 list = List @@ ToExpression[str]
(* {-30.21, 0.97 x1, 0.52 x2, -0.07 x3}   *)

This list is transformed into required one as follows:

 list /. a_ /; Characters[ToString@a][[1]] == "x" -> 1

(*   {-30.21, 0.97, 0.52, -0.07}  *)

Here is another simple solution based on the assumption that you have always the numeration of x-s monotonously increasing,i.e. the list of three elements will be x1, x2 x3 and not x1, x28, x5. In this case one can do as follows:

   rule = Table[
  ToExpression[ToString[x] <> ToString[i]] -> 1, {i, 1, 
   Length[list] - 1}]

(*  {x1 -> 1, x2 -> 1, x3 -> 1}   *)

and then using the list from the previous solution:

    list /. rule

(*   {-30.21, 0.97, 0.52, -0.07}  *)

That' it. Have fun.

Answer 4

Using jVincent's ContextScope[]

m`str1 = "y = 0.97*x1 + 0.521*x2 - 30.21 - 0.07431*x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6";
ContextScope["m`", {SymbolName /@ Variables@#, 
                    Coefficient[#, Variables@#]} &@ToExpression[str1] // Transpose]
(*
{{"x1", 0.97`}, {"x2", 0.521`}, {"x3", -0.07431`}, 
 {"x4", -0.126`}, {"x5", -0.1939`}, {"x6", -0.361`}}
*)

Answer 5

Since I'm still new to String Patterns here is another entry using StringCases.

string = "y = 0.97*x1 + 0.521*x2 - 30.21 - 0.07431*x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6";

StringCases[string, s : ({" ", " + ", " - "} ~~ NumberString) ~~ "*" ~~ 
   x : ("x" ~~ DigitCharacter ..) :> {x, ToExpression@s}]

Gives:

{{"x1", 0.97}, {"x2", 0.521}, {"x3", -0.07431}, {"x4", -0.126}, {"x5", -0.1939}, {"x6",-0.361}}

Note the use of DigitCharacter .. for situations with variables like x10, x11 etc.

Kuba pointed out that cases like "y = x2" cannot be handled by the above method, so we do some StringReplacement before proceeding:

string2 = "y = 0.97*x1 + x2 - 30.21 - x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6";

Now

rp = StringReplace[string2, " " ~~ x : ("x" ~~ DigitCharacter ..) :> " 1" ~~ "*" ~~ x]

Then as before:

StringCases[rp, s : ({" ", " + ", " - "} ~~ NumberString) ~~ "*" ~~ 
                x : ("x" ~~ DigitCharacter ..) :> {x, ToExpression@s}]

{{"x1", 0.97}, {"x2", 1}, {"x3", -1}, {"x4", -0.126}, {"x5", -0.1939}, {"x6", -0.361}}

Answer 6

str = 
 "y = 0.97*x1 + 0.521*x2 - 30.21 - 0.07431*x3 - 0.126*x4 - 0.1939*x5 - 0.361*x6";

Using SequenceCases and SequenceReplace

SequenceCases[
 ToExpression @ SequenceReplace[
   StringSplit[str, {" ", "*"}][[3 ;;]],
   {{"-", x_} :> "-" <> x, {"+"} :> Nothing}],
 x : {_?NumericQ, _Symbol} :> ToString /@ x]

{{"0.97", "x1"}, {"0.521", "x2"}, {"-0.07431", "x3"}, {"-0.126", "x4"}, {"-0.1939", "x5"}, {"-0.361", "x6"}}