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Is there a simple way to apply a function to the RHS of a substitution?

Assign the Background rule in Grid (the positions can be described by a integer function)ReplaceAll performance problem: packed arrays on the LHS are unpacked when the RHS is too longHow to select the value of a substitution rule for a particular variable?replace RHS of ruleWhy won't the Rule work? And how to apply it to a combination of variables?How does one unpack the contents of a list while using rules to substitute values for each variable?Why does syntax highlighting in `Set` and `Rule` not color pattern names on the RHS?What is the function of OrderedQ in these expressions?Make Mathematica apply the same rule exhaustively in simplification

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6

1

$begingroup$

Suppose I have solved a system of equations, resulting in a solution of the form:

sol = f[a1] -> SomeComplicatedFunction[x, a1], f[a2] -> SomeComplicatedFunction[x, a2], f[a3] -> SomeComplicatedFunction[x, a3]

I want to use the list of substitutions sol later on, but first I want to apply some method myFunction to the rhs of the substitution. I.e., the desired output is

sol = f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> myFunction[SomeComplicatedFunction[x, a3]]

I have tried extracting all the RHSs from sol, applying myFunction to the list, then setting this back to the original f[]s, but this seems to be very inefficient. Is there some canonical Mathematica way of applying rules to solutions while keeping the solutions intact?

rule

share|improve this question

asked Oct 1 at 0:13

user366202user366202

14755 bronze badges

$endgroup$

add a comment
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6

1

$begingroup$

Suppose I have solved a system of equations, resulting in a solution of the form:

sol = f[a1] -> SomeComplicatedFunction[x, a1], f[a2] -> SomeComplicatedFunction[x, a2], f[a3] -> SomeComplicatedFunction[x, a3]

I want to use the list of substitutions sol later on, but first I want to apply some method myFunction to the rhs of the substitution. I.e., the desired output is

sol = f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> myFunction[SomeComplicatedFunction[x, a3]]

I have tried extracting all the RHSs from sol, applying myFunction to the list, then setting this back to the original f[]s, but this seems to be very inefficient. Is there some canonical Mathematica way of applying rules to solutions while keeping the solutions intact?

rule

share|improve this question

asked Oct 1 at 0:13

user366202user366202

14755 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

Suppose I have solved a system of equations, resulting in a solution of the form:

sol = f[a1] -> SomeComplicatedFunction[x, a1], f[a2] -> SomeComplicatedFunction[x, a2], f[a3] -> SomeComplicatedFunction[x, a3]

I want to use the list of substitutions sol later on, but first I want to apply some method myFunction to the rhs of the substitution. I.e., the desired output is

sol = f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> myFunction[SomeComplicatedFunction[x, a3]]

I have tried extracting all the RHSs from sol, applying myFunction to the list, then setting this back to the original f[]s, but this seems to be very inefficient. Is there some canonical Mathematica way of applying rules to solutions while keeping the solutions intact?

rule

share|improve this question

asked Oct 1 at 0:13

user366202user366202

14755 bronze badges

$endgroup$

sol = f[a1] -> SomeComplicatedFunction[x, a1], f[a2] -> SomeComplicatedFunction[x, a2], f[a3] -> SomeComplicatedFunction[x, a3]

sol = f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> myFunction[SomeComplicatedFunction[x, a3]]

share|improve this question

asked Oct 1 at 0:13

user366202user366202

14755 bronze badges

share|improve this question

asked Oct 1 at 0:13

user366202user366202

14755 bronze badges

asked Oct 1 at 0:13

user366202user366202

14755 bronze badges

asked Oct 1 at 0:13

user366202user366202

14755 bronze badges

2 Answers
2

active

oldest

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7

$begingroup$

sol = 
 f[a1] -> SomeComplicatedFunction[x, a1],
 f[a2] -> SomeComplicatedFunction[x, a2],
 f[a3] -> SomeComplicatedFunction[x, a3];

sol2 = sol /. Rule[lhs_, rhs_] :> Rule[lhs, myFunction[rhs]]

(* f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> 
 myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> 
 myFunction[SomeComplicatedFunction[x, a3]] *)

share|improve this answer

answered Oct 1 at 0:19

Bob HanlonBob Hanlon

70.4k33 gold badges4040 silver badges110110 bronze badges

$endgroup$

add a comment
 | 

7

$begingroup$

Additional alternatives:

You can use MapAt to map myFunction at positions All, -1, -1:

sol3 = MapAt[myFunction, sol, All, -1, -1]

f[a1] -> myFunction[SomeComplicatedFunction[x, a1]],

f[a2] ->
myFunction[SomeComplicatedFunction[x, a2]],

f[a3] ->
myFunction[SomeComplicatedFunction[x, a3]]

You can assign new values at desired positions using Part assignment:

sol4 = sol;
sol4[[All, -1, -1]] = myFunction /@ sol4[[All, -1, -1]];
sol4

same result

share|improve this answer

answered Oct 1 at 1:04

kglrkglr

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add a comment
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7

$begingroup$

sol = 
 f[a1] -> SomeComplicatedFunction[x, a1],
 f[a2] -> SomeComplicatedFunction[x, a2],
 f[a3] -> SomeComplicatedFunction[x, a3];

sol2 = sol /. Rule[lhs_, rhs_] :> Rule[lhs, myFunction[rhs]]

(* f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> 
 myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> 
 myFunction[SomeComplicatedFunction[x, a3]] *)

share|improve this answer

answered Oct 1 at 0:19

Bob HanlonBob Hanlon

70.4k33 gold badges4040 silver badges110110 bronze badges

$endgroup$

add a comment
 | 

7

$begingroup$

sol = 
 f[a1] -> SomeComplicatedFunction[x, a1],
 f[a2] -> SomeComplicatedFunction[x, a2],
 f[a3] -> SomeComplicatedFunction[x, a3];

sol2 = sol /. Rule[lhs_, rhs_] :> Rule[lhs, myFunction[rhs]]

(* f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> 
 myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> 
 myFunction[SomeComplicatedFunction[x, a3]] *)

share|improve this answer

answered Oct 1 at 0:19

Bob HanlonBob Hanlon

70.4k33 gold badges4040 silver badges110110 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

sol = 
 f[a1] -> SomeComplicatedFunction[x, a1],
 f[a2] -> SomeComplicatedFunction[x, a2],
 f[a3] -> SomeComplicatedFunction[x, a3];

sol2 = sol /. Rule[lhs_, rhs_] :> Rule[lhs, myFunction[rhs]]

(* f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> 
 myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> 
 myFunction[SomeComplicatedFunction[x, a3]] *)

share|improve this answer

answered Oct 1 at 0:19

Bob HanlonBob Hanlon

70.4k33 gold badges4040 silver badges110110 bronze badges

$endgroup$

sol = 
 f[a1] -> SomeComplicatedFunction[x, a1],
 f[a2] -> SomeComplicatedFunction[x, a2],
 f[a3] -> SomeComplicatedFunction[x, a3];

sol2 = sol /. Rule[lhs_, rhs_] :> Rule[lhs, myFunction[rhs]]

(* f[a1] -> myFunction[SomeComplicatedFunction[x, a1]], f[a2] -> 
 myFunction[SomeComplicatedFunction[x, a2]], f[a3] -> 
 myFunction[SomeComplicatedFunction[x, a3]] *)

share|improve this answer

answered Oct 1 at 0:19

Bob HanlonBob Hanlon

70.4k33 gold badges4040 silver badges110110 bronze badges

answered Oct 1 at 0:19

Bob HanlonBob Hanlon

70.4k33 gold badges4040 silver badges110110 bronze badges

answered Oct 1 at 0:19

Bob HanlonBob Hanlon

70.4k33 gold badges4040 silver badges110110 bronze badges

7

$begingroup$

Additional alternatives:

You can use MapAt to map myFunction at positions All, -1, -1:

sol3 = MapAt[myFunction, sol, All, -1, -1]

f[a1] -> myFunction[SomeComplicatedFunction[x, a1]],

f[a2] ->
myFunction[SomeComplicatedFunction[x, a2]],

f[a3] ->
myFunction[SomeComplicatedFunction[x, a3]]

You can assign new values at desired positions using Part assignment:

sol4 = sol;
sol4[[All, -1, -1]] = myFunction /@ sol4[[All, -1, -1]];
sol4

same result

share|improve this answer

answered Oct 1 at 1:04

kglrkglr

229k1010 gold badges259259 silver badges522522 bronze badges

$endgroup$

add a comment
 | 

7

$begingroup$

Additional alternatives:

You can use MapAt to map myFunction at positions All, -1, -1:

sol3 = MapAt[myFunction, sol, All, -1, -1]

f[a1] -> myFunction[SomeComplicatedFunction[x, a1]],

f[a2] ->
myFunction[SomeComplicatedFunction[x, a2]],

f[a3] ->
myFunction[SomeComplicatedFunction[x, a3]]

You can assign new values at desired positions using Part assignment:

sol4 = sol;
sol4[[All, -1, -1]] = myFunction /@ sol4[[All, -1, -1]];
sol4

same result

share|improve this answer

answered Oct 1 at 1:04

kglrkglr

229k1010 gold badges259259 silver badges522522 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

Additional alternatives:

You can use MapAt to map myFunction at positions All, -1, -1:

sol3 = MapAt[myFunction, sol, All, -1, -1]

f[a1] -> myFunction[SomeComplicatedFunction[x, a1]],

f[a2] ->
myFunction[SomeComplicatedFunction[x, a2]],

f[a3] ->
myFunction[SomeComplicatedFunction[x, a3]]

You can assign new values at desired positions using Part assignment:

sol4 = sol;
sol4[[All, -1, -1]] = myFunction /@ sol4[[All, -1, -1]];
sol4

same result

share|improve this answer

answered Oct 1 at 1:04

kglrkglr

229k1010 gold badges259259 silver badges522522 bronze badges

$endgroup$

sol3 = MapAt[myFunction, sol, All, -1, -1]

sol4 = sol;
sol4[[All, -1, -1]] = myFunction /@ sol4[[All, -1, -1]];
sol4

share|improve this answer

answered Oct 1 at 1:04

kglrkglr

229k1010 gold badges259259 silver badges522522 bronze badges

answered Oct 1 at 1:04

kglrkglr

229k1010 gold badges259259 silver badges522522 bronze badges

answered Oct 1 at 1:04

kglrkglr

229k1010 gold badges259259 silver badges522522 bronze badges