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RE: Beginner question on local vars./scoping

  • To: mathgroup at
  • Subject: [mg33674] RE: [mg33660] Beginner question on local vars./scoping
  • From: "Wolf, Hartmut" <Hartmut.Wolf at>
  • Date: Sat, 6 Apr 2002 00:48:49 -0500 (EST)
  • Sender: owner-wri-mathgroup at

> -----Original Message-----
> From: Mark Pilloff [mailto:mdp1REMOVETHIS at]
To: mathgroup at
> Sent: Friday, April 05, 2002 2:41 AM
> To: mathgroup at
> Subject: [mg33674] [mg33660] Beginner question on local vars./scoping
> Hi,
> I've written a function of the sort:
> function := Do some stuff
> The situation is that the 'Do some stuff' depends upon 
> various global vars.
> but some of the 'stuff' yields the same result unless some of 
> the global
> vars have changed.  I'd like to memoize the results and have 
> some local vars
> to function that will remember the value of the global vars 
> when function
> was last called and only recompute if necessary.  Right now I 
> have global
> vars like lastValueOfVarSeen and lastResultOfStep2 but I'd 
> prefer to make
> them local to function but still permanent.
> 1.  How can I do this?
> 2.  Is there a better / more standard way to achieve the goal 
> described
> above?
> Thanks for any help,
> Mark


certainly the subject of your post doesn't adequately describe your problem!
Or perhaps I didn't understand right... Anyway, I'll give you two
suggestions, which, hopefully, might help you.

I assume that you want to memorize the results of a function, let's call it
f, perhaps dependent on some parameters *and* some global variables. The
function will be evaluated (anew) if new values of the parameters occur *or*
if one of the global variables has changed.

Your (current) global variables are ValueOfVarSeen, ResultOfStep2.

Proposal (1) The definitions:

In[2]:= f[some_, thing_] := 
    f[some, thing, ValueOfVarSeen, ResultOfStep2]

In[3]:= f[some_, thing_, _, _] := 
    (Print["calculated anew!"]; 
    With[{newvalue = some * ValueOfVarSeen + thing * ResultOfStep2}, 
        f[some, thing, ValueOfVarSeen, ResultOfStep2] := 
        (Print["reused!"]; newvalue); 

In[4]:= f[__] := Print["storage error"]
In[5]:= ?f

You see: the values of the globals are stored together with the parameter
values of your calculation. I have inserted some Print statements as to
monitor whether stored or new values are returned. For the (tested and
running!) application you may remove them.


In[6]:= ValueOfVarSeen = 1;
        ResultOfStep2 = 2;

In[8]:= f[4, 5]
>From In[8]:= "calculated anew!"
Out[8]= 14

In[9]:= f[4, 5]
>From In[9]:= "reused!"
Out[9]= 14

In[10]:= ValueOfVarSeen = 2;

In[11]:= f[4, 5]
>From In[11]:= "calculated anew!"
Out[11]= 18

In[12]:= f[5, 5]
>From In[12]:= "calculated anew!"
Out[12]= 20

In[13]:= f[4, 5]
>From In[13]:= "reused!"
Out[13]= 18

In[14]:= ValueOfVarSeen = 1;

In[15]:= f[4, 5]
>From In[15]:= "reused!"
Out[15]= 14

In[16]:= ?f

In[17]:= Quit[]

A characteristic of this solution is that all calculated values are kept,
such that, if you return to a prior value of a global variable, the
corresponding old calculated values are returned. This may be desirable or

If not, follow proposal (2).

This is a bit more tricky: all stored values are Cleared if the function is
called with changed global variables. But then the definitions are cleared
too, so they have to be renewed immediately after. This is done with the
conditional call to f; of course we now have to store the old global values.
The definitions:

In[1]:= Clear[f, ff, lastValueOfVarSeen, lastResultOfStep2]

In[2]:= f[some_, thing_] /; (ValueOfVarSeen =!= lastValueOfVarSeen || 
        ResultOfStep2 =!= lastResultOfStep2) := 
    ff[s_, t_] := (Print["calculated anew!"]; 
        With[{newvalue = s * ValueOfVarSeen + t * ResultOfStep2}, 
          ff[s, t] := (Print["reused!"]; newvalue); newvalue]); 
    lastValueOfVarSeen = ValueOfVarSeen ; 
    lastResultOfStep2 = ResultOfStep2;
    ff[some, thing])

In[3]:= f[some_, thing_] := ff[some, thing]

In[4]:= ff[__] := Print["storage error"]

In[5]:= ?f
In[6]:= ?? ff


In[7]:= ValueOfVarSeen = 1;
        ResultOfStep2 = 2;

In[9]:= f[4, 5]
>From In[9]:= "calculated anew!"
Out[9]= 14

In[10]:= f[4, 5]
>From In[10]:= "reused!"
Out[10]= 14

In[11]:= f[5, 5]
>From In[11]:= "calculated anew!"
Out[11]= 15

In[12]:= ValueOfVarSeen = 2;

In[13]:= f[4, 5]
>From In[13]:= "calculated anew!"
Out[13]= 18

In[14]:= f[4, 5]
>From In[14]:= "reused!"
Out[14]= 18

In[15]:= ValueOfVarSeen = 1;

In[16]:= f[4, 5]
>From In[16]:= "calculated anew!"
Out[16]= 14

In[17]:= ?ff

In[18]:= Quit[]

Hartmut Wolf

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