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Re: Replacements and NIntegrate

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  Re: Replacements and NIntegrate Andrew Moylan <amoylan@wolfram.com> - 2011-05-03 12:22 +0000
    Re: Replacements and NIntegrate Giacomo Ciani <jackspam79@gmail.com> - 2011-05-04 10:33 +0000

#2070 — Re: Replacements and NIntegrate

There are different ways to do it.

As an example:

In[1]:= h[z_] := a + b + z

In[2]:= vals = {a -> 1, b -> 2, L -> 3};

The easiest way is to use Block instead of replacement rules:

In[3]:= Block[{a = 1, b = 2, L = 3}, 
 NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]

Out[3]= 4.79556

A good way is to make h depend on the parameters a and b:

In[4]:= h[{a_, b_}, z_] := a + b + z

Then you want NIntegrate to not be evaluated until after the replacement rules are applied by ReplaceAll. Thus:

In[5]:= Unevaluated[
  NIntegrate[h[{a, b}, z] z/Sqrt[L^2 + z^2], {z, -L, L}]] /. vals

Out[5]= 4.79556

If you don't want to make either of these changes, you can construct the Block from the replacement rules:

In[6]:= Block @@ 
 Append[Apply[Set, Hold[Evaluate[vals]], {2}], 
  Unevaluated[NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]]

Out[6]= 4.79556

Take it apart piece by piece to see how it works:

In[7]:= Hold[Evaluate[vals]]

Out[7]= Hold[{a -> 1, b -> 2, L -> 3}]


In[8]:= Apply[Set, Hold[Evaluate[vals]], {2}]

Out[8]= Hold[{a = 1, b = 2, L = 3}]


In[9]:= Append[Apply[Set, Hold[Evaluate[vals]], {2}], 
 Unevaluated[NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]]

Out[9]= Hold[{a = 1, b = 2, L = 3}, 
 NIntegrate[(h[z] z)/Sqrt[L^2 + z^2], {z, -L, L}]]

You can easily make a function to do this:

In[10]:= SetAttributes[BlockRules, HoldRest];

In[11]:= BlockRules[rules_, expr_] := 
 Block @@ Append[Apply[Set, Hold@rules, {2}], Unevaluated[expr]]

Use it like this:

In[12]:= BlockRules[vals, 
 NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]

Out[12]= 4.79556

You can also make another useful variant, WithRules, which works the same way but with With instead of Block.

Hope this helps.

Andrew Moylan
Wolfram Research


----- Original Message -----
> From: "Giacomo Ciani" <jackspam79@gmail.com>
> To: mathgroup@smc.vnet.net
> Sent: Tuesday, May 3, 2011 7:44:43 PM
> Subject:  Replacements and NIntegrate
> 
> Hi all,
> 
> I've been reading quite a bit in the Mathematica docs and in this
> newsgroup, but didn't find (or didn't recognize...) an answer to my
> problem.
> 
> I want to evaluate the following expression:
> 
> NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]
> 
> where h[z] has a delayed value set previously in the notebook. Also,
> I
> have previously defined a set of replacement rules in the form:
> 
> vals = {a->1, b->2, ec....}
> 
> to be used to specify the numerical values of the various parameters
> (including those present in the delayed value of h[z]).
> 
> As for now, the only (brute force) way I found to have my expression
> correctly evaluated is to apply replacement rules separately to each
> argument of NIntegrate (including integration limits):
> 
> NIntegrate[ h[z] z / Sqrt[L^2 + z^2]  /.vals, {z, -L /.vals,
> L/.vals}]
> 
> I think you agree with me that this does not look very elegant.
> Instead, I would like to be able to write something like this:
> 
> NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]/.vals
> 
> I know this can't work, as Mathematica tries to evaluate NIntegrate
> and then apply the replacement rules... but how can I ask Mathematica
> to apply all the replacement rules and delayed values to an
> expression
> without (or before) actually trying to evaluate it?
> 
> I found a lot of commands to hold the function from evaluating the
> arguments, while I need pretty much the opposite...
> 
> Maybe there is something very simple I am overlooking...
> 
> Thanks
> 
> Giacomo
> 
> 

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#2080

Thanks! That's a bit convoluted, but it does what I wanted. And it has
been an occasion to learn more functions... :-)

Giacomo

On May 3, 8:22 am, Andrew Moylan <amoy...@wolfram.com> wrote:
> There are different ways to do it.
>
> As an example:
>
> In[1]:= h[z_] := a + b + z
>
> In[2]:= vals = {a -> 1, b -> 2, L -> 3};
>
> The easiest way is to use Block instead of replacement rules:
>
> In[3]:= Block[{a = 1, b = 2, L = 3},
>  NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]
>
> Out[3]= 4.79556
>
> A good way is to make h depend on the parameters a and b:
>
> In[4]:= h[{a_, b_}, z_] := a + b + z
>
> Then you want NIntegrate to not be evaluated until after the replacement rules are applied by ReplaceAll. Thus:
>
> In[5]:= Unevaluated[
>   NIntegrate[h[{a, b}, z] z/Sqrt[L^2 + z^2], {z, -L, L}]] /. vals
>
> Out[5]= 4.79556
>
> If you don't want to make either of these changes, you can construct the Block from the replacement rules:
>
> In[6]:= Block @@
>  Append[Apply[Set, Hold[Evaluate[vals]], {2}],
>   Unevaluated[NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]]
>
> Out[6]= 4.79556
>
> Take it apart piece by piece to see how it works:
>
> In[7]:= Hold[Evaluate[vals]]
>
> Out[7]= Hold[{a -> 1, b -> 2, L -> 3}]
>
> In[8]:= Apply[Set, Hold[Evaluate[vals]], {2}]
>
> Out[8]= Hold[{a = 1, b = 2, L = 3}]
>
> In[9]:= Append[Apply[Set, Hold[Evaluate[vals]], {2}],
>  Unevaluated[NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]]
>
> Out[9]= Hold[{a = 1, b = 2, L = 3},
>  NIntegrate[(h[z] z)/Sqrt[L^2 + z^2], {z, -L, L}]]
>
> You can easily make a function to do this:
>
> In[10]:= SetAttributes[BlockRules, HoldRest];
>
> In[11]:= BlockRules[rules_, expr_] :=
>  Block @@ Append[Apply[Set, Hold@rules, {2}], Unevaluated[expr]]
>
> Use it like this:
>
> In[12]:= BlockRules[vals,
>  NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]]
>
> Out[12]= 4.79556
>
> You can also make another useful variant, WithRules, which works the same way but with With instead of Block.
>
> Hope this helps.
>
> Andrew Moylan
> Wolfram Research
>
> ----- Original Message -----
> > From: "Giacomo Ciani" <jackspa...@gmail.com>
> > To: mathgr...@smc.vnet.net
> > Sent: Tuesday, May 3, 2011 7:44:43 PM
> > Subject:  Replacements and NIntegrate
>
> > Hi all,
>
> > I've been reading quite a bit in the Mathematica docs and in this
> > newsgroup, but didn't find (or didn't recognize...) an answer to my
> > problem.
>
> > I want to evaluate the following expression:
>
> > NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]
>
> > where h[z] has a delayed value set previously in the notebook. Also,
> > I
> > have previously defined a set of replacement rules in the form:
>
> > vals = {a->1, b->2, ec....}
>
> > to be used to specify the numerical values of the various parameters
> > (including those present in the delayed value of h[z]).
>
> > As for now, the only (brute force) way I found to have my expression
> > correctly evaluated is to apply replacement rules separately to each
> > argument of NIntegrate (including integration limits):
>
> > NIntegrate[ h[z] z / Sqrt[L^2 + z^2]  /.vals, {z, -L /.vals,
> > L/.vals}]
>
> > I think you agree with me that this does not look very elegant.
> > Instead, I would like to be able to write something like this:
>
> > NIntegrate[h[z] z/Sqrt[L^2 + z^2], {z, -L, L}]/.vals
>
> > I know this can't work, as Mathematica tries to evaluate NIntegrate
> > and then apply the replacement rules... but how can I ask Mathematica
> > to apply all the replacement rules and delayed values to an
> > expression
> > without (or before) actually trying to evaluate it?
>
> > I found a lot of commands to hold the function from evaluating the
> > arguments, while I need pretty much the opposite...
>
> > Maybe there is something very simple I am overlooking...
>
> > Thanks
>
> > Giacomo

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