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Re: hints to speed up numerical integration?

• To: mathgroup at smc.vnet.net
• Subject: [mg60138] Re: [mg60114] hints to speed up numerical integration?
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sun, 4 Sep 2005 03:02:01 -0400 (EDT)
• References: <200509030606.CAA19051@smc.vnet.net>
• Reply-to: chris.chiasson at gmail.com
• Sender: owner-wri-mathgroup at wolfram.com

I can't get your code to work :-[

On 9/3/05, Ruth Lazkoz <ruth.lazkoz at ehu.es> wrote:
> 
> Dear colleagues,
> 
> I would like to speed up this code, because I have to minimize the
> function chi2mar defined below. I have tried Compiled -> True in the
> numerical integrals but it would only make things worse.
> 
> Thanks for your cooperation,
> 
> Ruth Lazkoz
> 
> In[1]:=
> datanw = {{0.0400, 36.38, 0.19}, {0.050, 36.84, 0.21}, {0.0307, 35.90,
> 0.20},
> {0.0560, 37.31, 0.18}, {0.0331, 35.54, 0.20}, {0.0141, 34.13, 0.25},
> {0.0460,
> 36.35, 0.21}, {0.0265, 35.64, 0.20}, {0.101, 38.73, 0.20}, {0.075,
> 37.77, 0.19}};
> 
> In[2]:=
> ndat = 10;
> 
> In[3]:=
> z = datanw[[#1, 1]] & ; mi = datanw[[#1, 2]] & ; smi
> datanw[[#1, 3]] & ; SetAttributes[smi, Listable];
> f[x_, om_, w_] := 1/Sqrt[om*(1 + x)^3 + ( 1 - om)*(1 + x)^(3*(1 +
> w))];
> rr[1, om_, w_] :=
> rr[1, om, w] = NIntegrate[f[x, om, w], {x, 0, z [1]}, Compiled ->
> False];
> rr[i_?IntegerQ, om_, w_] :=
> rr[i, om, w] =
> rr[i - 1, om, w] +
> NIntegrate[f[x, om, w], {x, z[i - 1], z[i]}, Compiled -> False];
> ff[i_?IntegerQ, om_, w_] := 5*Log[ 10, rr[i, om, w]*(1 + z[i])]; ci =
> Sum[1/smi[i]^2, {i, 1, ndat}];
> chi2f2[(om_)? NumericQ, (w_)?NumericQ] :=
> Module[{vec = ((mi[#1] - ff[#1, om, w])/ smi[#1] & ) /@ Range[ndat]},
> vec . vec - Total[vec/smi[Range[ndat]]]^2/ci]
> 
> In[4]:=
> chi2mar[w_] := -2*
> Log[NIntegrate[Exp[-chi2f2[0.23 + omvar, w]/2], {omvar, -0.07, 0.07},
> Compiled -> False]]
> 
> 
> In[5]:=
> chi2mar[0.1] // Timing
> Out[5]=
> {0.078 Second, 15.5573}
> 
> 
> In[6]:=
> chi2mar[0.3] // Timing
> Out[6]=
> {0.078 Second, 15.7998}
> 
> 


-- 
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

• References:
  • hints to speed up numerical integration?
    • From: "Ruth Lazkoz" <ruth.lazkoz@ehu.es>