Re: question

• To: mathgroup at smc.vnet.net
• Subject: [mg132527] Re: question
• From: Sseziwa Mukasa <mukasa at gmail.com>
• Date: Tue, 8 Apr 2014 03:37:05 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-outx@smc.vnet.net
• Delivered-to: mathgroup-newsendx@smc.vnet.net
• References: <20140405054854.566716A57@smc.vnet.net>

```NIntegrate evaluates its arguments symbolically before it does numerical evaluation.  So the problem is F1 and factor2 are being evaluated symbolically when g is evaluated and it's that you want to suppress not the evaluation of g with non-numeric arguments.  That said there are other issues with evaluating your expressions numerically:

(Debug) In[1]:= r1=1;
r2=2;
beta2[t_]:={r1*Cos[2*Pi*t],r2*Sin[2*Pi*t]}

beta1[t_]:=beta2[t+4.8*t^2*(t-1)^2]

=
q2[t_]:=FunctionExpand[beta2'[t]/Sqrt[Norm[beta2'[t]]],Assumptions->t\[Element]Reals&&beta2'\[Element]Vectors[2,Reals]]

=
q1[s_]:=FunctionExpand[beta1'[s]/Sqrt[Norm[beta1'[s]]],Assumptions->s\[Element]Reals&&beta2'\[Element]Vectors[2,Reals]]

a[t_,z_]:=2*q1[t].q2'[z]//FunctionExpand
b[t_,z_]:=q1[t].q2[z]//FunctionExpand
c[t_,z_]:=2*q1'[t].q2[z]//FunctionExpand

F1[t_,z_?NumericQ]:=c[t,z]/b[t,z]
F2[t_,z_]:=a[t,z]/b[t,z]

factor1[s_,z_]:=Exp[-NIntegrate[F2[s,u],{u,0,z}]]

factor2[s_,z_?NumericQ]:=Exp[NIntegrate[F2[s,u],{u,0,z}]]

g[s_,z_]:=NIntegrate[factor2[s,tau]*F1[s,tau],{tau,0,z}]

y[s_,z_]:=factor1[s,z]*g[s,z]

y[.2,.3]
(Debug) During evaluation of In[1]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
(Debug) During evaluation of In[1]:= NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in u near {u} = {0.175777}. NIntegrate obtained -2.75436 and 6.834469819790337` for the integral and error estimates. >>
(Debug) During evaluation of In[1]:= NIntegrate::errprec: Catastrophic loss of precision in the global error estimate due to insufficient WorkingPrecision or divergent integral. >>
(Debug) Out[16]= 15.7109 NIntegrate[factor2[0.2,tau] F1[0.2,tau],{tau,0,0.3}]

You may want to plot your function and choose different regions of integration.

On Apr 5, 2014, at 1:48 AM, Hagwood, Charles R <charles.hagwood at nist.gov> wrote:

>
> I am so sick of Mathematica.  It no longer seems to be a  package to do applied work, but more for the university types.  I have spent several hours using several combinations
> of ?NumberQ  in the following code, but still I get an error.  Last weekend I spend several hours using FunctionExpand to get results I can read.
>
> Any help appreciated.
>
>
>
> r1=1;
> r2=2;
> beta2[t_]:={r1*Cos[2*Pi*t],r2*Sin[2*Pi*t]}
>
> beta1[t_]:=beta2[t+4.8*t^2*(t-1)^2]
>
> q2[t_]:=
> =
FunctionExpand[beta2'[t]/Sqrt[Norm[beta2'[t]]],Assumptions->t\[Element] Reals && beta2'\[Element]Vectors[2,Reals]]
>
> q1[s_]:=FunctionExpand[
> beta1'[s]/Sqrt[Norm[beta1'[s]]],Assumptions->s\[Element] Reals&& beta2'\[Element]Vectors[2,Reals]]
>
>
> a[t_, z_] := 2*q1[t].q2'[z] // FunctionExpand
> b[t_, z_] := q1[t].q2[z] // FunctionExpand
> c[t_, z_] := 2*q1'[t].q2[z] // FunctionExpand
>
>
> F1[t_, z_] := c[t, z]/b[t, z]
> F2[t_, z_] := a[t, z]/b[t, z]
>
>
>
> factor1[s_, z_] := Exp[-NIntegrate[F2[s, u], {u, 0, z}]]
>
> factor2[s_, z_] := Exp[NIntegrate[F2[s, u], {u, 0, z}]]
>
> g[s_, z_?NumberQ] :=  NIntegrate[factor2[s, tau]*F1[s, tau], {tau, 0, z}]
>
> y[s_, z_] := factor1[s, z]*g[s, z]
>
> y[.2, .3]
>
>
> I get the error
>
> NIntegrate::nlim: _u_ = _tau_ is not a valid limit of integration
>
>

```

• References:
• question
• From: "Hagwood, Charles R" <charles.hagwood@nist.gov>
• Prev by Date: Re: Copying Text From CDFs
• Next by Date: Re: question