       Re: MathKernel crashes

• To: mathgroup at smc.vnet.net
• Subject: [mg72860] Re: MathKernel crashes
• From: "nandan" <joshi.nandan at gmail.com>
• Date: Tue, 23 Jan 2007 04:31:06 -0500 (EST)
• References: <eosgop\$9ai\$1@smc.vnet.net><eovesf\$rlp\$1@smc.vnet.net>

```Hi:

On Jan 21, 11:22 am, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com>
wrote:
> nandan wrote:
> > Hallo:
>
> > MathKernel crashes, since I use recursive function for calculation. I
> > have 2 of the important functions for my calculation as given below:
> > \$RecursionLimit=Infinity;
>
> > pi[0, \[Theta]_] := 0;
> > pi[1, \[Theta]_] := 1;
> > pi[i_, \[Theta]_]\  := pi[i, \[Theta]]  = ((2  i - 1)/(i - 1))-------------------^
> Extra backslash must be removed
>
> > Cos[\[Theta]] pi[i - 1, \[Theta]] - (i/(i - 1)) pi[i - 2,\[Theta]]);--------------------------------------------------------------------^
> Extra parentheses must be removed
>
> > \[Tau][i_, \[Theta]_] := \[Tau][i, \[Theta]] = i Cos[\[Theta]] pi[i,
> > \[Theta]] - (i + 1)pi[i - 1, \[Theta]];

The syntax problem was due to wrong copying of the Mathematica code in
StandardForm. Is there any better way of copying it in InputForm?

> Here is a corrected version of the code:
>
> In:=
> pi[0, Î¸_] = 0;
> pi[1, Î¸_] = 1;
> pi[i_, Î¸_] := pi[i, Î¸] =
>      ((2*i - 1)/(i - 1))*Cos[Î¸]*pi[i - 1, Î¸] -
>       (i/(i - 1))*pi[i - 2, Î¸];
> Ï?[i_, Î¸_] := Ï?[i, Î¸] = i*Cos[Î¸]*pi[i, Î¸] -
>       (i + 1)*pi[i - 1, Î¸];
>
> In:=
> pi[14, Pi/3]
>
> Out=
> 30439185
> --------
> 8388608
>
> > In this case, I can get solution to any numerical value like pi[14,
> > \[Pi]/3]. But quite a few times, it happened that MathKernel quitted,IIt would have been nice that you provided an example of such a call.
>
> > started again, but it started another processor parallel to that. LaterNot sure to understand what you mean: if the kernel really quits, you
> have no more kernel process loaded into memory.

The kernel simply quits, if the depth of recursion is big. The same
problem has be observed by Johan and reported here:

>
> > I wanted to calculate another function as follows:
> > S1Temp[i_, \[Theta]_] := ((2 l + 1)/(l (l + 1))) (an[l] pi[l, \[Theta]]---------^
> Inconsistent syntax: i is never used in the code: do you mean l? At any
> rate, this definition will cause an infinite recursion whenever it is
> called. Increasing \$RecursionLimit will do nothing.

I'm sorry, 'i' was meant for 'l'. Too many equations with different
sums, makes it difficult to report.

>
> >  + bn[l]  \[Tau][l, \[Theta]]);
>
> > But in this case, whenever I try to calculate S1Temp[14, \[Pi]/3], it
> > simply quits and, sometimes crashes. I have to always restart
> > Mathematica to start over again.Here is a corrected version of the code:
>
> In:=
> S1Temp[l_, Î¸_] := ((2*l + 1)/(l*(l + 1)))*
>      (an[l]*pi[l, Î¸] + bn[l]*Ï?[l, Î¸]);
>
> In:=
> S1Temp[14, Pi/3]
>
> Out=
> 29   30439185 an   115937115 bn
> --- (--------------- - ----------------)
> 210      8388608           8388608
>
> Now, the above result might or might not be what you expected since you
> did not provide any definition for an[i] and bn[i]. (Are they functions
> or arrays of values?)

The Solution for Pi/3 is faster, but in case of 'Pi/4' and higher 'l'
it simply quits. I provide u the correct version of the code and also
for a[i] and b[i], well, probably copying it as InputForm in
Mathematica can give better understanding...:

\[Psi][l_, \[Rho]_] := \[Rho]*Sqrt[Pi/(2*\[Rho])]*BesselJ[l + 1/2,
\[Rho]]
\[Psi]Prime[l_, \[Rho]_] := Evaluate[D[\[Psi][l, \[Rho]], \[Rho]]];
\[Zeta][l_, \[Rho]_] := \[Psi][l, \[Rho]] +
I*\[Rho]*Sqrt[Pi/(2*\[Rho])]*BesselY[l + 1/2, \[Rho]];
\[Zeta]Prime[l_, \[Rho]_] := Evaluate[D[\[Zeta][l, \[Rho]], \[Rho]]];

In:=
an[l_] := Evaluate[(Subscript[m, 2]*\[Psi]Prime[l, Subscript[s,
1][r]]*\[Psi][l, Subscript[s, 2][r]] -
Subscript[m, 1]*\[Psi][l, Subscript[s, 1][r]]*\[Psi]Prime[l,
Subscript[s, 2][r]])/
(Subscript[m, 2]*\[Zeta]Prime[l, Subscript[s, 1][r]]*\[Psi][l,
Subscript[s, 2][r]] - Subscript[m, 1]*\[Zeta][l, Subscript[s, 1][r]]*
\[Psi]Prime[l, Subscript[s, 2][r]])]
bn[l_] := Evaluate[(Subscript[m, 2]*\[Psi][l, Subscript[s,
1][r]]*\[Psi]Prime[l, Subscript[s, 2][r]] -
Subscript[m, 1]*\[Psi]Prime[l, Subscript[s, 1][r]]*\[Psi][l,
Subscript[s, 2][r]])/
(Subscript[m, 2]*\[Zeta][l, Subscript[s, 1][r]]*\[Psi]Prime[l,
Subscript[s, 2][r]] - Subscript[m, 1]*\[Zeta]Prime[l, Subscript[s,
1][r]]*
\[Psi][l, Subscript[s, 2][r]])]
cn[l_] := Evaluate[(Subscript[m, 2]*\[Zeta][l, Subscript[s,
1][r]]*\[Psi]Prime[l, Subscript[s, 1][r]] -
Subscript[m, 2]*\[Zeta]Prime[l, Subscript[s, 1][r]]*\[Psi][l,
Subscript[s, 1][r]])/
(Subscript[m, 2]*\[Zeta][l, Subscript[s, 1][r]]*\[Psi]Prime[l,
Subscript[s, 2][r]] - Subscript[m, 1]*\[Zeta]Prime[l, Subscript[s,
1][r]]*
\[Psi][l, Subscript[s, 2][r]])]
dn[l_] := Evaluate[(Subscript[m, 2]*\[Zeta]Prime[l, Subscript[s,
1][r]]*\[Psi][l, Subscript[s, 1][r]] -
Subscript[m, 2]*\[Zeta][l, Subscript[s, 1][r]]*\[Psi]Prime[l,
Subscript[s, 1][r]])/
(Subscript[m, 2]*\[Zeta]Prime[l, Subscript[s, 1][r]]*\[Psi][l,
Subscript[s, 2][r]] - Subscript[m, 1]*\[Zeta][l, Subscript[s, 1][r]]*
\[Psi]Prime[l, Subscript[s, 2][r]])]

pi[0, \[Theta]_] := 0;
pi[1, \[Theta]_] := 1;
pi[i_, \[Theta]_] := pi[i, \[Theta]] = ((2*i - 1)/(i -
1))*Cos[\[Theta]]*pi[i - 1, \[Theta]] - (i/(i - 1))*pi[i - 2,
\[Theta]];
\[Tau][i_, \[Theta]_] := \[Tau][i, \[Theta]] = i*Cos[\[Theta]]*pi[i,
\[Theta]] - (i + 1)*pi[i - 1, \[Theta]];

S1[\[Theta]_] := Sum[((2*l + 1)/(l*(l + 1)))*(an[l]*pi[l, \[Theta]] +
bn[l]*\[Tau][l, \[Theta]]), {l, 1, LastTerm[r]}];
S2[\[Theta]_] := Sum[((2*l + 1)/(l*(l + 1)))*(an[l]*\[Tau][l, \[Theta]]
+ bn[l]*pi[l, \[Theta]]), {l, 1, LastTerm[r]}];

>
> Regards,
> Jean-Marc

Thanx again!

nandan

```

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