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[1]:= > pi[0, θ_] = 0; > pi[1, θ_] = 1; > pi[i_, θ_] := pi[i, θ] = > ((2*i - 1)/(i - 1))*Cos[θ]*pi[i - 1, θ] - > (i/(i - 1))*pi[i - 2, θ]; > Ï?[i_, θ_] := Ï?[i, θ] = i*Cos[θ]*pi[i, θ] - > (i + 1)*pi[i - 1, θ]; > > In[5]:= > pi[14, Pi/3] > > Out[5]= > 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: http://groups-beta.google.com/group/comp.soft-sys.math.mathematica/browse_frm/thread/922e6b5d1a472346 > > > 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[6]:= > S1Temp[l_, θ_] := ((2*l + 1)/(l*(l + 1)))* > (an[l]*pi[l, θ] + bn[l]*Ï?[l, θ]); > > In[7]:= > S1Temp[14, Pi/3] > > Out[7]= > 29 30439185 an[14] 115937115 bn[14] > --- (--------------- - ----------------) > 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[81]:= 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