Re: How to free memory?
- To: mathgroup at smc.vnet.net
- Subject: [mg59786] Re: How to free memory?
- From: "Carl K. Woll" <carlw at u.washington.edu>
- Date: Sun, 21 Aug 2005 03:51:34 -0400 (EDT)
- Organization: University of Washington
- References: <de46jr$r62$1@smc.vnet.net> <de6lru$cg5$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Wonseok Shin" <wssaca at gmail.com> wrote in message news:de6lru$cg5$1 at smc.vnet.net... > Now I want to be more specific. > > I've read the "Garbage Collection" thread that has been going on for > the past few days, and tried all solutions in there. But those > couldn't resolve my problem. > > Here goes my code: > -------------------------------------------------------------------------- > In[1]:= > $HistoryLength = 0; > > In[1]:= > n1=3.5; n2=1.5; d1=0.5; d2=1.0; a = d1 + d2; > > In[2]:= > eig[x_]:= > Module[{eigVal, eigVec, T1, T2, T, k1=2Pi n1/x, k2 = 2Pi n2/x, A1, > B1, A2, > B2, e1, e2, h1, h2,coeff, e, de1, de2, de}, > > (* Calculates the matrix. *) > T1={{Cos[2Pi n1 d1/x], -I Sin[2Pi n1 d1/x] /n1}, {-I Sin[2Pi n1 > d1/x] n1, Cos[2Pi n1 d1/x]}}; > T2={{Cos[2Pi n2 d2/x], -I Sin[2Pi n2 d2/x] /n2}, {-I Sin[2Pi n2 > d2/x] n2, Cos[2Pi n2 d2/x]}}; > T=T2.T1; > > (* Calculates the eigenvalue and eigenvector of T. *) > eigVal = Eigenvalues[T][[1]]; > eigVec = Eigenvectors[T][[1]]; > > (* Defines the equations for the eigenmodes in 0 = z = a. *) > e1[z_]:= A1 Exp[I k1 z] + B1 Exp[-I k1 z]; > e2[z_]:= A2 Exp[I k2 z] + B2 Exp[-I k2 z]; > h1[z_]:=-n1 (A1 Exp[I k1 z] - B1 Exp[-I k1 z]); > h2[z_]:=-n2 (A2 Exp[I k2 z] - B2 Exp[-I k2 z]); > > (* Determines the coefficients using the boundary conditions *) > coeff=Solve[{{e1[0], h1[0]} == eigVec, e1[d1]==e2[0], > h1[d1]==h2[0]}, {A1, B1, A2, B2 }]; > > (* Redefines the functions. *) > DownValues[e1] = DownValues[e1] /. coeff; > DownValues[e2] = DownValues[e2] /. coeff; > > (* Gets the eigenmode. *) > e[z_ /; 0 = Mod[z, a] < d1] := eigVal^Quotient[z,a] * e1[z - a ^ | should be <= as well as a few more times below > Quotient[z, a]]; > e[z_ /; d1 = Mod[z, a] < a] := eigVal^Quotient[z,a] * e2[z - (a > Quotient[z, a] + d1)]; > > (* Takes the derivatives of the eigenmode. *) > de1[z_] = D[e1[z], z]; > de2[z_] = D[e2[z], z]; > > de[z_ /; 0 = Mod[z, a] < d1] := eigVal^Quotient[z, a] * de1[z - a > Quotient[z, a]]; > de[z_ /; d1 = Mod[z, a] < a] := eigVal^Quotient[z, a] * de2[z - > (a Quotient[z, a] + d1)]; > > (* Returns the eigenmode and its derivative functions. *) > {e, de} > ] > Your function eig returns two new functions e and de (actually e$nnn and de$nnn). These functions in turn depend on e1,e2,de1,de2,k1,k2 and eigVal. > In[3]:= > eig[0.1][[2]][30] (* Checks if the function eig[x] works well. *) > > Out[3]= > -2.3088026412307006`*^-11 - 56.97491898475945 I > > In[4]:= > MemoryInUse[] > > Out[4]= > 3033832 > > In[5]:= > data = Table[eig[x], {x, 5, 10, 0.001}]; (* Generate a huge list of > eigenmodes and its derivative pairs *) > You've created ~5000 definitions of e and de, and set data equal to a list of these functions. > In[6]:= > MemoryInUse[] > > Out[6]= > 52423632 > > In[7]:= > data=.; Clear[data]; Remove[data]; > > In[8]:= > MemoryInUse[] > > Out[8]= > 52425096 > (* data was not released. *) > -------------------------------------------------------------------------- > > So, why isn't data released here? > Clearing data doesn't clear the function definitions. For example: f[x_]:=1 data=f; Clear[data] In[63]:= f[x] Out[63]= 1 and we see that f is still defined. If you want to clear all of the new functions you've created, you need to use Clear on those functions. In your case we need to do the following: Clear["e$*", "de$*", "e1$*", "e2$*", "de1$*", "de2$*", "k1$*", "k2$*", \ "eigVal$*"] Let's see how memory usage works in your case. We start out with a memory in use of ~7MB: In[21]:= MemoryInUse[] Out[21]= 6723448 Creating data increases memory used ~55MB: In[22]:= data = Table[eig[x], {x, 5, 10, 0.001}]; //Timing MemoryInUse[] Out[22]= {16.297 Second,Null} Out[23]= 55634032 Clearing data doesn't do much since function definitions remain: In[24]:= Clear[data] MemoryInUse[] Out[25]= 55453680 Clearing function definitions and internal variables helps: In[26]:= Clear["e$*","de$*","e1$*","e2$*","de1$*","de2$*","k1$*","k2$*","eigVal$*"] MemoryInUse[] Out[27]= 18776968 The final bit of memory usage is tied up with the cache: In[28]:= Developer`ClearCache[] MemoryInUse[] Out[29]= 6724176 And we are almost back to where we started. Carl Woll Wolfram Research