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MathGroup Archive 2001

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"No more memory "

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30165] "No more memory "
  • From: zosi <zosi at to.infn.it>
  • Date: Wed, 1 Aug 2001 02:19:20 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

We are working with the Takagi equations
(see attached simplified notebook).
To avoid the following Mathematica message

"No more memory available
 Mathematica kernel has shut down
 Try quitting other applications and try again"

 we have updated our platform which now is

   1 GB RAM, 2 GB swap, 23 GB free HD
   Version 4.1
   Linux RedHat 7.1, Kernel 2.4.2-2

Unfortunately, we meet the same message when we set
         (in NDSolve in our nb)

      AccuracyGoal -> 25
      PrecisionGoal -> 25
      WorkingPrecision -> 30
      MaxSteps -> 500000      and

      Zmax = 0.000800  ( 800 micrometers)

If we reduce Zmax (e.g. Zmax = 0.000400) it works.

Our question is: How can we avoid the message
                   "No more memory available" ?

For patient and kind people we annexe the summary
of the results shown by the "top" Linux command.

Any interested people can contact us directly.
Many thanks for any suggestion.

Gianfranco ZOSI
Dip Fisica Generale "A. Avogadro"
Universita di Torino
v. P. Giuria 1 - 10125 - Italy
ph + 39 011 670 7426


              **** ANNEXE *****

At the beginning we have

           Start   Phase 1
  3:48pm  up  3:36,  4 users,  load average: 2.19, 1.94, 2.24
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 37.5% user, 32.1% system,  0.0% nice, 30.3% idle
Mem:  1028792K av,  174788K used,  854004K free,                        <-------
Swap: 2096440K av,       4K used, 2096436K free, 73712K cached          <-------
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  5304 5304  2900 S     0.0  0.5   0:01 Mathematica
 2158 zosi   19   0 22124  21M  2572 R    53.3  2.1   0:19 MathKernel
---
  3:49pm  up  3:37,  4 users,  load average: 2.54, 2.07, 2.27
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 73.4% user, 26.5% system,  0.0% nice,  0.0% idle
Mem:  1028792K av,  203496K used,  825296K free,                        <-------
Swap: 2096440K av,       4K used, 2096436K free, 73716K cached          <-------
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  5332 5332  2928 S     0.0  0.5   0:01 Mathematica
 2158 zosi   20   0  790M 790M  2572 R    53.9 78.6  14:47 MathKernel

In Phase 1 the used Mem raises regularly until the Mem is saturated
as apperas in the following Phase 2

*********************  Phase 2

  4:16pm  up  4:04,  4 users,  load average: 2.88, 2.89, 2.72
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 74.3% user, 25.6% system,  0.0% nice,  0.0% idle
Mem:  1028792K av,  991644K used,   37148K free,
Swap: 2096440K av,       4K used, 2096436K free, 73736K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  5332 5332  2928 S     0.0  0.5   0:01 Mathematica
 2158 zosi   15   0  818M 818M  2572 R    53.9 81.5  15:20 MathKernel
---
  4:17pm  up  4:05,  4 users,  load average: 2.99, 2.92, 2.74
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 76.4% user, 23.5% system,  0.0% nice,  0.0% idle
Mem:  1028792K av, 1020736K used,    8056K free,
Swap: 2096440K av,       4K used, 2096436K free, 73736K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  5332 5332  2928 S     0.0  0.5   0:01 Mathematica
 2158 zosi   20   0  847M 847M  2572 R    54.0 84.3  15:52 MathKernel

We remark here, from 4:17 to 4:18pm, a jump of the swap area;
the used swap area raises mildly and does not saturate
the total 2 GB swap area

  4:18pm  up  4:06,  4 users,  load average: 2.79, 2.87, 2.73
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 70.2% user, 29.7% system,  0.0% nice,  0.0% idle
Mem:  1028792K av, 1024308K used,    4484K free,                       <--------
Swap: 2096440K av,  890816K used, 1205624K free, 941940K cached        <-------- jump
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  2404    4     4 S     0.0  0.0   0:01 Mathematica
 2158 zosi   19   0  874M  34M   436 R    50.0  3.4  16:22 MathKernel

  4:19pm  up  4:07,  4 users,  load average: 2.78, 2.85, 2.73
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 73.0% user, 26.9% system,  0.0% nice,  0.0% idle
Mem:  1028792K av, 1024104K used,    4688K free,
Swap: 2096440K av,  890816K used, 1205624K free, 928764K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  2552  328   284 S     0.0  0.0   0:02 Mathematica
 2158 zosi   20   0 1243M 241M   436 R    39.2 24.0  22:47 MathKernel
---
  4:34pm  up  4:22,  4 users,  load average: 4.26, 3.86, 3.27
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 50.6% user, 49.3% system,  0.0% nice,  0.0% idle
Mem:  1028792K av, 1025136K used,    3656K free,
Swap: 2096440K av, 1102668K used,  993772K free, 784808K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  2456  232   188 S     0.0  0.0   0:02 Mathematica
 2158 zosi   20   0 1263M 216M   436 R    35.0 21.5  23:08 MathKernel
---
  4:35pm  up  4:23,  4 users,  load average: 4.39, 3.96, 3.34
2 processes: 1 sleeping, 1 running, 0 zombie, 0 stopped
CPU states: 57.7% user, 42.2% system,  0.0% nice,  0.0% idle
Mem:  1028792K av, 1024916K used,    3876K free,
Swap: 2096440K av, 1103460K used,  992980K free, 762540K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    9   0  2404    4     4 S     0.0  0.0   0:02 Mathematica
 2158 zosi   14   0 1394M 246M   436 R    37.0 24.5  25:27 MathKernel

************       (MathKernel lost)   Phase 3                           <-------

In the following phase the MathKernel disappears

  4:41pm  up  4:29,  4 users,  load average: 4.04, 4.13, 3.61
1 processes: 1 sleeping, 0 running, 0 zombie, 0 stopped
CPU states: 37.8% user, 62.1% system,  0.0% nice,  0.0% idle
Mem:  1028792K av,  803984K used,  224808K free,
Swap: 2096440K av,  798372K used, 1298068K free, 785628K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    8   0  4036 2928  2276 S     0.5  0.2   0:02 Mathematica
---
  4:42pm  up  4:30,  4 users,  load average: 3.18, 3.86, 3.55
1 processes: 1 sleeping, 0 running, 0 zombie, 0 stopped
CPU states: 37.9% user, 62.0% system,  0.0% nice,  0.0% idle
Mem:  1028792K av,  804364K used,  224428K free,
Swap: 2096440K av,  798372K used, 1298068K free, 786172K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    8   0  4036 2928  2276 S     0.0  0.2   0:02 Mathematica
---
  4:55pm  up  4:43,  4 users,  load average: 2.42, 2.64, 2.96
1 processes: 1 sleeping, 0 running, 0 zombie, 0 stopped
CPU states: 38.1% user, 61.8% system,  0.0% nice,  0.0% idle
Mem:  1028792K av,  806696K used,  222096K free,
Swap: 2096440K av,  798312K used, 1298128K free, 788484K cached
  PID USER  PRI  NI  SIZE  RSS SHARE STAT %CPU %MEM   TIME COMMAND
32614 zosi    8   0  4036 2928  2276 S     0.0  0.2   0:02 Mathematica

and after nearly one hour (from 3:48 to 4:55pm)
the message "No more memory" appears, even though the swap area is NOT saturated                                        <-------

Final comment. We have also remarked that SOMETIMES quitting Mathematica
               does not clear the used Mem area; in these cases
               the message "No more memory" appears quite soon



Here is the notebook containing the NDSolve command.
In this case we know the analytical solution.

(************** Content-type: application/mathematica **************

                    Mathematica-Compatible Notebook

This notebook can be used with any Mathematica-compatible
application, such as Mathematica, MathReader or Publicon. The data
for the notebook starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do
one of the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the
  application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing
the word CacheID, otherwise Mathematica-compatible applications may
try to use invalid cache data.

For more information on notebooks and Mathematica-compatible
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info at wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from
Wolfram Research.
*******************************************************************)

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(*WindowFrame->Normal*)

Notebook[{

Cell[CellGroupData[{
Cell["Takagi1.nb ", "Section"],

Cell[BoxData[
    \(\(\(Clear["\<Global`*\>"]\)\(\ \ \)\( (*\ \(.\)\(nb\)\ *) \)\)\)], \
"Input"],

Cell[BoxData[
    \(Needs["\<Algebra`ReIm`\>"]\)], "Input"],

Cell[BoxData[
    \(Off[General::spell1]\)], "Input"],

Cell[BoxData[
    \(\(\[Theta]b = 185456\/10\^6;\)\)], "Input"],

Cell[BoxData[
    \(\(\[Lambda]mo = 708\/10\^13;\)\)], "Input"],

Cell[BoxData[
    \(\(re\[Chi]conh = \(-\(1901\/10\^9\)\);\)\)], "Input"],

Cell[BoxData[
    \(\(im\[Chi]conh = 1589\/10\^11;\)\)], "Input"],

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
    \(\(c = \((\(2*\[Pi]\)\/\[Lambda]mo*2*
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Cell[BoxData[{
    \(\(\(\[Xi] = 1/1000000;\)\(\[IndentingNewLine]\)
    \)\), "\[IndentingNewLine]",
    \(\(Zmax\  = \ 800\/10\^6;\)\)}], "Input"],

Cell[BoxData[
    \(eq5 =
      Timing[NDSolve[{\(d05'\)[z] \[Equal] \((a + \[ImaginaryI]*b)\)*
                dh5[z], \ \ \ \ \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(dh5'\)[
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              0}, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
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            dh5[z]}, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
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            Zmax}, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ AccuracyGoal \
\[Rule] 16, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ PrecisionGoal \[Rule]
            16, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ WorkingPrecision \
\[Rule] 30, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ MaxSteps \[Rule]
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Cell[BoxData[
    \(\(d005[z_] = d05[z] /. First[Rest[eq5]];\)\)], "Input"],

Cell[BoxData[
    \(\(dhh5[z_] = dh5[z] /. First[Rest[eq5]];\)\)], "Input"],

Cell[BoxData[
    \( (*stacchetto*******) \)], "Input"],

Cell[BoxData[
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          PlotPoints \[Rule] 200, PlotRange \[Rule] All, Frame \[Rule] True,
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Cell[BoxData[
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          PlotPoints \[Rule] 200, PlotRange \[Rule] All, Frame \[Rule] True,
          GridLines \[Rule] Automatic];\)\)], "Input"]
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FrontEndVersion->"4.1 for X",
ScreenRectangle->{{0, 1024}, {0, 768}},
WindowSize->{601, 678},
WindowMargins->{{Automatic, 28}, {Automatic, 1}},
ShowCellLabel->False
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(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
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(*******************************************************************
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