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How to prevent memory leak when solving a linear system of equations using left_kernel ?

asked 2013-07-08 02:00:19 -0600

M. H. M. gravatar image

updated 2013-07-09 03:08:44 -0600

I am having a problem when running the left_kernel function multiple times. Every time I call the function It takes a new part of the memory although I do not create new variables. I tried finding out where does the memory disappear, but without any luck. here is an example code:

    sage: mat
    69 x 70 dense matrix over Symbolic Ring (type 'print mat.str()' to see all of the entries)
    sage: get_memory_usage() #memory check before call
    1170.34765625
    sage: Inter_mat=mat.transpose() 
    sage: Solution=Inter_mat.left_kernel()
    sage: get_memory_usage() #memory check after 1st call
    1190.5390625
    sage: Inter_mat=mat.transpose()
    sage: Solution=Inter_mat.left_kernel()
    sage: get_memory_usage()  #memory check after 2nd call
    1194.73828125
    sage: Inter_mat=mat.transpose()
    sage: Solution=Inter_mat.left_kernel()
    sage: get_memory_usage()  #memory check after 3rd call
    1217.76953125

As you can see every time I call the function, the memory usage increases. Is there a way to release the memory that was used in a previous call ? My program stops after a few iterations because of lack of memory.

Update: (Creating the matrix "mat")

mat=[]
for Coord in range(len(M_col)):
  if(M[M_row[Coord],M_col[Coord]]!=0):
    s=M[M_row[Coord],M_col[Coord]]
    if(s==1):
      temp_v=vector(Poly)(x=a^M_col[Coord],y=FIELDinfoBook[M_row[Coord]])
      mat.append(vector(W,temp_v))
    else:
      up=[i for i in range(s)]
      down=list(up)
      down.reverse()
      for Cup in range(s):
        for Cdown in range(s):
          if(up[Cup]+down[Cdown]<s):
            temp_v=list(zero_vector(sum(Len_Poly)))
            for j in range(down[Cdown],l+1):
              for i in range(up[Cup],Len_Poly[j]):
            comb1=len(Combinations(j,down[Cdown]).list())
            comb2=len(Combinations(i,up[Cup]).list())
            temp=comb1*comb2*x^(i-up[Cup])*y^(j-down[Cdown])
            temp=temp(x=a^M_col[Coord],y=FIELDinfoBook[M_row[Coord]])
            temp_v[Len_Poly_inc[j]+i]=(temp)
              mat.append(vector(temp_v))

The matrix M is a sparse matrix with integers (mostly ones) at certain positions. M_col and M_row are lists with the locations of nonzero elements.

sage: M
64 x 63 dense matrix over Integer Ring (type 'print M.str()' to see all of the entries)

Poly is a list of bivariate polynomials created like this:

Poly=[]
    for j in range(l+1):
      for i in range(Len_Poly[j]):
        Poly.append(x^i*y^j)

And l=1 , Len_poly=[63, 7] and Len_poly_inc=[0, 63, 70]

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answered 2013-07-08 03:05:31 -0600

tmonteil gravatar image

updated 2013-07-08 03:13:35 -0600

You can force the garbage collection as follows:

import gc
gc.enable()
mat = random_matrix(SR,69,70)
for i in range(100):
    Inter_mat=mat.transpose()
    Solution=Inter_mat.left_kernel()
    print get_memory_usage()
    gc.collect()

1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
1109.7109375
....

You can also collect less often, set a frequency, and so on. See this page.

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Comments

I tried it before but it didnt help. This is the result I get when I use your code: (using my mat of course) 1133.46875 1153.5234375 1174.0078125 1178.21875 1198.9296875 .....

M. H. M. gravatar imageM. H. M. ( 2013-07-08 04:33:34 -0600 )edit

Could you provide your matrix so that i can test further ?

tmonteil gravatar imagetmonteil ( 2013-07-08 04:55:18 -0600 )edit

I changed the type of the elements inside the matrix from Symbolic ring to Univariate Polynomial Ring in x over Finite Field in a of size 2^6. Now it works fine without a leak. I do not know why. Thanks for the help. You gave me the idea to change it. What should I do now that I have my problem solved. Also I would like to point out the problem when it was Symbolic?

M. H. M. gravatar imageM. H. M. ( 2013-07-08 05:09:49 -0600 )edit

If there is still a problem with symbolic entries, you should give us details on how to reproduce it, so that we can have a look and eventually report it as a bug.

tmonteil gravatar imagetmonteil ( 2013-07-08 05:14:14 -0600 )edit

I start with a list of vectors and then transform it to a matrix. So I write mat=matrix(W,mat) instead of mat=matrix(mat). where: m=6 q=2^m P=GF(q,'a') W.<x> = PolynomialRing(P)

M. H. M. gravatar imageM. H. M. ( 2013-07-08 05:17:33 -0600 )edit
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answered 2013-07-08 05:16:19 -0600

M. H. M. gravatar image

I solved my problem by changing the type of the elements from Symbolic ring to Univariate Polynomial Ring in x over Finite Field in a of size 2^6.

However, if it remained as a matrix with elements from the Symbolic ring. The leak would still exist.

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Comments

1

Since it seems i cannot reproduce your problem with mat = random_matrix(SR,69,70) I need a precise procedure to construct a bad matrix over the symbolic ring.

tmonteil gravatar imagetmonteil ( 2013-07-08 06:07:45 -0600 )edit

I am new to this system. How can I paste a code in the comment part. In the answer part I can just click on "Insert code" icon.

M. H. M. gravatar imageM. H. M. ( 2013-07-08 23:48:28 -0600 )edit

You can just paste it as you did for your first question. The comments field is not very convenient since you can not hit <enter>. Another possibility is to edit this question and add your code there. To have a nicely printed code, it suffice to add four spaces before each line of code.

tmonteil gravatar imagetmonteil ( 2013-07-09 00:31:48 -0600 )edit

I added my code in the question. I tried to upload the matrix for you but I do not have enough karma

M. H. M. gravatar imageM. H. M. ( 2013-07-09 03:10:12 -0600 )edit

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Asked: 2013-07-08 02:00:19 -0600

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Last updated: Jul 09 '13