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

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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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.

more

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 .....

( 2013-07-08 11:33:34 +0200 )edit

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

( 2013-07-08 11:55:18 +0200 )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?

( 2013-07-08 12:09:49 +0200 )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.

( 2013-07-08 12:14:14 +0200 )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)

( 2013-07-08 12:17:33 +0200 )edit

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.

more

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.

( 2013-07-08 13:07:45 +0200 )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.

( 2013-07-09 06:48:28 +0200 )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.

( 2013-07-09 07:31:48 +0200 )edit

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

( 2013-07-09 10:10:12 +0200 )edit