method to get the left-lower and right-upper triangular parts of a matrix

[Huayi Wei]

Hi, everyone,

I have a sage matrix, and I want to get its left-lower and right-upper
triangular parts. Does there exist any method to get them directly?

In matlab, there are two functions `triu` and `tril` to do such things.
Does sage have the similar functions?

Best

Huayi

[Vincent Delecroix]

Hi Huayi,

It does not seem to exists. Sage only has a `diagonal` method to return
the list of entries on the diagonal.

Do you know how to implement it in Sage? Otherwise the small function
below does the job

def triu(m):
t = matrix(m.base_ring(), m.nrows())
for i in range(m.nrows()):
t[i,i:] = m[i,i:]
return t

Though, if your matrices are sparse, there are more efficient ways for sure.

Best,
Vincent

[Huayi Wei]

Hi, Vincent,

Yes, my matrix is sparse. I just move here from matlab, so I am a
newbie for sage and python.

The function you have offered can do the job. But I am worried about its
efficiency, because my sparse matrix
maybe very large which comes from Finite Element method.

So about the efficient ways for sparse matrix, can you give me some
suggestion? Thanks very much.

Best

Huayi

[Vincent Delecroix]

Hi,

On 20/05/15 08:54, Huayi Wei wrote:
> Hi, Vincent,
>
> Yes, my matrix is sparse. I just move here from matlab, so I am a
> newbie for sage and python.
>
> The function you have offered can do the job. But I am worried about its
> efficiency, because my sparse matrix
> maybe very large which comes from Finite Element method.

The function I gave is not so bad, because if you have a sparse matrix
accessing to a row (or even a slice of a row) gives you a sparse vector:

sage: m = matrix(100, sparse=True)
sage: v = m[5,5:]
sage: v.is_sparse()
True

Thouh I am not sure about the efficiency of

sage: m[5,5:] = v

when m is a sparse matrix and v a sparse vector. I quickly look at the
code and it seems to run through all entries of v which is very stupid.

> So about the efficient ways for sparse matrix, can you give me some
> suggestion? Thanks very much.

If your matrix is sparse I would do

def triu(m):
t = matrix(m.base_ring(), m.nrows(), sparse=True)
for (i,j) in m.nonzero_positions():
if i <= j:
t[i,j] = m[i,j]
return t

Depending whether you want the diagonal or not you have to adjust the
inequality for being strict or not.

Best,
Vincent

[魏华祎]

Hi, Vincent,

Thanks for your reply. I will try it following your suggestion.

Best

Huayi

 

 

------------------ Original ------------------

From:  "Vincent Delecroix"<20100.d...@gmail.com>;

Date:  Wed, May 20, 2015 03:55 PM

To:  "sage-support"<sage-s...@googlegroups.com>;

Subject:  Re: [sage-support] method to get the left-lower and right-uppertriangular parts of a matrix

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