I went through the link.
It also returns perm_c and perm_r and the solution is represented as
Pr * (R^-1) * A * Pc = L * U
It is similar to one returned by scipy
>>> lu.perm_r
array([0, 2, 1, 3], dtype=int32)
>>> lu.perm_c
array([2, 0, 1, 3], dtype=int32)
I think it doesn't support square matrix too. Link
<https://github.com/scikit-umfpack/scikit-umfpack/blob/ce77944bce003a29771ae07be182af348c3eadce/scikits/umfpack/interface.py#L199C1-L200C81>
On Wednesday, February 28, 2024 at 6:17:26 PM UTC+5:30 Max Alekseyev wrote:
> One more option would be umfack via scikits.umfpack:
>
> https://scikit-umfpack.github.io/scikit-umfpack/reference/scikits.umfpack.UmfpackLU.html
>
> Regards,
> Max
> On Wednesday, February 28, 2024 at 7:07:53 AM UTC-5 Animesh Shree wrote:
>
>> One thing I would like to suggest.
>>
>> We can provide multiple ways to compute the sparse LU
>> 1. scipy
>> 2. sage original implementation in src.sage.matrix.matrix2.LU
>> <https://github.com/sagemath/sage/blob/acbe15dcd87085d4fa177705ec01107b53a026ef/src/sage/matrix/matrix2.pyx#L13160>
>> (Note
>> - link
>> <https://github.com/sagemath/sage/blob/acbe15dcd87085d4fa177705ec01107b53a026ef/src/sage/matrix/matrix2.pyx#L13249C1-L13254C51>
>> )
>> 3. convert to dense then factor
>>
>> It will be up to user to choose based on the complexity.
>> Is it fine?
>>
>> On Wednesday, February 28, 2024 at 4:30:51 PM UTC+5:30 Animesh Shree
>> wrote:
>>
>>> Thank you for reminding
>>> I went through.
>>> We need to Decompose A11 only and rest can be calculated via taking
>>> inverse of L11 or U11.
>>> Here A11 is square matrix and we can use scipy to decompose square
>>> matrices.
>>> Am I correct?
>>>
>>> New and only problem that I see is the returned LU decomposition of
>>> scipy's splu is calculated by full permutation of row and column as pointed
>>> out by *Nils Bruin*. We will be returning row and col permutation
>>> array/matrix separately instead of single row permutation which sage
>>> usage generally for plu decomposition.
>>> User will have to manage row and col permutations.
>>> or else
>>> We can return handler function for reconstruction of matrix from L, U
>>> & p={perm_r, perm_c}
>>> or
>>> We can leave that to user
>>> User will have to permute its input data according to perm_c (like :
>>> perm_c * input) before using the perm_r^(-1) * L * U
>>> as perm_r^(-1) * L * U is PLU decomposition of Original_matrix*perm_c
>>>
>>> https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.SuperLU.html
>>> >>> A = Pr^(-1) *L*U * Pc^(-1) # as told by *Nils Bruin*
>>> or
>>> scipy's splu will not do.
>>>
>>> On Tuesday, February 27, 2024 at 11:57:02 PM UTC+5:30 Dima Pasechnik
>>> wrote:
>>>
>>>>
>>>>
>>>> On 27 February 2024 17:25:51 GMT, 'Animesh Shree' via sage-devel <
>>>> sage-...@googlegroups.com> wrote:
>>>> >This works good if input is square and I also checked on your idea of
>>>> >padding zeros for non square matrices.
>>>> >I am currently concerned about the permutation matrix and L, U in case
>>>> of
>>>> >padded 0s. Because if we pad then how will they affect the outputs, so
>>>> that
>>>> >we can extract p,l,u for unpadded matrix.
>>>>
>>>> please read details I wrote on how to deal with the non-square case.
>>>> There is no padding needed.
>>>>
>>>>
>>>> >
>>>> >On Tuesday, February 27, 2024 at 10:03:25 PM UTC+5:30 Dima Pasechnik
>>>> wrote:
>>>> >
>>>> >>
>>>> >>
>>>> >> On 27 February 2024 15:34:20 GMT, 'Animesh Shree' via sage-devel <
>>>> >> sage-...@googlegroups.com> wrote:
>>>> >> >I tried scipy which uses superLU. We get the result but there is
>>>> little
>>>> >> bit
>>>> >> >of issue.
>>>> >> >
>>>> >> >
>>>> >> >--For Dense--
>>>> >> >The dense matrix factorization gives this output using permutation
>>>> matrix
>>>> >> >sage: a = Matrix(RDF, [[1, 0],[2, 1]], sparse=True)
>>>> >> >sage: a
>>>> >> >[1.0 0.0]
>>>> >> >[2.0 1.0]
>>>> >> >sage: p,l,u = a.dense_matrix().LU()
>>>> >> >sage: p
>>>> >> >[0.0 1.0]
>>>> >> >[1.0 0.0]
>>>> >> >sage: l
>>>> >> >[1.0 0.0]
>>>> >> >[0.5 1.0]
>>>> >> >sage: u
>>>> >> >[ 2.0 1.0]
>>>> >> >[ 0.0 -0.5]
>>>> >> >
>>>> >>
>>>> >> you'd probably want to convert the permutation matrix into a
>>>> permutation.
>>>> >>
>>>> >>
>>>> >> >--For Sparse--
>>>> >> >But the scipy LU decomposition uses permutations which involves
>>>> taking
>>>> >> >transpose, also the output permutations are represented as array.
>>>> >>
>>>> >> It is very normal to represent permutations as arrays.
>>>> >> One can reconstruct the permutation matrix from such an array
>>>> trivially
>>>> >> (IIRC, Sage even has a function for it)
>>>> >>
>>>> >> I am not sure what you mean by "taking transpose".
>>>> >>
>>>> >> >sage: p,l,u = a.LU(force=True)
>>>> >> >sage: p
>>>> >> >{'perm_r': [1, 0], 'perm_c': [1, 0]}
>>>> >> >sage: l
>>>> >> >[1.0 0.0]
>>>> >> >[0.0 1.0]
>>>> >> >sage: u
>>>> >> >[1.0 2.0]
>>>> >> >[0.0 1.0]
>>>> >> >
>>>> >> >
>>>> >> >Shall I continue with this?
>>>> >>
>>>> >> sure, you are quite close to getting it all done it seems.
>>>> >>
>>>> >>
>>>> >> >On Tuesday, February 6, 2024 at 11:29:07 PM UTC+5:30 Dima Pasechnik
>>>> wrote:
>>>> >> >
>>>> >> >> Non-square case for LU is in fact easy. Note that if you have
>>>> A=LU as
>>>> >> >> a block matrix
>>>> >> >> A11 A12
>>>> >> >> A21 A22
>>>> >> >>
>>>> >> >> then its LU-factors L and U are
>>>> >> >> L11 0 and U11 U12
>>>> >> >> L21 L22 0 U22
>>>> >> >>
>>>> >> >> and A11=L11 U11, A12=L11 U12, A21=L21 U11, A22=L21 U12+L22 U22
>>>> >> >>
>>>> >> >> Assume that A11 is square and full rank (else one may apply
>>>> >> >> permutations of rows and columns in the usual way). while A21=0
>>>> and
>>>> >> >> A22=0. Then one can take L21=0, L22=U22=0, while A12=L11 U12
>>>> >> >> implies U12=L11^-1 A12.
>>>> >> >> That is, we can first compute LU-decomposition of a square matrix
>>>> A11,
>>>> >> >> and then compute U12 from it and A.
>>>> >> >>
>>>> >> >> Similarly, if instead A12=0 and A22=0, then we can take U12=0,
>>>> >> >> L22=U22=0, and A21=L21 U11,
>>>> >> >> i.e. L21=A21 U11^-1, and again we compute LU-decomposition of
>>>> A11, and
>>>> >> >> then L21=A21 U11^-1.
>>>> >> >>
>>>> >> >> ----------------
>>>> >> >>
>>>> >> >> Note that in some cases one cannot get LU, but instead must go
>>>> for an
>>>> >> >> PLU,with P a permutation matrix.
>>>> >> >> For non-square matrices this seems a bit more complicated, but,
>>>> well,
>>>> >> >> still doable.
>>>> >> >>
>>>> >> >> HTH
>>>> >> >> Dima
>>>> >> >>
>>>> >> >>
>>>> >> >>
>>>> >> >>
>>>> >> >> On Mon, Feb 5, 2024 at 6:00 PM Nils Bruin <nbr...@sfu.ca> wrote:
>>>> >> >> >
>>>> >> >> > On Monday 5 February 2024 at 02:31:04 UTC-8 Dima Pasechnik
>>>> wrote:
>>>> >> >> >
>>>> >> >> >
>>>> >> >> > it is the matter of adding extra zero rows or columns to the
>>>> matrix
>>>> >> you
>>>> >> >> want to decompose. This could be a quick fix.
>>>> >> >> >
>>>> >> >> > (in reference to computing LU decompositions of non-square
>>>> matrices)
>>>> >> --
>>>> >> >> in a numerical setting, adding extra zero rows/columns may not be
>>>> such
>>>> >> an
>>>> >> >> attractive option: if previously you know you had a maximal rank
>>>> >> matrix,
>>>> >> >> you have now ruined it by the padding. It's worth checking the
>>>> >> >> documentation and literature if padding is appropriate/desirable
>>>> for
>>>> >> the
>>>> >> >> target algorithm/implementation.
>>>> >> >> >
>>>> >> >> > --
>>>> >> >> > You received this message because you are subscribed to the
>>>> Google
>>>> >> >> Groups "sage-devel" group.
>>>> >> >> > To unsubscribe from this group and stop receiving emails from
>>>> it,
>>>> >> send
>>>> >> >> an email to sage-devel+...@googlegroups.com.
>>>> >> >> > To view this discussion on the web visit
>>>> >> >>
>>>> >>
>>>> https://groups.google.com/d/msgid/sage-devel/622a01e0-9197-40c5-beda-92729c4e4a32n%40googlegroups.com
>>>>
>>>> >> >> .
>>>> >> >>
>>>> >> >
>>>> >>
>>>> >
>>>>
>>>
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