See the documentation:
https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.SuperLU.html
As you can see there it computes permutation matrices Pr and Pc and lower
and upper triangular matrices L,U such that
Pr*A*Pc = L*U
so it's not computing a normal LU decomposition of a PLU decomposition:
it's doing both row- and column permutations on A; presumably to condition
it to get a more numerically stable L,U.
It's a different decomposition. You may be able to solve similar problems
with it, but you'll have to expose the computed data to the user. I don't
think it's suitable for wrapping as a normal LU-decomposition, as it won't
be a drop-in substitute for it.
You do get
A = Pr^(-1) *L*U * Pc^(-1)
On Tuesday 27 February 2024 at 10:02:19 UTC-8 Animesh Shree wrote:
> Sorry for multiple messages
>
> I just want to say
>
> >sage: p,l,u = a.LU(force=True)
> >sage: p
> >{'perm_r': [1, 0], 'perm_c': [1, 0]}
>
> It ( {'perm_r': [1, 0], 'perm_c': [1, 0]} ) represents transpose and
> it cannot be represented as permutation matrix.
> Similar cases may arise for other matrices.
>
> On Tuesday, February 27, 2024 at 11:29:44 PM UTC+5:30 Animesh Shree wrote:
>
>> For transpose :
>>
>> In the example we can see permutations are provided as arrays for rows
>> and cols.
>> The permutation is equivalent of taking transpose of matrix.
>> But we cant represent transpose as a permutation matrix.
>>
>>
>> >>> a = np.matrix([[1,2],[3,5]])
>> >>> # a * perm = a.T
>> >>> # perm = a.I * a.T
>> >>> a.I*a.T
>> matrix([[-1., -5.],
>> [ 1., 4.]])
>> >>>
>>
>> the output is not permutation matrix.
>>
>> 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.
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>>> 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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