
Ublas : 
From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 20060414 02:39:36
Hi,
Usually, factorization methods do not crash, but deliver a complete
factorization. The singularity is usually pivoted to the bottom of the
matrix. Some information is passed on to the user. See the manual for
LAPACK that I added below.
Karl
*SYNOPSIS*
SUBROUTINE DGETRF(M, N, A, LDA, IPIVOT, INFO)
INTEGER M, N, LDA, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION A(LDA,*)
SUBROUTINE DGETRF_64(M, N, A, LDA, IPIVOT, INFO)
INTEGER*8 M, N, LDA, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION A(LDA,*)
*PURPOSE*
dgetrf computes an LU factorization of a general MbyN
matrix A using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with
unit diagonal elements (lower trapezoidal if m > n), and U
is upper triangular (upper trapezoidal if m < n).
This is the rightlooking Level 3 BLAS version of the algo
rithm.
*ARGUMENTS*
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrix A. N >= 0.
A (input/output)
On entry, the MbyN matrix to be factored. On
exit, the factors L and U from the factorization A
= P*L*U; the unit diagonal elements of L are not
stored.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
IPIVOT (output)
The pivot indices; for 1 <= i <= min(M,N), row i
of the matrix was interchanged with row IPIVOT(i).
INFO (output)
= 0: successful exit
< 0: if INFO = i, the ith argument had an ille
gal value
> 0: if INFO = i, U(i,i) is exactly zero. The
factorization has been completed, but the factor U
is exactly singular, and division by zero will
occur if it is used to solve a system of equa
tions.
Sohail Somani wrote:
>Im sure it can, but perhaps the author assumed you knew whether or not
>the matrix was singular (I tend not to assume this)
>
>
>
>>Original Message
>>From: ublasbounces_at_[hidden]
>>[mailto:ublasbounces_at_[hidden]] On Behalf Of Manoj Rajagopalan
>>Sent: Thursday, April 13, 2006 12:53 PM
>>To: ublas mailing list
>>Subject: Re: [ublas] Solving linear equations of the form Ax = b ?
>>
>>I can confirm that this code will crash on singular matrices
>>:) Can't
>>ublas be modified to throw an exception or return an error value like
>>INFO in the original FORTRAN version?
>>
>>
>>Sohail Somani wrote:
>>
>>
>>>Warning: I think the wiki says that this code will crash on
>>>
>>>
>>a singular
>>
>>
>>>matrix.
>>>
>>>Just fyi.
>>>
>>>
>>>
>>>
>>>>Original Message
>>>>From: ublasbounces_at_[hidden]
>>>>[mailto:ublasbounces_at_[hidden]] On Behalf Of Manoj
>>>>
>>>>
>>Rajagopalan
>>
>>
>>>>Sent: Thursday, April 13, 2006 7:06 AM
>>>>To: ublas mailing list
>>>>Subject: Re: [ublas] Solving linear equations of the form Ax = b ?
>>>>
>>>>you can solve Ax=b using three lines of ublas code:
>>>>
>>>>permutation_matrix<> piv;
>>>>lu_factorize(A, piv);
>>>>lu_substitute(A, piv, x);
>>>>
>>>>Then x will contain the solution and A is overwritten with its LU
>>>>decomposition. i.e., the original values of A and x are
>>>>destroyed so the
>>>>above lines are actually the inplace_solve(A, x) for a dense,
>>>>generic A.
>>>>
>>>>BTW, I've come across this in many places  what does
>>>>"boilerplate code"
>>>>mean and why is it called so?
>>>>
>>>>cheers!
>>>>Manoj
>>>>
>>>>
>>>>
>>>>John Maddock wrote:
>>>>
>>>>
>>>>
>>>>>I gather from a quick web search that ublas does have LUP
>>>>>
>>>>>
>>>>decomposition
>>>>
>>>>
>>>>
>>>>>routines, however a grep of the docs failed to find any
>>>>>
>>>>>
>>>>mention of the
>>>>
>>>>
>>>>
>>>>>routine in question, and how they should be used.
>>>>>
>>>>>So.... does anyone have the boiler plate code needed to
>>>>>
>>>>>
>>>>solve for x given
>>>>
>>>>
>>>>
>>>>>matrix A and vector b ?
>>>>>
>>>>>Many thanks,
>>>>>
>>>>>John Maddock.
>>>>>
>>>>>_______________________________________________
>>>>>ublas mailing list
>>>>>ublas_at_[hidden]
>>>>>http://lists.boost.org/mailman/listinfo.cgi/ublas
>>>>>
>>>>>
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>>>>
>>>>
>>>>
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>>>
>>>
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>>
>>
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>
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