gsl_multifit_fdfsolver_lsmder memory usage
Peter Verveer
verveer@embl-heidelberg.de
Sun Mar 16 19:54:00 GMT 2003
Hi Brian,
> > I recently started converting some numerical code to GSL and
> > replaced a Levenberg-Marquardt routine which was a C translation of
> > lmdif from MINPACK. However, I found that the GSL solver
> > gsl_multifit_fdfsolver_lsmder uses a lot of memory, since it
> > appears to allocate a matrix of m times m, where m is the number of
> > functions. This causes me many problems since I work with large
> > data sets (10,000-100.000 data points is not unusual) and obviously
> > memory requirements quickly get out of hand then. I had a look at
> > the original fortran MINPACK which does not seem to require
> > this. Is there a particular reason gsl_multifit_fdfsolver_lsmder
> > needs so much memory, and could this eventually be changed?
>
> When I implemented the algorithm I believe I stored the full Q matrix
> from the QR decomposition because it was easier to implement that way.
>
> Maybe you could look at what is needed to avoid storing the full Q
> matrix, as in MINPACK. I don't think it's too complicated now that the
> basic algorithm is there.
You are right. It turns out that the changes are very minor. I replaced the QR
decomposition by its in-place version, and used the resulting encoded QR
matrix to calculate qtf. Then the q matrix in the solver can be eliminated,
saving huge amounts of memory in my case.
Below are the patches that I applied. They are quite small, so maybe they can
be included in future versions of GSL? I hope they are correct and don't
introduce any problems I did not discover.
I should note that I do not actually unpack the QR matrix to get R. The packed
matrix QR can be used directly instead of R since its upper triangular matrix
is equal to that of R (at least I think...). This seems to work since the
rest of the code does not access the lower triangular matrix of R. If that
seems a problem, R should be extracted, or the lower triangular part of QR
set to zero to get R.
Thanks for the hint, the code works now fine for me.
Cheers, Peter
-------------------------------------------------------------------------------------------------------------------------------
Here are the patches:
In lmset.c just replace the QR decomposition with its in-place version:
6d5
< gsl_matrix *q = state->q;
41c40,41
< gsl_linalg_QRPT_decomp2 (J, q, r, tau, perm, &signum, work1);
---
> gsl_matrix_memcpy (r, J);
> gsl_linalg_QRPT_decomp (r, tau, perm, &signum, work1);
In lmder.c, remove the allocation and deallocation of q:
43d42
< gsl_matrix *q;
84,92d82
< q = gsl_matrix_calloc (n, n);
<
< if (q == 0)
< {
< GSL_ERROR ("failed to allocate space for q", GSL_ENOMEM);
< }
<
< state->q = q;
<
389d378
< gsl_matrix_free (state->q);
In lmiterate replace compute_qtf() and gsl_linalg_QRPT_decomp2():
6d5
< gsl_matrix *q = state->q;
31,32c30,31
<
< compute_qtf (q, f, qtf);
---
> gsl_vector_memcpy (qtf, f);
> gsl_linalg_QR_QTvec (r, tau, qtf);
187c186,187
< gsl_linalg_QRPT_decomp2 (J, q, r, tau, perm, &signum, work1);
---
> gsl_matrix_memcpy (r, J);
> gsl_linalg_QRPT_decomp (r, tau, perm, &signum, work1);
In lmutils, remove the definition of compute_qtf():
100,113d99
< static void
< compute_qtf (const gsl_matrix * q, const gsl_vector * f, gsl_vector * qtf)
< {
< size_t i, j, N = f->size;
<
< for (j = 0; j < N; j++)
< {
< double sum = 0;
< for (i = 0; i < N; i++)
< sum += gsl_matrix_get (q, i, j) * gsl_vector_get (f, i);
<
< gsl_vector_set (qtf, j, sum);
< }
< }
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