ivan-pi / libdogleg-f

Fortran bindings to libdogleg - a large-scale nonlinear least-squares optimization library
GNU Lesser General Public License v3.0
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Add sparse matrix support #4

Open ivan-pi opened 2 years ago

ivan-pi commented 2 years ago

The biggest advantage of libdogleg is it supports problems with sparse Jacobians. This can result in huge savings for large least squares problems.

Generally speaking, we just need to recover the sparse storage buffers of the compressed-column sparse (CCS) matrix of type cholmod_sparse and fill them with our Jacobian values. In C, the unpacking is done as follows:

static void optimizerCallback(const double*   p,
                              double*         x,
                              cholmod_sparse* Jt,
                              void*           cookie __attribute__ ((unused)) )
{

  // These are convenient so that I only apply the casts once
  int*    Jrowptr = (int*)Jt->p;
  int*    Jcolidx = (int*)Jt->i;
  double* Jval    = (double*)Jt->x;

Notably, the Jacobian matrix is referenced as J^T. The array Jrowptr is of size Nmeas + 1 (recall the output vector is of size Nmeas). The arrays Jcolidx and Jval are of size Jnnz, which is the number of non-zero values in the sparse matrix.

The number of non-zeros must be given explicitly to the libdogleg optimizer:

    optimum = dogleg_optimize2(p, Nstate, Nmeasurements, Jnnz,
                               &optimizerCallback, NULL,
                               &dogleg_parameters, NULL);

A full description of the CHOLMOD sparse storage format is given in the user guide: https://github.com/DrTimothyAldenDavis/SuiteSparse/blob/master/CHOLMOD/Doc/CHOLMOD_UserGuide.pdf

ivan-pi commented 2 years ago

One more observation, in the Fortran interface we should add support for 1-based indexing.

Since CHOLMOD is a C library, it expects 0-based indexing. This should be handled as an (optional) argument in the call to the optimizer.

By default we'd assume Fortran indexing is used.