Add qr build option for numerically stable GAP fitting

[7albertoh]

Summary

Add a new meson build option qr (default: true) that enables the -DHAVE_QR compiler flag.
This activates the QR decomposition solve path in gp_predict.F90, which is numerically stable
for ill-conditioned kernel matrices that cause Cholesky (dpotrf) to fail with
LA_Matrix_Factorise: cannot factorise.

Problem

gap_fit routinely crashes with LA_Matrix_Factorise: cannot factorise, error: 8/9 when fitting
SOAP descriptors with moderate sparse point counts (500–2000). The Cholesky factorization of
the kernel matrix Q = C_MM + C_MN * Λ⁻¹ * C_NM fails when Q is ill-conditioned. This is a
known issue — see #229, #132, #312.

The only documented workaround (sparse_jitter) does not reliably fix it. I tested 4
combinations of sparse_jitter (1e-10 to 1e-2), zeta (2–4), n_sparse (500–2000), and
default_sigma — all crashed at the same point.

Solution

QUIP already contains a complete QR decomposition solve path in src/GAP/gp_predict.F90 (lines
782–905), gated behind #ifdef HAVE_QR. This path reformulates the system as a tall
least-squares problem solved via LAPACK's dgeqrf, which is numerically stable for
ill-conditioned matrices. The required LAPACK routines are already provided by
OpenBLAS/LAPACK.

This PR adds a meson build option to enable it, following the existing pattern of gap and mpi
options:

meson.options

option('qr', type: 'boolean', value: true, description: 'Use QR decomposition for numerically
stable GAP fitting (requires GAP)')

Usage

Default (QR enabled)

meson setup builddir -Dgap=true

Explicitly disable QR (old Cholesky behavior)

meson setup builddir -Dgap=true -Dqr=false

Test Results

Cu FCC, 108-atom supercell, 350 training frames, SOAP cutoff=5.28 Å:

Before (Cholesky): SYSTEM ABORT: LA_Matrix_Factorise: cannot factorise, error: 9 — crashed on
every attempt.

After (QR, -Dqr=true):

┌─────────────────┬──────────────────────┬───────────────────────┐
│ │ n_sparse=500, zeta=2 │ n_sparse=2000, zeta=4 │
├─────────────────┼──────────────────────┼───────────────────────┤
│ SOAP covariance │ 26 min │ 101 min │
├─────────────────┼──────────────────────┼───────────────────────┤
│ QR solve │ 1 sec │ 7 sec │
├─────────────────┼──────────────────────┼───────────────────────┤
│ Result │ ✅ Success │ ✅ Success │
├─────────────────┼──────────────────────┼───────────────────────┤
│ Energy RMSE │ — │ 2.5 meV/atom │
├─────────────────┼──────────────────────┼───────────────────────┤
│ Force RMSE │ — │ 0.25 eV/Å │
└─────────────────┴──────────────────────┴───────────────────────┘

Log output confirms: Using LAPACK to solve QR

Changes

• meson.options: Add qr boolean option (default true)
• meson.build: Conditionally add -DHAVE_QR when qr=true and gap=true

2 files changed, 7 insertions, 2 deletions. No Fortran source changes — the QR code path
already exists.