DFTInterpolator for singular integral gives bad results

[unalmis]

When the DFTInterpolator is used in the singular integral routine the results are not correct, and also not deterministic on my machine. Running this test multiple times gives different results. Attached is example output.

@pytest.mark.unit
def test_singular_integral_vac_estell(self):
    """Test calculating Bplasma for vacuum estell, which should be near 0."""
    eq = get("ESTELL")
    grid = LinearGrid(M=25, N=25, NFP=eq.NFP)
    keys = [
        "K_vc",
        "B",
        "|B|^2",
        "R",
        "phi",
        "Z",
        "e^rho",
        "n_rho",
        "|e_theta x e_zeta|",
    ]
    data = eq.compute(keys, grid=grid)
    k = min(grid.num_theta, grid.num_zeta * grid.NFP)
    s = k - 1
    q = k // 2 + int(np.sqrt(k))
    interpolator = DFTInterpolator(grid, grid, s, q)
    Bplasma = virtual_casing_biot_savart(data, data, interpolator, loop=True)
    # need extra factor of B/2 bc we're evaluating on plasma surface
    Bplasma += data["B"] / 2
    Bplasma = np.linalg.norm(Bplasma, axis=-1)
    # scale by total field magnitude
    B = Bplasma / np.linalg.norm(data["B"], axis=-1).mean()
    np.testing.assert_allclose(B, 0, atol=0.005)

[unalmis]

• The issue occurs more often on larger problem sizes.
• I suspect there might be a numerics issue caused by computing the pseudoinverse of the vandermonde matrix A. A solution would be to compute $c = A^{-1} f$ directly with a Fourier transform and then retain the other basis matrix to interpolate via B@c.