Troubleshooting

Common errors, what causes them, and how to fix them.

MethodError: no method matching... when creating an operator

Your data is a Matrix instead of a Vector of vectors. Every point must be its own vector with a compile-time-inferrable dimension.

# WRONG — a Matrix
points = rand(100, 2)

# CORRECT
using StaticArrays
points = rand(SVector{2,Float64}, 100)

# Converting from a Matrix
matrix_data = rand(100, 2)
points = map(SVector{2}, eachrow(matrix_data))

ArgumentError: n must be 1, 3, 5, or 7

Polyharmonic spline order must be odd and ≤ 7.

PHS(2)  # ✗ even
PHS(9)  # ✗ too high

PHS(1)  # linear   (least smooth)
PHS(3)  # cubic    (default, good balance)
PHS(5)  # quintic  (smoother)
PHS(7)  # septic   (smoothest)

ArgumentError: Shape parameter should be > 0

The shape parameter ε of IMQ and Gaussian must be positive.

IMQ(-1.0)      # ✗
Gaussian(0.0)  # ✗

IMQ(1.0)       # typical range 0.1 – 10.0
Gaussian(0.5)  # smaller ε ⇒ wider basis function

Poor accuracy or oscillations

Work through these in order: 2. Stencil too small — increase k:

lap = laplacian(points; k = 50)

3. Polynomial degree too low — increase poly_deg:

basis = PHS(3; poly_deg = 4)

4. Wrong basis for the problem — for very smooth functions, try a higher-order PHS:

basis = PHS(5; poly_deg = 4)

5. Shape parameter ill-suited (IMQ / Gaussian) — tune ε; smaller is smoother:

basis = IMQ(0.1)

SingularException or an ill-conditioned system

2. Duplicate or near-duplicate points. Two points at (nearly) the same location make the collocation matrix singular. Detect them with a KDTree and remove them.

3. Stencil too large for the local point density — reduce k:

lap = laplacian(points; k = 20)

4. Polynomial degree too high for the stencil size — reduce poly_deg:

basis = PHS(3; poly_deg = 1)

As a rule of thumb, keep poly_deg ≤ (k - 1) / dim so the polynomial block stays determined.