SGP: numpy.linalg.LinAlgError: 58-th leading minor of the array is not positive definite

[NAThompson]

If the number of inducing inputs in SGP is >=~58, we get the following exception from numpy:

numpy.linalg.LinAlgError: 58-th leading minor of the array is not positive definite

To reproduce run:

#!/usr/bin/env python3
import random
from math import sin
from math import pi as π
import numpy as np
import random
from smt.surrogate_models import SGP

np.random.seed(41)
random.seed(41)

def generate_sin_volume(samples: int):
    abscissas = np.ndarray(shape=(samples, 3))
    ordinates = np.ndarray(shape=samples)
    for i in range(samples):
        x = random.uniform(-0.5, 0.5)
        y = random.uniform(-1, 1)
        z = random.uniform(-2, 2)
        abscissas[i] = np.array([x, y, z])
        ordinates[i] = sin(2 * π * x) * sin(π * y) * sin(π * z / 2)

    return abscissas, ordinates


def test_sgp_principle_minor():
    # samples = 57 # works
    samples = 58 
    xs, ys = generate_sin_volume(samples)
    sgp = SGP(
        print_global=False,
        inducing_method="kmeans",
        n_inducing=samples,
        random_state=41,
    )
    sgp.set_training_values(xs, ys)
    sgp.train()

    x = np.array([np.array([0.3, -0.4, 0.6])])
    y1 = sgp.predict_values(x)[0][0]


if __name__ == "__main__":
    test_sgp_principle_minor()

Now, arguably the error is here:

capi_return is NULL
Call-back cb_calcfc_in__cobyla__user__routines failed.
Optimization failed. Try increasing the 'nugget' above its current value of 2.220446049250313e-13.

But this error is buried in the subsequent error stack, which I believe is simply continuing with garbage data.