def interp(x, xp, fp):
"""
Simple equivalent of np.interp that compute a linear interpolation.
We are not doing any checks, so make sure your query points are lying
inside the array.
TODO: Implement proper interpolation!
x, xp, fp need to be 1d arrays
"""
# First we find the nearest neighbour
ind = np.argmin((x - xp) ** 2)
# Perform linear interpolation
ind = np.clip(ind, 1, len(xp) - 2)
xi = xp[ind]
# Figure out if we are on the right or the left of nearest
s = np.sign(np.clip(x, xp[1], xp[-2]) - xi).astype(np.int64)
a = (fp[ind + np.copysign(1, s)] - fp[ind]) / (
xp[ind + np.copysign(1, s)] - xp[ind]
)
b = fp[ind] - a * xp[ind]
return a * x + b
def get_boundaries_intersections(z: jnp.ndarray, d: jnp.ndarray,
trust_radius: Union[float, jnp.ndarray]):
"""
ported from scipy
Solve the scalar quadratic equation ||z + t d|| == trust_radius.
This is like a line-sphere intersection.
Return the two values of t, sorted from low to high.
"""
a = _dot(d, d)
b = 2 * _dot(z, d)
c = _dot(z, z) - trust_radius**2
sqrt_discriminant = jnp.sqrt(b * b - 4 * a * c)
# The following calculation is mathematically
# equivalent to:
# ta = (-b - sqrt_discriminant) / (2*a)
# tb = (-b + sqrt_discriminant) / (2*a)
# but produce smaller round off errors.
# Look at Matrix Computation p.97
# for a better justification.
aux = b + jnp.copysign(sqrt_discriminant, b)
ta = -aux / (2 * a)
tb = -2 * c / aux
# (ta, tb) if ta < tb else (tb, ta)
ra = jnp.where(ta < tb, ta, tb)
rb = jnp.where(ta < tb, tb, ta)
return (ra, rb)
def copysign(x1, x2): if isinstance(x1, JaxArray): x1 = x1.value if isinstance(x2, JaxArray): x2 = x2.value return JaxArray(jnp.copysign(x1, x2))