def mesh_nist3_direct(r_min, r_max, N):
"""
Calculates the NIST III mesh directly.
"""
exp = numpy.exp
log = math.log
# Uniform mesh in rho:
rho = mesh_exp(log(r_min), log(r_max), a=1, N=N)
r = exp(rho)
return r
def mesh_exp2(r_min, r_max, a, N):
"""
Calculates the exponential mesh using a formula:
r_n = (a**(n/N) - 1) / (a - 1)
with a > 1. By substitution a -> a**((N-1.)/N), we can just call
mesh_exp().
"""
a = float(a)
assert a > 1
assert N >= 1
return mesh_exp(r_min, r_max, a**((N-1.)/N), N)