small simplication in bisect_alignment

[stestoll]

No description provided.

[stestoll]

Unclear why tests don't pass with 1e-7 tolerance. Precision of the two methods appears comparable:

import numpy as np
r = 4   # angstrom
n = 100000
err1 = np.empty(n)
err2 = np.empty(n)
for i in range(n):
  N = np.random.random_sample(3,)*r
  CA = np.random.random_sample(3,)*r
  C = np.random.random_sample(3,)*r

  CA_N = N - CA
  CA_N /= np.linalg.norm(CA_N)
  CA_C = C - CA
  CA_C /= np.linalg.norm(CA_C)
  z = CA_N + CA_C
  z /= np.linalg.norm(z)

  # unit vectors
  y = CA_N - CA_C
  y /= np.linalg.norm(y)
  
  # projection
  y2 = N - C
  y2 = y2 - np.dot(y2,z)*z
  y2 /= np.linalg.norm(y2)
  
  err1[i] = np.dot(z,y)
  err2[i] = np.dot(z,y2)

print(f"""
unitvectors (new):  mean {np.mean(err1)} std {np.std(err1)}
projection (old):   mean {np.mean(err2)} std {np.std(err2)}
""")

unitvectors (new):  mean -3.742426358502478e-19 std 4.0585430030246706e-16
projection (old):   mean 2.586048995625379e-19 std 1.7544848971476776e-16

[mtessmer]

It looks like terminal atoms are the biggest failures. In my experience, rotation matrices amplify numerical instabilities.