def cal_transformation_kabsch(src_points, dst_points):
'''
Calculates the optimal rigid transformation from src_points to dst_points.
(Regarding the least squares error)
Args:
------
src_points: array, (N, 3) matrix.
dst_points: array, (N, 3) matrix.
Returns:
------
R: rotaion matrix, array.
T: translation vector, array.
rmsd_value: float.
'''
assert src_points.shape == dst_points.shape
if src_points.shape[1] != 3:
raise Exception(
"The input data matrix had to be transposed in order to compute transformation."
)
#src_points = src_points.transpose()
#dst_points = dst_points.transpose()
src_points_centered = src_points - rmsd.centroid(src_points)
dst_points_centered = dst_points - rmsd.centroid(dst_points)
R = rmsd.kabsch(src_points_centered, dst_points_centered)
rmsd_value = rmsd.kabsch_rmsd(src_points_centered, dst_points_centered)
T = rmsd.centroid(dst_points) - np.matmul(rmsd.centroid(src_points), R)
return R.transpose(), T.transpose(), rmsd_value
def rmsd_dist(A, B):
#REMOVE CENTER OF MASS
A -= rmsd.centroid(A)
B -= rmsd.centroid(B)
#FIND ROTATION MATRIX
U = rmsd.kabsch(A, B)
# ROTATE TOWARDS B
A = np.dot(A, U)
#RETURN ROOT MEAN SQUARE DEVIATION
return rmsd.rmsd(A, B)
def rmsd_VEC(A, B):
#REMOVE CENTER OF MASS
A -= rmsd.centroid(A)
B -= rmsd.centroid(B)
#FIND ROTATION MATRIX
U = rmsd.kabsch(A, B)
# ROTATE TOWARDS B
A = np.dot(A, U)
#RETURN ROTATED ARRAY
return A
def write_rmsd(fp, fp2, A, B):
A -= rmsd.centroid(A)
B -= rmsd.centroid(B)
fp2.write('%d\n' % (len(A)))
fp2.write('\n')
for i in range(len(A)):
fp2.write('A %f %f %f\n' % (A[i, 0], A[i, 1], A[i, 2]))
#FIND ROTATION MATRIX
U = rmsd.kabsch(A, B)
# ROTATE TOWARDS B
A = np.dot(A, U)
fp.write('%d\n' % (len(A)))
fp.write('\n')
for i in range(len(A)):
fp.write('A %f %f %f\n' % (A[i, 0], A[i, 1], A[i, 2]))
return fp
def arrange(ref, to):
ref -= rmsd.centroid(ref)
to -= rmsd.centroid(to)
U = rmsd.kabsch(to[:3, :], ref[:3, :])
to = np.dot(to, U)
dist = []
ref_CT_taken = []
to_CT_taken = []
unordered_results = []
for i in range(3, len(ref)):
for j in range(3, len(to)):
ref_CT = ref[i, :]
to_CT = to[j, :]
dist.append([i - 3, j - 3, abs(np.linalg.norm(ref_CT - to_CT))])
while len(ref_CT_taken) != len(ref) - 3:
min_index = min_dist_index(dist)
unordered_results.append([dist[min_index][0], dist[min_index][1]])
ref_lmo = dist[min_index][0]
to_lmo = dist[min_index][1]
ref_CT_taken.append(ref_lmo)
to_CT_taken.append(to_lmo)
to_be_deleted = []
for i in range(len(dist)):
if dist[i][0] == ref_lmo:
if i not in to_be_deleted:
to_be_deleted.append(dist[i])
continue
if dist[i][1] == to_lmo:
if i not in to_be_deleted:
to_be_deleted.append(dist[i])
for i in range(len(to_be_deleted)):
dist.remove(to_be_deleted[i])
return order(unordered_results, len(ref) - 3)