def numpy_svd_rmsd_rot(in_crds1, in_crds2):
"""
Returns rmsd and optional rotation between 2 sets of [nx3] arrays.
This requires numpy for svd decomposition.
The transform direction: transform(m, ref_crd) => target_crd.
"""
crds1 = numpy.array(in_crds1)
crds2 = numpy.array(in_crds2)
assert (crds1.shape[1] == 3)
assert (crds1.shape == crds2.shape)
n_vec = numpy.shape(crds1)[0]
correlation_matrix = numpy.dot(numpy.transpose(crds1), crds2)
v, s, w = numpy.linalg.svd(correlation_matrix)
is_reflection = (numpy.linalg.det(v) * numpy.linalg.det(w)) < 0.0
if is_reflection:
s[-1] = -s[-1]
E0 = sum(sum(crds1 * crds1)) + \
sum(sum(crds2 * crds2))
rmsd_sq = (E0 - 2.0 * sum(s)) / float(n_vec)
rmsd_sq = max([rmsd_sq, 0.0])
rmsd = numpy.sqrt(rmsd_sq)
if is_reflection:
v[-1, :] = -v[-1, :]
rot33 = numpy.dot(v, w)
m = v3.identity()
m[:3, :3] = rot33.transpose()
return rmsd, m
def numpy_svd_rmsd_rot(in_crds1, in_crds2):
"""
Returns rmsd and optional rotation between 2 sets of [nx3] arrays.
This requires numpy for svd decomposition.
The transform direction: transform(m, ref_crd) => target_crd.
"""
crds1 = numpy.array(in_crds1)
crds2 = numpy.array(in_crds2)
assert(crds1.shape[1] == 3)
assert(crds1.shape == crds2.shape)
n_vec = numpy.shape(crds1)[0]
correlation_matrix = numpy.dot(numpy.transpose(crds1), crds2)
v, s, w = numpy.linalg.svd(correlation_matrix)
is_reflection = (numpy.linalg.det(v) * numpy.linalg.det(w)) < 0.0
if is_reflection:
s[-1] = - s[-1]
E0 = sum(sum(crds1 * crds1)) + \
sum(sum(crds2 * crds2))
rmsd_sq = (E0 - 2.0*sum(s)) / float(n_vec)
rmsd_sq = max([rmsd_sq, 0.0])
rmsd = numpy.sqrt(rmsd_sq)
if is_reflection:
v[-1,:] = -v[-1,:]
rot33 = numpy.dot(v, w)
m = v3.identity()
m[:3,:3] = rot33.transpose()
return rmsd, m
def pyqcprot_rmsd_rot(crds1, crds2):
"""
Returns rmsd and optional rotation between 2 sets of [nx3] arrays.
This requires Joshua Adelman's pyqcrot library for quaternion-based
calculation of Theobauld. The transform direction:
transform(m, ref_crd) => target_crd.
"""
rms, rot9 = lib.pyqcprot.calc_rms_rot(crds1, crds2)
matrix = v3.identity()
for i in range(3):
for j in range(3):
v3.matrix_elem(matrix, i, j, rot9[i * 3 + j])
return rms, matrix
def pyqcprot_rmsd_rot(crds1, crds2):
"""
Returns rmsd and optional rotation between 2 sets of [nx3] arrays.
This requires Joshua Adelman's pyqcrot library for quaternion-based
calculation of Theobauld. The transform direction:
transform(m, ref_crd) => target_crd.
"""
rms, rot9 = lib.pyqcprot.calc_rms_rot(crds1, crds2)
matrix = v3.identity()
for i in range(3):
for j in range(3):
v3.matrix_elem(matrix, i, j, rot9[i*3+j])
return rms, matrix