def rmsd_to(self, other):
import forgi.threedee.model.similarity as ftms #This import is here to avoid circular imports.
if self._elem_names == other._elem_names:
return ftms.rmsd(self._coordinates, other._coordinates,
self.is_centered & other.is_centered)
else:
common_keys = set(self._elem_names.keys()) & set(
other._elem_names.keys())
if len(common_keys) == len(self._elem_names):
rev_lookup = list(x for x in sorted(
self._elem_names.keys(), key=self._elem_names.__getitem__))
other_array = np.array([
coord_line for d in rev_lookup
for coord_line in [other[d][0], other[d][1]]
])
return ftms.rmsd(self._coordinates, other_array,
self.is_centered & other.is_centered)
else:
common_keys = list(common_keys)
this_array = np.array([
coord_line for d in common_keys
for coord_line in [self[d][0], self[d][1]]
])
other_array = np.array([
coord_line for d in common_keys
for coord_line in [other[d][0], other[d][1]]
])
return ftms.rmsd(this_array, other_array, False)
def rmsd_to(self, other):
# This import is here to avoid circular imports.
import forgi.threedee.model.similarity as ftms
if self._elem_names == other._elem_names:
return ftms.rmsd(self._coordinates,
other._coordinates,
self.is_centered & other.is_centered)
else:
common_keys = set(self._elem_names.keys()) & set(
other._elem_names.keys())
if len(common_keys) == len(self._elem_names):
rev_lookup = list(x for x in sorted(
self._elem_names.keys(), key=self._elem_names.__getitem__))
other_array = np.array(
[coord_line for d in rev_lookup for coord_line in [other[d][0], other[d][1]]])
return ftms.rmsd(self._coordinates,
other_array,
self.is_centered & other.is_centered)
else:
common_keys = list(common_keys)
this_array = np.array(
[coord_line for d in common_keys for coord_line in [self[d][0], self[d][1]]])
other_array = np.array(
[coord_line for d in common_keys for coord_line in [other[d][0], other[d][1]]])
return ftms.rmsd(this_array,
other_array,
False)
def test_rmsd_to_same(self):
a1 = np.array([[1., 1., 1.], [0., 0., 0.], [-1., -1., -1.]])
a2 = np.array([[1., 2., 1.], [0., -1., 0.], [-1., -1., -1.]])
self.assertAlmostEqual(ftme.drmsd(a1, a1), 0)
self.assertAlmostEqual(ftme.drmsd(a2, a2), 0)
self.assertAlmostEqual(ftme.rmsd(a1, a1), 0)
self.assertAlmostEqual(ftme.rmsd(a2, a2), 0)
def test_rmsd_to_same(self):
a1 = np.array([[1., 1., 1.], [0., 0., 0.], [-1., -1., -1.]])
a2 = np.array([[1., 2., 1.], [0., -1., 0.], [-1., -1., -1.]])
self.assertAlmostEqual(ftme.drmsd(a1, a1), 0)
self.assertAlmostEqual(ftme.drmsd(a2, a2), 0)
self.assertAlmostEqual(ftme.rmsd(a1, a1), 0)
self.assertAlmostEqual(ftme.rmsd(a2, a2), 0)
def realatom_vatom_rmsd(cg):
"""
The RMSD between the real atoms and the virtual atoms of the stems.
"""
vposs = []
rposs = []
for stem in cg.stem_iterator():
stemv = []
stemr = []
resseqs = cg.get_resseqs(stem)
resseqs = resseqs[0] + resseqs[1]
for posCg, idPdb in zip(cg.define_residue_num_iterator(stem), resseqs):
chainPdb, posPdb = idPdb
vas = cg.virtual_atoms(posCg)
for a, coords in vas.items():
try:
rp = cg.chains[chainPdb][posPdb][a].get_vector(
).get_array()
except KeyError:
pass
else:
rposs.append(rp)
vposs.append(coords)
assert len(vposs) == len(rposs)
return ftme.rmsd(np.array(vposs), np.array(rposs))
def main(parser):
args = parser.parse_args()
with fuc.hide_traceback():
cg1, cg2 = fuc.cgs_from_args(args,
nargs=2,
rna_type="3d",
enable_logging=True)
dir1 = np.array(args.directions[0].split(","), dtype=float)
dir2 = np.array(args.directions[1].split(","), dtype=float)
proj1 = ftmp.Projection2D(cg1, dir1)
proj2 = ftmp.Projection2D(cg2, dir2)
vrs1 = np.array(
[x for p in sorted(proj1._coords.keys()) for x in proj1._coords[p]])
vrs2 = np.array(
[x for p in sorted(proj2._coords.keys()) for x in proj2._coords[p]])
print(ftms.rmsd(vrs1, vrs2))
if args.plot:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
proj1.plot(ax, line2dproperties={"color": "green"})
proj2.plot(ax, line2dproperties={"color": "red"})
plt.show()
def realatom_vatom_rmsd(cg):
"""
The RMSD between the real atoms and the virtual atoms of the stems.
"""
vposs = []
rposs = []
for stem in cg.stem_iterator():
stemv = []
stemr = []
resseqs = cg.get_resseqs(stem)
resseqs = resseqs[0] + resseqs[1]
for posCg, idPdb in zip(cg.define_residue_num_iterator(stem), resseqs):
chainPdb, posPdb = idPdb
vas = cg.virtual_atoms(posCg)
for a, coords in vas.items():
try:
rp = cg.chains[chainPdb][posPdb][a].get_vector().get_array(
)
except KeyError:
pass
else:
rposs.append(rp)
vposs.append(coords)
assert len(vposs) == len(rposs)
return ftme.rmsd(np.array(vposs), np.array(rposs))
def update(self, sm, step):
if not self.silent:
curr_vress=sm.bg.get_ordered_virtual_residue_poss()
if self.mode=="RMSD":
rmsd=ftme.rmsd(self._reference, curr_vress)
elif self.mode=="dRMSD":
rmsd=ftme.drmsd(self._reference, curr_vress)
if self.best_cgs.can_insert_right((None, rmsd)):
self.best_cgs.insert_right((sm.bg.to_cg_string(),rmsd))
if step % 10 == 0:
for i, bg in enumerate(self.best_cgs):
with open(os.path.join(conf.Configuration.sampling_output_dir,
'best_rmsd{:d}.coord'.format(i)), 'w') as f:
f.write(bg[0])
if self._showMinMax:
if rmsd>self._maxRMSD:
self._maxRMSD=rmsd
if self._showMinMax==True:
if rmsd<self._minRMSD:
self._minRMSD=rmsd
self.history[1].append( self._minRMSD )
self.history[0].append( rmsd )
self.history[-1].append( self._maxRMSD )
if self._showMinMax=="max":
return "{:6.3f} A\t{:6.3f} A".format(rmsd, self._maxRMSD)
else:
return "{:6.3f} A\t{:6.3f} A\t{:6.3f} A".format(rmsd, self._minRMSD, self._maxRMSD)
else:
self.history[0].append( rmsd )
return "{:6.3f} A".format(rmsd)
else:
return
def main(parser):
args = parser.parse_args()
with fuc.hide_traceback():
cg1, cg2 = fuc.cgs_from_args(
args, rna_type="3d", enable_logging=True)
dir1 = np.array(args.directions[0].split(","), dtype=float)
dir2 = np.array(args.directions[1].split(","), dtype=float)
proj1 = ftmp.Projection2D(cg1, dir1)
proj2 = ftmp.Projection2D(cg2, dir2)
vrs1 = np.array([x for p in sorted(proj1._coords.keys())
for x in proj1._coords[p]])
vrs2 = np.array([x for p in sorted(proj2._coords.keys())
for x in proj2._coords[p]])
print(ftms.rmsd(vrs1, vrs2))
if args.plot:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
proj1.plot(ax, line2dproperties={"color": "green"})
proj2.plot(ax, line2dproperties={"color": "red"})
plt.show()
def test_cg_rmsd(self):
cg1 = ftmc.CoarseGrainRNA('test/forgi/threedee/data/1GID_A.cg')
cg2 = ftmc.CoarseGrainRNA('test/forgi/threedee/data/1GID_A_sampled.cg')
residues1 = ftug.bg_virtual_residues(cg1)
residues2 = ftug.bg_virtual_residues(cg2)
self.assertAlmostEqual(ftme.rmsd(residues1, residues2),
ftme.cg_rmsd(cg1, cg2))
def realatom_vatom_rmsd(cg):
"""
The RMSD between the real atoms and the virtual atoms of the stems.
"""
vposs = []
rposs = []
#print(cg.seq)
#print("".join(r.get_segid() for r in chain.get_residues()))
#print(cg.seq[1], chain[2])
for stem in cg.stem_iterator():
stemv = []
stemr = []
resseqs = cg.get_resseqs(stem)
resseqs = resseqs[0] + resseqs[1]
for posCg, posPdb in zip(cg.define_residue_num_iterator(stem),
resseqs):
#try:
# print( posCg, posPdb, cg.seq[posCg-1], cg.chain[posPdb] )
#except KeyError as e: print(e)
vas = cg.virtual_atoms(posCg)
for a, coords in vas.items():
try:
rposs.append(cg.chain[posPdb][a].get_vector().get_array())
stemr.append(cg.chain[posPdb][a].get_vector().get_array())
except KeyError:
pass
else:
vposs.append(coords)
stemv.append(coords)
assert len(vposs) == len(rposs)
#print (np.array(vposs).shape, file=sys.stderr)
return ftme.rmsd(np.array(vposs), np.array(rposs))
def test_cg_rmsd(self):
cg1 = ftmc.CoarseGrainRNA.from_bg_file(
'test/forgi/threedee/data/1GID_A.cg')
cg2 = ftmc.CoarseGrainRNA.from_bg_file(
'test/forgi/threedee/data/1GID_A_sampled.cg')
cg1.add_all_virtual_residues()
cg2.add_all_virtual_residues()
residues1 = cg1.get_ordered_virtual_residue_poss()
residues2 = cg2.get_ordered_virtual_residue_poss()
self.assertAlmostEqual(
ftme.rmsd(residues1, residues2), ftme.cg_rmsd(cg1, cg2))
def main(parser):
args = parser.parse_args()
cg1 = ftmc.CoarseGrainRNA(args.files[0])
cg2 = ftmc.CoarseGrainRNA(args.files[1])
dir1 = np.array(args.directions[0].split(","), dtype=float)
dir2 = np.array(args.directions[1].split(","), dtype=float)
proj1 = ftmp.Projection2D(cg1, dir1)
proj2 = ftmp.Projection2D(cg2, dir2)
vrs1 = np.array([x for p in sorted(proj1._coords.keys()) for x in proj1._coords[p]])
vrs2 = np.array([x for p in sorted(proj2._coords.keys()) for x in proj2._coords[p]])
print ftms.rmsd(vrs1, vrs2)
if args.plot:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
proj1.plot(ax, line2dproperties={"color": "green"})
proj2.plot(ax, line2dproperties={"color": "red"})
plt.show()
def test_rmsd_in_2D(self):
a1 = np.array([[1., 1.], [0., 0.], [-1., -1.]])
a2 = np.array([[2., 2.], [0., 0.], [-2., -2.]])
a3 = np.array([[2., 4.], [0., 6.], [-1., 0.]])
self.assertAlmostEqual(ftme.rmsd(a1, a1), 0)
self.assertAlmostEqual(ftme.rmsd(a2, a2), 0)
self.assertAlmostEqual(ftme.rmsd(a3, a3), 0)
self.assertAlmostEqual(ftme.rmsd(a1, a2), math.sqrt(4. / 3.))
self.assertGreater(ftme.rmsd(a1, a3), ftme.rmsd(a1, a2))
def test_rmsd_in_2D(self):
a1 = np.array([[1., 1.], [0., 0.], [-1., -1.]])
a2 = np.array([[2., 2.], [0., 0.], [-2., -2.]])
a3 = np.array([[2., 4.], [0., 6.], [-1., 0.]])
self.assertAlmostEqual(ftme.rmsd(a1, a1), 0)
self.assertAlmostEqual(ftme.rmsd(a2, a2), 0)
self.assertAlmostEqual(ftme.rmsd(a3, a3), 0)
self.assertAlmostEqual(ftme.rmsd(a1, a2), math.sqrt(4. / 3.))
self.assertGreater(ftme.rmsd(a1, a3), ftme.rmsd(a1, a2))
def main(args):
cgs = []
projs = []
for file_ in args.files:
cgs.append(ftmc.CoarseGrainRNA(file_))
try:
projs.append(ftmp.Projection2D(cgs[-1]))
except ValueError:
projs.append(None)
p_rmsds = OrderedDict()
cg_rmsds = OrderedDict()
p_rmsds[0] = 0.0
cg_rmsds[0] = 0.0
if "," in args.max_diff:
diffs = map(int, args.max_diff.split(","))
else:
diffs = range(1, int(args.max_diff) + 1)
for diff in diffs:
print ("diff {}".format(diff))
prmsd = 0
cgrmsd = 0
count = 0
pcount = 0
for i in range(0, len(cgs) - diff):
count += 1
try:
vrs1 = np.array([x for p in sorted(projs[i]._coords.keys()) for x in projs[i]._coords[p]])
vrs2 = np.array([x for p in sorted(projs[i + diff]._coords.keys()) for x in projs[i + diff]._coords[p]])
prmsd += ftms.rmsd(vrs1, vrs2)
pcount += 1
except:
pass
cgrmsd += ftms.cg_rmsd(cgs[i], cgs[i + diff])
if count:
cg_rmsds[diff] = cgrmsd / count
if pcount:
p_rmsds[diff] = prmsd / pcount
print "projection RMSDs:", p_rmsds
print "3D-RMSDs:", cg_rmsds
import matplotlib.pyplot as plt
if args.target_structure and args.hausdorff_reference:
fig, (ax, axT, axH) = plt.subplots(3)
elif args.target_structure:
fig, (ax, axT) = plt.subplots(2)
elif args.hausdorff_reference:
fig, (ax, axH) = plt.subplots(2)
else:
fig, ax = plt.subplots()
if args.target_structure:
target = ftmc.CoarseGrainRNA(args.target_structure)
target_rmsds = []
target_proj_rmsds = []
try:
target_proj = ftmp.Projection2D(target)
except ValueError:
pass
else:
target_vrs = np.array([x for p in sorted(target_proj._coords.keys()) for x in target_proj._coords[p]])
for proj in projs:
try:
vrs1 = np.array([x for p in sorted(proj._coords.keys()) for x in proj._coords[p]])
prmsd = ftms.rmsd(vrs1, target_vrs)
target_proj_rmsds.append(prmsd)
except:
target_proj_rmsds.append(float("nan"))
target_vrs = ftug.bg_virtual_residues(target)
for cg in cgs:
vrs1 = ftug.bg_virtual_residues(cg)
cgrmsd = ftms.rmsd(vrs1, target_vrs)
target_rmsds.append(cgrmsd)
xval = np.arange(len(cgs)) * args.step_size
if target_proj_rmsds:
axT.plot(xval, target_proj_rmsds, label="Projection", color="green")
axT.plot(xval, target_rmsds, label="3D", color="blue")
axT.set_title("RMSD to target structure")
axT.set_xlabel("step")
axT.set_ylabel("RMSD")
leg = axT.legend(framealpha=0.8, fancybox=True)
leg.get_frame().set_linewidth(0.0)
plt.subplots_adjust(hspace=0.4)
if args.hausdorff_reference:
ref_img = scipy.ndimage.imread(args.hausdorff_reference)
ref_quarter = scipy.ndimage.zoom(ref_img, 0.3) > 150
degrees = get_refimg_longest_axis(ref_img)
global_optima = []
local_optima = []
for cg in cgs:
score, img, params = fph.try_parameters(ref_img, args.hausdorff_scale, cg, degrees)
local_optima.append(score)
s, i, params = fph.globally_minimal_distance(
ref_quarter, args.hausdorff_scale, cg, start_points=40, starting_rotations=degrees, virtual_atoms=False
)
score, img, params = fph.locally_minimal_distance(
ref_img, args.hausdorff_scale, cg, params[1], params[2], params[0], maxiter=200
)
global_optima.append(score)
axH.plot(xval, global_optima, label="Global Minimization", color="red")
axH.plot(xval, local_optima, label="Local Minimization", color="lavender")
axH.set_title("Hausdorff Distance to reference image")
axH.set_xlabel("step")
axH.set_ylabel("Hausdorff Distance")
leg = axH.legend(framealpha=0.8, fancybox=True)
leg.get_frame().set_linewidth(0.0)
plt.subplots_adjust(hspace=0.4)
p_rmsds = np.array(p_rmsds.items())
cg_rmsds = np.array(cg_rmsds.items())
ax.plot(p_rmsds[:, 0] * args.step_size, p_rmsds[:, 1], label="Projection", color="green", marker="o")
ax.plot(cg_rmsds[:, 0] * args.step_size, cg_rmsds[:, 1], label="3D", color="blue", marker="o")
ax.set_title("Average RMSD between structures X steps apart.")
ax.set_xlabel("steps apart")
ax.set_ylabel("RMSD")
leg = ax.legend(framealpha=0.8, fancybox=True)
leg.get_frame().set_linewidth(0.0)
fig.patch.set_facecolor("white")
if args.save_fig:
with open(args.save_fig, "w") as f:
pickle.dump(fig, f)
plt.show()
def update(self, sm, step):
if not self.silent:
if self.res_ids:
curr_vress = []
for res in self.res_ids:
curr_vress.append(
sm.bg.get_virtual_residue(res,
allow_single_stranded=True))
curr_vress = np.array(curr_vress)
else:
curr_vress = sm.bg.get_ordered_virtual_residue_poss()
if self.mode == "RMSD":
try:
rmsd = ftme.rmsd(self._reference, curr_vress)
except Exception as e:
self.res_ids = set(self.reference_cg.seq._seqids) & set(
sm.bg.seq._seqids)
self._reference = []
curr_vress = []
for res in self.res_ids:
curr_vress.append(
sm.bg.get_virtual_residue(
res, allow_single_stranded=True))
self._reference.append(
self.reference_cg.get_virtual_residue(
res, allow_single_stranded=True))
curr_vress = np.array(curr_vress)
self._reference = np.array(self._reference)
log.error("Calculating rmsd between %s and %s",
self._reference, curr_vress)
rmsd = ftme.rmsd(self._reference, curr_vress)
elif self.mode == "dRMSD":
rmsd = ftme.drmsd(self._reference, curr_vress)
if self.best_cgs.can_insert_right((None, rmsd)):
self.best_cgs.insert_right((sm.bg.to_cg_string(), rmsd))
if step % 10 == 0:
for i, bg in enumerate(self.best_cgs):
with open(
os.path.join(
conf.Configuration.sampling_output_dir,
'best_rmsd{:d}.coord'.format(i)), 'w') as f:
f.write(bg[0])
if self._showMinMax:
if rmsd > self._maxRMSD:
self._maxRMSD = rmsd
if self._showMinMax == True:
if rmsd < self._minRMSD:
self._minRMSD = rmsd
self.history[1].append(self._minRMSD)
self.history[0].append(rmsd)
self.history[-1].append(self._maxRMSD)
if self._showMinMax == "max":
return "{:6.3f} A\t{:6.3f} A".format(rmsd, self._maxRMSD)
else:
return "{:6.3f} A\t{:6.3f} A\t{:6.3f} A".format(
rmsd, self._minRMSD, self._maxRMSD)
else:
self.history[0].append(rmsd)
return "{:6.3f} A".format(rmsd)
else:
return
def main(args):
cgs = []
projs = []
for file_ in args.files:
cgs.append(ftmc.CoarseGrainRNA(file_))
try:
projs.append(ftmp.Projection2D(cgs[-1]))
except ValueError:
projs.append(None)
p_rmsds = OrderedDict()
cg_rmsds = OrderedDict()
p_rmsds[0] = 0.
cg_rmsds[0] = 0.
if "," in args.max_diff:
diffs = map(int, args.max_diff.split(","))
else:
diffs = range(1, int(args.max_diff) + 1)
for diff in diffs:
print("diff {}".format(diff))
prmsd = 0
cgrmsd = 0
count = 0
pcount = 0
for i in range(0, len(cgs) - diff):
count += 1
try:
vrs1 = np.array([
x for p in sorted(projs[i]._coords.keys())
for x in projs[i]._coords[p]
])
vrs2 = np.array([
x for p in sorted(projs[i + diff]._coords.keys())
for x in projs[i + diff]._coords[p]
])
prmsd += ftms.rmsd(vrs1, vrs2)
pcount += 1
except:
pass
cgrmsd += ftms.cg_rmsd(cgs[i], cgs[i + diff])
if count:
cg_rmsds[diff] = cgrmsd / count
if pcount:
p_rmsds[diff] = prmsd / pcount
print("projection RMSDs:", p_rmsds)
print("3D-RMSDs:", cg_rmsds)
import matplotlib.pyplot as plt
if args.target_structure and args.hausdorff_reference:
fig, (ax, axT, axH) = plt.subplots(3)
elif args.target_structure:
fig, (ax, axT) = plt.subplots(2)
elif args.hausdorff_reference:
fig, (ax, axH) = plt.subplots(2)
else:
fig, ax = plt.subplots()
if args.target_structure:
target = ftmc.CoarseGrainRNA(args.target_structure)
target_rmsds = []
target_proj_rmsds = []
try:
target_proj = ftmp.Projection2D(target)
except ValueError:
pass
else:
target_vrs = np.array([
x for p in sorted(target_proj._coords.keys())
for x in target_proj._coords[p]
])
for proj in projs:
try:
vrs1 = np.array([
x for p in sorted(proj._coords.keys())
for x in proj._coords[p]
])
prmsd = ftms.rmsd(vrs1, target_vrs)
target_proj_rmsds.append(prmsd)
except:
target_proj_rmsds.append(float("nan"))
target_vrs = target.get_ordered_virtual_residue_poss()
for cg in cgs:
vrs1 = cg.get_ordered_virtual_residue_poss()
cgrmsd = ftms.rmsd(vrs1, target_vrs)
target_rmsds.append(cgrmsd)
xval = np.arange(len(cgs)) * args.step_size
if target_proj_rmsds:
axT.plot(xval,
target_proj_rmsds,
label="Projection",
color="green")
axT.plot(xval, target_rmsds, label="3D", color="blue")
axT.set_title("RMSD to target structure")
axT.set_xlabel("step")
axT.set_ylabel("RMSD")
leg = axT.legend(framealpha=0.8, fancybox=True)
leg.get_frame().set_linewidth(0.0)
plt.subplots_adjust(hspace=0.4)
if args.hausdorff_reference:
ref_img = scipy.ndimage.imread(args.hausdorff_reference)
ref_quarter = (scipy.ndimage.zoom(ref_img, 0.3) > 150)
degrees = get_refimg_longest_axis(ref_img)
global_optima = []
local_optima = []
for cg in cgs:
score, img, params = fph.try_parameters(ref_img,
args.hausdorff_scale, cg,
degrees)
local_optima.append(score)
s, i, params = fph.globally_minimal_distance(
ref_quarter,
args.hausdorff_scale,
cg,
start_points=40,
starting_rotations=degrees,
virtual_atoms=False)
score, img, params = fph.locally_minimal_distance(
ref_img,
args.hausdorff_scale,
cg,
params[1],
params[2],
params[0],
maxiter=200)
global_optima.append(score)
axH.plot(xval, global_optima, label="Global Minimization", color="red")
axH.plot(xval,
local_optima,
label="Local Minimization",
color="lavender")
axH.set_title("Hausdorff Distance to reference image")
axH.set_xlabel("step")
axH.set_ylabel("Hausdorff Distance")
leg = axH.legend(framealpha=0.8, fancybox=True)
leg.get_frame().set_linewidth(0.0)
plt.subplots_adjust(hspace=0.4)
p_rmsds = np.array(list(p_rmsds.items()))
cg_rmsds = np.array(list(cg_rmsds.items()))
ax.plot(p_rmsds[:, 0] * args.step_size,
p_rmsds[:, 1],
label="Projection",
color="green",
marker="o")
ax.plot(cg_rmsds[:, 0] * args.step_size,
cg_rmsds[:, 1],
label="3D",
color="blue",
marker="o")
ax.set_title("Average RMSD between structures X steps apart.")
ax.set_xlabel("steps apart")
ax.set_ylabel("RMSD")
leg = ax.legend(framealpha=0.8, fancybox=True)
leg.get_frame().set_linewidth(0.0)
fig.patch.set_facecolor('white')
if args.save_fig:
with open(args.save_fig, "w") as f:
pickle.dump(fig, f)
plt.show()
def test_rmsd(self):
a1 = np.array([[1., 1., 1.], [0., 0., 0.], [-1., -1., -1.]])
a3 = np.array([[2., 2., 2.], [0., 0., 0.], [-2., -2., -2.]])
self.assertAlmostEqual(ftme.rmsd(a1, a3), math.sqrt(2))
def test_rmsd(self):
a1 = np.array([[1., 1., 1.], [0., 0., 0.], [-1., -1., -1.]])
a3 = np.array([[2., 2., 2.], [0., 0., 0.], [-2., -2., -2.]])
self.assertAlmostEqual(ftme.rmsd(a1, a3), math.sqrt(2))