def get_grads_reps_pca2_tangent(experiment, nreps, nsel, cores, projector):
experiments = {}
dim = experiment.dim
dimnoise = experiment.dimnoise
for i in range(nreps):
experiments[i] = copy.copy(experiment)
experiments[i].M.selected_points = np.random.choice(list(
range(experiment.n)),
nsel,
replace=False)
tangent_bases = experiments[i].M.get_wlpca_tangent_sel(
experiments[i].Mpca, experiments[i].M.selected_points, dimnoise)
subM = RiemannianManifold(
experiments[i].Mpca.data[experiments[i].M.selected_points], dim)
subM.tb = TangentBundle(subM, tangent_bases)
experiments[i].N.tangent_bundle = TangentBundle(
experiments[i].N,
experiments[i].N.geom.rmetric.embedding_eigenvectors)
#experiments[i].df_M = experiments[i].get_dF_js_idM(experiments[i].Mpca, experiments[i].N, subM.tb, experiments[i].N.tangent_bundle,
# experiments[i].M.selected_points,dimnoise)
#experiments[i].df_M = experiments[i].df_M / np.linalg.norm(experiments[i].df_M, axis=1).sum(axis=0)
#experiments[i].df_M2 = experiments[i].df_M / np.linalg.norm(experiments[i].df_M) ** 2
experiments[i].df_M = np.asarray(
[np.identity(dim) for i in range(nsel)])
experiments[i].dg_x = experiments[i].get_dx_g_full(
experiments[i].M.data[experiments[i].M.selected_points])
experiments[i].W = ShapeSpace(experiments[i].positions,
experiments[i].M.data)
experiments[i].dw = experiments[i].W.get_dw(
cores, experiments[i].atoms3, experiments[i].natoms,
experiments[i].M.selected_points)
experiments[i].dg_w = experiments[i].project(
np.swapaxes(experiments[i].dw, 1, 2),
experiments[i].project(experiments[i].dw, experiments[i].dg_x))
experiments[i].dg_w_pca = np.asarray([
np.matmul(projector,
experiments[i].dg_w[j].transpose()).transpose()
for j in range(nsel)
])
experiments[i].dgw_norm = experiments[i].normalize(
experiments[i].dg_w_pca)
# tb_w_tangent_bases = experiment.project(experiment.dw_pca, np.swapaxes(subM.tb.tangent_bases,1,2))
# experiment.dgw_norm = experiment.normalize(experiment.dg_w)
#experiment[i].dg_M = experiment.project(subM.tb.tangent_bases, experiment.dgw_norm)
experiments[i].dg_M = experiments[i].project(subM.tb.tangent_bases,
experiments[i].dgw_norm)
#experiments[i].dw_pca = np.asarray([np.matmul(projector, experiments[i].dw[j]) for j in range(nsel)])
#experiments[i].dg_w = experiments[i].project(experiments[i].dw_pca, np.swapaxes(experiments[i].dg_x_pca,1,2))
#tb_w_tangent_bases = experiments[i].project(experiments[i].dw_pca, np.swapaxes(subM.tb.tangent_bases, 1, 2))
#experiments[i].dw_norm = experiments[i].normalize(experiments[i].dg_w)
#experiments[i].dg_M = experiments[i].project(np.swapaxes(tb_w_tangent_bases, 1, 2), experiments[i].dw_norm)
#experiments[i].coeffs = experiments[i].get_betas_spam2(experiments[i].xtrain, experiments[i].ytrain, experiments[i].groups, lambdas,
# nsel, experiments[i].q, itermax, tol)
return (experiments)
def load_data(self, angles=False):
n = self.n
#d = self.d
dim = self.dim
natoms = self.natoms
atoms3 = self.atoms3
filename_xyz = workingdirectory + '/untracked_data/chemistry_data/eMDA-H-H-Me.Rusinska-Roszak-DB.DFT.PBE-TS.light.MD.500K.99k.R_E_F_D_Q.npz'
#filename_angle_indices = workingdirectory + '/untracked_data/chemistry_data/eMDA-H-H-Me_all2indices.npy'
filename_angle_indices = workingdirectory + '/untracked_data/chemistry_data/eMDA-H-H-Mindices.npy'
#filename_angles = workingdirectory + '/untracked_data/chemistry_data/eMDA-H-H-Me_all2angles.npy'
filename_angles = workingdirectory + '/untracked_data/chemistry_data/eMDA-H-H-Mangles.npy'
data_xyz_loaded = np.load(filename_xyz)
angle_indices = np.load(filename_angle_indices)
n = len(angle_indices)
self.n = n
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
dat = np.load(filename_angles)
d = int(dat.shape[0] * dat.shape[1] / n)
self.d = d
data = np.reshape(dat, (n, d))
data = np.arccos(data)
return (RiemannianManifold(data, dim))
def generate_data(self, n, theta):
self.n = n
d = self.d
xvar = self.xvar
dim = self.dim
noise = self.noise
self.theta = theta
ts = 1.5 * np.pi * (1 +
2 * np.random.uniform(low=0.0, high=1.0, size=n))
x = ts * np.cos(ts)
y = 21 * np.random.uniform(low=0.0, high=1.0, size=n)
self.ys = y
z = ts * np.sin(ts)
self.ts = ts
X = np.vstack((x, y, z))
#X += noise * generator.randn(3, n_samples)
X = X.T
unrotated_data = np.zeros((n, 49))
unrotated_data[:, :3] = X
rotator = special_ortho_group.rvs(49)
#rotator = np.identity(49)
self.rotator = rotator
data = np.matmul(unrotated_data, rotator)
#data = rotator(X,theta)
#data = dup_cols(data, indx=0, num_dups=46)
#data = np.reshape(results, (n, (d)))
return (RiemannianManifold(data, dim))
def load_data(self):
# filename = 'tolueneangles.npz'
atoms3 = self.atoms3
dim = self.dim
# cor = self.cor
# xvar = self.xvar
filename_xyz = workingdirectory + '/untracked_data/chemistry_data/ethanol.mat'
filename_angle_indices = workingdirectory + '/untracked_data/chemistry_data/ethanolindices022119.npy'
data_xyz_loaded = scipy.io.loadmat(filename_xyz)
# print(data_xyz_loaded['R'].shape)
angle_indices = np.load(filename_angle_indices)
self.timeindices = angle_indices
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
filename_angles = workingdirectory + '/untracked_data/chemistry_data/ethanolangles022119.npy'
data = np.reshape(np.load(filename_angles), (50000, 3 * len(atoms3)))
data = np.arccos(data)
# print(positions[0])
# if angles == True:
# p = Pool(cores)
# results = p.map(lambda i: compute3angles(position = positions[i[0],atoms3[i[1]],:]),data_stream(10,84))
# data2 = np.reshape(results, (10,(d)))
# else:
# data = np.reshape(positions,(n,d))
return (RiemannianManifold(data, dim))
def load_data(self):
# filename = 'tolueneangles.npz'
dim = self.dim
n = self.n
atoms3 = self.atoms3
subset = self.subset
# cor = self.cor
# xvar = self.xvar
filename_xyz = '/Users/samsonkoelle/Downloads/aspirin.mat'
filename_angle_indices = '/Users/samsonkoelle/Downloads/aspirinindices020619.npy'
data_xyz_loaded = scipy.io.loadmat(filename_xyz)
# print(data_xyz_loaded['R'].shape)
angle_indices = np.load(filename_angle_indices)
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
filename_angles = '/Users/samsonkoelle/Downloads/aspirinangles020619.npy'
data = np.reshape(np.load(filename_angles), (50000, len(atoms3)*3))
data = np.arccos(data)
data = data[subset]
# print(positions[0])
# if angles == True:
# p = Pool(cores)
# results = p.map(lambda i: compute3angles(position = positions[i[0],atoms3[i[1]],:]),data_stream(10,84))
# data2 = np.reshape(results, (10,(d)))
# else:
# data = np.reshape(positions,(n,d))
return (RiemannianManifold(data, dim))
def get_grads_reps(experiment, nreps, nsel, cores):
experiments = {}
dim = experiment.dim
for i in range(nreps):
experiments[i] = copy.copy(experiment)
experiments[i].M.selected_points = np.random.choice(list(
range(experiment.n)),
nsel,
replace=False)
tangent_bases = experiments[i].M.get_wlpca_tangent_sel(
experiments[i].M, experiments[i].M.selected_points)
subM = RiemannianManifold(
experiments[i].M.data[experiments[i].M.selected_points], dim)
subM.tb = TangentBundle(subM, tangent_bases)
experiments[i].N.tangent_bundle = TangentBundle(
experiments[i].N,
experiments[i].N.geom.rmetric.embedding_eigenvectors)
experiments[i].df_M = experiments[i].get_dF_js_idM(
experiments[i].M, experiments[i].N, subM.tb,
experiments[i].N.tangent_bundle, experiments[i].M.selected_points)
#experiments[i].df_M = experiments[i].df_M / np.linalg.norm(experiments[i].df_M, axis=1).sum(axis=0)
experiments[i].df_M2 = experiments[i].df_M / np.linalg.norm(
experiments[i].df_M)**2
experiments[i].dg_x = experiments[i].get_dx_g_full(
experiments[i].M.data[experiments[i].M.selected_points])
experiments[i].W = ShapeSpace(experiments[i].positions,
experiments[i].M.data)
experiments[i].dw = experiments[i].W.get_dw(
cores, experiments[i].atoms3, experiments[i].natoms,
experiments[i].M.selected_points)
experiments[i].dg_w = experiments[i].project(experiments[i].dw,
experiments[i].dg_x)
tb_w_tangent_bases = experiments[i].project(
experiments[i].dw, np.swapaxes(subM.tb.tangent_bases, 1, 2))
experiments[i].dw_norm = experiments[i].normalize(experiments[i].dg_w)
experiments[i].dg_M = experiments[i].project(
np.swapaxes(tb_w_tangent_bases, 1, 2), experiments[i].dw_norm)
#experiments[i].coeffs = experiments[i].get_betas_spam2(experiments[i].xtrain, experiments[i].ytrain, experiments[i].groups, lambdas,
# nsel, experiments[i].q, itermax, tol)
return (experiments)
def load_data(self, angles=False):
n = self.n
d = self.d
dim = self.dim
natoms = self.natoms
atoms3 = self.atoms3
filename_xyz = workingdirectory + '/untracked_data/chemistry_data/toluene.mat'
filename_angle_indices = workingdirectory + '/untracked_data/chemistry_data/tolueneindices020619.npy'
data_xyz_loaded = scipy.io.loadmat(filename_xyz)
angle_indices = np.load(filename_angle_indices)
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
filename_angles = workingdirectory + '/untracked_data/chemistry_data/tolueneangles020619.npy'
data = np.reshape(np.load(filename_angles), (50000, 50))
data = np.arccos(data)
return (RiemannianManifold(data, dim))
def load_data(self, angles=False):
n = self.n
d = self.d
dim = self.dim
natoms = self.natoms
atoms3 = self.atoms3
filename_xyz = workingdirectory + '/untracked_data/chemistry_data/p-xylene.DFT.PBE-TS.l1t.MD.500K.01.npz'
filename_angle_indices = workingdirectory + '/untracked_data/chemistry_data/p-xyleneindices060319.npy'
data_xyz_loaded = np.load(filename_xyz)
angle_indices = np.load(filename_angle_indices)
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
filename_angles = workingdirectory + '/untracked_data/chemistry_data/p-xyleneangles060319.npy'
data = np.reshape(np.load(filename_angles), (50000, 2448))
data = np.arccos(data)
return (RiemannianManifold(data, dim))
def generate_data(self, n, theta):
self.n = n
d = self.d
xvar = self.xvar
dim = self.dim
noise = self.noise
self.theta = theta
ts = 1.5 * np.pi * (1 +
2 * np.random.uniform(low=0.0, high=1.0, size=n))
x = ts * np.cos(ts)
y = 21 * np.random.uniform(low=0.0, high=1.0, size=n)
z = ts * np.sin(ts)
self.ts = ts
X = np.vstack((x, y, z))
#X += noise * generator.randn(3, n_samples)
X = X.T
data = rotator(X, theta)
#data = np.reshape(results, (n, (d)))
return (RiemannianManifold(data, dim))
def load_data(self):
n = self.n
d = self.d
dim = self.dim
natoms = self.natoms
atoms3 = self.atoms3
angle_indices = self.angle_indices
filename_xyz = xyz
filename_angle_indices = angle_indices
print(filename_xyz[-4:])
if filename_xyz[-4:] == '.mat':
data_xyz_loaded = scipy.io.loadmat(filename_xyz)
if filename_xyz[-4:] == '.npz':
data_xyz_loaded = np.load(filename_xyz)
print(filename_angle_indices)
angle_indices = np.load(filename_angle_indices)
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
filename_angles = angles
data = np.reshape(np.load(filename_angles), (n, 3 * len(atoms3)))
data = np.arccos(data)
return (RiemannianManifold(data, dim))
def load_data(self, angles=False):
n = self.n
#d = self.d
dim = self.dim
natoms = self.natoms
atoms3 = self.atoms3
filename_xyz = workingdirectory + '/untracked_data/chemistry_data/BIPHENYLENEDIOL.fullerene.DFT.PBE-TS.light.MD.500K.102k.R_E_F_D_Q.npz'
filename_angle_indices = workingdirectory + '/untracked_data/chemistry_data/BIPHENYLENEDIOLindices.npy'
filename_angles = workingdirectory + '/untracked_data/chemistry_data/BIPHENYLENEDIOLangles.npy'
data_xyz_loaded = np.load(filename_xyz)
angle_indices = np.load(filename_angle_indices)
n = len(angle_indices)
self.n = n
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
dat = np.load(filename_angles)
d = int(dat.shape[0] * dat.shape[1] / n)
self.d = d
data = np.reshape(dat, (n, d))
data = np.arccos(data)
return (RiemannianManifold(data, dim))
cores = 16 #number of cores for parallel processing
natoms = 26
ii = np.asarray(list(range(natoms)), dtype=int)
jj = np.asarray(list(range(natoms)), dtype=int)
#run experiment
#atoms4 = np.asarray([[9,0,1,2],[0,1,2,3],[1,2,3,4],[2,3,4,5],[3,4,5,6],[4,5,6,1],[5,6,1,0]],dtype = int)
atoms4 = np.asarray([[14, 0, 1, 15], [14, 0, 3, 4], [15, 1, 9, 10],
[9, 1, 15, 0], [3, 0, 14, 1], [0, 15, 14, 1]],
dtype=int)
experiment = BiphenylenediolAngles(dim, n, ii, jj, cores, atoms4)
experiment.M = experiment.load_data(
) #if noise == False then noise parameters are overriden
experiment.Mpca = RiemannianManifold(
np.load(
workingdirectory +
'/untracked_data/chemistry_data/BIPHENYLENEDIOLanglespca_pca50.npy'),
dim)
projector = np.load(
workingdirectory +
'/untracked_data/chemistry_data/BIPHENYLENEDIOLanglespca_pca50_components.npy'
)
folder = workingdirectory + '/Figures/biphenylenediol/' + now
experiment.q = n_components
experiment.dimnoise = dimnoise
n = experiment.n
experiment.Mpca.geom = experiment.Mpca.compute_geom(diffusion_time,
n_neighbors)
experiment.N = experiment.Mpca.get_embedding3(experiment.Mpca.geom,
n_components, diffusion_time,
savename = 'ethanol_013120'
savefolder = 'ethanol'
loadfolder = 'ethanol'
loadname = 'ethanol_013020'
nreps = 5
if new_MN == True:
experiment = EthanolAngles(dim, ii, jj, cores, atoms4)
projector = np.load(
workingdirectory +
'/untracked_data/chemistry_data/ethanolangles022119_pca50_components.npy'
)
experiment.M = experiment.load_data(
) # if noise == False then noise parameters are overriden
experiment.Mpca = RiemannianManifold(
np.load(
workingdirectory +
'/untracked_data/chemistry_data/ethanolangles022119_pca50.npy'),
dim)
experiment.q = n_components
experiment.dimnoise = dimnoise
n = experiment.n
experiment.Mpca.geom = experiment.Mpca.compute_geom(
diffusion_time, n_neighbors)
experiment.N = experiment.Mpca.get_embedding3(experiment.Mpca.geom,
n_components, diffusion_time,
dim)
with open(
workingdirectory + '/untracked_data/embeddings/' + savefolder +
'/' + savename + '.pkl', 'wb') as output:
pickle.dump(experiment, output, pickle.HIGHEST_PROTOCOL)
loadfolder = 'emdahhme'
loadname = 'emdahhme_013020'
nreps = 5
if new_MN == True:
experiment = EmdaHHMAngles(dim, n, ii, jj, cores, atoms4)
projector = np.load(
workingdirectory +
'/untracked_data/chemistry_data/eMDA-H-H-M_anglespca_pca50_components.npy'
)
experiment.M = experiment.load_data(
) # if noise == False then noise parameters are overriden
experiment.Mpca = RiemannianManifold(
np.load(
workingdirectory +
'/untracked_data/chemistry_data/eMDA-H-H-M_anglespca_pca50.npy'),
dim)
experiment.q = n_components
experiment.dimnoise = dimnoise
n = experiment.n
experiment.Mpca.geom = experiment.Mpca.compute_geom(
diffusion_time, n_neighbors)
experiment.N = experiment.Mpca.get_embedding3(experiment.Mpca.geom,
n_components, diffusion_time,
dim)
with open(
workingdirectory + '/untracked_data/embeddings/' + savefolder +
'/' + savename + '.pkl', 'wb') as output:
pickle.dump(experiment, output, pickle.HIGHEST_PROTOCOL)
n_neighbors = 1000 #number of neighbors in megaman n_components = 5 #number of embedding dimensions (diffusion maps) diffusion_time = 5. #diffusion time controls gaussian kernel radius per gradients paper dim = 2 #slow manifold dimension dimnoise = 2 #noise dimension cores = 16 #number of cores for parallel processing natoms = 9 ii = np.asarray(list(range(natoms)), dtype = int) jj = np.asarray(list(range(natoms)), dtype = int) #run experiment #atoms4 = np.asarray([[9,0,1,2],[0,1,2,3],[1,2,3,4],[2,3,4,5],[3,4,5,6],[4,5,6,1],[5,6,1,0]],dtype = int) atoms4 = np.asarray([[5,3,1,0],[3,1,0,6],[4,2,0,1],[8,2,0,6],[7,1,0,6]],dtype = int) experiment = EmdaHHHAngles(dim, n, ii, jj,cores,atoms4) experiment.M = experiment.load_data() #if noise == False then noise parameters are overriden experiment.Mpca = RiemannianManifold(pca_dat, dim) projector = np.load(workingdirectory + '/untracked_data/chemistry_data/eMDA-H-H-H_all2anglespca_pca50_components.npy') folder = workingdirectory + '/Figures/emdahhh/' + now experiment.q = n_components experiment.dimnoise = dimnoise n = experiment.n experiment.Mpca.geom = experiment.Mpca.compute_geom(diffusion_time, n_neighbors) experiment.N = experiment.Mpca.get_embedding3(experiment.Mpca.geom, n_components, diffusion_time, dim) #experiment.g0 = experiment.get_g_full_sub(experiment.M.data,experiment.atoms4[0]) #experiment.g1 = experiment.get_g_full_sub(experiment.M.data,experiment.atoms4[1]) #experiment.g2 = experiment.get_g_full_sub(experiment.M.data,experiment.atoms4[2]) #experiment.g3 = experiment.get_g_full_sub(experiment.M.data,experiment.atoms4[3]) #experiment.g4 = experiment.get_g_full_sub(experiment.M.data,experiment.atoms4[4]) experiment.gs = experiment.get_g_full(experiment.M.data) experiment.g0 = experiment.gs[:,0]
data_xyz_loaded = scipy.io.loadmat(filename_xyz)
if filename_xyz[-4:] == '.npz':
data_xyz_loaded = np.load(filename_xyz)
print(filename_angle_indices)
angle_indices = np.load(filename_angle_indices)
positions = data_xyz_loaded['R'][angle_indices]
self.positions = positions
filename_angles = angles
data = np.reshape(np.load(filename_angles), (n, 3 * len(atoms3)))
data = np.arccos(data)
return (RiemannianManifold(data, dim))
lambdas = np.asarray(np.hstack([np.asarray([0]),np.logspace(lambdamin,lambdamax,nlambdas)]), dtype = np.float16)
experiment = AtomicRegressionLoader( angles,angle_indices, xyz,dim, dimnoise,itermax,tol,lambdas,n_neighbors, n_components, atoms4, ncores, diffusion_time)
experiment.M = experiment.load_data() #if noise == False then noise parameters are overriden
experiment.Mpca = RiemannianManifold(np.load(projected), dim)
experiment.q = n_components
experiment.dimnoise = dimnoise
projector = np.load(pca_projector)
print(n_neighbors, type(n_neighbors), 'nebstuff')
experiment.Mpca.geom = experiment.Mpca.compute_geom(diffusion_time, n_neighbors)
experiment.N = experiment.Mpca.get_embedding3(experiment.Mpca.geom, n_components, diffusion_time, dim)
#experiment.g0 = experiment.get_g_full_sub(experiment.M.data,experiment.atoms4[0])
folder = output_folder + now
os.mkdir(folder)
axislist = list(combinations_with_replacement(list(range(n_components)), 3))
for i in range(len(axislist)):
experiment.N.plot(axislist[i], list(range(n)),np.ones(n),.1,.1, folder + '/' + str(axislist[i]))
#print('pregrad',datetime.datetime.now().strftime("%B_%d_%Y_%H_%M_%S"))
#experiments = get_grads_reps_pca2(experiment, nreps, nsel,cores,projector)
#print('precoeff',datetime.datetime.now().strftime("%B_%d_%Y_%H_%M_%S"))
def generate_data(self, noise=False):
n = self.n
d = self.d
cor = self.cor
xvar = self.xvar
natoms = self.natoms
cores = self.cores
atoms3 = self.atoms3
dim = self.dim
noise = self.noise
positions = np.zeros((n, 9, 3))
# positions[0,0,:] = np.asarray([0.,0.,0.])
# positions[0,1,:] = np.asarray([-10.,0.,0.])
# positions[0,2,:] = np.asarray([1.,10.,0.])
# #positions[0,8,:] = np.asarray([1.,1.,0.])
# positions[0,8,:] = np.asarray([2.,10.,-0])
# positions[0,3,:] = np.asarray([1., np.cos(2/3 * np.pi), np.sin(2/3 * np.pi)])
# positions[0,4,:] = np.asarray([1., np.cos(2/3 * np.pi), np.sin(4/3 * np.pi)])
# positions[0,5,:] = np.asarray([-12.,1.,0.])
# positions[0,6,:] = np.asarray([-12., np.cos(2/3 * np.pi),np.sin(2/3 * np.pi)])
# positions[0,7,:] = np.asarray([-12.,np.cos(2/3 * np.pi), np.sin(4/3 * np.pi)])
positions[0, 0, :] = np.asarray([0., 0., 0.])
positions[0, 1, :] = np.asarray([-10., 0., np.sqrt(2) / 100])
positions[0, 2, :] = np.asarray([0., 10., np.sqrt(3) / 100])
#positions[0,8,:] = np.asarray([1.,1.,0.])
positions[0, 8, :] = np.asarray([1., 10., np.sqrt(5) / 100])
positions[0, 3, :] = np.asarray(
[np.sqrt(7) / 100,
np.cos(2 / 3 * np.pi),
np.sin(2 / 3 * np.pi)])
positions[0, 4, :] = np.asarray(
[np.sqrt(11) / 100,
np.cos(2 / 3 * np.pi),
np.sin(4 / 3 * np.pi)])
positions[0, 5, :] = np.asarray([-11., 1., np.sqrt(13) / 100])
positions[0, 6, :] = np.asarray(
[-11., np.cos(2 / 3 * np.pi),
np.sin(2 / 3 * np.pi)])
positions[0, 7, :] = np.asarray(
[-11., np.cos(2 / 3 * np.pi),
np.sin(4 / 3 * np.pi)])
angles1 = np.tile(
np.linspace(start=0.,
stop=2 * math.pi,
num=int(np.sqrt(n)),
endpoint=False), int(np.sqrt(n)))
angles2 = np.repeat(
np.linspace(start=0.,
stop=2 * math.pi,
num=int(np.sqrt(n)),
endpoint=False), int(np.sqrt(n)))
for i in range(1, n):
rotationmatrix1 = np.zeros((3, 3))
rotationmatrix1[1, 1] = 1
rotationmatrix1[0, 0] = np.cos(angles1[i])
rotationmatrix1[0, 2] = -np.sin(angles1[i])
rotationmatrix1[2, 2] = np.cos(angles1[i])
rotationmatrix1[2, 0] = np.sin(angles1[i])
rotationmatrix2 = np.zeros((3, 3))
rotationmatrix2[0, 0] = 1
rotationmatrix2[1, 1] = np.cos(angles2[i])
rotationmatrix2[1, 2] = -np.sin(angles2[i])
rotationmatrix2[2, 2] = np.cos(angles2[i])
rotationmatrix2[2, 1] = np.sin(angles2[i])
positions[i,
np.asarray([3, 4]), :] = positions[0,
np.asarray([3, 4]), :]
positions[i, np.asarray([2, 8]), :] = np.matmul(
rotationmatrix1,
positions[0, np.asarray([2, 8]), :].transpose()).transpose()
positions[i, np.asarray([1, 5, 6, 7]), :] = np.matmul(
rotationmatrix2, positions[
0, np.asarray([1, 5, 6, 7]), :].transpose()).transpose()
covariance = np.identity(natoms)
for i in range(natoms):
for j in range(natoms):
if i != j:
covariance[i, j] = cor
covariance = xvar * covariance
if noise == True:
for i in range(n):
for j in range(3):
positions[i, :, j] = np.random.multivariate_normal(
positions[i, :, j], covariance, size=1)
self.positions = positions
p = Pool(cores)
results = p.map(
lambda i: compute3angles(position=positions[i[0], atoms3[i[1]], :]
), data_stream(10000, 84))
data = np.reshape(results, (n, (d)))
svd = TruncatedSVD(n_components=50)
svd.fit(data)
data_pca = svd.transform(data)
return (RiemannianManifold(data, dim),
RiemannianManifold(data_pca, dim), svd.components_)
