def test_pca_noref_nofit(self):
'''no reference and do not do fitting
from drroe: " Also, not fitting at all should be considered a legitimate option -
you may want to include global rotational and translational motion in your eigenvectors."
pytraj: pt.pca(traj, mask, n_vecs=2, fit=False)
'''
command = '''
parm data/tz2.parm7
trajin data/tz2.nc
matrix covar name MyMatrix !@H=
createcrd CRD1
run
# Step three. Diagonalize matrix.
runanalysis diagmatrix MyMatrix vecs 2 name MyEvecs
# Step four. Project saved fit coordinates along eigenvectors 1 and 2
crdaction CRD1 projection evecs MyEvecs !@H= out project.dat beg 1 end 2
'''
traj = pt.load("data/tz2.nc", "data/tz2.parm7")
# no reference
state = pt.load_cpptraj_state(command)
state.run()
mask = '!@H='
data = pt.pca(traj, mask, n_vecs=2, fit=False)
data_ref = pt.pca(traj, mask, n_vecs=2, fit=False, ref=3, ref_mask='@CA')
cpp_data = state.data[-2:].values
# use absolute values
aa_eq(np.abs(data[0]), np.abs(cpp_data), decimal=3)
# if fit=True, ref will be ignored
aa_eq(np.abs(data_ref[0]), np.abs(cpp_data), decimal=3)
def test_traj_on_disk_fit_to_given_reference(self):
"""test_traj_on_disk_fit_to_given_reference
"""
fit = True
traj_on_disk = pt.iterload(fn('tz2.nc'), fn('tz2.parm7'))
traj_on_mem = pt.load(fn('tz2.nc'), fn('tz2.parm7'))
ref0 = traj_on_disk[0]
ref1 = traj_on_mem[0]
data0, _ = pt.pca(traj_on_disk,
mask='@CA',
n_vecs=2,
fit=fit,
ref=ref0)
data1, _ = pt.pca(traj_on_mem, mask='@CA', n_vecs=2, fit=fit, ref=ref1)
aa_eq(np.abs(data0), np.abs(data1))
# try again
# https://github.com/Amber-MD/pytraj/issues/1452
data2, _ = pt.pca(traj_on_disk,
mask='@CA',
n_vecs=2,
fit=fit,
ref=ref0)
aa_eq(np.abs(data0), np.abs(data2))
def test_pca_with_ref_with_different_mask_from_matrix(self):
'''has reference. Use !@H= for ref_mask and use * for covariance matrix and projection
from drroe: "You should be able to supply separate masks for fitting and creating the covariance matrix
It is common enough for example to only perform rms-fitting on heavy atoms while still wanting all atoms in eigenvectors."
pytraj: pt.pca(traj, mask=mask_matrix, n_vecs=2, ref=ref, ref_mask=mask_ref)
'''
command_ref_provided = '''
parm data/tz2.parm7
trajin data/tz2.nc
reference data/tz2.rst7
# only perform fitting on heavy atoms
rms reference !@H=
# all atoms
matrix covar name MyMatrix *
createcrd CRD1
run
# Step three. Diagonalize matrix.
runanalysis diagmatrix MyMatrix vecs 2 name MyEvecs
# Step four. Project saved fit coordinates along eigenvectors 1 and 2
# all atoms
crdaction CRD1 projection evecs MyEvecs * out project.dat beg 1 end 2
'''
traj = pt.load("data/tz2.nc", "data/tz2.parm7")
ref = pt.load('data/tz2.rst7', traj.top)
state = pt.load_cpptraj_state(command_ref_provided)
state.run()
mask_ref = '!@H='
mask_matrix = '*'
data = pt.pca(traj,
mask=mask_matrix,
n_vecs=2,
ref=ref,
ref_mask=mask_ref)
cpp_data = state.data[-2:].values
# use absolute values
aa_eq(np.abs(data[0]), np.abs(cpp_data), decimal=3)
def test_pca_with_ref_with_different_mask_from_matrix(self):
'''has reference. Use !@H= for ref_mask and use * for covariance matrix and projection
from drroe: "You should be able to supply separate masks for fitting and creating the covariance matrix
It is common enough for example to only perform rms-fitting on heavy atoms while still wanting all atoms in eigenvectors."
pytraj: pt.pca(traj, mask=mask_matrix, n_vecs=2, ref=ref, ref_mask=mask_ref)
'''
command_ref_provided = '''
parm data/tz2.parm7
trajin data/tz2.nc
reference data/tz2.rst7
# only perform fitting on heavy atoms
rms reference !@H=
# all atoms
matrix covar name MyMatrix *
createcrd CRD1
run
# Step three. Diagonalize matrix.
runanalysis diagmatrix MyMatrix vecs 2 name MyEvecs
# Step four. Project saved fit coordinates along eigenvectors 1 and 2
# all atoms
crdaction CRD1 projection evecs MyEvecs * out project.dat beg 1 end 2
'''
traj = pt.load("data/tz2.nc", "data/tz2.parm7")
ref = pt.load('data/tz2.rst7', traj.top)
state = pt.load_cpptraj_state(command_ref_provided)
state.run()
mask_ref = '!@H='
mask_matrix = '*'
data = pt.pca(traj, mask=mask_matrix, n_vecs=2, ref=ref, ref_mask=mask_ref)
cpp_data = state.data[-2:].values
# use absolute values
aa_eq(np.abs(data[0]), np.abs(cpp_data), decimal=3)
def test_pca_noref(self):
'''test_pca_noref: no reference
pytraj: pt.pca(traj, mask, n_vecs=2)
'''
command = '''
# Step one. Generate average structure.
# RMS-Fit to first frame to remove global translation/rotation.
parm {tz2_top}
trajin {tz2_trajin}
rms first !@H=
average crdset AVG
run
# Step two. RMS-Fit to average structure. Calculate covariance matrix.
# Save the fit coordinates.
rms ref AVG !@H=
matrix covar name MyMatrix !@H=
createcrd CRD1
run
# Step three. Diagonalize matrix.
runanalysis diagmatrix MyMatrix vecs 2 name MyEvecs
# Step four. Project saved fit coordinates along eigenvectors 1 and 2
crdaction CRD1 projection evecs MyEvecs !@H= out project.dat beg 1 end 2
'''.format(
tz2_top=tz2_top, tz2_trajin=tz2_trajin)
traj = pt.load(fn('tz2.nc'), fn('tz2.parm7'))
# no reference
state = pt.load_cpptraj_state(command)
state.run()
mask = '!@H='
data = pt.pca(traj, mask, n_vecs=2)
cpp_data = state.data[-2:].values
# use absolute values
aa_eq(np.abs(data[0]), np.abs(cpp_data), decimal=3)
def test_pca_noref(self):
'''no reference
pytraj: pt.pca(traj, mask, n_vecs=2)
'''
command = '''
# Step one. Generate average structure.
# RMS-Fit to first frame to remove global translation/rotation.
parm data/tz2.parm7
trajin data/tz2.nc
rms first !@H=
average crdset AVG
run
# Step two. RMS-Fit to average structure. Calculate covariance matrix.
# Save the fit coordinates.
rms ref AVG !@H=
matrix covar name MyMatrix !@H=
createcrd CRD1
run
# Step three. Diagonalize matrix.
runanalysis diagmatrix MyMatrix vecs 2 name MyEvecs
# Step four. Project saved fit coordinates along eigenvectors 1 and 2
crdaction CRD1 projection evecs MyEvecs !@H= out project.dat beg 1 end 2
'''
traj = pt.load("data/tz2.nc", "data/tz2.parm7")
# no reference
state = pt.load_cpptraj_state(command)
state.run()
mask = '!@H='
data = pt.pca(traj, mask, n_vecs=2)
cpp_data = state.data[-2:].values
# use absolute values
aa_eq(np.abs(data[0]), np.abs(cpp_data), decimal=3)
def test_pca_with_ref(self):
'''has reference
from drroe: "If the user provides their own reference structure, do not create an average structure"
pytraj: pt.pca(traj, mask, n_vecs=2, ref=ref)
'''
command_ref_provided = '''
parm data/tz2.parm7
trajin data/tz2.nc
reference data/tz2.rst7
rms reference !@H=
matrix covar name MyMatrix !@H=
createcrd CRD1
run
# Step three. Diagonalize matrix.
runanalysis diagmatrix MyMatrix vecs 2 name MyEvecs
# Step four. Project saved fit coordinates along eigenvectors 1 and 2
crdaction CRD1 projection evecs MyEvecs !@H= out project.dat beg 1 end 2
'''
traj = pt.load("data/tz2.nc", "data/tz2.parm7")
ref = pt.load('data/tz2.rst7', traj.top)
state = pt.load_cpptraj_state(command_ref_provided)
state.run()
mask = '!@H='
data = pt.pca(traj, mask, n_vecs=2, ref=ref)
cpp_data = state.data[-2:].values
# use absolute values
aa_eq(np.abs(data[0]), np.abs(cpp_data), decimal=3)
def test_pca_with_ref(self):
'''has reference
from drroe: "If the user provides their own reference structure, do not create an average structure"
pytraj: pt.pca(traj, mask, n_vecs=2, ref=ref)
'''
command_ref_provided = '''
parm data/tz2.parm7
trajin data/tz2.nc
reference data/tz2.rst7
rms reference !@H=
matrix covar name MyMatrix !@H=
createcrd CRD1
run
# Step three. Diagonalize matrix.
runanalysis diagmatrix MyMatrix vecs 2 name MyEvecs
# Step four. Project saved fit coordinates along eigenvectors 1 and 2
crdaction CRD1 projection evecs MyEvecs !@H= out project.dat beg 1 end 2
'''
traj = pt.load("data/tz2.nc", "data/tz2.parm7")
ref = pt.load('data/tz2.rst7', traj.top)
state = pt.load_cpptraj_state(command_ref_provided)
state.run()
mask = '!@H='
data = pt.pca(traj, mask, n_vecs=2, ref=ref)
cpp_data = state.data[-2:].values
# use absolute values
aa_eq(np.abs(data[0]), np.abs(cpp_data), decimal=3)
def test_pca_raise(self):
traj = pt.iterload('data/tz2.nc', 'data/tz2.parm7')
self.assertRaises(ValueError,
lambda: pt.pca(traj, n_vecs=2, mask='@CA'))
def test_pca_raise(self):
traj = pt.iterload('data/tz2.nc', 'data/tz2.parm7')
self.assertRaises(ValueError, lambda: pt.pca(traj, n_vecs=2, mask='@CA'))
def test_raises(self):
frame = pt.iterload(fn('tz2.nc'), fn('tz2.parm7'))[0]
with pytest.raises(ValueError):
pt.pca(frame, mask='@CA')
import pytraj as pt
traj = pt.load('../tests/data/tz2.nc', '../tests/data/tz2.parm7')
data = pt.pca(traj, mask='@CA', n_vecs=3)
print(pt.pca.__doc__)
print('##################')
print('output')
print(data)
def main():
traj = pt.load(args.traj, args.parm)
rnd_iter = args.riter
rnd_vecs = args.evec
pairs = list()
if args.mask_proj == None:
args.mask_proj = args.mask
print "Mask : ", args.mask
print "Mask proj: ", args.mask_proj
if rnd_vecs < 1:
rnd_vecs = 3 * traj[args.mask].xyz.shape[1] - 6
#make pairs
for n_i in range(rnd_vecs):
for n_j in range(rnd_vecs):
if n_i < n_j:
pairs.append((n_i, n_j))
sele = pt.select(traj.top, args.mask)
sele_txt = ""
for s_i, s in enumerate(sele):
sele_txt += "%d %s\n" % (s_i, traj.top.atomlist[s])
o = open("%s_sele.dat" % args.prefix, "w")
o.write(sele_txt)
o.close()
n_vecs = rnd_vecs
pca_data, eigen = pt.pca(traj[args.start:], mask=args.mask, n_vecs=n_vecs)
eigen_val = eigen[0]
eigen_vec = eigen[1]
np.savetxt("%s_eigen_vec.dat" % args.prefix,
np.c_[eigen_vec[0], eigen_vec[1], eigen_vec[2]])
np.savetxt("%s_pcadata.dat" % args.prefix, pca_data.T)
#h = hist(pca_data[0], pca_data[1])
#h.plot2d(xlab="PC1 [$\AA$]", ylab="PC2 [$\AA$]", title="PCA", name=args.out)
# Plot PCA
for pc_i, pc_j in pairs:
plt.scatter(pca_data[pc_i],
pca_data[pc_j],
marker='o',
c="r",
alpha=0.5)
plt.xlabel("PC%d [$\AA$]" % pc_i)
plt.ylabel("PC%d [$\AA$]" % pc_j)
plt.title("PCA PC%d vs. PC%d" % (pc_i, pc_j))
plt.savefig("PC%d-vs-PC%s_%s.png" % (pc_i, pc_j, args.prefix))
plt.close('all')
# Plot atom contritbuion
for pc_i in range(3):
l = eigen_vec[pc_i].shape[0]
c = np.linalg.norm(eigen_vec[pc_i].reshape((l / 3, 3)), axis=1)
a = np.arange(l / 3) + 1
plt.plot(a, c, label="PC%s" % pc_i, alpha=0.5)
plt.legend()
plt.xlim(0, l / 3 + 1)
plt.xlabel("Atom ID")
plt.ylabel("Eigenvector components")
plt.title("Eigenvectors")
plt.savefig("Eigenvectors_%s.png" % args.prefix)
plt.close('all')
total_var = np.sum(eigen_val)
plt.scatter(range(1, n_vecs + 1), (np.cumsum(eigen_val) / total_var) * 100,
label="Cumulative Variance")
plt.plot(range(1, n_vecs + 1), (eigen_val / total_var) * 100,
"g--",
label="Variance")
plt.legend()
#plt.xticks(range(1, n_vecs+1, 2))
plt.xlabel("Eigenvector #")
plt.ylabel("Variance explained [%]")
plt.title("Variance explained by PC Eigenvectors")
plt.savefig("Variance_%s.png" % args.prefix, dpi=1000)
plt.close('all')
if args.traj_proj != None and args.parm_proj != None:
traj_proj = pt.load(args.traj_proj, args.parm_proj)
pt.rmsd(traj_proj, mask=args.mask_proj)
#avg_proj = pt.mean_structure(traj_proj, mask=args.mask)
#pt.rmsd(traj_proj, mask=args.mask, ref=avg_proj)
projection_data = pt.projection(traj_proj[args.start_proj:], args.mask_proj, eigenvalues=eigen_val,\
eigenvectors=eigen_vec,\
scalar_type='covar')
np.savetxt("%s_pcadata_proj.dat" % args.prefix, projection_data.T)
#h = hist(projection_data[0], projection_data[1])
#h.plot2d(xlab="PC1 [$\AA$]", ylab="PC2 [$\AA$]", title="PCA projection", name=args.out_proj)
for pc_i, pc_j in pairs:
plt.scatter(pca_data[pc_i],
pca_data[pc_j],
marker='o',
c="r",
alpha=0.5)
plt.scatter(projection_data[pc_i],
projection_data[pc_j],
marker='o',
c="g",
alpha=0.5)
plt.xlabel("PC%d [$\AA$]" % pc_i)
plt.ylabel("PC%d [$\AA$]" % pc_j)
plt.title("PCA PC%d vs. PC%d with projection" % (pc_i, pc_j))
plt.savefig("PC%d-vs-PC%s_%s_projection.png" %
(pc_i, pc_j, args.prefix))
plt.close('all')
plt.scatter(projection_data[pc_i],
projection_data[pc_j],
marker='o',
c="g",
alpha=0.5)
plt.xlabel("PC%d [$\AA$]" % pc_i)
plt.ylabel("PC%d [$\AA$]" % pc_j)
plt.title("PCA PC%d vs. PC%d only projection" % (pc_i, pc_j))
plt.savefig("PC%d-vs-PC%d_%s_only_projection.png" %
(pc_i, pc_j, args.prefix))
plt.close('all')
pca_data_2, eigen_2 = pt.pca(traj_proj[args.start_proj:],
mask=args.mask_proj,
n_vecs=n_vecs)
eigen_val_2 = eigen_2[0]
eigen_vec_2 = eigen_2[1]
overlap = 0
for pc_i in range(rnd_vecs):
for pc_j in range(rnd_vecs):
overlap += (np.dot(eigen_vec[pc_i], eigen_vec_2[pc_j]) /
(np.linalg.norm(eigen_vec[pc_i]) *
np.linalg.norm(eigen_vec_2[pc_j])))**2
overlap /= rnd_vecs
print "Vector space spanned by traj-1 overlap with traj-2 subspace (%d vecs): %6.3f" % (
rnd_vecs, overlap)
if args.zscore != None:
overlap_rnd = np.zeros(rnd_iter)
for r in range(rnd_iter):
### make random traj
t1_rnd = traj
for f in range(t1_rnd.xyz[args.start:].shape[0]):
idxs = np.arange(t1_rnd.xyz[args.start + f, ].shape[0])
sele = np.random.permutation(idxs)
t1_rnd[f] = t1_rnd.xyz[args.start + f, ][sele]
pca_t1_rnd, eigen_t1_rnd = pt.pca(t1_rnd[args.start:],
mask=args.mask,
n_vecs=n_vecs)
eigen_vec_1_rnd = eigen_t1_rnd[1]
for pc_i in range(n_vecs):
for pc_j in range(n_vecs):
overlap_rnd[r] += (
np.dot(eigen_vec[pc_i], eigen_vec_1_rnd[pc_j]) /
(np.linalg.norm(eigen_vec[pc_i]) *
np.linalg.norm(eigen_vec_1_rnd[pc_j])))**2
overlap_rnd[r] /= n_vecs
z_score = (overlap - np.mean(overlap_rnd)) / np.std(overlap_rnd)
print "Z-score : %6.3f" % z_score
def main():
X = pt.load(args.traj, args.parm, stride=args.stride)
if args.pca == "no":
X = X[args.mask].xyz[args.start:]
shape = X.shape
X = X.reshape((shape[0], shape[1] * 3))
else:
n_vecs = 3 * X[args.mask].xyz[args.start:].shape[1] - 6
pca_data, eigen = pt.pca(X[args.start:], n_vecs=n_vecs, mask=args.mask)
eigen_val = eigen[0]
eigen_vec = eigen[1]
np.savetxt("%s_eigen_vec.dat" % args.prefix,
np.c_[eigen_vec[0], eigen_vec[1], eigen_vec[2]])
pairs = list()
#make pairs
for n_i in range(3):
for n_j in range(3):
if n_i < n_j:
pairs.append((n_i, n_j))
# Plot PCA
for pc_i, pc_j in pairs:
plt.scatter(pca_data[pc_i],
pca_data[pc_j],
marker='o',
c="r",
alpha=0.5)
plt.xlabel("PC%d [$\AA$]" % pc_i)
plt.ylabel("PC%d [$\AA$]" % pc_j)
plt.title("PCA PC%d vs. PC%d" % (pc_i, pc_j))
plt.savefig("PC%d-vs-PC%s_%s.png" % (pc_i, pc_j, args.prefix),
dpi=1000)
plt.close('all')
# Plot atom contritbuion
for pc_i in range(3):
l = eigen_vec[pc_i].shape[0]
c = np.linalg.norm(eigen_vec[pc_i].reshape((l / 3, 3)), axis=1)
a = np.arange(l / 3) + 1
plt.plot(a, c, label="PC%s" % pc_i, alpha=0.5)
plt.legend()
plt.xlim(0, l / 3 + 1)
plt.xlabel("Atom ID")
plt.ylabel("Eigenvector components")
plt.title("Eigenvectors")
plt.savefig("Eigenvectors_%s.png" % args.prefix, dpi=1000)
plt.close('all')
total_var = np.sum(eigen_val)
plt.scatter(range(1, n_vecs + 1),
(np.cumsum(eigen_val) / total_var) * 100,
label="Cumulative Variance")
plt.plot(range(1, n_vecs + 1), (eigen_val / total_var) * 100,
"g--",
label="Eigenvector Variance")
plt.legend()
#plt.xticks(range(1, n_vecs+1, 2))
plt.xlabel("Eigenvector #")
plt.ylabel("Fractional of Variance explained [%]")
plt.title("Explained total variance explained by PCA")
plt.savefig("Variance_%s.png" % args.prefix, dpi=1000)
plt.close('all')
X = pca_data
range_n_clusters = range(2, 20)
for n_clusters in range_n_clusters:
# Create a subplot with 1 row and 2 columns
if args.pca == "yes":
fig, (ax1, ax2) = plt.subplots(1, 2)
fig.set_size_inches(18, 7)
else:
fig, (ax1, ax2) = plt.subplots(1, 1)
# The 1st subplot is the silhouette plot
# The silhouette coefficient can range from -1, 1 but in this example all
# lie within [-0.1, 1]
ax1.set_xlim([-0.1, 1])
# The (n_clusters+1)*10 is for inserting blank space between silhouette
# plots of individual clusters, to demarcate them clearly.
ax1.set_ylim([0, len(X) + (n_clusters + 1) * 10])
# Initialize the clusterer with n_clusters value and a random generator
# seed of rand for reproducibility.
rand = np.random.randint(99999)
print("Random seed is %d." % rand)
clusterer = KMeans(n_clusters=n_clusters, random_state=rand)
cluster_labels = clusterer.fit_predict(X)
# The silhouette_score gives the average value for all the samples.
# This gives a perspective into the density and separation of the formed
# clusters
silhouette_avg = silhouette_score(X, cluster_labels)
print("For n_clusters =", n_clusters,
"The average silhouette_score is :", silhouette_avg)
# Compute the silhouette scores for each sample
sample_silhouette_values = silhouette_samples(X, cluster_labels)
y_lower = 10
for i in range(n_clusters):
# Aggregate the silhouette scores for samples belonging to
# cluster i, and sort them
ith_cluster_silhouette_values = \
sample_silhouette_values[cluster_labels == i]
ith_cluster_silhouette_values.sort()
size_cluster_i = ith_cluster_silhouette_values.shape[0]
y_upper = y_lower + size_cluster_i
color = cm.spectral(float(i) / n_clusters)
ax1.fill_betweenx(np.arange(y_lower, y_upper),
0,
ith_cluster_silhouette_values,
facecolor=color,
edgecolor=color,
alpha=0.7)
# Label the silhouette plots with their cluster numbers at the middle
ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))
# Compute the new y_lower for next plot
y_lower = y_upper + 10 # 10 for the 0 samples
ax1.set_title("The silhouette plot for the various clusters.")
ax1.set_xlabel("The silhouette coefficient values")
ax1.set_ylabel("Cluster label")
# The vertical line for average silhouette score of all the values
ax1.axvline(x=silhouette_avg, color="red", linestyle="--")
ax1.set_yticks([]) # Clear the yaxis labels / ticks
ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])
if args.pca == "yes":
# 2nd Plot showing the actual clusters formed
colors = cm.spectral(cluster_labels.astype(float) / n_clusters)
ax2.scatter(X[:, 0],
X[:, 1],
marker='.',
s=30,
lw=0,
alpha=0.7,
c=colors)
# Labeling the clusters
centers = clusterer.cluster_centers_
# Draw white circles at cluster centers
ax2.scatter(centers[:, 0],
centers[:, 1],
marker='o',
c="white",
alpha=1,
s=200)
for i, c in enumerate(centers):
ax2.scatter(c[0], c[1], marker='$%d$' % i, alpha=1, s=50)
ax2.set_title("The visualization of the clustered data.")
ax2.set_xlabel("Feature space for the 1st feature")
ax2.set_ylabel("Feature space for the 2nd feature")
plt.suptitle(
("Silhouette analysis for KMeans clustering on sample data "
"with n_clusters = %d" % n_clusters),
fontsize=14,
fontweight='bold')
plt.savefig("%s_silhouette_n=%d.png" % (args.prefix, n_clusters),
dpi=1000)
plt.close('all')
