def test_restart(self):
A = np.array([[1, 1, 0],
[1, 1, 1],
[0, 1, 1]])
# Do 3 iterations on A and gather the result
try:
Y = nearcorr(A, max_iterations=3)
except nearest_correlation.ExceededMaxIterationsError as e:
result3 = np.copy(e.matrix)
# Do 1 iteration on A
try:
X = nearcorr(A, max_iterations=1)
except nearest_correlation.ExceededMaxIterationsError as e:
restart = e
# restart from previous result and do another iteration
try:
X = nearcorr(restart, max_iterations=1)
except nearest_correlation.ExceededMaxIterationsError as e:
restart = e
# restart from previous result and do another iteration
try:
X = nearcorr(restart, max_iterations=1)
except nearest_correlation.ExceededMaxIterationsError as e:
result1 = e.matrix
self.assertTrue(np.all(result1 == result3))
def test_restart(self):
A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]])
# Do 3 iterations on A and gather the result
try:
Y = nearcorr(A, max_iterations=3)
except nearest_correlation.ExceededMaxIterationsError as e:
result3 = np.copy(e.matrix)
# Do 1 iteration on A
try:
X = nearcorr(A, max_iterations=1)
except nearest_correlation.ExceededMaxIterationsError as e:
restart = e
# restart from previous result and do another iteration
try:
X = nearcorr(restart, max_iterations=1)
except nearest_correlation.ExceededMaxIterationsError as e:
restart = e
# restart from previous result and do another iteration
try:
X = nearcorr(restart, max_iterations=1)
except nearest_correlation.ExceededMaxIterationsError as e:
result1 = e.matrix
self.assertTrue(np.all(result1 == result3))
def generate_cov_mat(size):
""" Generates a random size x size correlation matrix
Parameters
----------
size : int
Dimension of the square correlation matrix
Returns
----------
A : numpy.ndarray
Correlation matrix
"""
P = np.zeros((size, size))
for k in range(size):
for i in range(size):
if k == i:
P[k][i] = 1
elif k < i:
P[k][i] = random.uniform(-1, 1)
else:
P[k][i] = P[i][k]
A = nearcorr(P,
tol=[],
flag=0,
max_iterations=50000,
n_pos_eig=0,
weights=None,
verbose=False,
except_on_too_many_iterations=True)
return A
def test_HighamExample2002(self):
A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]])
X = nearcorr(A)
expected_result = np.array([[1., 0.76068985, 0.15729811],
[0.76068985, 1., 0.76068985],
[0.15729811, 0.76068985, 1.]])
self.assertTrue((np.abs((X - expected_result)) < 1e-8).all())
def test_Weights(self):
A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]])
weights = np.array([1, 2, 3])
X = nearcorr(A, weights=weights)
expected_result = np.array([[1., 0.66774961, 0.16723692],
[0.66774961, 1., 0.84557496],
[0.16723692, 0.84557496, 1.]])
self.assertTrue((np.abs((X - expected_result)) < 1e-8).all())
def test_NAGExample(self):
A = np.array([[2, -1, 0, 0], [-1, 2, -1, 0], [0, -1, 2, -1],
[0, 0, -1, 2]])
X = nearcorr(A)
expected_result = np.array([[1., -0.8084125, 0.1915875, 0.10677505],
[-0.8084125, 1., -0.65623269, 0.1915875],
[0.1915875, -0.65623269, 1., -0.8084125],
[0.10677505, 0.1915875, -0.8084125, 1.]])
self.assertTrue((np.abs((X - expected_result)) < 1e-8).all())
def test_HighamExample2002(self):
A = np.array([[1, 1, 0],
[1, 1, 1],
[0, 1, 1]])
X = nearcorr(A)
expected_result = np.array([[ 1. , 0.76068985, 0.15729811],
[ 0.76068985, 1. , 0.76068985],
[ 0.15729811, 0.76068985, 1. ]])
self.assertTrue((np.abs((X - expected_result)) < 1e-8).all())
def test_Weights(self):
A = np.array([[1, 1, 0],
[1, 1, 1],
[0, 1, 1]])
weights = np.array([1,2,3])
X = nearcorr(A, weights = weights)
expected_result = np.array([[ 1. , 0.66774961, 0.16723692],
[ 0.66774961, 1. , 0.84557496],
[ 0.16723692, 0.84557496, 1. ]])
self.assertTrue((np.abs((X - expected_result)) < 1e-8).all())
def test_NAGExample(self):
A = np.array([[2, -1, 0, 0],
[-1, 2, -1, 0],
[0, -1, 2, -1],
[0, 0, -1, 2]])
X = nearcorr(A)
expected_result = np.array([[ 1. , -0.8084125 , 0.1915875 , 0.10677505],
[-0.8084125 , 1. , -0.65623269, 0.1915875 ],
[ 0.1915875 , -0.65623269, 1. , -0.8084125 ],
[ 0.10677505, 0.1915875 , -0.8084125 , 1. ]])
self.assertTrue((np.abs((X - expected_result)) < 1e-8).all())
def test_ExceededMaxIterationsFalse(self):
A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]])
X = nearcorr(A, max_iterations=10, except_on_too_many_iterations=False)
def re():
#tm = np.load("TM_score_matrix.npy")
#tm = np.loadtxt("../Datasets/Fold_representation/TM_score/Gram_Matrix/TM_matrix/TM_matrix.fa")
tm = np.load("TM_matrix_2_pdbs-noTER_symmetric.npy")
print(tm.shape)
#tm = tm + np.identity(len(tm))*2.50
model = eigen()
tm_flat = np.reshape(tm, (-1, ))
print("original:", np.mean(tm_flat), np.std(tm_flat))
#plot_hist(tm_flat, "original")
from nearest_correlation import nearcorr
print(
"Frobenius norm:",
np.linalg.norm(tm - nearcorr(tm, max_iterations=2000, tol=[1E-5]),
'fro'))
tm = nearcorr(tm, max_iterations=2000, tol=[1E-5])
#tm = tm + np.identity(len(tm))*0.001
#print ("w", np.mean(w), np.std(w), np.min(w))
w, v = model.fit(tm)
print("w", np.mean(w), np.std(w), np.min(w))
tm_flat1 = np.reshape(tm, (-1, ))
print("before_centralized", np.mean(tm_flat1), np.std(tm_flat1))
#plot_hist(tm_flat1, "before_centralized")
print(sum(w[0:20]) / sum(w))
tm = model.center(tm, tm)
#tm = tm + np.identity(len(tm))*0.000001
tm = tm + np.identity(len(tm)) * 0.001
tm_flat2 = np.reshape(tm, (-1, ))
print("after centerlized", np.mean(tm_flat2), np.std(tm_flat2))
#plot_hist(tm_flat, tm_flat1, tm_flat2, "original", "before_centralized", "after_centralized")
#plot_relation(tm_flat, tm_flat1, tm_flat2, "original", "before_centralized", "after_centralized")
w, v = model.fit(tm)
print("w", np.mean(w), np.std(w), np.min(w))
print(sum(w[0:20]) / sum(w))
'''
sum_ne=0
for i in range(len(tm)):
if(w[i]<0):
w[i]=0.001
sum_ne+=1
#print (sum_ne, np.linalg.norm(v[0]), np.linalg.norm(v[33]))
tm_flat = np.reshape(tm, (-1,))
print ("previous", np.mean(tm_flat), np.std(tm_flat))
tm = np.zeros((len(tm), len(tm)))
for i in range(len(tm)):
ttt=np.reshape(v[i], (1, len(tm)))
y = np.multiply(ttt.T, ttt*w[i])
tm+=y
# geting the new tm matrix after truncation
tm = model.center(tm,tm)
w,v = model.fit(tm)
tm_flat = np.reshape(tm, (-1,))
print ("now", np.mean(tm_flat), np.std(tm_flat))
'''
np.save("../Results/eigenvalues", np.array(w))
np.save("../Results/eigenvectors", np.array(v))
#w=np.load("Results/eigenvalues.npy")
#v=np.load("Results/eigenvectors.npy")
print(sum(w[0:20]) / sum(w))
print("min:", min(w))
import matplotlib.pyplot as plt
plt.figure()
z1 = np.linspace(-500, 20)
z = np.linspace(0, 1.1)
x = np.arange(0, 1232, 1)
for i in range(len(x)):
plt.scatter(x[i], np.sum(w[0:(i + 1)]) / np.sum(w), color='blue', s=4)
plt.plot(np.zeros(z.shape) + 20, z, linestyle='--', color='black')
plt.plot(z1,
np.zeros(z1.shape) + np.sum(w[0:20]) / np.sum(w),
linestyle='--',
color='black')
plt.xlabel("Index", fontsize=12)
plt.ylabel("Cumulative explained Variance", fontsize=12)
plt.ylim([0, 1.1])
plt.xlim([-100, 1400])
plt.xticks([0, 200, 400, 600, 800, 1000, 1200],
(0, 200, 400, 600, 800, 1000, 1200))
plt.yticks([0.0, 0.20, 0.4, 0.6, 0.8, 1], (0.0, 0.20, 0.4, 0.6, 0.8, 1))
plt.savefig("../Results/explained_variance.eps", format='eps')
plt.savefig("../Results/explained_variance.png", format='png')
plt.show()
plt.close()
coor = []
dis = np.zeros((len(tm), len(tm)))
for i in range(len(tm)):
temp = []
temp1 = []
#temp.append(fold[i])
for j in range(len(tm)):
temp.append(str("%7.4f" % (np.dot(tm[i], v[j]) / np.sqrt(w[j]))))
temp1.append(np.dot(tm[i], v[j]) / np.sqrt(w[j]))
#top20.append(temp)
coor.append(temp1)
folds_name = np.loadtxt("folds_name", dtype='str')
with open("../Results/folds_coordinate", "w") as f:
for i in range(len(tm)):
f.write(folds_name[i])
f.write(" ")
for element in coor[i][0:20]:
f.write("%6.3f " % (element))
f.write("\n")
# save coordinates ---------------start
basis = []
for i in range(20):
basis.append(v[i] / np.sqrt(w[i]))
np.savetxt("../Results/folds_basis", basis, fmt='%s')
# save coordinates------------------end
for i in range(20):
print(np.var(coor, axis=0)[i], w[i] / 1232.)
#coor=np.loadtxt("Results/folds_coordinate")
from sklearn.cluster import KMeans
def fold_center_var(ncluster):
kmeans = KMeans(n_clusters=ncluster, random_state=0).fit(coor)
coor100 = kmeans.cluster_centers_ # coor100 shape (ncluster, 1232)
pca = PCA()
pca.fit(coor100)
# coor100 is the cluster heads coordinates
# we only need to consier two space: 1232d and n_cluster-dimensinal space
# project the original first 20 basis into these n_cluster-spanned subspace, which are [1,0...], [0,1...].. in 1232d space
pbasis = pca.components_ #pbasis (n_cluster, 1232)
coor20pbasis = [] # shape(20, n_cluster)
for i in range(20):
obasis = np.zeros((1232, ))
obasis[i] = 1.
cw = []
for j in range(len(pbasis)):
cw.append(
np.dot(obasis, pbasis[j]) / np.linalg.norm(pbasis[j]))
coor20pbasis.append(cw)
# calculate variance of n_cluster cluster heads along these 20 basis in n_clusterd
#1. first calculate the n_cluster cluster heads coordinate in n_cluster d
coorncluster = [] # shape(n_cluster, n_cluster)
for i in range(ncluster):
cw = []
for j in range(ncluster):
cw.append(
np.dot(coor100[i], pbasis[j]) / np.linalg.norm(pbasis[j]))
coorncluster.append(cw)
# then project those points along these 20 dimensional vectors.
nominator = 0.
for i in range(20):
cw = []
for j in range(ncluster):
cw.append(
np.dot(coor20pbasis[i], coorncluster[j]) /
np.linalg.norm(coor20pbasis[i]))
nominator += np.var(cw)
denominator = sum(pca.explained_variance_)
print(nominator / denominator)
return nominator / denominator
x = [20, 30, 40, 60, 80, 100, 120, 140, 160, 180, 200]
y = []
for xx in x:
y.append(fold_center_var(xx))
import matplotlib.pyplot as plt
plt.plot(x, y)
plt.yticks(fontsize=14)
plt.ylim([0, 1.1])
plt.xlim([0, 200])
plt.xticks(x, x)
plt.xlabel("#clusters", fontsize=14)
plt.ylabel("Cumulative explained Variance", fontsize=12)
plt.savefig("../Results/explained_variance_after_clustering.eps",
format='eps')
plt.savefig("../Results/explained_variance_after_clustering.png",
format='png')
plt.show()
exit(0)
'''
exit(0)
z1=np.linspace(-100,20)
z=np.linspace(0,1)
plt.plot(np.zeros(z.shape)+20, z , linestyle='--', color='black')
plt.plot(z1, np.zeros(z1.shape)+np.sum(w[0:20])/np.sum(w), linestyle='--', color='grey')
# plt.text(22, np.sum(w[0:20])/np.sum(w), "[%.1f, 20]" %())
for i in range(len(x)):
plt.scatter(x[i], np.sum(w[0:(i+1)])/np.sum(w), color='blue' , s=4)
print np.sum(w[0:20])/np.sum(w)
#plt.xticks(x, (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20))
plt.xlabel("Index", fontsize=12)
plt.ylabel("Cumulative explained Variance", fontsize=12)
plt.ylim([0,1])
plt.xlim([-100,1400])
plt.xticks([0, 200, 400, 600, 800, 1000, 1200],(0, 200, 400, 600, 800, 1000, 1200))
plt.yticks([0.0, 0.20, 0.4, 0.6, 0.8, 1], (0.0, 0.20,0.4,0.6,0.8,1))
plt.savefig("curve.eps", format='eps')
plt.show()
plt.close()
exit(0)
'''
classs = []
fold = []
top20 = []
for lines in open("../represent_file"):
classs.append(lines[5])
for b in range(8, 12):
if (lines[b] == '.'):
fold.append(lines[5:b])
break
# print fold, len(fold)
coor = []
dis = np.zeros((len(tm), len(tm)))
for i in range(len(tm)):
temp = []
temp1 = []
temp.append(fold[i])
for j in range(500):
temp.append(str("%7.4f" % (np.dot(tm[i], v[j]) / np.sqrt(w[j]))))
temp1.append(np.dot(tm[i], v[j]) / np.sqrt(w[j]))
top20.append(temp)
coor.append(temp1)
from sklearn.cluster import KMeans
kmeans = KMeans(n_clusters=100, random_state=0).fit(coor)
var = np.var(np.array(kmeans.cluster_centers_), axis=0)
print np.sum(var[0:20]) / np.sum(var[0:100])
# for i in range(1232):
# print ("%.2f %.3f %.3f" % (w[i], w[i]/len(w), np.var(np.array(coor).T[i]) ))
exit(0)
np.savetxt("folds_coordinate", top20, fmt='%s')
#basis
basis = []
for i in range(20):
basis.append(v[i] / np.sqrt(w[i]))
np.savetxt("folds_basis", basis, fmt='%s')
for i in range(len(w)):
print w[i]
minm = 1.0
'''
for i in range(len(tm)):
for j in range(len(tm)):
dis[i][j]=np.linalg.norm(np.subtract(coor[i],coor[j]))
if(i!=j and dis[i][j]<minm):
minm=dis[i][j]
print ("%.4f " %(dis[i][j])),
print ('\n')
'''
for i in range(20):
print("%.2f %.3f %.3f" %
(w[i], w[i] / len(w), np.var(np.array(coor).T[i])))
exit(0)
#----------------1/11/2019----------------------------
for threhold in np.linspace(0.3, 1, 8):
tm_new = delete_fold(tm)
#print len(tm_new), len(tm_new[0])
w, v = linalg.eig(tm_new)
#print np.min(w)
if (np.min(w) < 0):
tm_new = np.add(tm_new, -np.min(w) * np.identity(len(tm_new)))
w, v = linalg.eig(tm_new)
v = np.transpose(v)
#print np.min(w)
for i in range(len(w)):
for j in range(i + 1, len(w)):
if (w[i] < w[j]):
temp = w[i]
w[i] = w[j]
w[j] = temp
temp = v[i]
v[i] = v[j]
v[j] = temp
wnorm = w / np.sum(w)
for i in range(len(tm_new)):
if (np.sum(wnorm[0:i + 1]) > 0.5):
print("%.3f %.0f %.0f\n" % (threhold, i, len(tm_new))),
break
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
plt.figure()
x = np.arange(0, 20, 1)
for i in range(50):
print("%d %.4f %.4f" % (i + 1, wnorm[i], np.sum(wnorm[0:i + 1])))
exit(0)
for i in range(len(x)):
plt.bar(x[i], w[i], color='blue', width=0.7)
#plt.savefig("top20eigv.png", format='png')
plt.close()
x1 = []
x2 = []
x3 = []
top20 = []
for i in range(len(tm)):
x1.append(np.dot(tm[i], v[0]) / np.sqrt(w[0]))
x2.append(np.dot(tm[i], v[1]) / np.sqrt(w[1]))
x3.append(np.dot(tm[i], v[2]) / np.sqrt(w[2]))
#print x1[-1],x2[-1],x3[-1], v[0][i]*np.sqrt(w[0]), v[1][i]*np.sqrt(w[1]), v[2][i]*np.sqrt(w[2])
classs = []
fold = []
for lines in open("../represent_file"):
classs.append(lines[5])
for b in range(8, 12):
if (lines[b] == '.'):
fold.append(lines[5:b])
break
# print fold, len(fold)
for i in range(len(tm)):
temp = []
#temp.append(fold[i])
for j in range(20):
temp.append(str("%7.4f" % (np.dot(tm[i], v[j]) / np.sqrt(w[j]))))
top20.append(temp)
#np.savetxt("folds_coordinate", top20, fmt='%s')
#basis
basis = []
for i in range(20):
basis.append(v[i] / np.sqrt(w[i]))
#np.savetxt("fold_basis", basis)
c = []
colormap = 'rainbow'
class1 = {
'a': 'red',
'b': 'pink',
'c': 'orange',
'd': 'yellow',
'e': 'green',
'f': 'blue',
'g': 'purple'
}
fig = plt.figure()
ax = fig.gca(projection='3d')
label = {
'a': r'$\alpha$',
'b': r'$\beta$',
'c': r'$\alpha/\beta$',
'd': r'$\alpha+\beta$',
'e': r'$\alpha and \beta$',
'f': 'Membrane and cell surface',
'g': 'Small proteins'
}
judge = {}
for i in range(len(x1)):
if classs[i] in judge:
ax.scatter(x1[i], x2[i], x3[i], alpha=0.8, c=class1[classs[i]])
else:
ax.scatter(x1[i],
x2[i],
x3[i],
alpha=0.8,
c=class1[classs[i]],
label=label[classs[i]])
judge[classs[i]] = 1
ax.set_xlabel("PC1")
ax.set_ylabel("PC2")
ax.set_zlabel("PC3")
plt.legend(loc="upper left")
#plt.close()
fig = plt.figure()
ax = fig.gca(projection='3d')
withold = np.loadtxt("withhold_folds", dtype='str')
j = 0
for i in range(len(x1)):
if fold[i] in withold:
j += 1
# print j
ax.scatter(x1[i], x2[i], x3[i], alpha=0.8, c='blue')
else:
ax.scatter(x1[i], x2[i], x3[i], alpha=0.8, c='green')
ax.set_xlabel("PC1")
ax.set_ylabel("PC2")
ax.set_zlabel("PC3")
plt.legend(loc="upper left")
#plt.show()
plt.close()
# t-SNE
from sklearn.manifold import TSNE
t_embed = TSNE(n_components=3).fit_transform(top20)
# print t_embed.shape
judge = {}
for i in range(len(x1)):
if classs[i] in judge:
ax.scatter(t_embed[i][0],
t_embed[i][1],
t_embed[i][2],
alpha=0.8,
c=class1[classs[i]])
else:
ax.scatter(t_embed[i][0],
t_embed[i][1],
t_embed[i][2],
alpha=0.8,
c=class1[classs[i]],
label=label[classs[i]])
judge[classs[i]] = 1
ax.set_xlabel("PC1")
ax.set_ylabel("PC2")
ax.set_zlabel("PC3")
plt.legend(loc="upper left")
plt.show()
from scipy.stats import random_correlation
from knowledge_gradient import KG_Alg
from knowledge_gradient import KG_multi
from knowledge_gradient import update_mu_S
if __name__ == "__main__":
processes = mp.cpu_count()
pool = mp.Pool(processes)
np.random.seed(126)
g = 7/sum([.5, .8, 1.2, 2.5, 1.7, 2.1, 2.2])
G = np.round(random_correlation.rvs((g*.5, g*.8, g*1.2, g*2.5, g*1.7, g*2.1, g*2.2)), 3)
S = nearcorr(G, tol=[], flag=0, max_iterations=1000, n_pos_eig=0, weights=None,
verbose=False, except_on_too_many_iterations=True)
M = S.shape[0]
lambda_ = np.array([0.2, 1.1, 1.3, 0.12, 0.4, 0.3, 0.12])
mu = np.array([0.2, 0.21, 0.92, 0.11, 0.7, 0.2, -0.1])
print(KG_Alg(mu, S, lambda_))
print(KG_multi(mu, S, lambda_, pool))
y=0.22
x=3
mu_1, S_1 = update_mu_S(mu, S, lambda_, x, y)
print(mu_1.shape)
for tkr in good_tickers:
tmpdf = df[df.Ticker == tkr]["Adj Close"][dte1:dte2]
tmprtndf = ((tmpdf - tmpdf.shift(1)) / tmpdf).dropna()
rsdf = tmprtndf / tmprtndf.std()
rtndf = pd.concat([rtndf, rsdf], axis=1)
rtndf = rtndf.dropna()
rtndf.columns = good_tickers
t, m = rtndf.shape
cmat = rtndf.corr()
evls, evcs = LA.eig(cmat)
rcmat = abs(np.dot(np.dot(evcs, np.diag(evls)), LA.inv(evcs)))
evallst = map(abs, evls)
filtvals = [val for val in evallst if val < lamplus(t, m)]
sevlist = [np.mean(filtvals)] * len(filtvals)
feval = evallst[: (len(evallst) - len(sevlist))] + sevlist
rcmat = abs(np.dot(np.dot(evcs, np.diag(feval)), LA.inv(evcs)))
rcmat = (rcmat + rcmat.T) / 2
ncorr = nearcorr(rcmat, max_iterations=1000)
ncorrdf = pd.DataFrame(ncorr, columns=good_tickers, index=good_tickers)
# Start the clustering
sns.clustermap(1 - abs(ncorrdf))
plt.show()
for tkr in good_tickers:
tmpdf = df[df.Ticker == tkr]['Adj Close'][dte1:dte2]
tmprtndf = ((tmpdf - tmpdf.shift(1)) / tmpdf).dropna()
rsdf = tmprtndf / tmprtndf.std()
rtndf = pd.concat([rtndf, rsdf], axis=1)
rtndf = rtndf.dropna()
rtndf.columns = good_tickers
t, m = rtndf.shape
cmat = rtndf.corr()
evls, evcs = LA.eig(cmat)
rcmat = abs(np.dot(np.dot(evcs, np.diag(evls)), LA.inv(evcs)))
evallst = map(abs, evls)
filtvals = [val for val in evallst if val < lamplus(t, m)]
sevlist = [np.mean(filtvals)] * len(filtvals)
feval = evallst[:(len(evallst) - len(sevlist))] + sevlist
rcmat = abs(np.dot(np.dot(evcs, np.diag(feval)), LA.inv(evcs)))
rcmat = (rcmat + rcmat.T) / 2
ncorr = nearcorr(rcmat, max_iterations=1000)
ncorrdf = pd.DataFrame(ncorr, columns=good_tickers, index=good_tickers)
# Start the clustering
sns.clustermap(1 - abs(ncorrdf))
plt.show()
def test_ExceededMaxIterationsFalse(self):
A = np.array([[1,1,0],
[1,1,1],
[0,1,1]])
X = nearcorr(A,max_iterations=10,except_on_too_many_iterations=False)
