def CD(prot_sub, iter_num):
"""
Coordinate Descent Solver:
retrun inferred protein, Z, r^2, X, error
"""
S = prot_sub['S']
X = prot_sub['X']
if len(sys.argv) < 3:
iter_num = 1000
Num_pep, Num_prot = S.shape
Num_condition = X.shape[1]
# set IC
protein_ic = np.random.randn(Num_prot, Num_condition)
protein = protein_ic
# for loop iterations
for each in range(iter_num):
Prot = protein
dat = S.dot(protein).T
zeta = np.sum(dat * X.T, axis=0) / np.sum(dat * dat, axis=0)
if np.sum(zeta[:] < 0):
zeta[zeta < 0] = 1e-4
Zeta = np.diag(zeta)
Proteins = np.linalg.lstsq(Zeta.dot(S), X)[0]
if np.sum(Proteins[:] < 0):
Proteins[Proteins < 0] = 1e-4
protein = Proteins
if np.linalg.norm(Prot[:] - protein[:]) < 1e-8:
break
Model = Zeta.dot(S).dot(protein)
X_norm = hf.norm_mean(X, 0)
Rsq = 1 - (np.sum(X[:] - Model[:])**2) / np.sum(X_norm**2)
opt = dict()
opt['model'] = Model
opt['rsq'] = Rsq
opt['Z'] = Zeta
opt['error'] = np.linalg.norm(Prot[:] - protein[:])
return protein, opt
def QP(prot_sub):
"""
Quadratic Programming Solver:
Return the inferred protein level, Z, r^2
"""
S = prot_sub['S']
X = prot_sub['X']
N = X.shape[1]
A1 = np.kron(S, np.eye(N))
A2 = -block_diag(*X).T
A1 = matrix(A1)
A2 = matrix(A2)
AA = matrix([[A1], [A2]])
P = matrix(np.dot(AA.T, AA))
dim = P.size[0]
q = matrix(np.zeros(dim))
G = matrix(-np.eye(dim))
h = matrix(np.zeros(dim), (dim, 1))
A = matrix(np.ones(dim), (1, dim))
b = matrix(1.0)
sol = solvers.qp(P, q, G, h, A, b)
w = np.array(sol['x'])
if np.sum(w < 0) > np.sum(w > 0):
w = -1 * w
p_vect = w[0:S.shape[1] * X.shape[1]]
U_hat = np.array(p_vect).reshape(S.shape[1],
X.shape[1]) #♌ in test case reshape(2,6)
L_hat = np.concatenate(w[S.shape[1] * X.shape[1]::])
Z_hat = 1 / L_hat
protein = U_hat
X_rec = np.diag(Z_hat).dot(S).dot(U_hat)
Model = X_rec * np.median(X_rec[:] / X[:])
X_norm = hf.norm_mean(X, 0)
Rsq = 1 - (np.sum(X[:] - Model[:])**2) / np.sum(X_norm**2)
opt = dict()
opt['model'] = Model
opt['rsq'] = Rsq
opt['Z'] = np.diag(Z_hat)
return protein, opt
def SVD(prot_sub):
"""
SVD sovler:
Return the inferred protein level, Z, r^2
"""
S = prot_sub['S']
X = prot_sub['X']
N = X.shape[1]
M = S.shape[0]
K = S.shape[1]
A1 = np.kron(S, np.eye(N))
A2 = block_diag(*X).T
A = np.concatenate((A1, -A2), axis=1)
U, s, V = np.linalg.svd(A, full_matrices=True)
# U, s, V = svd(A, full_matrices=True, lapack_driver = 'gesvd')
w = V[-1, :] #♌
eigen_spacing = (s[-2] - s[-1]) / (s[-2] + s[-1])
if np.sum(w < 0) > np.sum(w > 0):
w = -1 * w
p_vect = w[0:K * N]
U_hat = p_vect.reshape(K, N)
L_hat = w[K * N::]
Z_hat = 1 / L_hat
protein = U_hat
X_rec = np.diag(Z_hat).dot(S).dot(U_hat)
Model = X_rec * np.median(X_rec[:] / X[:])
X_norm = hf.norm_mean(X, 0)
Rsq = 1 - (np.sum(X[:] - Model[:])**2) / np.sum(X_norm**2)
opt = dict()
opt['model'] = Model
opt['rsq'] = Rsq
opt['Z'] = np.diag(Z_hat)
opt['V'] = w # last eigen vector
opt['eigen_spacing'] = eigen_spacing
return protein, opt
CD_homo_P = dict()
SVD_homo_P = dict()
QP_homo_P = dict()
U_true_set = dict()
for each in range(num_problem):
Z_true = 1 + np.array([random.expovariate(1) for rand in range(M)])
U_true = np.random.rand(K, N)
X_clean = np.diag(Z_true).dot(S).dot(U_true)
X = X_clean + (X_clean * sigma_n) * np.array(mtl.randn(M, N))
U_true_set[str(each)] = U_true
prot_sub = dict()
prot_sub['S'] = S
prot_sub['X'] = X
hf.null_sp_dim(prot_sub)
# SVD sovler
SVD_solution = Solvers.SVD(prot_sub)
SVD_protein, SVD_opt = SVD_solution
SVD_homo_P[str(each)] = SVD_protein
# QP solver
QP_solution = Solvers.QP(prot_sub)
QP_protein, QP_opt = QP_solution
QP_homo_P[str(each)] = QP_protein
# CD sovler
CD_solution = Solvers.CD(prot_sub, 1000)
CD_protein, CD_opt = CD_solution
CD_homo_P[str(each)] = CD_protein
import HIquant_functions as hf
import Solvers
from cvxopt import solvers, matrix, lapack
import matplotlib.pyplot as plt
import HIquant_test_path_set as ts
from sklearn.ensemble import RandomForestRegressor
import seaborn as sns
os.getcwd()
print( 'Importing data from the directory below ...')
st=time.time()
test_path = ts.test_set['TMT2_MQ_Phospho']
#test_path = '/Users/chentianchi/Desktop/alex_all_proteoform_IL4_hiquant_input.txt'
Mat_A , Mat_S, Mat_CC , Mat_nC, Dat_data, Dat_textdata, Dat_proteins, Data_isunique, Num_peptides, Num_proteins = hf.GetData(test_path)
ed=time.time()
print('Time:',ed-st)
Mat_nC
Num_proteins
Num_peptides
Dat_data
## 2. Complie a list protein having unique peptde and common peptides.
proteins_uniq_pep = Dat_textdata[Data_isunique==1].iloc[:,0].tolist()
# proteins_uniq_indx = pd.DataFrame(Dat_proteins).isin(proteins_uniq_pep)
# print('The number of proteins with unique peptides is :', proteins_uniq_indx.sum().values) % redundont, use the following
print('The number of proteins with unique peptides is :', len(np.unique(proteins_uniq_pep)))
print('Number of proteins ONLY with common peptides:', Num_proteins-len(np.unique(proteins_uniq_pep)))