def update_terminals(self):
self.terminals = sp.zeros(self.vertices.shape, dtype='int')
self.terminals[0,
sp.where(
sp.sum(sp.tril(self.edges), axis=1) == 0)[0]] = 1
self.terminals[1,
sp.where(
sp.sum(sp.triu(self.edges), axis=1) == 0)[0]] = 1
def Calculate_NCG(X, Pi, alpha, beta1, beta2, d_old, g_norm_old):
# Probability of observing an edge between clusters
eps = 1e-10
N = X.shape[0]
k = Pi.shape[1]
psi = sc.special.psi
Y = sc.ones((N, N)) - sc.identity(N) - X
d_log_B1 = psi(beta1) - psi(beta1 + beta2)
d_log_B2 = psi(beta2) - psi(beta1 + beta2)
d_log_B1 = sc.diag(
sc.diag(d_log_B1)) + sc.log(eps) * sc.triu(sc.ones(
(k, k)), 1) + sc.log(eps) * sc.tril(sc.ones((k, k)), -1)
d_log_B2 = sc.diag(
sc.diag(d_log_B2)) + sc.log(1 - eps) * sc.triu(sc.ones(
(k, k)), 1) + sc.log(1 - eps) * sc.tril(sc.ones((k, k)), -1)
# L_prime_i,j = dL / dPi_i,j
L_prime = X.dot(Pi.dot(d_log_B1.T)) + Y.dot(Pi.dot(d_log_B2.T)) \
+ sc.outer(sc.ones(N), psi(alpha)) - sc.log(Pi) - sc.outer(sc.ones(N), sc.ones(k))
u = sc.concatenate([sc.identity(k - 1), -sc.ones((1, k - 1))], axis=0)
# Natural gradient
g = L_prime.dot(u)
# Norm of natural gradient
g_norm = 0
for i in range(N):
l = L_prime[i, :]
p = Pi[i, :]
B = sc.diag(p) - sc.outer(p, p)
g_norm += l.dot(B.dot(l))
# Natural Conjugate Gradient
d = g + g_norm / g_norm_old * d_old
return d, g_norm
def __init__(self,
matA,
matB,
xguess=None,
eps_flux=EPS_INNER,
eps_source=EPS_OUTER,
eps_k=EPS_OUTER):
super().__init__(matA, matB, xguess, eps_flux, eps_source, eps_k)
self.matL = scipy.tril(matA)
self.matU = matA - self.matL
del matA
def factLU(A):
n=len(A)
for k in range(n-1):
if s.absolute(A[k][k])<1e-20:
print('Pivote cercano a cero en k=%d' % k)
L=[[0.0]*n for i in range(n)]
U=[[0.0]*n for i in range(n)]
return L,U
else:
for i in range(k+1,n):
A[i][k] = A[i][k]/A[k][k]
for j in range(k+1,n):
A[i][j] = A[i][j]-A[i][k]*A[k][j]
#==================================
#OBSERVE QUE:
#Las siguientes lineas en realidad no hacen falta
U=s.triu(A)
L=s.tril(A,-1)
for i in range(n):
L[i][i] =1.0
return L,U
def Log_Likelihood(X, Pi, alpha, beta1, beta2):
# Probability of observing an edge between clusters
eps = 1e-10
k = Pi.shape[1]
N = X.shape[0]
ones = sc.ones((k, k))
Y = sc.ones((N, N)) - sc.identity(N) - X
Z = sc.log(eps) * Pi.T.dot(X.dot(Pi)) + sc.log(1 - eps) * Pi.T.dot(
Y.dot(Pi))
Z = sc.tril(Z, -1)
A = sc.sum(Pi * sc.log(Pi))
B_alpha = sc.log(nbeta(alpha) / nbeta(sc.ones(alpha.shape[0])))
B_beta = sc.special.beta(beta1, beta2) / sc.special.beta(1, 1)
B_beta = sc.diag(sc.log(B_beta))
L = sc.sum(Z) + A + B_alpha + sc.sum(B_beta)
return L
def gen_unrelated_eur_1k_data(input_file='/home/bjarni/TheHonestGene/faststorage/1Kgenomes/phase3/1k_genomes_hg.hdf5' ,
out_file='/home/bjarni/PCMA/faststorage/1_DATA/1k_genomes/1K_genomes_phase3_EUR_unrelated.hdf5',
maf_thres=0.01, max_relatedness=0.05, K_thinning_frac=0.1, debug=False):
h5f = h5py.File(input_file)
num_indivs = len(h5f['indivs']['continent'])
eur_filter = h5f['indivs']['continent'][...] == 'EUR'
num_eur_indivs = sp.sum(eur_filter)
print 'Number of European individuals: %d', num_eur_indivs
K = sp.zeros((num_eur_indivs, num_eur_indivs), dtype='single')
num_snps = 0
std_thres = sp.sqrt(2.0 * (1 - maf_thres) * (maf_thres))
print 'Calculating kinship'
for chrom in range(1, 23):
print 'Working on Chromosome %d' % chrom
chrom_str = 'chr%d' % chrom
print 'Loading SNPs and data'
snps = sp.array(h5f[chrom_str]['calldata']['snps'][...], dtype='int8')
print 'Loading NTs'
ref_nts = h5f[chrom_str]['variants']['REF'][...]
alt_nts = h5f[chrom_str]['variants']['ALT'][...]
print 'Filtering multi-allelic SNPs'
multi_allelic_filter = sp.negative(h5f[chrom_str]['variants']['MULTI_ALLELIC'][...])
snps = snps[multi_allelic_filter]
ref_nts = ref_nts[multi_allelic_filter]
alt_nts = alt_nts[multi_allelic_filter]
if K_thinning_frac < 1:
print 'Thinning SNPs for kinship calculation'
thinning_filter = sp.random.random(len(snps)) < K_thinning_frac
snps = snps[thinning_filter]
alt_nts = alt_nts[thinning_filter]
ref_nts = ref_nts[thinning_filter]
print 'Filter SNPs with missing NT information'
nt_filter = sp.in1d(ref_nts, ok_nts)
nt_filter = nt_filter * sp.in1d(alt_nts, ok_nts)
if sp.sum(nt_filter) < len(nt_filter):
snps = snps[nt_filter]
print 'Filtering non-European individuals'
snps = snps[:, eur_filter]
print 'Filtering SNPs with MAF <', maf_thres
snp_stds = sp.std(snps, 1)
maf_filter = snp_stds.flatten() > std_thres
snps = snps[maf_filter]
snp_stds = snp_stds[maf_filter]
print '%d SNPs remaining after all filtering steps.' % len(snps)
print 'Normalizing SNPs'
snp_means = sp.mean(snps, 1)
norm_snps = (snps - snp_means[sp.newaxis].T) / snp_stds[sp.newaxis].T
print 'Updating kinship'
K += sp.dot(norm_snps.T, norm_snps)
num_snps += len(norm_snps)
assert sp.isclose(sp.sum(sp.diag(K)) / (num_snps * num_eur_indivs), 1.0)
K = K / float(num_snps)
print 'Kinship calculation done using %d SNPs\n' % num_snps
# Filter individuals
print 'Filtering individuals'
keep_indiv_set = set(range(num_eur_indivs))
for i in range(num_eur_indivs):
if i in keep_indiv_set:
for j in range(i + 1, num_eur_indivs):
if K[i, j] > max_relatedness:
if j in keep_indiv_set:
keep_indiv_set.remove(j)
keep_indivs = list(keep_indiv_set)
keep_indivs.sort()
print 'Retained %d individuals\n' % len(keep_indivs)
# Checking that everything is ok!
K_ok = K[keep_indivs]
K_ok = K_ok[:, keep_indivs]
assert (K_ok - sp.tril(K_ok)).max() < max_relatedness
indiv_filter = sp.zeros(num_indivs, dtype='bool8')
indiv_filter[(sp.arange(num_indivs)[eur_filter])[keep_indivs]] = 1
assert sp.sum(indiv_filter) == len(keep_indivs)
# Store in new file
print 'Now storing data.'
oh5f = h5py.File(out_file, 'w')
indiv_ids = h5f['indivs']['indiv_ids'][indiv_filter]
oh5f.create_dataset('indiv_ids', data=indiv_ids)
for chrom in range(1, 23):
print 'Working on Chromosome %d' % chrom
chrom_str = 'chr%d' % chrom
print 'Loading SNPs and data'
snps = sp.array(h5f[chrom_str]['calldata']['snps'][...], dtype='int8')
snp_ids = h5f[chrom_str]['variants']['ID'][...]
positions = h5f[chrom_str]['variants']['POS'][...]
print 'Loading NTs'
ref_nts = h5f[chrom_str]['variants']['REF'][...]
alt_nts = h5f[chrom_str]['variants']['ALT'][...]
print 'Filtering multi-allelic SNPs'
multi_allelic_filter = sp.negative(h5f[chrom_str]['variants']['MULTI_ALLELIC'][...])
snps = snps[multi_allelic_filter]
ref_nts = ref_nts[multi_allelic_filter]
alt_nts = alt_nts[multi_allelic_filter]
positions = positions[multi_allelic_filter]
snp_ids = snp_ids[multi_allelic_filter]
print 'Filter individuals'
snps = snps[:, indiv_filter]
print 'Filter SNPs with missing NT information'
nt_filter = sp.in1d(ref_nts, ok_nts)
nt_filter = nt_filter * sp.in1d(alt_nts, ok_nts)
if sp.sum(nt_filter) < len(nt_filter):
snps = snps[nt_filter]
ref_nts = ref_nts[nt_filter]
alt_nts = alt_nts[nt_filter]
positions = positions[nt_filter]
snp_ids = snp_ids[nt_filter]
print 'filter monomorphic SNPs'
snp_stds = sp.std(snps, 1)
mono_morph_filter = snp_stds > 0
snps = snps[mono_morph_filter]
ref_nts = ref_nts[mono_morph_filter]
alt_nts = alt_nts[mono_morph_filter]
positions = positions[mono_morph_filter]
snp_ids = snp_ids[mono_morph_filter]
snp_stds = snp_stds[mono_morph_filter]
snp_means = sp.mean(snps, 1)
if debug:
if K_thinning_frac < 1:
print 'Thinning SNPs for kinship calculation'
thinning_filter = sp.random.random(len(snps)) < K_thinning_frac
k_snps = snps[thinning_filter]
k_snp_stds = snp_stds[thinning_filter]
print 'Filtering SNPs with MAF <', maf_thres
maf_filter = k_snp_stds.flatten() > std_thres
k_snps = k_snps[maf_filter]
k_snp_stds = k_snp_stds[maf_filter]
k_snp_means = sp.mean(k_snps)
print 'Verifying that the Kinship makes sense'
norm_snps = (k_snps - k_snp_means[sp.newaxis].T) / k_snp_stds[sp.newaxis].T
K = sp.dot(norm_snps.T, norm_snps)
num_snps += len(norm_snps)
if sp.isclose(sp.sum(sp.diag(K)) / (num_snps * num_eur_indivs), 1.0) and (K - sp.tril(K)).max() < (max_relatedness * 1.5):
print 'It looks OK!'
else:
raise Exception('Kinship looks wrong?')
nts = sp.array([[nt1, nt2] for nt1, nt2 in izip(ref_nts, alt_nts)])
print 'Writing to disk'
cg = oh5f.create_group(chrom_str)
cg.create_dataset('snps', data=snps)
cg.create_dataset('snp_means', data=snp_means[sp.newaxis].T)
cg.create_dataset('snp_stds', data=snp_stds[sp.newaxis].T)
cg.create_dataset('snp_ids', data=snp_ids)
cg.create_dataset('positions', data=positions)
cg.create_dataset('nts', data=nts)
oh5f.flush()
print 'Done writing to disk'
# centimorgans = h5f[chrom_str]['centimorgans'][...]
# cg.create_dataset('centimorgans',data=centimorgans)
#
# centimorgan_rates = h5f[chrom_str]['centimorgan_rates'][...]
# cg.create_dataset('centimorgan_rates',data=centimorgan_rates)
oh5f.close()
h5f.close()
print 'Done'
def gen_unrelated_eur_1k_data(
input_file='/home/bjarni/TheHonestGene/faststorage/1Kgenomes/phase3/1k_genomes_hg.hdf5',
out_file='/home/bjarni/PCMA/faststorage/1_DATA/1k_genomes/1K_genomes_phase3_EUR_unrelated.hdf5',
maf_thres=0.01,
max_relatedness=0.05,
K_thinning_frac=0.1,
debug=False):
h5f = h5py.File(input_file)
num_indivs = len(h5f['indivs']['continent'])
eur_filter = h5f['indivs']['continent'][...] == 'EUR'
num_eur_indivs = sp.sum(eur_filter)
print 'Number of European individuals: %d', num_eur_indivs
K = sp.zeros((num_eur_indivs, num_eur_indivs), dtype='float64')
num_snps = 0
std_thres = sp.sqrt(2.0 * (1 - maf_thres) * (maf_thres))
print 'Calculating kinship'
for chrom in range(1, 23):
print 'Working on Chromosome %d' % chrom
chrom_str = 'chr%d' % chrom
print 'Loading SNPs and data'
snps = sp.array(h5f[chrom_str]['calldata']['snps'][...], dtype='int8')
print 'Loading NTs'
ref_nts = h5f[chrom_str]['variants']['REF'][...]
alt_nts = h5f[chrom_str]['variants']['ALT'][...]
print 'Filtering multi-allelic SNPs'
multi_allelic_filter = sp.negative(
h5f[chrom_str]['variants']['MULTI_ALLELIC'][...])
snps = snps[multi_allelic_filter]
ref_nts = ref_nts[multi_allelic_filter]
alt_nts = alt_nts[multi_allelic_filter]
if K_thinning_frac < 1:
print 'Thinning SNPs for kinship calculation'
thinning_filter = sp.random.random(len(snps)) < K_thinning_frac
snps = snps[thinning_filter]
alt_nts = alt_nts[thinning_filter]
ref_nts = ref_nts[thinning_filter]
print 'Filter SNPs with missing NT information'
nt_filter = sp.in1d(ref_nts, ok_nts)
nt_filter = nt_filter * sp.in1d(alt_nts, ok_nts)
if sp.sum(nt_filter) < len(nt_filter):
snps = snps[nt_filter]
print 'Filtering non-European individuals'
snps = snps[:, eur_filter]
print 'Filtering SNPs with MAF <', maf_thres
snp_stds = sp.std(snps, 1)
maf_filter = snp_stds.flatten() > std_thres
snps = snps[maf_filter]
snp_stds = snp_stds[maf_filter]
print '%d SNPs remaining after all filtering steps.' % len(snps)
print 'Normalizing SNPs'
snp_means = sp.mean(snps, 1)
norm_snps = (snps - snp_means[sp.newaxis].T) / snp_stds[sp.newaxis].T
print 'Updating kinship'
K += sp.dot(norm_snps.T, norm_snps)
num_snps += len(norm_snps)
assert sp.isclose(
sp.sum(sp.diag(K)) / (num_snps * num_eur_indivs), 1.0)
K = K / float(num_snps)
print 'Kinship calculation done using %d SNPs\n' % num_snps
# Filter individuals
print 'Filtering individuals'
keep_indiv_set = set(range(num_eur_indivs))
for i in range(num_eur_indivs):
if i in keep_indiv_set:
for j in range(i + 1, num_eur_indivs):
if K[i, j] > max_relatedness:
if j in keep_indiv_set:
keep_indiv_set.remove(j)
keep_indivs = list(keep_indiv_set)
keep_indivs.sort()
print 'Retained %d individuals\n' % len(keep_indivs)
# Checking that everything is ok!
K_ok = K[keep_indivs]
K_ok = K_ok[:, keep_indivs]
assert (K_ok - sp.tril(K_ok)).max() < max_relatedness
indiv_filter = sp.zeros(num_indivs, dtype='bool8')
indiv_filter[(sp.arange(num_indivs)[eur_filter])[keep_indivs]] = 1
assert sp.sum(indiv_filter) == len(keep_indivs)
# Store in new file
print 'Now storing data.'
oh5f = h5py.File(out_file, 'w')
indiv_ids = h5f['indivs']['indiv_ids'][indiv_filter]
oh5f.create_dataset('indiv_ids', data=indiv_ids)
for chrom in range(1, 23):
print 'Working on Chromosome %d' % chrom
chrom_str = 'chr%d' % chrom
print 'Loading SNPs and data'
snps = sp.array(h5f[chrom_str]['calldata']['snps'][...], dtype='int8')
snp_ids = h5f[chrom_str]['variants']['ID'][...]
positions = h5f[chrom_str]['variants']['POS'][...]
print 'Loading NTs'
ref_nts = h5f[chrom_str]['variants']['REF'][...]
alt_nts = h5f[chrom_str]['variants']['ALT'][...]
print 'Filtering multi-allelic SNPs'
multi_allelic_filter = sp.negative(
h5f[chrom_str]['variants']['MULTI_ALLELIC'][...])
snps = snps[multi_allelic_filter]
ref_nts = ref_nts[multi_allelic_filter]
alt_nts = alt_nts[multi_allelic_filter]
positions = positions[multi_allelic_filter]
snp_ids = snp_ids[multi_allelic_filter]
print 'Filter individuals'
snps = snps[:, indiv_filter]
print 'Filter SNPs with missing NT information'
nt_filter = sp.in1d(ref_nts, ok_nts)
nt_filter = nt_filter * sp.in1d(alt_nts, ok_nts)
if sp.sum(nt_filter) < len(nt_filter):
snps = snps[nt_filter]
ref_nts = ref_nts[nt_filter]
alt_nts = alt_nts[nt_filter]
positions = positions[nt_filter]
snp_ids = snp_ids[nt_filter]
print 'filter monomorphic SNPs'
snp_stds = sp.std(snps, 1)
mono_morph_filter = snp_stds > 0
snps = snps[mono_morph_filter]
ref_nts = ref_nts[mono_morph_filter]
alt_nts = alt_nts[mono_morph_filter]
positions = positions[mono_morph_filter]
snp_ids = snp_ids[mono_morph_filter]
snp_stds = snp_stds[mono_morph_filter]
snp_means = sp.mean(snps, 1)
if debug:
if K_thinning_frac < 1:
print 'Thinning SNPs for kinship calculation'
thinning_filter = sp.random.random(len(snps)) < K_thinning_frac
k_snps = snps[thinning_filter]
k_snp_stds = snp_stds[thinning_filter]
print 'Filtering SNPs with MAF <', maf_thres
maf_filter = k_snp_stds.flatten() > std_thres
k_snps = k_snps[maf_filter]
k_snp_stds = k_snp_stds[maf_filter]
k_snp_means = sp.mean(k_snps)
print 'Verifying that the Kinship makes sense'
norm_snps = (k_snps -
k_snp_means[sp.newaxis].T) / k_snp_stds[sp.newaxis].T
K = sp.dot(norm_snps.T, norm_snps)
num_snps += len(norm_snps)
if sp.isclose(
sp.sum(sp.diag(K)) / (num_snps * num_eur_indivs),
1.0) and (K - sp.tril(K)).max() < (max_relatedness * 1.5):
print 'It looks OK!'
else:
raise Exception('Kinship looks wrong?')
nts = sp.array([[nt1, nt2] for nt1, nt2 in izip(ref_nts, alt_nts)])
print 'Writing to disk'
cg = oh5f.create_group(chrom_str)
cg.create_dataset('snps', data=snps)
cg.create_dataset('snp_means', data=snp_means[sp.newaxis].T)
cg.create_dataset('snp_stds', data=snp_stds[sp.newaxis].T)
cg.create_dataset('snp_ids', data=snp_ids)
cg.create_dataset('positions', data=positions)
cg.create_dataset('nts', data=nts)
oh5f.flush()
print 'Done writing to disk'
# centimorgans = h5f[chrom_str]['centimorgans'][...]
# cg.create_dataset('centimorgans',data=centimorgans)
#
# centimorgan_rates = h5f[chrom_str]['centimorgan_rates'][...]
# cg.create_dataset('centimorgan_rates',data=centimorgan_rates)
oh5f.close()
h5f.close()
print 'Done'
def from_gene(self, gene):
for transcript_idx in range(len(gene.transcripts)):
exon_start_end = gene.exons[transcript_idx]
### only one exon in the transcript
if exon_start_end.shape[0] == 1:
exon1_start = exon_start_end[0, 0]
exon1_end = exon_start_end[0, 1]
if self.vertices.shape[1] == 0:
self.vertices = sp.array([[exon1_start], [exon1_end]], dtype='int')
self.edges = sp.array([[0]], dtype='int')
else:
self.vertices = sp.c_[self.vertices, [exon1_start, exon1_end]]
self.new_edge()
### more than one exon in the transcript
else:
for exon_idx in range(exon_start_end.shape[0] - 1):
exon1_start = exon_start_end[exon_idx , 0]
exon1_end = exon_start_end[exon_idx, 1]
exon2_start = exon_start_end[exon_idx + 1, 0]
exon2_end = exon_start_end[exon_idx + 1, 1]
if self.vertices.shape[1] == 0:
self.vertices = sp.array([[exon1_start, exon2_start], [exon1_end, exon2_end]], dtype='int')
self.edges = sp.array([[0, 1], [1, 0]], dtype='int')
else:
exon1_idx = -1
exon2_idx = -1
### check if current exon already occurred
for idx in range(self.vertices.shape[1]):
if ((self.vertices[0, idx] == exon1_start) and (self.vertices[1, idx] == exon1_end)):
exon1_idx = idx
if ((self.vertices[0, idx] == exon2_start) and (self.vertices[1, idx] == exon2_end)):
exon2_idx = idx
### both exons already occured -> only add an edge
if (exon1_idx != -1) and (exon2_idx != -1):
self.edges[exon1_idx, exon2_idx] = 1
self.edges[exon2_idx, exon1_idx] = 1
else:
### 2nd exon occured
if ((exon1_idx == -1) and (exon2_idx != -1)):
self.vertices = sp.c_[self.vertices, [exon1_start, exon1_end]]
self.new_edge()
self.edges[exon2_idx, -1] = 1
self.edges[-1, exon2_idx] = 1
### 1st exon occured
elif ((exon2_idx == -1) and (exon1_idx != -1)):
self.vertices = sp.c_[self.vertices, [exon2_start, exon2_end]]
self.new_edge()
self.edges[exon1_idx, -1] = 1
self.edges[-1, exon1_idx] = 1
### no exon occured
else:
assert((exon1_idx == -1) and (exon2_idx == -1))
self.vertices = sp.c_[self.vertices, [exon1_start, exon1_end]]
self.vertices = sp.c_[self.vertices, [exon2_start, exon2_end]]
self.new_edge()
self.new_edge()
self.edges[-2, -1] = 1
self.edges[-1, -2] = 1
### take care of the sorting by exon start
s_idx = sp.argsort(self.vertices[0, :])
self.vertices = self.vertices[:, s_idx]
self.edges = self.edges[s_idx, :][:, s_idx]
self.terminals = sp.zeros(self.vertices.shape, dtype='int')
self.terminals[0, sp.where(sp.tril(self.edges).sum(axis=1) == 0)[0]] = 1
self.terminals[1, sp.where(sp.triu(self.edges).sum(axis=1) == 0)[0]] = 1
def update_terminals(self):
self.terminals = sp.zeros(self.vertices.shape, dtype='int')
self.terminals[0, sp.where(sp.sum(sp.tril(self.edges), axis=1) == 0)[0]] = 1
self.terminals[1, sp.where(sp.sum(sp.triu(self.edges), axis=1) == 0)[0]] = 1
def newton(self, v=None, maxit=100, tol=EPS, verbose=False,
gauss_seidel=False):
"""Solve Bellman equations via Newton method (policy iteration)
Parameters
--------------
v : array, shape (n, ), optional
Initial guess for values.
x : array, shape (n, ), optional
Initial guess for policy.
maxit : int, optional
Maximum number of iterations
tol : float, optional
Convergence tolerance
gauss_seidel : bool, optional
Use Gauss-Seidel to solve the linear equation.
Returns
------------
info : int
Exit status. 0 if converged. -1 if not.
t : int
Number of iterations
relres : float
Residual variance
v : array, shape (n, )
x : array, shape
pstar : array, shape
Notes
--------
Also called policy iteration.
"""
if v is None:
v = sp.zeros(self.n)
## Set initial values of x to such
x = sp.zeros(self.n)
info = -1
t = 0
for it in range(maxit):
t += 1
xold = x.copy()
v, x = self.valmax(v)
pstar, fstar, ind = self.valpol(x)
Q = pstar * self.discount
eyeminus(Q)
if not gauss_seidel:
vold = v.copy()
v = la.solve(Q, fstar)
relres = la.norm(v - vold)
else:
## Gauss Seidel
L = sp.tril(Q)
dv = la.solve(L, fstar - sp.dot(Q, v))
relres = la.norm(dv)
v += dv
if verbose:
print("%d, %f" % (it, relres))
if sp.all(x == xold):
info = 0
break
return (info, t, relres, v, x, pstar)