def autocor_two_time(self,print_=False,save_=True,filename=None):
global buf,num,cts,cur,g12, countl
global Ndel,Npix
global time_ind #generate a time-frame for each level
global g12x, g12y, g12z #for interpolate
start_time = time.time()
buf=zeros([nolev,nobuf,nopixels]) #// matrix of buffers, for store img
cts=zeros(nolev)
cur=ones(nolev) * nobuf
countl = array(zeros( nolev ),dtype='int')
g12 = zeros( [ noframes,noframes, noqs] )
g12x=[]
g12y=[]
g12z=[]
num= array(zeros( nolev ),dtype='int')
time_ind ={key: [] for key in range(nolev)}
ttx=0
for n in range(1,noframes +1 ): ##do the work here
self.insertimg_twotime(begframe+n-1, print_=print_)
if n %(noframes/10) ==0:
sys.stdout.write("#")
sys.stdout.flush()
for q in range(noqs):
x0 = g12[:,:,q]
g12[:,:,q] = tril(x0) + tril(x0).T - diag(diag(x0))
elapsed_time = time.time() - start_time
print 'Total time: %.2f min' %(elapsed_time/60.)
if save_:
if filename==None:
filename = 'g12_-%s-%s_ImgReadMethod_'%(
begframe,begframe+noframes-1)+FOUT
save( RES_DIR + filename+FOUT, g12)
print 'the %s was stored in %s'%(filename,RES_DIR)
return g12, (elapsed_time/60.)
def _chol_blocked_fwd(L, Adot, NB=256, inplace=False):
"""
Forwards-mode differentiation through the Cholesky decomposition
Obtain L_dot from Sigma_dot, where "_dot" means sensitivities in
forwards-mode differentiation, and Sigma = L @ L.T.
This version uses a blocked algorithm to update sensitivities Adot
in place. tril(Adot) should start containing Sigma_dot, and will
end containing the L_dot. Take tril() of the answer if
triu(Adot,1) did not start out filled with zeros. Unlike the
unblocked routine, if the upper triangular part of Adot started
with non-zero values, some of these will be overwritten.
If inplace=False, a copy of Adot is modified instead of the
original. The Abar that was modified is returned.
"""
if not inplace:
Adot = Adot.copy()
for j in range(0, L.shape[0], NB):
k = min(N, j + NB)
R, D, B, C = _level3partition(L, j, k)
Rdot, Ddot, Bdot, Cdot = _level3partition(Adot, j, k)
Ddot[:] = tril(Ddot) - tril(np.dot(Rdot, R.T) + np.dot(R, Rdot.T))
#chol_unblocked_fwd(D, Ddot, inplace=True) # slow in Python
Ddot[:] = _chol_symbolic_fwd(D, Ddot + tril(Ddot, -1).T)
Cdot -= (np.dot(Bdot, R.T) + np.dot(B, Rdot.T))
#Cdot[:] = (Cdot - [email protected]) @ inv(tril(D)).T
Cdot[:] = _st(D, Cdot.T - np.dot(Ddot, C.T)).T
return Adot
def _chol_blocked_rev(L, Abar, NB=256, inplace=False):
"""
Reverse-mode differentiation through the Cholesky decomposition
Obtain tril(Sigma_bar) from L_bar, where "_bar" means sensitivities
in reverse-mode differentiation, and Sigma = L @ L.T.
This version uses a blocked algorithm to update sensitivities Abar
in place. tril(Abar) should start containing L_bar, and will end
containing the tril(Sigma_bar). Take tril(Abar) at the end if
triu(Abar,1) did not start out filled with zeros. Alternatively,
(tril(Abar) + tril(Abar).T) will give the symmetric, redundant
matrix of sensitivities.
Unlike the unblocked routine, if the upper triangular part of Abar
started with non-zero values, some of these will be overwritten.
If inplace=False, a copy of Abar is modified instead of the
original. The Abar that was modified is returned.
"""
if not inplace:
Abar = Abar.copy()
for k in range(L.shape[0], -1, -NB):
j = max(0, k - NB)
R, D, B, C = _level3partition(L, j, k)
Rbar, Dbar, Bbar, Cbar = _level3partition(Abar, j, k)
#Cbar[:] = Cbar @ inv(tril(D))
Cbar[:] = _st(D, Cbar.T, trans=1).T
Bbar -= np.dot(Cbar, R)
Dbar[:] = tril(Dbar) - tril(np.dot(Cbar.T, C))
#chol_unblocked_rev(D, Dbar, inplace=True) # slow in Python
Dbar[:] = _chol_symbolic_rev(D, Dbar)
Rbar -= (np.dot(Cbar.T, B) + np.dot(Dbar + Dbar.T, R))
return Abar
def test_al_mohy_higham_2012_experiment_1(self):
# Matrix square root of a tricky upper triangular matrix.
A = _get_al_mohy_higham_2012_experiment_1()
A_sqrtm, info = sqrtm(A, disp=False)
A_round_trip = A_sqrtm.dot(A_sqrtm)
assert_allclose(A_round_trip, A, rtol=1e-5)
assert_allclose(np.tril(A_round_trip), np.tril(A))
def q150():
x = numpy.arange(2**20, dtype=numpy.int64)
x = (615949*x + 797807) % 2**20
s = numpy.empty(500500+1,dtype=numpy.int64)
t = 0
s[0] = 0
for k in xrange(1,500500+1):
t = x[t]
s[k] = t - 2**19
del x
print s[1:4]
r,c = numpy.mgrid[:1000,:1000]
s = s[numpy.tril(r*(r+1)/2 + c + 1)]
del r,c
s0 = s
best = s.min()
t = s
p = numpy.zeros((1001,1001), dtype=numpy.int64)
for i in xrange(1,1000):
n = s[:-1,:-1] + numpy.tril(t[1:,:-1]) + t[1:,1:] - numpy.tril(p[2:,1:-1])
#n = s[:-1,:-1] +t[1:,:-1] + t[1:,1:] - p[2:,1:-1]
print i,best,t[0,0]
p,t,s = t,n,s[:-1,:-1]
best = min(best, t.min())
print best
def plot_distance_matrix(distance_csv_file, outfile="similarity_matrix_plot.pdf"):
"""
plotting distance matrix between organisms
the distance between the organisms are calculated based on the difference in their sequence composition
"""
distance = pandas.read_csv(distance_csv_file, header=0)
C = numpy.tril(distance)
sim = 1-distance
C = numpy.tril(sim)
N = sim.shape[1]
C = numpy.ma.masked_array(C, C == 0)
A = numpy.array([(y, x) for x in range(N, -1, -1) for y in range(N + 1)])
t = numpy.array([[0.5, 1], [0.5, -1]])
A = numpy.dot(A, t)
X = A[:, 1].reshape(N + 1, N + 1)
Y = A[:, 0].reshape(N + 1, N + 1)
fig = pylab.figure(figsize=(20,20))
ax = fig.add_subplot(121, frame_on=False, aspect=2.0)
ax.set_xticks([])
ax.set_yticks([])
caxes = pylab.pcolormesh(X, Y, np.flipud(C), axes=ax)
ax.set_xlim(right=0)
fig.savefig(outfile, bbox_inches='tight')
def getMechStiffStatistic(self, rangeK, minAA=0, AA='all'):
"""Return number of effective spring constant with set range of
amino acids of protein structure.
``AA`` can be a list with a range of analysed amino acids as:
[first_aa, last_aa, first_aa2, last_aa2],
minAA - eliminate amino acids that are within 20aa and
``rangeK`` is a list [minK, maxK]"""
model = self.getModel()
if AA == 'all':
sm = model.getStiffness()
elif type(AA) == int:
sm = model.getStiffness()[0: AA, (-1)*AA-1:-1]
elif type(AA) == list and len(AA) == 1:
sm = model.getStiffness()[0: AA, (-1)*AA-1:-1]
elif type(AA) == list and len(AA) == 4:
sm = model.getStiffness()[AA[0]:AA[1],AA[2]:AA[3]]
if minAA > 0:
sm2 = sm[minAA:-1,0:-1-minAA] # matrix without close contacts
sm3 = np.tril(sm2, k=-1)
#sort_sm2 = np.sort((np.tril(sm2, k=-1)1).flatten())
a = np.where(np.logical_and(sm3>rangeK[0], sm3<rangeK[1]))
if minAA == 0:
sm2 = np.tril(sm, k=-1)
a = np.where(np.logical_and(sm2>rangeK[0], sm2<rangeK[1]))
return len(a[0])
def __init__(self, batch_size, mem_size, hidden_size):
self.hidden_size = hidden_size
self.mem_size = mem_size
self.batch_size = batch_size
N, M, d = batch_size, mem_size, hidden_size
self.L = np.tril(np.ones([M, M], dtype='float32'))
self.sL = np.tril(np.ones([M, M], dtype='float32'), k=-1)
def cmat_for_key(connectome, key, number_of_nodes=None,
force_symmetric=True):
"""Return a N x N connection matrix for given connectome and
key. The connection matrix is returned as a numpy ndarray.
"""
# create our new shiny connection matrix
import numpy
if number_of_nodes is None:
n = max(connectome.nodes())
else:
n = number_of_nodes
new_cmat = numpy.zeros((n,n))
# extract the value for key for every edge in the given connectome
for i,j in connectome.edges_iter():
new_cmat[i-1][j-1] = connectome[i][j][key]
# do we need to do anything regarding symmetry?
if force_symmetric and (new_cmat - new_cmat.T != 0).any():
#...if one-sided (no information below diagonal)
if (numpy.tril(new_cmat,-1) == 0).all():
# project above diagonal onto below diagonal
new_cmat += numpy.tril(new_cmat.T, -1)
#...else, we will assume two-sided unequal
else:
# our solution will be to take the mean of each pair of
# reflected indices
new_cmat = (new_cmat + new_cmat.T ) / 2.0
# return the cmat
return new_cmat
def connectionParameterMatrix(self, parameter): if utils.isCallable(parameter): matrix = parameter((self.noNodes, self.noNodes)) * self.connections matrix = np.tril(matrix) + np.tril(matrix).T # ensure symmetry else: matrix = parameter * np.ones((self.noNodes, self.noNodes)) * self.connections return matrix
def test_separate_independent_mok(session_tf):
"""
We use different independent kernels for each of the output dimensions.
We can achieve this in two ways:
1) efficient: SeparateIndependentMok with Shared/SeparateIndependentMof
2) inefficient: SeparateIndependentMok with InducingPoints
However, both methods should return the same conditional,
and after optimization return the same log likelihood.
"""
# Model 1 (INefficient)
q_mu_1 = np.random.randn(Data.M * Data.P, 1)
q_sqrt_1 = np.tril(np.random.randn(Data.M * Data.P, Data.M * Data.P))[None, ...] # 1 x MP x MP
kern_list_1 = [RBF(Data.D, variance=0.5, lengthscales=1.2) for _ in range(Data.P)]
kernel_1 = mk.SeparateIndependentMok(kern_list_1)
feature_1 = InducingPoints(Data.X[:Data.M,...].copy())
m1 = SVGP(Data.X, Data.Y, kernel_1, Gaussian(), feature_1, q_mu=q_mu_1, q_sqrt=q_sqrt_1)
m1.set_trainable(False)
m1.q_sqrt.set_trainable(True)
m1.q_mu.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Data.MAXITER)
# Model 2 (efficient)
q_mu_2 = np.random.randn(Data.M, Data.P)
q_sqrt_2 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M
kern_list_2 = [RBF(Data.D, variance=0.5, lengthscales=1.2) for _ in range(Data.P)]
kernel_2 = mk.SeparateIndependentMok(kern_list_2)
feature_2 = mf.SharedIndependentMof(InducingPoints(Data.X[:Data.M, ...].copy()))
m2 = SVGP(Data.X, Data.Y, kernel_2, Gaussian(), feature_2, q_mu=q_mu_2, q_sqrt=q_sqrt_2)
m2.set_trainable(False)
m2.q_sqrt.set_trainable(True)
m2.q_mu.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Data.MAXITER)
check_equality_predictions(session_tf, [m1, m2])
def _test(n):
"""Do an nxn test case worth 5 points."""
A = self._luTestCase(n)
L1, U1 = lu(A)
if not np.allclose(L1.dot(U1), A):
return _test(n)
stu = s.lu(A.copy())
try:
L2, U2 = stu
except(TypeError, ValueError):
raise ValueError("lu() failed to return two arrays")
pts = 5
if not all(np.allclose(*x) for x in [(np.tril(L2), L2),
(np.triu(U2), U2), (L1, L2), (U1, U2), (A, L2.dot(U2))]):
pts = 2
self.feedback += "\n\n{}\nA =\n{}".format('- '*20, A)
if not np.allclose(np.tril(L2), L2):
self.feedback += "\nL not lower triangular:\n{}".format(L2)
pts -= 1
if not np.allclose(np.triu(U2), U2):
self.feedback += "\nU not upper triangular:\n{}".format(U2)
pts -= 1
pts += self._eqTest(L1, L2, "lu() failed (L incorrect)")
pts += self._eqTest(U1, U2, "lu() failed (U incorrect)")
pts += self._eqTest(A, L2.dot(U2), "lu() failed (A != LU)")
return pts
def hessian(self, x, lagrange, obj_factor):
H = np.zeros((2*self._m, 2*self._m))
H[:self._m, :self._m] = np.tril(np.tril(np.dot(self._A.T, self._A)))
row, col = self.hessianstructure()
return obj_factor*H[row, col]
def vec_to_sym(vec, shape):
mask = np.tril(np.ones(shape)).astype(np.bool)
sym = np.zeros(vec.shape[:-1] + mask.shape, vec.dtype)
sym[..., mask] = vec
sym -= (1 - np.sqrt(2))*np.diag(np.diag(sym))
sym /= np.sqrt(2)
sym += np.tril(sym, k=-1).T
return sym
def absMDS(distmat, Z, weights, Vp): dZ = eucD(Z) dZ[dZ==0] = 1E-5 bZ = Bcalc(weights, distmat, dZ) Xu = Vp.dot(bZ).dot(Z) dXu = eucD(Xu) stress = np.sqrt(np.tril(weights*(distmat-dXu)**2).sum() / np.tril(dXu**2).sum()) return stress, Xu
def test_riemann():
"""Simple test of the Riemann matrix."""
n = 10
a = rogues.riemann(n)
b = np.tril(-np.ones((n, n)), -1)
c = np.tril(a, -1)
# Kind of a goofy prop to check, but it's simple
npt.assert_array_equal(b, c)
def run_tril(dtype, shape, order, inplace):
ac, ag = gen_gpuarray(shape, dtype, order=order, ctx=context)
result = tril(ag, inplace=inplace)
assert numpy.all(numpy.tril(ac) == result)
if inplace:
assert numpy.all(numpy.tril(ac) == ag)
else:
assert numpy.all(ac == ag)
def test_compute_epochs_csd():
"""Test computing cross-spectral density from epochs
"""
epochs, epochs_sin = _get_data()
# Check that wrong parameters are recognized
assert_raises(ValueError, compute_epochs_csd, epochs, mode="notamode")
assert_raises(ValueError, compute_epochs_csd, epochs, fmin=20, fmax=10)
assert_raises(ValueError, compute_epochs_csd, epochs, fmin=20, fmax=20.1)
assert_raises(ValueError, compute_epochs_csd, epochs, tmin=0.15, tmax=0.1)
assert_raises(ValueError, compute_epochs_csd, epochs, tmin=0, tmax=10)
assert_raises(ValueError, compute_epochs_csd, epochs, tmin=10, tmax=11)
data_csd_mt = compute_epochs_csd(epochs, mode="multitaper", fmin=8, fmax=12, tmin=0.04, tmax=0.15)
data_csd_fourier = compute_epochs_csd(epochs, mode="fourier", fmin=8, fmax=12, tmin=0.04, tmax=0.15)
# Check shape of the CSD matrix
n_chan = len(data_csd_mt.ch_names)
assert_equal(data_csd_mt.data.shape, (n_chan, n_chan))
assert_equal(data_csd_fourier.data.shape, (n_chan, n_chan))
# Check if the CSD matrix is hermitian
assert_array_equal(np.tril(data_csd_mt.data).T.conj(), np.triu(data_csd_mt.data))
assert_array_equal(np.tril(data_csd_fourier.data).T.conj(), np.triu(data_csd_fourier.data))
# Computing induced power for comparison
epochs.crop(tmin=0.04, tmax=0.15)
power, _ = induced_power(epochs.get_data(), epochs.info["sfreq"], [10], n_cycles=0.6)
power = np.mean(power, 2)
# Maximum PSD should occur for specific channel
max_ch_power = power.argmax()
max_ch_mt = data_csd_mt.data.diagonal().argmax()
max_ch_fourier = data_csd_fourier.data.diagonal().argmax()
assert_equal(max_ch_mt, max_ch_power)
assert_equal(max_ch_fourier, max_ch_power)
# Maximum CSD should occur for specific channel
ch_csd_mt = [np.abs(data_csd_mt.data[max_ch_power][i]) if i != max_ch_power else 0 for i in range(n_chan)]
max_ch_csd_mt = np.argmax(ch_csd_mt)
ch_csd_fourier = [np.abs(data_csd_fourier.data[max_ch_power][i]) if i != max_ch_power else 0 for i in range(n_chan)]
max_ch_csd_fourier = np.argmax(ch_csd_fourier)
assert_equal(max_ch_csd_mt, max_ch_csd_fourier)
# Check a list of CSD matrices is returned for multiple frequencies within
# a given range when fsum=False
csd_fsum = compute_epochs_csd(epochs, mode="fourier", fmin=8, fmax=20, fsum=True)
csds = compute_epochs_csd(epochs, mode="fourier", fmin=8, fmax=20, fsum=False)
freqs = [csd.frequencies[0] for csd in csds]
csd_sum = np.zeros_like(csd_fsum.data)
for csd in csds:
csd_sum += csd.data
assert len(csds) == 2
assert len(csd_fsum.frequencies) == 2
assert_array_equal(csd_fsum.frequencies, freqs)
assert_array_equal(csd_fsum.data, csd_sum)
def test_tfttr_trttf():
"""
Test conversion routines between the Rectengular Full Packed (RFP) format
and Standard Triangular Array (TR)
"""
seed(1234)
for ind, dtype in enumerate(DTYPES):
n = 20
if ind > 1:
A_full = (rand(n, n) + rand(n, n)*1j).astype(dtype)
transr = 'C'
else:
A_full = (rand(n, n)).astype(dtype)
transr = 'T'
trttf, tfttr = get_lapack_funcs(('trttf', 'tfttr'), dtype=dtype)
A_tf_U, info = trttf(A_full)
assert_(info == 0)
A_tf_L, info = trttf(A_full, uplo='L')
assert_(info == 0)
A_tf_U_T, info = trttf(A_full, transr=transr, uplo='U')
assert_(info == 0)
A_tf_L_T, info = trttf(A_full, transr=transr, uplo='L')
assert_(info == 0)
# Create the RFP array manually (n is even!)
A_tf_U_m = zeros((n+1, n//2), dtype=dtype)
A_tf_U_m[:-1, :] = triu(A_full)[:, n//2:]
A_tf_U_m[n//2+1:, :] += triu(A_full)[:n//2, :n//2].conj().T
A_tf_L_m = zeros((n+1, n//2), dtype=dtype)
A_tf_L_m[1:, :] = tril(A_full)[:, :n//2]
A_tf_L_m[:n//2, :] += tril(A_full)[n//2:, n//2:].conj().T
assert_array_almost_equal(A_tf_U, A_tf_U_m.reshape(-1, order='F'))
assert_array_almost_equal(A_tf_U_T,
A_tf_U_m.conj().T.reshape(-1, order='F'))
assert_array_almost_equal(A_tf_L, A_tf_L_m.reshape(-1, order='F'))
assert_array_almost_equal(A_tf_L_T,
A_tf_L_m.conj().T.reshape(-1, order='F'))
# Get the original array from RFP
A_tr_U, info = tfttr(n, A_tf_U)
assert_(info == 0)
A_tr_L, info = tfttr(n, A_tf_L, uplo='L')
assert_(info == 0)
A_tr_U_T, info = tfttr(n, A_tf_U_T, transr=transr, uplo='U')
assert_(info == 0)
A_tr_L_T, info = tfttr(n, A_tf_L_T, transr=transr, uplo='L')
assert_(info == 0)
assert_array_almost_equal(A_tr_U, triu(A_full))
assert_array_almost_equal(A_tr_U_T, triu(A_full))
assert_array_almost_equal(A_tr_L, tril(A_full))
assert_array_almost_equal(A_tr_L_T, tril(A_full))
def ratioMDS(distmat, b, Z, weights, Vp): dHat = distmat*b dZ = eucD(Z) dZ[dZ==0] = 1E-5 bZ = Bcalc(weights, dHat, dZ) Xu = Vp.dot(bZ).dot(Z) dXu = eucD(Xu) stress = np.sqrt(np.tril(weights*(dHat-dXu)**2).sum() / np.tril(dXu**2).sum()) b = np.tril(weights*distmat*dXu).sum() / np.tril(weights*distmat**2).sum() return stress, Xu, b
def passed_test(dtype, as_matrix, provide_C, uplo, trans):
"""
Run one symmetric rank-2k update test.
Arguments:
dtype: either 'float64' or 'float32', the NumPy dtype to test
as_matrix: True to test a NumPy matrix, False to test a NumPy ndarray
provide_C: True if C is to be provided to the BLASpy function, False otherwise
uplo: BLASpy 'uplo' parameter to test
trans: BLASpy 'trans' parameter to test
Returns:
True if the expected result is within the margin of error of the actual result,
False otherwise.
"""
transpose_a = trans == 't' or trans == 'T'
upper = uplo == 'u' or uplo == 'U'
# generate random sizes for matrix dimensions
m_A = randint(N_MIN, N_MAX)
n_A = randint(N_MIN, N_MAX)
n = m_A if not transpose_a else n_A
# create random scalars and matrices to test
alpha = uniform(SCAL_MIN, SCAL_MAX)
beta = uniform(SCAL_MIN, SCAL_MAX)
A = random_matrix(m_A, n_A, dtype, as_matrix)
B = random_matrix(m_A, n_A, dtype, as_matrix)
C = random_symmetric_matrix(n, dtype, as_matrix) if provide_C else None
# create a copy of C that can be used to calculate the expected result
C_2 = copy(C) if C is not None else zeros((n, n))
# compute the expected result
if not transpose_a:
C_2 = (beta * C_2) + (alpha * dot(A, B.T)) + (alpha * dot(B, A.T))
else:
C_2 = (beta * C_2) + (alpha * dot(A.T, B)) + (alpha * dot(B.T, A))
# ensure C and C_2 are upper or lower triangular representations of symmetric matrices
if upper:
C_2 = triu(C_2)
if provide_C:
C = triu(C)
else:
C_2 = tril(C_2)
if provide_C:
C = tril(C)
# get the actual result
C = syr2k(A, B, C, uplo, trans, alpha, beta)
# compare the actual result to the expected result and return result of the test
return allclose(C, C_2, RTOL, ATOL)
def __init__(self, s):
"""Initialize the elastic tensor from a string"""
if not s:
raise ValueError("no matrix was provided")
# Remove braces and pipes
s = s.replace("|", " ").replace("(", " ").replace(")", " ")
# Remove empty lines
lines = [line for line in s.split('\n') if line.strip()]
if len(lines) != 6:
raise ValueError("should have six rows")
# Convert to float
try:
mat = [map(float, line.split()) for line in lines]
except:
raise ValueError("not all entries are numbers")
# Make it into a square matrix
mat = np.array(mat)
if mat.shape != (6,6):
# Is it upper triangular?
if map(len, mat) == [6,5,4,3,2,1]:
mat = [ [0]*i + mat[i] for i in range(6) ]
mat = np.array(mat)
# Is it lower triangular?
if map(len, mat) == [1,2,3,4,5,6]:
mat = [ mat[i] + [0]*(5-i) for i in range(6) ]
mat = np.array(mat)
if mat.shape != (6,6):
raise ValueError("should be a square matrix")
# Check that is is symmetric, or make it symmetric
if la.norm(np.tril(mat, -1)) == 0:
mat = mat + np.triu(mat, 1).transpose()
if la.norm(np.triu(mat, 1)) == 0:
mat = mat + np.tril(mat, -1).transpose()
if la.norm(mat - mat.transpose()) > 0:
raise ValueError("should be symmetric, or triangular")
# Store it
self.CVoigt = mat
# Put it in a more useful representation
self.SVoigt = la.inv(self.CVoigt)
VoigtMat = [[0, 5, 4], [5, 1, 3], [4, 3, 2]]
def SVoigtCoeff(p,q): return 1. / ((1+p/3)*(1+q/3))
self.Smat = [[[[ SVoigtCoeff(VoigtMat[i][j], VoigtMat[k][l]) * self.SVoigt[VoigtMat[i][j]][VoigtMat[k][l]]
for i in range(3) ] for j in range(3) ] for k in range(3) ] for l in range(3) ]
return
def nMDS(distmat, Z, weights, Vp): dZ = eucD(Z) dZ[dZ==0] = 1E-5 diss_f = distmat.ravel() dhat_f = dZ.ravel() dhat = isotonic(dhat_f, diss_f) dhat = dhat.prediction.reshape(distmat.shape) stress = np.sqrt(np.tril((weights*(dZ - dhat)**2)).sum() / np.tril(weights*dZ**2).sum()) bZ = Bcalc(weights, dhat, dZ) Xu = Vp.dot(bZ).dot(Z) return stress, Xu
def collocate_at_nodes(mesh):
for d in mesh.dList:
# Set up collXYZ with an initial value
coll_store = d.eList[0].vals(d.eList[0].limits[0], d.eList[0].limits[2])
for e in d.eList:
xi1 = np.linspace(e.limits[0], e.limits[1], e.m + 1)
xi2 = np.linspace(e.limits[2], e.limits[3], e.n + 1)
xi1, xi2 = np.meshgrid(xi1, xi2)
e.collocationXi = np.vstack([xi1.reshape(-1), xi2.reshape(-1)])
if e.__class__.__name__ == "SerendipityQuadraticElement":
e.collocationXi = np.delete(e.collocationXi, 4, axis=1)
e.collocation_points = e.vals(e.collocationXi[0], e.collocationXi[1])
# Check for repeated points in new set
px, py, pz = e.collocation_points
px = px.reshape(-1, 1)
py = py.reshape(-1, 1)
pz = pz.reshape(-1, 1)
qx, qy, qz = e.collocation_points
rx = px - qx
ry = py - qy
rz = pz - qz
rx = np.tril(rx, -1)[:, :-1] + np.triu(rx, 1)[:, 1:]
ry = np.tril(ry, -1)[:, :-1] + np.triu(ry, 1)[:, 1:]
rz = np.tril(rz, -1)[:, :-1] + np.triu(rz, 1)[:, 1:]
r = np.sqrt(rx ** 2 + ry ** 2 + rz ** 2)
delete = np.where(np.any(r < 1e-10, axis=1))[0]
e.collocation_points = np.delete(e.collocation_points, delete[1:], axis=1)
e.collocationXi = np.delete(e.collocationXi, delete[1:], axis=1)
# Check for repeated points in large set
px, py, pz = e.collocation_points
px = px.reshape(-1, 1)
py = py.reshape(-1, 1)
pz = pz.reshape(-1, 1)
qx, qy, qz = coll_store
r = np.sqrt((qx - px) ** 2 + (qy - py) ** 2 + (qz - pz) ** 2)
delete = np.where(np.any(r < 1e-10, axis=1))[0]
coll_store = np.hstack([coll_store, np.delete(e.collocation_points, delete, axis=1)])
d.collocation_points = coll_store
# Apply to mesh
mesh.collocation_points = np.hstack([d.collocation_points for d in mesh.dList])
mesh.numBoundaryCollocation = mesh.collocation_points.shape[1]
def passed_test(dtype, as_matrix, x_is_row, y_is_row, provide_A, stride, uplo):
"""
Run one symmetric rank-2 update test.
Arguments:
dtype: either 'float64' or 'float32', the NumPy dtype to test
as_matrix: True to test a NumPy matrix, False to test a NumPy ndarray
x_is_row: True to test a row vector as parameter x, False to test a column vector
y_is_row: True to test a row vector as parameter y, False to test a column vector
provide_A: True if A is to be provided to the BLASpy function, False otherwise
stride: stride of x and y to test; if None, a random stride is assigned
uplo: BLASpy uplo parameter to test
Returns:
True if the expected result is within the margin of error of the actual result,
False otherwise.
"""
# generate random sizes for matrix/vector dimensions and vector stride (if necessary)
n = randint(N_MIN, N_MAX)
stride = randint(N_MIN, STRIDE_MAX) if stride is None else stride
n_A = n / stride + (n % stride > 0)
# create random scalars, vectors, and matrices to test
alpha = uniform(SCAL_MIN, SCAL_MAX)
x = random_vector(n, x_is_row, dtype, as_matrix)
y = random_vector(n, y_is_row, dtype, as_matrix)
A = random_symmetric_matrix(n_A, dtype, as_matrix) if provide_A else None
# create copies/views of A, x, and y that can be used to calculate the expected result
x_2 = x.T if x_is_row else x
y_2 = y.T if y_is_row else y
A_2 = zeros((n_A, n_A)) if A is None else copy(A)
# compute the expected result
if stride == 1:
A_2 += alpha * dot(x_2, y_2.T)
A_2 += alpha * dot(y_2, x_2.T)
else:
for i in range(0, n_A):
for j in range(0, n_A):
A_2[i, j] += alpha * (x_2[i * stride, 0] * y_2[j * stride, 0])
A_2[i, j] += alpha * (y_2[i * stride, 0] * x_2[j * stride, 0])
# get the actual result
A = syr2(x, y, A, uplo, alpha, inc_x=stride, inc_y=stride)
# make A and A_2 triangular so that they can be compared
A = triu(A) if uplo == 'u' else tril(A)
A_2 = triu(A_2) if uplo == 'u' else tril(A_2)
# compare the actual result to the expected result and return result of the test
return allclose(A, A_2, RTOL, ATOL)
def test_tril():
for shape in [(10, 5), (5, 10), (10, 10)]:
for order in ['c', 'f']:
for inplace in [True, False]:
ac, ag = gen_gpuarray(shape, 'float32',
order=order, ctx=context)
result = tril(ag, inplace=inplace)
assert numpy.all(numpy.tril(ac) == result)
if inplace:
assert numpy.all(numpy.tril(ac) == ag)
else:
assert numpy.all(ac == ag)
def test_tril_triu():
A = np.random.randn(20, 20)
for chk in [5, 4]:
dA = da.from_array(A, (chk, chk))
assert np.allclose(da.triu(dA).compute(), np.triu(A))
assert np.allclose(da.tril(dA).compute(), np.tril(A))
for k in [-25, -20, -19, -15, -14, -9, -8, -6, -5, -1,
1, 4, 5, 6, 8, 10, 11, 15, 16, 19, 20, 21]:
assert np.allclose(da.triu(dA, k).compute(), np.triu(A, k))
assert np.allclose(da.tril(dA, k).compute(), np.tril(A, k))
def train(self, sample, trg=None, err=None, d=None, e=None):
"""Train the regression on one or more samples.
``sample``
Input samples. Array of size (K, input_dim)
``trg``
Sample target. Array of size (K, output_dim)
``err``
Sample error terms. Array of size (K, output_dim)
"""
if self._stop_training:
return
if d is not None:
warnings.warn("Use of argument 'd' is deprecated. Use 'trg' instead.")
trg = d
if e is not None:
warnings.warn("Use of argument 'e' is deprecated. Use 'err' instead.")
err = e
if self.with_bias:
sample = self._add_constant(sample)
for i in range(sample.shape[0]):
# preliminaries
sample_i = np.atleast_2d(sample[i]).T
psi_x = self._psi_inv.dot(sample_i)
gain = 1.0 / (self.lambda_ + sample_i.T.dot(psi_x)) * psi_x
# error
if err is None:
trg_i = np.atleast_2d(trg[i]).T
pred = self.beta.T.dot(sample_i)
err_i = trg_i - pred
else:
err_i = np.atleast_2d(err[i]).T
# update
self.beta += gain.dot(err_i.T)
tri = np.tril(self._psi_inv)
tri -= np.tril(gain*psi_x.T)
tri /= self.lambda_
#self._psi_inv = tri + tri.T - np.diag(tri.diagonal())
# FIXME: (numpy bug) tri.diagonal() introduces a memory leak
self._psi_inv = np.tril(tri, -1).T + tri
# Diagonal stabilization
self.cnt_train += 1
if self.cnt_train % self.tau == 0:
np.fill_diagonal(self._psi_inv, self.diag_default)
def _process_data(self, data):
"""data array into usable data structures
Create empty spin array
Create structures for couplings between spins
Create adjacency list for spins and neighbours
"""
# map spins to contiguous positive integer values
max_spin = np.amax(data[:,:-1]).astype(int)
unique_spins = np.unique(data[:,:-1]).astype(int)
spin_map = np.zeros((max_spin + 1), dtype=int)
for i, spin in enumerate(unique_spins):
spin_map[spin] = i
# build couplings matrix, spin array and adjacency list
self.size = unique_spins.size
self.J = np.zeros((self.size, self.size), dtype=float)
# this is lower triangular with self-couplings on the diagonal
for i, j, J in data[data[:,0].argsort()]:
i = spin_map[int(i)]
j = spin_map[int(j)]
# print "i: {}, j: {}, J: {}".format(i, j, J)
if i >= j:
self.J[i,j] = J
else:
self.J[j,i] = J
if np.max(np.absolute(self.J)) > 1:
self.scaling_factor = 1e5
self.J /= self.scaling_factor
self.h = np.diag(self.J).copy()
np.fill_diagonal(self.J, 0)
# ensure J is formed properly
assert(self.J.any() == True)
assert(np.triu(self.J).any() == False)
assert(np.tril(self.J).any() == True)
self.J = np.tril(self.J)
assert(np.triu(self.J).any() == False)
self.J += np.tril(self.J).T
# about the adjacency list:
# it is possible to just use h and J with the spins array
# in order to do all the calculations using linear algebra,
# but when these problems are sparse, an adjacency list works
# much faster -- and in a spinglass, spins often have only two or
# three neighbours
self.adjacency = [[j for j, x in enumerate(self.J[i]) if x != 0] for i in xrange(self.size)]
# lock arrays to prevent accidental mutations
self.J.flags.writeable = False
self.h.flags.writeable = False
def test_syr2k(self):
for f in _get_func('syr2k'):
c = f(a=self.a, b=self.b, alpha=1.)
assert_array_almost_equal(np.triu(c), np.triu(self.t))
c = f(a=self.a, b=self.b, alpha=1., lower=1)
assert_array_almost_equal(np.tril(c), np.tril(self.t))
c0 = np.ones(self.t.shape)
c = f(a=self.a, b=self.b, alpha=1., beta=1., c=c0)
assert_array_almost_equal(np.triu(c), np.triu(self.t+c0))
c = f(a=self.a, b=self.b, alpha=1., trans=1)
assert_array_almost_equal(np.triu(c), np.triu(self.tt))
def args_maker():
a = rng(lhs_shape, dtype)
if sym_pos:
a = onp.matmul(a, onp.conj(T(a)))
a = onp.tril(a) if lower else onp.triu(a)
return [a, rng(rhs_shape, dtype)]
def compute_similarity(F, inds_to_compare): # inds_to_compare: feature indices
features_to_compare = F[inds_to_compare, :]
CORRMAT = np.corrcoef(features_to_compare)
similarity = np.mean(np.ma.masked_equal(np.tril(CORRMAT, -1), 0))
#np.mean(np.ma.masked_equal(np.tril(CORRMAT, -1), 0))#(np.tril(CORRMAT)) # (np.ma.masked_equal(np.tril(CORRMAT, -1), 0))
return similarity
def klip_math(sci,
ref_psfs,
numbasis,
covar_psfs=None,
return_basis=False,
return_basis_and_eig=False):
"""
Helper function for KLIP that does the linear algebra
Args:
sci: array of length p containing the science data
ref_psfs: N x p array of the N reference PSFs that
characterizes the PSF of the p pixels
numbasis: number of KLIP basis vectors to use (can be an int or an array of ints of length b)
covar_psfs: covariance matrix of reference psfs passed in so you don't have to calculate it here
return_basis: If true, return KL basis vectors (used when onesegment==True)
return_basis_and_eig: If true, return KL basis vectors as well as the eigenvalues and eigenvectors of the
covariance matrix. Used for KLIP Forward Modelling of Laurent Pueyo.
Returns:
sub_img_rows_selected: array of shape (p,b) that is the PSF subtracted data for each of the b KLIP basis
cutoffs. If numbasis was an int, then sub_img_row_selected is just an array of length p
KL_basis: array of shape (max(numbasis),p). Only if return_basis or return_basis_and_eig is True.
evals: Eigenvalues of the covariance matrix. The covariance matrix is assumed NOT to be normalized by (p-1).
Only if return_basis_and_eig is True.
evecs: Eigenvectors of the covariance matrix. The covariance matrix is assumed NOT to be normalized by (p-1).
Only if return_basis_and_eig is True.
"""
# for the science image, subtract the mean and mask bad pixels
sci_mean_sub = sci - np.nanmean(sci)
# sci_nanpix = np.where(np.isnan(sci_mean_sub))
# sci_mean_sub[sci_nanpix] = 0
# do the same for the reference PSFs
# playing some tricks to vectorize the subtraction
ref_psfs_mean_sub = ref_psfs - np.nanmean(ref_psfs, axis=1)[:, None]
ref_psfs_mean_sub[np.where(np.isnan(ref_psfs_mean_sub))] = 0
# calculate the covariance matrix for the reference PSFs
# note that numpy.cov normalizes by p-1 to get the NxN covariance matrix
# we have to correct for that a few lines down when consturcting the KL
# vectors since that's not part of the equation in the KLIP paper
if covar_psfs is None:
covar_psfs = np.cov(ref_psfs_mean_sub)
# maximum number of KL modes
tot_basis = covar_psfs.shape[0]
# only pick numbasis requested that are valid. We can't compute more KL basis than there are reference PSFs
# do numbasis - 1 for ease of indexing since index 0 is using 1 KL basis vector
numbasis = np.clip(
numbasis - 1, 0, tot_basis -
1) # clip values, for output consistency we'll keep duplicates
max_basis = np.max(
numbasis
) + 1 # maximum number of eigenvectors/KL basis we actually need to use/calculate
# calculate eigenvalues and eigenvectors of covariance matrix, but only the ones we need (up to max basis)
evals, evecs = la.eigh(covar_psfs,
eigvals=(tot_basis - max_basis, tot_basis - 1))
# check if there are negative eignevalues as they will cause NaNs later that we have to remove
# the eigenvalues are ordered smallest to largest
#check_nans = evals[-1] < 0 # currently this checks that *all* the evals are neg, but we want just one.
# also, include 0 because that is a bad value too
check_nans = np.any(
evals <= 0) # alternatively, check_nans = evals[0] <= 0
# scipy.linalg.eigh spits out the eigenvalues/vectors smallest first so we need to reverse
# we're going to recopy them to hopefully improve caching when doing matrix multiplication
evals = np.copy(evals[::-1])
evecs = np.copy(
evecs[:, ::-1], order='F'
) #fortran order to improve memory caching in matrix multiplication
# keep an index of the negative eignevalues for future reference if there are any
if check_nans:
neg_evals = (np.where(evals <= 0))[0]
# calculate the KL basis vectors
kl_basis = np.dot(ref_psfs_mean_sub.T, evecs)
# JB question: Why is there this [None, :]? (It adds an empty first dimension)
kl_basis = kl_basis * (1. / np.sqrt(
evals * (np.size(sci) - 1)))[None, :] #multiply a value for each row
# sort to KL basis in descending order (largest first)
# kl_basis = kl_basis[:,eig_args_all]
# duplicate science image by the max_basis to do simultaneous calculation for different k_KLIP
sci_mean_sub_rows = np.tile(sci_mean_sub, (max_basis, 1))
sci_rows_selected = np.tile(
sci_mean_sub,
(np.size(numbasis), 1)) # this is the output image which has less rows
# bad pixel mask
# do it first for the image we're just doing computations on but don't care about the output
sci_nanpix = np.where(np.isnan(sci_mean_sub_rows))
sci_mean_sub_rows[sci_nanpix] = 0
# now do it for the output image
sci_nanpix = np.where(np.isnan(sci_rows_selected))
sci_rows_selected[sci_nanpix] = 0
# do the KLIP equation, but now all the different k_KLIP simultaneously
# calculate the inner product of science image with each of the different kl_basis vectors
# TODO: can we optimize this so it doesn't have to multiply all the rows because in the next lines we only select some of them
inner_products = np.dot(sci_mean_sub_rows,
np.require(kl_basis, requirements=['F']))
# select the KLIP modes we want for each level of KLIP by multiplying by lower diagonal matrix
lower_tri = np.tril(np.ones([max_basis, max_basis]))
inner_products = inner_products * lower_tri
# if there are NaNs due to negative eigenvalues, make sure they don't mess up the matrix multiplicatoin
# by setting the appropriate values to zero
if check_nans:
needs_to_be_zeroed = np.where(lower_tri == 0)
inner_products[needs_to_be_zeroed] = 0
# make a KLIP PSF for each amount of klip basis, but only for the amounts of klip basis we actually output
kl_basis[:, neg_evals] = 0
klip_psf = np.dot(inner_products[numbasis, :], kl_basis.T)
# for KLIP PSFs that use so many KL modes that they become nans, we have to put nan's back in those
badbasis = np.where(
numbasis >=
np.min(neg_evals)) #use basis with negative eignevalues
klip_psf[badbasis[0], :] = np.nan
else:
# make a KLIP PSF for each amount of klip basis, but only for the amounts of klip basis we actually output
klip_psf = np.dot(inner_products[numbasis, :], kl_basis.T)
# make subtracted image for each number of klip basis
sub_img_rows_selected = sci_rows_selected - klip_psf
# restore NaNs
sub_img_rows_selected[sci_nanpix] = np.nan
if return_basis is True:
return sub_img_rows_selected.transpose(), kl_basis.transpose()
elif return_basis_and_eig is True:
return sub_img_rows_selected.transpose(), kl_basis.transpose(
), evals * (np.size(sci) - 1), evecs
else:
return sub_img_rows_selected.transpose()
def create_synth_data(data_type='bool', noise_factor=0):
n_data = N_DATA
n_dim = N_DIM
S = np.zeros((n_dim, n_data, n_data)) # Similarity tensor
cluster_members = [50, 100, 200]
# Contruct labels
y = []
for i, c in enumerate(cluster_members):
y.extend(np.ones(c) * i)
intra_c_prob = np.array([[0.8, 0.1, 0.7], [0.05, 0.4, 0.06],
[0.6, 0.8, 0.67], [0.6, 0.4, 0.1]])
# noise_d = np.array([0.25,0.15,0.45,0.22]) + noise_factor
noise_d = np.array([0, 0, 0, 0]) + noise_factor
intra_cluster_proba = 0.1
for d in range(n_dim):
i = 0
for c in range(len(cluster_members)):
if data_type == "bool":
S[d][i:i + cluster_members[c],
i:i + cluster_members[c]] = np.random.binomial(
1, intra_c_prob[d][c],
size=cluster_members[c]**2).reshape(
(cluster_members[c], cluster_members[c]))
elif data_type == 'linear':
S[d][i:i + cluster_members[c],
i:i + cluster_members[c]] = np.random.normal(
loc=intra_c_prob[d][c],
scale=0.2,
size=cluster_members[c]**2).reshape(
(cluster_members[c], cluster_members[c]))
else:
raise ValueError
i = i + cluster_members[c]
# Add noise
if data_type == "bool":
S[d] = S[d] + np.random.binomial(
1, noise_d[d], size=S[d].size
).reshape(
S[d].shape
) #np.random.normal(loc=noise_d[d],scale=0.9,size=S[d].size).reshape(S[d].shape)
elif data_type == 'linear':
S[d] = S[d] + np.random.normal(
loc=0, scale=noise_d[d], size=S[d].size).reshape(S[d].shape)
else:
raise ValueError
# Make symmetric
S[d] = (np.tril(S[d]) + np.triu(S[d].T, 1))
S[d] = np.where(S[d] < 0, 0, S[d]) # remove negative
if data_type == "bool":
S[d] = np.where(S[d] > 1, 1, S[d]) # Remove val > 1
elif data_type == "linear":
S[d] = np.where(S[d] > 1, 0, S[d]) # Remove val > 1
# Set diag to single value
di, dj = np.diag_indices_from(S[d])
S[d][di, dj] = 1
return S, y
def norm_distance(distance):
L = np.tril(distance, -1)
min_max_scaler = preprocessing.MinMaxScaler()
distance_tran = min_max_scaler.fit_transform(L)
distance_tran = distance_tran + np.transpose(distance_tran)
return distance_tran
inputs = np.concatenate((full_X_jets, full_X_mu, full_X_el), axis=1) weights = np.concatenate((full_jet_w, full_mu_w, full_el_w), axis=1) labels = np.concatenate((full_jet_labels, full_mu_labels, full_el_labels)) koop = np.linspace(0, 69, 70) correlation = np.abs(np.corrcoef(weights.transpose())) correlation_in = np.abs(np.corrcoef(inputs.transpose())) rms_val = rms(weights) select_rms = rms_val < 0.008 matrix_rms = rms_val * np.transpose(rms_val) selection = (correlation < 0.1) | (correlation_in > 0.6) correlation_in = np.abs(np.tril(correlation_in, -1)) correlation = np.abs(np.tril(correlation, -1)) correlation[selection] = 0 correlation[select_rms, :] = 0 correlation[:, select_rms] = 0 rms_corr = np.multiply(matrix_rms, correlation) idx = largest_indices(rms_corr, 10) print labels[idx[0]] print labels[idx[1]] #print labels[idx_in[0]] #print labels[idx_in[1]] plt.figure(figsize=(14, 14)) plt.imshow(rms_corr, cmap='jet', interpolation='nearest') plt.xticks(koop, labels, rotation=90) plt.yticks(koop, labels)
if len(B.shape) != 1:
raise ValueError('B no es un vector')
if fA != B.shape[0]:
raise ValueError('No coinciden la matriz A y el vector B')
if not diago.all():
raise ValueError('A es una matriz singular')
x = np.zeros_like(B, dtype=float)
for k in np.arange(fA):
suma = np.dot(A[k, :k], x[:k])
x[k] = (B[k] - suma) / A[k, k]
return A, x
print('Matriz triangular inferior:')
E = np.tril(A)
print(sltrinf(E, B))
soltrinf = la.solve(E, B)
print(soltrinf)
#MÉTODO GAUSS
def slgauss(A, b):
A = A.astype(float)
b = b.astype(float)
x = np.zeros_like(b, dtype=float)
fA, cA = A.shape
for i in range(fA):
if A[i, i] == 0:
raise ValueError('pivot becomes null')
def sample_trajectory(self, T=10000, sample_freq=10):
n = self.n_balls
assert (T % sample_freq == 0)
T_save = int(T / sample_freq - 1)
diag_mask = np.ones((n, n), dtype=bool)
np.fill_diagonal(diag_mask, 0)
counter = 0
if self.uniform_draw:
total_num_edges = int(0.5 * self.n_balls * (self.n_balls - 1))
num_edges = random.randint(0, total_num_edges)
edges = [0 for i in range(total_num_edges)]
for i in range(num_edges):
edges[i] = 1
random.shuffle(edges)
spring_edges = np.zeros((self.n_balls, self.n_balls))
spring_edges[np.triu_indices(self.n_balls, 1)] = np.array(edges)
spring_edges.T[np.triu_indices(self.n_balls, 1)] = np.array(edges)
charges = [0 for i in range(self.n_balls)]
n_c = random.randint(
1, self.n_balls) # choose a random number of charges, 1 to 5
for i in range(n_c):
charges[i] = 1
random.shuffle(charges)
charges = np.expand_dims(np.array(charges), -1)
charge_edges = charges.dot(charges.transpose()).astype('float')
else:
spring_edges = np.random.choice(
self.
spring_types, # self.spring_types is an array of relative spring strengths eg. [0., 0.5, 1.]
size=(self.n_balls, self.n_balls),
p=self.spring_prob) # prob. of each spring type
spring_edges = np.tril(spring_edges) + np.tril(
spring_edges, -1).T # this makes the edges matrix symmetric
np.fill_diagonal(spring_edges, 0) # remove self loops
# Sample charge edges
charges = np.random.choice(self.charge_types,
size=(self.n_balls, 1),
p=self.charge_prob)
charge_edges = charges.dot(charges.transpose())
#np.fill_diagonal(charge_edges, 0) # remove self loops
# Initialize location and velocity
loc = np.zeros((T_save, 2, n))
vel = np.zeros((T_save, 2, n))
loc_next = np.random.randn(
2, n) * self.loc_std # randn samples from a unit normal dist.
vel_next = np.random.randn(2, n)
v_norm = np.sqrt((vel_next**2).sum(axis=0)).reshape(1, -1)
vel_next = vel_next * self.vel_norm / v_norm
loc[0, :, :], vel[0, :, :] = self._clamp(loc_next, vel_next)
# disables division by zero warning, since I fix it with fill_diagonal
with np.errstate(divide='ignore', invalid='ignore'):
spring_forces_size = -self.spring_interaction_strength * spring_edges
#np.fill_diagonal(spring_forces_size, 0) # self forces are zero (fixes division by zero)
l2_dist_power3 = np.power(
self._l2(loc_next.transpose(), loc_next.transpose()), 3. / 2.)
# size of forces up to a 1/|r| factor
# since I later multiply by an unnormalized r vector
charge_forces_size = -self.charge_interaction_strength * charge_edges / l2_dist_power3
np.fill_diagonal(
charge_forces_size,
0) # self forces are zero (fixes division by zero)
#assert (np.abs(charge_forces_size[diag_mask]).min() > 1e-10)
F_s = (spring_forces_size.reshape(1, n, n) * np.concatenate(
(np.subtract.outer(loc_next[0, :], loc_next[0, :]).reshape(
1, n, n), np.subtract.outer(loc_next[1, :],
loc_next[1, :]).reshape(
1, n, n)))).sum(axis=-1)
#assert (np.abs(charge_forces_size[diag_mask]).min() > 1e-10)
F_c = (charge_forces_size.reshape(1, n, n) * np.concatenate(
(np.subtract.outer(loc_next[0, :], loc_next[0, :]).reshape(
1, n, n), np.subtract.outer(loc_next[1, :],
loc_next[1, :]).reshape(
1, n, n)))).sum(axis=-1)
F = F_s + F_c
F[F > self._max_F] = self._max_F
F[F < -self._max_F] = -self._max_F
vel_next += self._delta_T * F
for i in range(1, T):
loc_next += self._delta_T * vel_next
loc_next, vel_next = self._clamp(loc_next, vel_next)
if i % sample_freq == 0:
loc[counter, :, :], vel[counter, :, :] = loc_next, vel_next
counter += 1
l2_dist_power3 = np.power(
self._l2(loc_next.transpose(), loc_next.transpose()),
3. / 2.)
# size of forces up to a 1/|r| factor
# since I later multiply by an unnormalized r vector
charge_forces_size = self.charge_interaction_strength * charge_edges / l2_dist_power3
np.fill_diagonal(
charge_forces_size,
0) # self forces are zero (fixes division by zero)
F_s = (spring_forces_size.reshape(1, n, n) * np.concatenate(
(np.subtract.outer(loc_next[0, :], loc_next[0, :]).reshape(
1, n, n),
np.subtract.outer(loc_next[1, :], loc_next[1, :]).reshape(
1, n, n)))).sum(axis=-1)
#assert (np.abs(charge_forces_size[diag_mask]).min() > 1e-10)
F_c = (charge_forces_size.reshape(1, n, n) * np.concatenate(
(np.subtract.outer(loc_next[0, :], loc_next[0, :]).reshape(
1, n, n),
np.subtract.outer(loc_next[1, :], loc_next[1, :]).reshape(
1, n, n)))).sum(axis=-1)
F = F_s + F_c
F[F > self._max_F] = self._max_F
F[F < -self._max_F] = -self._max_F
vel_next += self._delta_T * F
# Add noise to observations
loc += np.random.randn(T_save, 2, self.n_balls) * self.noise_var
vel += np.random.randn(T_save, 2, self.n_balls) * self.noise_var
np.fill_diagonal(charge_edges, 0)
edges = np.concatenate((np.expand_dims(
spring_edges, 0), np.expand_dims(charge_edges, 0)),
axis=0)
return loc, vel, edges
def compute_and_plot_specrad():
"""
Compute and plot spectral radius of smoother iteration matrix for a whole range of eigenvalues
Returns:
"""
# setup_list = [('LU', 'to0'), ('LU', 'toinf'), ('IE', 'to0'), ('IE', 'toinf')]
# setup_list = [('LU', 'to0'), ('LU', 'toinf')]
# setup_list = [('IE', 'to0'), ('IE', 'toinf')]
# setup_list = [('LU', 'toinf'), ('IE', 'toinf')]
setup_list = [('IE', 'full'), ('LU', 'full')]
setup_list = [('EX', 'to0'), ('PIC', 'to0')]
# set up plotting parameters
params = {'legend.fontsize': 20,
'figure.figsize': (12, 8),
'axes.labelsize': 20,
'axes.titlesize': 20,
'xtick.labelsize': 16,
'ytick.labelsize': 16,
'lines.linewidth': 3
}
plt.rcParams.update(params)
Nnodes = 5
Nsteps = 1
coll = CollGaussRadau_Right(Nnodes, 0, 1)
Qmat = coll.Qmat[1:, 1:]
Nmat = np.zeros((Nnodes, Nnodes))
Nmat[:, -1] = 1
Emat = np.zeros((Nsteps, Nsteps))
np.fill_diagonal(Emat[1:, :], 1)
for qd_type, conv_type in setup_list:
if qd_type == 'LU':
QT = coll.Qmat[1:, 1:].T
[_, _, U] = LA.lu(QT, overwrite_a=True)
QDmat = U.T
elif qd_type == 'IE':
QI = np.zeros(np.shape(coll.Qmat))
for m in range(coll.num_nodes + 1):
QI[m, 1:m + 1] = coll.delta_m[0:m]
QDmat = QI[1:, 1:]
elif qd_type == 'EE':
QE = np.zeros(np.shape(coll.Qmat))
for m in range(coll.num_nodes + 1):
QE[m, 0:m] = coll.delta_m[0:m]
QDmat = QE[1:, 1:]
elif qd_type == 'PIC':
QDmat = np.zeros(np.shape(coll.Qmat[1:, 1:]))
elif qd_type == 'EX':
QT = coll.Qmat[1:, 1:].T
[_, _, U] = LA.lu(QT, overwrite_a=True)
QDmat = np.tril(U.T, k=-1)
print(QDmat)
else:
raise NotImplementedError('qd_type %s is not implemented' % qd_type)
# lim_specrad = max(abs(np.linalg.eigvals(np.eye(Nnodes) - np.linalg.inv(QDmat).dot(Qmat))))
# print('qd_type: %s -- lim_specrad: %6.4e -- conv_type: %s' % (qd_type, lim_specrad, conv_type))
if conv_type == 'to0':
ilim_left = -4
ilim_right = 2
rlim_left = 2
rlim_right = -4
elif conv_type == 'toinf':
ilim_left = 0
ilim_right = 11
rlim_left = 6
rlim_right = 0
elif conv_type == 'full':
ilim_left = -10
ilim_right = 11
rlim_left = 10
rlim_right = -11
else:
raise NotImplementedError('conv_type %s is not implemented' % conv_type)
ilam_list = 1j * np.logspace(ilim_left, ilim_right, 201)
rlam_list = -1 * np.logspace(rlim_left, rlim_right, 201)
assert (rlim_right - rlim_left + 1) % 5 == 0
assert (ilim_right - ilim_left - 1) % 5 == 0
assert (len(rlam_list) - 1) % 5 == 0
assert (len(ilam_list) - 1) % 5 == 0
Prho = np.zeros((len(rlam_list), len(ilam_list)))
for idr, rlam in enumerate(rlam_list):
for idi, ilam in enumerate(ilam_list):
dxlam = rlam + ilam
mat = np.linalg.inv(np.eye(Nnodes * Nsteps) - dxlam * np.kron(np.eye(Nsteps), QDmat)).dot(
dxlam * np.kron(np.eye(Nsteps), (Qmat - QDmat)) + np.kron(Emat, Nmat))
mat = np.linalg.matrix_power(mat, Nnodes)
Prho[idr, idi] = max(abs(np.linalg.eigvals(mat)))
print(np.amax(Prho))
fig, ax = plt.subplots(figsize=(15, 10))
ax.set_xticks([i + 0.5 for i in range(0, len(rlam_list), int(len(rlam_list) / 5))])
ax.set_xticklabels([r'-$10^{%d}$' % i for i in range(rlim_left, rlim_right,
int((rlim_right - rlim_left + 1) / 5))])
ax.set_yticks([i + 0.5 for i in range(0, len(ilam_list), int(len(ilam_list) / 5))])
ax.set_yticklabels([r'$10^{%d}i$' % i for i in range(ilim_left, ilim_right,
int((ilim_right - ilim_left - 1) / 5))])
cmap = plt.get_cmap('Reds')
pcol = plt.pcolor(Prho.T, cmap=cmap, norm=LogNorm(vmin=1E-09, vmax=1E-00))
plt.colorbar(pcol)
plt.xlabel(r'$Re(\Delta t\lambda)$')
plt.ylabel(r'$Im(\Delta t\lambda)$')
fname = 'data/heatmap_smoother_' + conv_type + '_Nsteps' + str(Nsteps) + '_M' + \
str(Nnodes) + '_' + qd_type + '.png'
plt.savefig(fname, rasterized=True, transparent=True, bbox_inches='tight')
def __init__(self, xTr, yTr, xTe=None, yTe=None, **kwargs):
self.xTr = xTr
self.yTr = yTr
self.xTe = xTe
self.yTe = yTe
if 'num_inducing_points' in kwargs.keys():
self.num_inducing_points = min(xTr.shape[0], \
kwargs['num_inducing_points'])
else:
self.num_inducing_points = min(xTr.shape[0], 10)
if 'quad_deg' in kwargs.keys():
self.quad = GaussHermiteQuadrature(kwargs['quad_deg'])
else:
self.quad = GaussHermiteQuadrature(30)
if 'kernel_type' in kwargs.keys():
self.kernel_type = kwargs['kernel_type']
else:
self.kernel_type = 'rbf'
if 'kernel_args' in kwargs.keys():
self.kernel_args = kwargs['kernel_args']
else:
self.kernel_args = {'gamma': None}
if 'learning_rate' in kwargs.keys():
self.learning_rate = kwargs['learning_rate']
else:
self.learning_rate = 0.01
self.r0 = self.learning_rate
if 'alpha' in kwargs.keys():
self.alpha = kwargs['alpha']
else:
self.alpha = 0.2
if 'verbose' in kwargs.keys():
self.verbose = kwargs['verbose']
else:
self.verbose = 0
if 'max_iter' in kwargs.keys():
self.max_iter = kwargs['max_iter']
else:
self.max_iter = 10000
if 'tolerance' in kwargs.keys():
self.tolerance = kwargs['tolerance']
else:
self.tolerance = 1.0
if xTr is None or yTr is None:
raise Exception('None training data error')
else:
M = self.num_inducing_points
self.labels = np.unique(yTr)
self.num_classes = len(self.labels)
C = self.num_classes
self.labels_dist = []
for i in range(C):
indices, = np.where(self.yTr == self.labels[i])
self.labels_dist.append(indices)
self.inducing_points = xTr[self.sample_x(M)]
if self.verbose > 0:
print('computing kernel matrices...')
self.Kmm = self.kernel(self.inducing_points, self.inducing_points)
self.Kmm_inv = cho_inverse(self.Kmm)
self.Knn = self.kernel(xTr, xTr)
self.Knm = self.kernel(xTr, self.inducing_points)
self.A = self.Knm.dot(self.Kmm_inv)
self.mask = np.tril(np.ones((M, M))).ravel()
if self.verbose > 0:
print('finished.')
self.parameters = np.zeros(M * C + M * M * C)
self.parameters_best = None
for j in range(C):
self.parameters[M * j:M * (j + 1)] = np.ones(M)
self.parameters[M * C + M * M * j:M * C + M * M *
(j + 1)] = np.eye(M).ravel()
def test_triul(shape, k):
s = sparse.random(shape, density=0.5)
x = s.todense()
assert_eq(np.triu(x, k), sparse.triu(s, k))
assert_eq(np.tril(x, k), sparse.tril(s, k))
fname = sys.argv[1] # tsv filename: gen,clusterid,cost,genestart,chromid
dirpng = "Plots/"
label = fname.split('/')[-1].split('-')[0]
dirpng = dirpng + label
path = Path(dirpng).mkdir(parents=True, exist_ok=True)
logprint("Plot dir: %s" % dirpng)
logprint("Label: %s" % label)
# ALL CHROMOSOME WORK
print("Getting correlation")
df = pd.read_csv(fname, sep = "\t")
cor = df.iloc[:,1:df.shape[1]-2].T.corr()
print("Ploting")
plt.figure(figsize=(10,10),dpi=300)
masking = np.tril(cor)
sns.heatmap(cor ,xticklabels=False, yticklabels=False,
mask=masking, vmin=-1., vmax=1., square=True,
# cbar_kws={"shrink": 0.75}, cmap=RdBu_11.mpl_colormap)
cbar_kws={"shrink": 0.75}, cmap=plt.get_cmap('seismic'))
plt.title('Pearson correlation' + label)
plt.ylabel('Gene start position')
plt.xlabel('Gene start position')
plt.tight_layout()
pngname = dirpng + '/' + label + '-allchroms.png'
plt.savefig(pngname)
plt.clf()
plt.close() # to clean memory
# BY CROMOSOME WORK
def simulate_match(foot_model, homeTeam, awayTeam, max_goals=10):
home_goals_avg = foot_model.predict(
pd.DataFrame(data={
'team': homeTeam,
'opponent': awayTeam,
'home': 1
},
index=[1])).values[0]
away_goals_avg = foot_model.predict(
pd.DataFrame(data={
'team': awayTeam,
'opponent': homeTeam,
'home': 0
},
index=[1])).values[0]
team_pred = [[poisson.pmf(i, team_avg) for i in range(0, max_goals + 1)]
for team_avg in [home_goals_avg, away_goals_avg]]
return (np.outer(np.array(team_pred[0]), np.array(team_pred[1])))
prob = simulate_match(poisson_model, hteam, ateam, max_goals=10)
win = np.sum(np.tril(prob, -1))
draw = np.sum(np.diag(prob))
loss = np.sum(np.triu(prob, 1))
print("home team win percentage")
print(win * 100)
print("Away team win percentage")
print(loss * 100)
print("Draw percentage")
print(draw * 100)
def _get_symmat(size):
np.random.seed(1)
A = np.random.randint(1, 21, (size, size))
lA = np.tril(A)
return lA.dot(lA.T)
def simulate_dags(d, s0, K, rho, graph_type):
"""Simulate random DAG with some expected number of edges.
Args:
d (int): num of nodes
s0 (int): expected num of edges
K (int): number of groups
rho (double): [0,1)- variations of DAGs in different groups
graph_type (str): ER, SF
Returns:
B (np.ndarray): [K, d, d] binary adj matrix of DAG
"""
def _random_permutation(M):
# np.random.permutation permutes first axis only
P = np.random.permutation(np.eye(M.shape[0]))
return P.T @ M @ P
def _random_acyclic_orientation(B_und):
return np.tril(_random_permutation(B_und), k=-1)
def _graph_to_adjmat(G):
return np.array(G.get_adjacency().data)
if graph_type == 'ER':
# Erdos-Renyi
G_und = ig.Graph.Erdos_Renyi(n=d, m=s0)
B_und = _graph_to_adjmat(G_und)
B = _random_acyclic_orientation(B_und)
elif graph_type == 'SF':
# Scale-free, Barabasi-Albert
G = ig.Graph.Barabasi(n=d, m=int(round(s0 / d)), directed=True)
B = _graph_to_adjmat(G)
elif graph_type == 'BP':
# Bipartite, Sec 4.1 of (Gu, Fu, Zhou, 2018)
top = int(0.2 * d)
G = ig.Graph.Random_Bipartite(top,
d - top,
m=s0,
directed=True,
neimode=ig.OUT)
B = _graph_to_adjmat(G)
else:
raise ValueError('unknown graph type')
# add group variations
B_list = []
Btemp = np.triu(-np.ones([d, d]), k=0)
Btemp = Btemp + B
avai_index = np.where(Btemp == 0)
E = np.shape(np.where(Btemp == 1))[1]
L = np.shape(avai_index)[1]
P = np.random.permutation(np.eye(d))
for k in range(K):
Bk = Btemp
vedge_flag = np.random.rand(L) <= rho * E / (2 * L)
Bk[avai_index[0][vedge_flag], avai_index[1][vedge_flag]] = 1
Bk = np.tril(Bk, k=-1)
B_perm = P.T @ Bk @ P
B_list.append(B_perm)
assert ig.Graph.Adjacency(B_perm.tolist()).is_dag()
return B_list
print('\n\n')
print(np.logspace(3,10,50))
#Building matrices
#Let X = np.array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]). Get the diagonal of X, that is, [0, 5, 10].
print('\n\n')
X = np.array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]])
print(np.diag(X))
print('\n\n')
#Create a 2-D array whose diagonal equals [1, 2, 3, 4] and 0's elsewhere.
print(np.diagflat([1,2,3,4]))
print('\n\n')
#Create an array which looks like below. array([[ 0, 0, 0], [ 4, 0, 0], [ 7, 8, 0], [10, 11, 12]])
print(np.tril(np.arange(1,13).reshape(4,3),-1))
print('\n\n')
#Create an array which looks like below. array([[ 1, 2, 3], [ 4, 5, 6], [ 0, 8, 9], [ 0, 0, 12]])
print(np.triu(np.arange(1,13).reshape(4,3),-1))
def testTrilExecution(self):
a = arange(24, chunk_size=2).reshape(2, 3, 4)
t = tril(a)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(24).reshape(2, 3, 4))
np.testing.assert_equal(res, expected)
t = tril(a, k=1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(24).reshape(2, 3, 4), k=1)
np.testing.assert_equal(res, expected)
t = tril(a, k=2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(24).reshape(2, 3, 4), k=2)
np.testing.assert_equal(res, expected)
t = tril(a, k=-1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(24).reshape(2, 3, 4), k=-1)
np.testing.assert_equal(res, expected)
t = tril(a, k=-2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(24).reshape(2, 3, 4), k=-2)
np.testing.assert_equal(res, expected)
a = arange(12, chunk_size=2).reshape(3, 4).tosparse()
t = tril(a)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(12).reshape(3, 4))
self.assertIsInstance(res, SparseNDArray)
np.testing.assert_equal(res, expected)
t = tril(a, k=1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(12).reshape(3, 4), k=1)
self.assertIsInstance(res, SparseNDArray)
np.testing.assert_equal(res, expected)
t = tril(a, k=2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(12).reshape(3, 4), k=2)
self.assertIsInstance(res, SparseNDArray)
np.testing.assert_equal(res, expected)
t = tril(a, k=-1)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(12).reshape(3, 4), k=-1)
self.assertIsInstance(res, SparseNDArray)
np.testing.assert_equal(res, expected)
t = tril(a, k=-2)
res = self.executor.execute_tensor(t, concat=True)[0]
expected = np.tril(np.arange(12).reshape(3, 4), k=-2)
self.assertIsInstance(res, SparseNDArray)
np.testing.assert_equal(res, expected)
def _Phi(A):
"""Return lower-triangle of matrix and halve the diagonal"""
A = tril(A)
A[np.diag_indices_from(A)] *= 0.5
return A
def generate_structure(
num_nodes: int,
degree: float,
graph_type: str = "erdos-renyi",
w_min: float = 0.5,
w_max: float = 0.5,
) -> StructureModel:
"""Simulate random DAG with some expected degree.
Notes:
graph_type (str):
- erdos-renyi: constructs a graph such that the probability of any given edge is degree / (num_nodes - 1)
- barabasi-albert: constructs a scale-free graph from an initial connected graph of (degree / 2) nodes
- full: constructs a fully-connected graph - degree has no effect
Args:
num_nodes: number of nodes
degree: expected node degree, in + out
graph_type (str):
- erdos-renyi: constructs a graph such that the probability of any given edge is degree / (num_nodes - 1)
- barabasi-albert: constructs a scale-free graph from an initial connected graph of (degree / 2) nodes
- full: constructs a fully-connected graph - degree has no effect
w_min (float): min absolute weight of an edge in the graph
w_max (float): max absolute weight of an edge in the graph
Raises:
ValueError: if invalid arguments are provided
Returns:
weighted DAG
"""
if num_nodes < 2:
raise ValueError("DAG must have at least 2 nodes")
w_min, w_max = abs(w_min), abs(w_max)
if w_min > w_max:
raise ValueError(
"Absolute minimum weight must be less than or equal to maximum weight: {} > {}".format(
w_min, w_max
)
)
if graph_type == "erdos-renyi":
p_threshold = float(degree) / (num_nodes - 1)
p_edge = (np.random.rand(num_nodes, num_nodes) < p_threshold).astype(float)
edge_flags = np.tril(p_edge, k=-1)
elif graph_type == "barabasi-albert":
m = int(round(degree / 2))
edge_flags = np.zeros([num_nodes, num_nodes])
bag = [0]
for i in range(1, num_nodes):
dest = np.random.choice(bag, size=m)
for j in dest:
edge_flags[i, j] = 1
bag.append(i)
bag.extend(dest)
elif graph_type == "full": # ignore degree
edge_flags = np.tril(np.ones([num_nodes, num_nodes]), k=-1)
else:
raise ValueError("unknown graph type")
# randomly permute edges - required because we limited ourselves to lower diagonal previously
perms = np.random.permutation(np.eye(num_nodes, num_nodes))
edge_flags = perms.T.dot(edge_flags).dot(perms)
# random edge weights between w_min, w_max or between -w_min, -w_max
edge_weights = np.random.uniform(low=w_min, high=w_max, size=[num_nodes, num_nodes])
edge_weights[np.random.rand(num_nodes, num_nodes) < 0.5] *= -1
adj_matrix = (edge_flags != 0).astype(float) * edge_weights
graph = StructureModel(adj_matrix)
return graph
def _testme(N):
"""Exercise each function using NxN matrices"""
import scipy as sp
from time import time
if N > 1:
Sigma = np.cov(sp.randn(N, 2*N))
Sigma_dot = np.cov(sp.randn(N, 2*N))
elif N == 1:
Sigma = np.array([[sp.rand()]])
Sigma_dot = np.array([[sp.rand()]])
else:
assert(False)
tic = time()
L = np.linalg.cholesky(Sigma)
toc = time() - tic
print('Running np.linalg.cholesky:')
print(' Time taken: %0.4f s' % toc)
tic = time()
L_ub = tril(_chol_unblocked(Sigma))
toc = time() - tic
print('Unblocked chol works: %r'
% np.all(np.isclose(L, L_ub)))
print(' Time taken: %0.4f s' % toc)
tic = time()
L_bl = tril(_chol_blocked(Sigma))
toc = time() - tic
print('Blocked chol works: %r'
% np.all(np.isclose(L, L_bl)))
print(' Time taken: %0.4f s' % toc)
tic = time()
Ldot = _chol_symbolic_fwd(L, Sigma_dot)
toc = time() - tic
hh = 1e-5 # finite-difference step-size
L2 = np.linalg.cholesky(Sigma + Sigma_dot*hh/2)
L1 = np.linalg.cholesky(Sigma - Sigma_dot*hh/2)
Ldot_fd = (L2 - L1) / hh
print('Symbolic chol_fwd works: %r'
% np.all(np.isclose(Ldot, Ldot_fd)))
print(' Time taken: %0.4f s' % toc)
tic = time()
Ldot_ub = tril(_chol_unblocked_fwd(L, Sigma_dot))
toc = time() - tic
print('Unblocked chol_fwd works: %r'
% np.all(np.isclose(Ldot, Ldot_ub)))
print(' Time taken: %0.4f s' % toc)
tic = time()
Ldot_bl = tril(_chol_blocked_fwd(L, Sigma_dot))
toc = time() - tic
print('Blocked chol_fwd works: %r'
% np.all(np.isclose(Ldot, Ldot_bl)))
print(' Time taken: %0.4f s' % toc)
Lbar = tril(sp.randn(N, N))
tic = time()
Sigma_bar = _chol_symbolic_rev(L, Lbar)
toc = time() - tic
Delta1 = _trace_dot(Lbar, Ldot)
Delta2 = _trace_dot(Sigma_bar, Sigma_dot)
print('Symbolic chol_rev works: %r'
% np.all(np.isclose(Delta1, Delta2)))
print(' Time taken: %0.4f s' % toc)
tic = time()
Sigma_bar_ub = _chol_unblocked_rev(L, Lbar)
toc = time() - tic
Delta3 = _trace_dot(Sigma_bar_ub, Sigma_dot)
print('Unblocked chol_rev works: %r'
% np.all(np.isclose(Delta1, Delta3)))
print(' Time taken: %0.4f s' % toc)
tic = time()
Sigma_bar_bl = _chol_blocked_rev(L, Lbar)
toc = time() - tic
Delta4 = _trace_dot(Sigma_bar_bl, Sigma_dot)
print('Blocked chol_rev works: %r'
% np.all(np.isclose(Delta1, Delta4)))
print(' Time taken: %0.4f s' % toc)
if FORTRAN_COMPILED:
tic = time()
Sigma_bar_f = chol_rev(L, Lbar)
toc = time() - tic
Delta5 = _trace_dot(Sigma_bar_f, Sigma_dot)
print('Fortran chol_rev works: %r'
% np.all(np.isclose(Delta1, Delta5)))
print(' Time taken: %0.4f s' % toc)
tic = time()
Sigma_bar_fub = _chol_unblocked_fortran_rev(L, Lbar)
toc = time() - tic
Delta6 = _trace_dot(Sigma_bar_fub, Sigma_dot)
print('Fortran unblocked chol_rev works: %r'
% np.all(np.isclose(Delta1, Delta6)))
print(' Time taken: %0.4f s' % toc)
else:
print('Fortran chol_rev not compiled.')
X = X.drop(var, axis=1)
# remove unused datetime features
X = X.drop([
'Charge Off Date', 'Funded Date', 'Loan Maturity Date',
'Loan Paid In Full Date'
],
axis=1)
# for simplicity, drop the null rows
X = X.dropna()
X = X.reset_index(drop=True)
# check correlations among features
corr = X.corr()
corr.loc[:, :] = np.tril(corr, k=-1)
corr = corr.stack()
print('Large Correlations:')
print(corr[(corr > 0.55) | (corr < -0.55)])
var = X.var()
print('Small Variance')
print(var[var == 0.0])
print(X.columns)
# drop features with small variance + remove one column of each variable to ensure there is no multicollinearity
X = X.drop(['Other', 'LC-F', 'Rent'], axis=1)
# visualize
cph.fit(X, duration_col='T', event_col='Loan Status')
M = 10 #牧场数量
F = 3 #工厂数量
L = 10 # 牛奶登记数量
G = 64 # 出产时刻
N = 10 # 每时刻产奶上限
T = 50;#工厂需要的l级奶量上限
V = 200;#牧场的车辆的上限
# 生产时刻
g = list(range(1, G+1))
# 等级，12级伟a++
l = list(range(1, L+1))
# 每吨牛奶的降级成本
C_l = np.array(l)
C_l = np.tile(C_l, (L, 1)).T
C_l = np.tril(C_l)
temp = np.diag(range(1, 11))
C_l = C_l - temp
#工厂：编号：需求
f = list(range(1, F+1))
# 牧场：编号，产量
m = list(range(1, M+1))
# 路线时间矩阵
H_fm = np.random.randint(high=20, low=1, size=(F, M))
# 每个牧场的车辆
V_m = np.random.randint(high=V, low=1, size=(M, 1))
# 每个牧场的车的装载量
v_m = {}
#每个牧场车的平均荷载量
W_m = {}
for i in range(1, M+1):
def CausalMask(x, params, axis=-1, **kwargs):
del params, kwargs
size = x.shape[axis]
return onp.tril(onp.ones((1, size, size), dtype=x.dtype), k=0)
def causal_mask(size, dtype=np.uint8):
"""Causal attention mask."""
return onp.tril(onp.ones((1, size, size), dtype=dtype), k=0)
def testBasic(self):
rng = np.random.RandomState(0)
a = np.tril(rng.randn(5, 5))
b = rng.randn(5, 7)
for dtype in self.float_types:
self._VerifyTriangularSolveCombo(a.astype(dtype), b.astype(dtype))
def sample_trajectory(self,
T=10000,
sample_freq=10,
spring_prob=[
1. / 3, 1. / 3, 1. / 3
]): #### spring_prob=[1. / 2, 0, 1. / 2]
n = self.n_balls
assert (T % sample_freq == 0)
T_save = int(T / sample_freq - 1)
diag_mask = np.ones((n, n), dtype=bool)
np.fill_diagonal(diag_mask, 0)
counter = 0
# Sample edges
edges = np.random.choice(
self.
_spring_types, # self._spring_types is an array of relative spring strengths eg. [0., 0.5, 1.]
size=(self.n_balls, self.n_balls),
p=spring_prob) # prob. of each spring type
# ^ this edges returns an NxN matrix of relative spring strengths
edges = np.tril(edges) + np.tril(
edges, -1).T # this makes the edges matrix symmetric
np.fill_diagonal(edges, 0) # remove self loops
# Initialize location and velocity
loc = np.zeros((T_save, 2, n))
vel = np.zeros((T_save, 2, n))
loc_next = np.random.randn(
2, n) * self.loc_std # randn samples from a unit normal dist.
vel_next = np.random.randn(2, n)
v_norm = np.sqrt((vel_next**2).sum(axis=0)).reshape(1, -1)
vel_next = vel_next * self.vel_norm / v_norm
loc[0, :, :], vel[0, :, :] = self._clamp(loc_next, vel_next)
# disables division by zero warning, since I fix it with fill_diagonal
with np.errstate(divide='ignore'):
forces_size = -self.interaction_strength * edges
np.fill_diagonal(
forces_size,
0) # self forces are zero (fixes division by zero)
F = (forces_size.reshape(1, n, n) * np.concatenate(
(np.subtract.outer(loc_next[0, :], loc_next[0, :]).reshape(
1, n, n), np.subtract.outer(loc_next[1, :],
loc_next[1, :]).reshape(
1, n, n)))).sum(axis=-1)
F[F > self._max_F] = self._max_F
F[F < -self._max_F] = -self._max_F
vel_next += self._delta_T * F
# run leapfrog
for i in range(1, T):
loc_next += self._delta_T * vel_next
loc_next, vel_next = self._clamp(loc_next, vel_next)
if i % sample_freq == 0:
loc[counter, :, :], vel[counter, :, :] = loc_next, vel_next
counter += 1
forces_size = -self.interaction_strength * edges
np.fill_diagonal(forces_size, 0)
# assert (np.abs(forces_size[diag_mask]).min() > 1e-10)
F = (forces_size.reshape(1, n, n) * np.concatenate(
(np.subtract.outer(loc_next[0, :], loc_next[0, :]).reshape(
1, n, n),
np.subtract.outer(loc_next[1, :], loc_next[1, :]).reshape(
1, n, n)))).sum(axis=-1)
F[F > self._max_F] = self._max_F
F[F < -self._max_F] = -self._max_F
vel_next += self._delta_T * F
# Add noise to observations
loc += np.random.randn(T_save, 2, self.n_balls) * self.noise_var
vel += np.random.randn(T_save, 2, self.n_balls) * self.noise_var
return loc, vel, edges
def compute_score_full(self, L, tau):
s = -abs(np.arange(0, L - 1)[:, None] / 2 - np.arange(L)[None, :]) / tau
s = np.tril(s, 0) + np.triu(s - float("inf"), 1)
s = np.exp(s - s.max(1, keepdims=True))
return s / s.sum(1, keepdims=True)
import numpy as np import scipy.linalg from chainer_optnet import pivots A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]]) lu, piv = scipy.linalg.lu_factor(A) p = pivots.pivots_to_perm(piv) q = pivots.inv_perm(p) print(piv) print(p) print(pivots.pivots_to_perm(pivots.perm_to_pivots(p)) == p) print(pivots.perm_to_pivots(pivots.pivots_to_perm(piv)) == piv) L, U = np.tril(lu, k=-1) + np.eye(4), np.triu(lu) print(A - pivots.permute(L @ U, p)) print(pivots.bpermute(A, p) - L @ U) print(pivots.permute(A, q) - L @ U) print(A - pivots.bpermute(L @ U, q)) print(pivots.comp_perm(pivots.inv_perm(p), p)) print(pivots.comp_perm(p, pivots.inv_perm(p)))
def cren1D(etaC,nulamC,M):
" fonction crÈneau "
eta1, eta2 =vstack([0,etaC.reshape(-1,1)]), vstack([etaC.reshape(-1,1),1]) # remise sous forme colonne : .reshape(-1,1) ; remise sous forme ligne : .reshape(1,-1)
epr, m_ =nulamC.reshape(-1,1)**2, -2*pi*(arange(2*M)+1)
#print (eta1, eta2, epr)
epr0 = npsum( (eta2-eta1) * epr )
eprm = dot(epr,ones((1,2*M)))
m = m_.reshape(1,-1)
e1m, e2m =1j*dot(eta1,m), 1j*dot(eta2,m)
epr_m =hstack([0., -1j* npsum( (exp(e2m) -exp(e1m)) *eprm ,0) /m_ ])
epr_p =hstack([0., 1j* npsum( (exp(-e2m)-exp(-e1m))*eprm ,0) /m_ ])
return diagflat(epr0*ones(2*M+1)) + triu( toeplitz(epr_m.real)+1j*toeplitz(epr_m.imag) ) + tril( toeplitz(epr_p.real)+1j*toeplitz(epr_p.imag) )
def _random_acyclic_orientation(B_und):
return np.tril(_random_permutation(B_und), k=-1)