def __init__(self, value):
self.value = value
self.value_ = np.linalg.cholesky(value)[np.tril_indices(value.shape[0])]
self.shape = value.shape
self.size = value.size
self.free = np.resize(True, self.value_.shape)
self.to_external = lambda val: np.linalg.cholesky(val)[np.tril_indices(self.shape[0])]
def actor_critic_update(X0, A, R, X1, gamma=0.99, learnrate=0.0001):
global WP1, WP2, WV_A, WV_b, WV
global grad_WP1, grad_WP2, grad_N
global grad_WP1s, grad_WP2s
global noise_cov
S0 = XtoS(X0)
S1 = XtoS(X1)
SS0 = np.outer(S0, S0)[np.tril_indices(7)]
SS1 = np.outer(S1, S1)[np.tril_indices(7)]
deltaV = SS0 - gamma * SS1
WV_A += np.outer(deltaV, deltaV)
WV_b += R * deltaV
WV = np.linalg.solve(WV_A, WV_b)
advantage = R + gamma * np.dot(SS1, WV) - np.dot(SS0, WV)
g1 = -0.5*np.outer(A, A) * advantage
grad_WP1 += g1
grad_WP1s += g1*g1
g2 = np.outer(A, SS0) * advantage
grad_WP2 += g2
grad_WP2s += g2*g2
grad_N += 1
# if X0[4] > 4:
# print 'V(s0)', np.dot(SS0, WV), 'V(s1)', np.dot(SS1, WV), 'R', R
# print 'A', A, 'adv', advantage # , 'g_wp1\n', grad_WP1, 'g_wp2\n', grad_WP2
noise_cov = np.linalg.inv(np.linalg.cholesky(
WP1 + 1e-2 + np.eye(2))).T
def test_frozen(self):
# Test that the frozen and non-frozen inverse Wishart gives the same
# answers
# Construct an arbitrary positive definite scale matrix
dim = 4
scale = np.diag(np.arange(dim)+1)
scale[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
scale = np.dot(scale.T, scale)
# Construct a collection of positive definite matrices to test the PDF
X = []
for i in range(5):
x = np.diag(np.arange(dim)+(i+1)**2)
x[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
x = np.dot(x.T, x)
X.append(x)
X = np.array(X).T
# Construct a 1D and 2D set of parameters
parameters = [
(10, 1, np.linspace(0.1, 10, 5)), # 1D case
(10, scale, X)
]
for (df, scale, x) in parameters:
iw = invwishart(df, scale)
assert_equal(iw.var(), invwishart.var(df, scale))
assert_equal(iw.mean(), invwishart.mean(df, scale))
assert_equal(iw.mode(), invwishart.mode(df, scale))
assert_allclose(iw.pdf(x), invwishart.pdf(x, df, scale))
def amplitudes_to_cisdvec(c0, c1, c2):
nocc, nvir = c1.shape
ooidx = numpy.tril_indices(nocc, -1)
vvidx = numpy.tril_indices(nvir, -1)
c2tril = lib.take_2d(c2.reshape(nocc**2,nvir**2),
ooidx[0]*nocc+ooidx[1], vvidx[0]*nvir+vvidx[1])
return numpy.hstack((c0, c1.ravel(), c2tril.ravel()))
def find_stationary_var(amat=None, bmat=None, cmat=None):
"""Find fixed point of H = CC' + AHA' + BHB' given A, B, C.
Parameters
----------
amat, bmat, cmat : (nstocks, nstocks) arrays
Parameter matrices
Returns
-------
(nstocks, nstocks) array
Unconditional variance matrix
"""
nstocks = amat.shape[0]
kwargs = {'amat': amat, 'bmat': bmat, 'ccmat': cmat.dot(cmat.T)}
fun = partial(ParamGeneric.fixed_point, **kwargs)
try:
with np.errstate(divide='ignore', invalid='ignore'):
hvar = np.eye(nstocks)
sol = sco.fixed_point(fun, hvar[np.tril_indices(nstocks)])
hvar[np.tril_indices(nstocks)] = sol
hvar[np.triu_indices(nstocks, 1)] \
= hvar.T[np.triu_indices(nstocks, 1)]
return hvar
except RuntimeError:
# warnings.warn('Could not find stationary varaince!')
return None
def test_tril_indices():
# indices without and with offset
il1 = tril_indices(4)
il2 = tril_indices(4, 2)
a = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
# indexing:
yield (assert_array_equal, a[il1],
array([ 1, 5, 6, 9, 10, 11, 13, 14, 15, 16]) )
# And for assigning values:
a[il1] = -1
yield (assert_array_equal, a,
array([[-1, 2, 3, 4],
[-1, -1, 7, 8],
[-1, -1, -1, 12],
[-1, -1, -1, -1]]) )
# These cover almost the whole array (two diagonals right of the main one):
a[il2] = -10
yield (assert_array_equal, a,
array([[-10, -10, -10, 4],
[-10, -10, -10, -10],
[-10, -10, -10, -10],
[-10, -10, -10, -10]]) )
def test_equivalence(self):
"""
The Equivalence covariance structure can represent an
exchangeable covariance structure. Here we check that the
results are identical using the two approaches.
"""
np.random.seed(3424)
endog = np.random.normal(size=20)
exog = np.random.normal(size=(20, 2))
exog[:, 0] = 1
groups = np.kron(np.arange(5), np.ones(4))
groups[12:] = 3 # Create unequal size groups
# Set up an Equivalence covariance structure to mimic an
# Exchangeable covariance structure.
pairs = {}
start = [0, 4, 8, 12]
for k in range(4):
pairs[k] = {}
# Diagonal values (variance parameters)
if k < 3:
pairs[k][0] = (start[k] + np.r_[0, 1, 2, 3],
start[k] + np.r_[0, 1, 2, 3])
else:
pairs[k][0] = (start[k] + np.r_[0, 1, 2, 3, 4, 5, 6, 7],
start[k] + np.r_[0, 1, 2, 3, 4, 5, 6, 7])
# Off-diagonal pairs (covariance parameters)
if k < 3:
a, b = np.tril_indices(4, -1)
pairs[k][1] = (start[k] + a, start[k] + b)
else:
a, b = np.tril_indices(8, -1)
pairs[k][1] = (start[k] + a, start[k] + b)
ex = sm.cov_struct.Exchangeable()
model1 = sm.GEE(endog, exog, groups, cov_struct=ex)
result1 = model1.fit()
for return_cov in False, True:
ec = sm.cov_struct.Equivalence(pairs, return_cov=return_cov)
model2 = sm.GEE(endog, exog, groups, cov_struct=ec)
result2 = model2.fit()
# Use large atol/rtol for the correlation case since there
# are some small differences in the results due to degree
# of freedom differences.
if return_cov == True:
atol, rtol = 1e-6, 1e-6
else:
atol, rtol = 1e-3, 1e-3
assert_allclose(result1.params, result2.params, atol=atol, rtol=rtol)
assert_allclose(result1.bse, result2.bse, atol=atol, rtol=rtol)
assert_allclose(result1.scale, result2.scale, atol=atol, rtol=rtol)
def full_to_unique(y_full, feedmap, feedmask=None):
if feedmask is None:
feedmask = np.ones(feedmap.shape, dtype=np.bool)
y_full[np.tril_indices(feedmap.shape[0])] = y_full[np.tril_indices(feedmap.shape[0])].conj()
y_unique = y_full[np.where(feedmask)][np.unique(feedmap[np.where(feedmask)], return_index=True)[1]]
return y_unique
def tril_index_matrix(self):
n = self.global_size
num_tril_entries = self.num_tril_entries
tril_index_matrix = np.zeros([n, n], dtype=int)
tril_index_matrix[np.tril_indices(n)] = np.arange(num_tril_entries)
tril_index_matrix[
np.tril_indices(n)[::-1]
] = np.arange(num_tril_entries)
return tril_index_matrix
def unique_to_full(y_unique, feedmap, feedmask=None):
y_full = y_unique[feedmap]
y_full[np.tril_indices(feedmap.shape[0])] = y_full[np.tril_indices(feedmap.shape[0])].conj()
if feedmask is not None:
y_full[np.where(np.logical_not(feedmask))] = 0.0
return y_full
def scrape_args(self, records, scale=1, guide_tree=None, niters=10, keep_topology=False):
# local lists
distances = []
variances = []
headers = []
for rec in records:
distances.append(rec.parameters.partitions.distances)
variances.append(rec.parameters.partitions.variances)
headers.append(rec.get_names())
num_matrices = len(records)
label_set = reduce(lambda x, y: x.union(y), (set(l) for l in headers))
labels_len = len(label_set)
# labels string can be built straight away
labels_string = '{0}\n{1}\n'.format(labels_len, ' '.join(label_set))
# distvar and genome_map need to be built up
distvar_list = [str(num_matrices)]
genome_map_list = ['{0} {1}'.format(num_matrices, labels_len)]
# build up lists to turn into strings
for i in range(num_matrices):
labels = headers[i]
dim = len(labels)
dmatrix = np.array(distances[i])
vmatrix = np.array(variances[i])
matrix = np.zeros(dmatrix.shape)
matrix[np.triu_indices(len(dmatrix), 1)] = dmatrix[np.triu_indices(len(dmatrix), 1)]
matrix[np.tril_indices(len(vmatrix), -1)] = vmatrix[np.tril_indices(len(vmatrix), -1)]
if scale:
matrix[np.triu_indices(dim, 1)] *= scale
matrix[np.tril_indices(dim, -1)] *= scale * scale
if isinstance(matrix, np.ndarray):
matrix_string = '\n'.join([' '.join(str(x) for x in row)
for row in matrix]) + '\n'
else:
matrix_string = matrix
distvar_list.append('{0} {0} {1}\n{2}'.format(dim, i + 1,
matrix_string))
genome_map_entry = ' '.join((str(labels.index(lab) + 1)
if lab in labels else '-1')
for lab in label_set)
genome_map_list.append(genome_map_entry)
distvar_string = '\n'.join(distvar_list)
genome_map_string = '\n'.join(genome_map_list)
if guide_tree is None:
guide_tree = Tree.new_iterative_rtree(labels_len, names=label_set, rooted=True)
tree_string = guide_tree.scale(scale).newick.replace('\'', '')
return distvar_string, genome_map_string, labels_string, tree_string, niters, keep_topology
def test_cl_ldl(AA):
""" Test the CL implentation of LDL algorithm.
This tests a series (cl_size) of matrices against the Python implementation.
"""
# Convert to single float
AA = AA.astype(DTYPE)
# First calculate the Python based values for each matrix in AA
py_ldl_D = np.empty((AA.shape[0], AA.shape[2]), dtype=AA.dtype)
py_ldl_L = np.empty(AA.shape, dtype=AA.dtype)
for i in range(AA.shape[2]):
py_ldl_D[..., i], py_ldl_L[..., i] = ldl(AA[..., i])
# Setup CL context
import pyopencl as cl
from pycllp.ldl import cl_krnl_ldl
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
# Result arrays
m, n, cl_size = AA.shape
L = np.empty(cl_size*m*(m+1)/2, dtype=DTYPE)
D = np.empty(cl_size*m, dtype=DTYPE)
mf = cl.mem_flags
A_g = cl.Buffer(ctx, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=AA)
# Create and compile kernel
prg = cl_krnl_ldl(ctx)
L_g = cl.Buffer(ctx, mf.READ_WRITE, L.nbytes)
D_g = cl.Buffer(ctx, mf.READ_WRITE, D.nbytes)
# Test normal LDL (unmodified)
prg.ldl(queue, (cl_size,), None, np.int32(m), np.int32(n), A_g, L_g, D_g)
cl.enqueue_copy(queue, L, L_g)
cl.enqueue_copy(queue, D, D_g)
# Compare each matrix decomposition with the python equivalent.
for i in range(cl_size):
np.testing.assert_allclose(py_ldl_D[..., i], D[i::cl_size], rtol=1e-6, atol=1e-7)
np.testing.assert_allclose(py_ldl_L[..., i][np.tril_indices(m)], L[i::cl_size], rtol=1e-6, atol=1e-7)
# Now test the modified algorithm ...
beta = np.sqrt(np.amax(AA))
prg.modified_ldl(queue, (cl_size,), None, np.int32(m), np.int32(n), A_g, L_g, D_g,
DTYPE(beta), DTYPE(1e-6))
cl.enqueue_copy(queue, L, L_g)
cl.enqueue_copy(queue, D, D_g)
# Compare each matrix decomposition with the python equivalent.
for i in range(cl_size):
np.testing.assert_allclose(py_ldl_D[..., i], D[i::cl_size], rtol=1e-6, atol=1e-7)
np.testing.assert_allclose(py_ldl_L[..., i][np.tril_indices(m)], L[i::cl_size], rtol=1e-6, atol=1e-7)
def impute_missing_bins(hic_matrix, regions=None, per_chromosome=True, stat=np.ma.mean):
"""
Impute missing contacts in a Hi-C matrix.
For inter-chromosomal data uses the mean of all inter-chromosomal contacts,
for intra-chromosomal data uses the mean of intra-chromosomal counts at the corresponding diagonal.
:param hic_matrix: A square numpy array
:param regions: A list of :class:`~GenomicRegion`s - if omitted, will create a dummy list
:param per_chromosome: Do imputation on a per-chromosome basis (recommended)
:param stat: The aggregation statistic to be used for imputation, defaults to the mean.
"""
if regions is None:
for i in range(hic_matrix.shape[0]):
regions.append(GenomicRegion(chromosome='', start=i, end=i))
chr_bins = dict()
for i, region in enumerate(regions):
if region.chromosome not in chr_bins:
chr_bins[region.chromosome] = [i, i]
else:
chr_bins[region.chromosome][1] = i
n = len(regions)
if not hasattr(hic_matrix, "mask"):
hic_matrix = masked_matrix(hic_matrix)
imputed = hic_matrix.copy()
if per_chromosome:
for c_start, c_end in chr_bins.itervalues():
# Correcting intrachromoc_startmal contacts by mean contact count at each diagonal
for i in range(c_end - c_start):
ind = kth_diag_indices(c_end - c_start, -i)
diag = imputed[c_start:c_end, c_start:c_end][ind]
diag[diag.mask] = stat(diag)
imputed[c_start:c_end, c_start:c_end][ind] = diag
# Correcting interchromoc_startmal contacts by mean of all contact counts between
# each set of chromoc_startmes
for other_start, other_end in chr_bins.itervalues():
# Only correct upper triangle
if other_start <= c_start:
continue
inter = imputed[c_start:c_end, other_start:other_end]
inter[inter.mask] = stat(inter)
imputed[c_start:c_end, other_start:other_end] = inter
else:
for i in range(n):
diag = imputed[kth_diag_indices(n, -i)]
diag[diag.mask] = stat(diag)
imputed[kth_diag_indices(n, -i)] = diag
# Copying upper triangle to lower triangle
imputed[np.tril_indices(n)] = imputed.T[np.tril_indices(n)]
return imputed
def structure_function(self, bins): """ compute the structure function of the light curve at given time lags """ dt = np.subtract.outer(self.t,self.t)[np.tril_indices(self.t.shape[0], k=-1)] dm = np.subtract.outer(self.y,self.y)[np.tril_indices(self.y.shape[0], k=-1)] sqrsum, bins, _ = binned_statistic(dt, dm**2, bins=bins, statistic='sum') n, _, _ = binned_statistic(dt, dm**2, bins=bins, statistic='count') SF = np.sqrt(sqrsum/n) lags = 0.5*(bins[1:] + bins[:-1]) return lags, SF
def get_grad_tril(mo_coeff_kpts, mo_occ_kpts, fock):
if is_khf:
grad_kpts = []
for k, mo in enumerate(mo_coeff_kpts):
f_mo = reduce(numpy.dot, (mo.T.conj(), fock[k], mo))
nmo = f_mo.shape[0]
grad_kpts.append(f_mo[numpy.tril_indices(nmo, -1)])
return numpy.hstack(grad_kpts)
else:
f_mo = reduce(numpy.dot, (mo_coeff_kpts.T.conj(), fock, mo_coeff_kpts))
nmo = f_mo.shape[0]
return f_mo[numpy.tril_indices(nmo, -1)]
def get_y_matrix(self, projectile, daughter):
"""Returns a ``DIM x DIM`` yield matrix.
Args:
projectile (int): PDG ID of projectile particle
daughter (int): PDG ID of final state daughter/secondary particle
Returns:
numpy.array: yield matrix
Note:
In the current version, the matrices have to be multiplied by the
bin widths. In later versions they will be stored with the multiplication
carried out.
"""
# TODO: modify yields to include the bin size
if not self.band:
return self.yields[(projectile, daughter)].dot(self.weights)
else:
m = self.yields[(projectile, daughter)].dot(self.weights)
# set all elements except those inside selected xf band to 0
m[np.tril_indices(self.dim, -2 - self.band[1])] = 0
if self.band[0] < 0:
m[np.triu_indices(self.dim, -self.band[0])] = 0
return m
def threePointsToStandard(e, p, q, r):
"""Return a projective transformation that maps three points on a conic to
the conic xy + yz + xz = 0.
Keyword arguments:
e -- a projective conic
p -- the first point on e
q -- the second point on e
r -- the third point on e
"""
coeffs = e
p, q, r = np.matrix(p), np.matrix(q), np.matrix(r)
# Determine a matrix A associated with a projective transformation that
# maps P, Q, and R onto [1, 0, 0], [0, 1, 0], and [0, 0, 1], respectively.
A = np.linalg.inv(np.vstack([p, q, r]))
# Determine the equation bx'y' + fx'z' + gy'z' = 0 of t(E), for some real
# numbers b, f, and g.
M = sum([coeff * u.T * v
for coeff, (u, v)
in zip(coeffs, combinations_with_replacement((p, q, r), 2))])
# Get B from M by adding like terms to find b, f, and g and then
# constructing a diagonal matrix from the flat [1/g, 1/f, 1/b].
B = np.diagflat([1 / (u + v)
for u, v
in reversed(zip(np.array(M)[np.triu_indices(3, 1)],
np.array(M)[np.tril_indices(3, -1)]))])
return B * A
def update_nogrid(self, params):
endog = self.model.endog_li
cached_means = self.model.cached_means
varfunc = self.model.family.variance
dep_params = np.zeros(self.max_lag + 1)
dn = np.zeros(self.max_lag + 1)
for i in range(self.model.num_group):
expval, _ = cached_means[i]
stdev = np.sqrt(varfunc(expval))
resid = (endog[i] - expval) / stdev
j1, j2 = np.tril_indices(len(expval))
dx = np.abs(self.time[i][j1] - self.time[i][j2])
ii = np.flatnonzero(dx <= self.max_lag)
j1 = j1[ii]
j2 = j2[ii]
dx = dx[ii]
vs = np.bincount(dx, weights=resid[
j1] * resid[j2], minlength=self.max_lag + 1)
vd = np.bincount(dx, minlength=self.max_lag + 1)
ii = np.flatnonzero(vd > 0)
dn[ii] += 1
if len(ii) > 0:
dep_params[ii] += vs[ii] / vd[ii]
dep_params /= dn
self.dep_params = dep_params[1:] / dep_params[0]
def multivar_norm_cdf(upper, cov_matrix):
"""CDF of multivariate Gaussian centered at 0 with covariance matrix cov_matrix. CDF is taken from -inf to u."""
if upper.size == 1:
return scipy.stats.norm.cdf(upper[0], 0, numpy.sqrt(cov_matrix[0, 0]))
# Standardize the upper bound u using the standard deviation
std = numpy.sqrt(numpy.diag(cov_matrix))
std_upper = upper / std
# Convert covariance matrix into correlation matrix: http://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_matrices
corr_matrix = cov_matrix / std / std.reshape(upper.size, 1) # standardize -> correlation matrix
# Indices for traversing the strict lower triangular elements of corr_matrix in column major, as required by the fortran mvndst function.
strict_lower_diag_indices = numpy.tril_indices(upper.size, -1)
# Call into the scipy wrapper for the fortran method "mvndst"
# Link: http://www.math.wsu.edu/faculty/genz/software/fort77/mvtdstpack.f
out = scipy.stats.kde.mvn.mvndst(
numpy.zeros(upper.size, dtype=int), # The lower bound of integration. We initialize with 0 because it is ignored (because of the third argument).
std_upper, # The upper bound of integration
numpy.zeros(upper.size, dtype=int), # For each dim, 0 means -inf for lower bound
corr_matrix[strict_lower_diag_indices], # The vector of strict lower triangular correlation coefficients
maxpts=self._mvndst_parameters.maxpts_per_dim * upper.size, # Maximum number of iterations for the mvndst function
releps=self._mvndst_parameters.releps, # The error allowed relative to actual value
abseps=self._mvndst_parameters.abseps, # The absolute error allowed
)
return out[1] # Index 1 corresponds to the actual value. 0 has the error, and 2 is a flag denoting whether releps was reached
def vector_from_array(array):
"""Get triangle of output in vector from a correlation-type array.
Parameters
----------
array : np.array
Returns
-------
vector (np.array)
Notes
-----
Old Matlab code indexes by column (aka.Fortran-style), so to get the indices
of the top triangle, we have to do some reshaping.
Otherwise, if the vector made up by rows is OK, then simply :
triangle = np.triu_indices(array.size, k=1), out = array[triangle]
"""
triangle_lower = np.tril_indices(array.shape[0], k=-1)
flatten_idx = np.arange(array.size).reshape(array.shape)[triangle_lower]
triangle = np.unravel_index(flatten_idx, array.shape, order='F')
# triangle = np.triu_indices(array.size, k=1)
# out = array[triangle]
return array[triangle]
def _getSignificantData(self, sig_lvl):
'''Find which edges significant at passed level and set self properties.
'''
rows,cols = self.data.shape #rows = cols
mask = zeros((rows,cols))
mask[tril_indices(rows,0)] = 1 #preparing mask
cvals = unique(self.data[triu_indices(rows,1)]) # cvals is sorted
# calculate upper bound, i.e. what value in the distribution of values
# has sig_lvl fraction of the data higher than or equal to it. this is
# not guaranteed to be precise because of repeated values. for instance
# assume the distribution of dissimilarity values is:
# [.1, .2, .2, .2, .2, .3, .4, .5, .6, .6, .6, .6, .6, .6, .7]
# and you want sig_lvl=.2, i.e. you get 20 percent of the linkages as
# significant. this would result in choosing the score .6 since its the
# third in the ordered list (of 15 elements, 3/15=.2). but, since there
# is no a-priori way to tell which of the multiple .6 linkages are
# significant, we select all of them, forcing our lower bound to
# encompass 7/15ths of the data. the round call on the ub is to avoid
# documented numpy weirdness where it will misassign >= calls for long
# floats.
ub = round(cvals[-round(sig_lvl*len(cvals))],7)
mdata = ma(self.data, mask)
self.actual_sig_lvl = \
(mdata >= ub).sum()/float(mdata.shape[0]*(mdata.shape[0]-1)/2)
self.sig_edges = where(mdata >= ub, 1, 0).nonzero()
self.otu1 = [self.otu_ids[i] for i in self.sig_edges[0]]
self.otu2 = [self.otu_ids[i] for i in self.sig_edges[1]]
self.sig_otus = list(set(self.otu1+self.otu2))
self.edges = zip(self.otu1, self.otu2)
self.cvals = mdata[self.sig_edges[0], self.sig_edges[1]]
def scoring2B_behavior():
t_clusters = np.zeros((600,3))
t_clusters[0:200,0] = 1
t_clusters[200:400,1] = 1
t_clusters[400:,2] = 1
t_ccm = np.dot(t_clusters,t_clusters.T)
n_uniq = len(np.triu_indices(t_ccm.shape[0],k=1)[0])
res = []
concentrations = [1000,100,50,25,10,5,3,1]
for c in concentrations:
for i in range(50):
ccm = np.copy(t_ccm)
ccm[np.triu_indices(t_ccm.shape[0],k=1)] -= np.random.beta(1,c,n_uniq)
#ccm[np.tril_indices(t_ccm.shape[0],k=-1)] = ccm[np.triu_indices(t_ccm.shape[0],k=1)]
ccm[np.tril_indices(t_ccm.shape[0],k=-1)] = 0
ccm = ccm + ccm.T
np.fill_diagonal(ccm,1)
ccm = np.abs(ccm)
res.append([c,calculate2(ccm,t_ccm)])
res = [map(str,x) for x in res]
res = ['\t'.join(x) for x in res]
f = open('scoring2B_beta.tsv', 'w')
f.write('\n'.join(res))
f.close()
def test_overlap(xSer):
'test the set overlap among items in a Series \
-return set of all pairwise overlap values'
ns = len(xSer)
if ns >1:
# overlapMtrx = pd.DataFrame(data=np.zeros([ns,ns]),
# index=xSer.index,
# columns=xSer.index)
overlapMtrx = np.zeros([ns,ns])
for i1, ix1 in enumerate(xSer.index):
s1 = xSer[ix1]
for i2, ix2 in enumerate(xSer.index):
s2 = xSer[ix2]
nO = len(s1.intersection(s2))
# overlapMtrx.ix[ix1,ix2] = nO
# overlapMtrx.ix[ix2,ix1] = nO
overlapMtrx[i1,i2] = nO
overlapMtrx[i2,i1] = nO
iUp = np.tril_indices(ns)
overlapMtrx[iUp] = np.nan
overlapArray = overlapMtrx.flatten()
overlapArray = overlapArray[~np.isnan(overlapArray)]
#
return overlapArray
else:
# return pd.DataFrame()
return np.zeros(0)
def calculate_forces(clf, numbers, coords, meta=None, h=1e-6):
"""
A function that uses finite differences to calculate forces of a molecule
using the given clf. The default feature vector for this to use is the
coulomb matrix.
"""
if meta is None:
meta = [1]
vectors = []
for i, coord in enumerate(coords):
for j in xrange(3):
for sign in [-1, 1]:
new_coords = coords.copy()
new_coords[i, j] += sign * h / 2
mat = get_coulomb_matrix(numbers, new_coords)
mat[mat < 0] = 0
vectors.append(mat[numpy.tril_indices(mat.shape[0])].tolist() + meta)
results = clf.predict(numpy.matrix(vectors))
forces = numpy.zeros(coords.shape)
for i, coord in enumerate(coords):
for j in xrange(3):
forces[i, j] = (results[i * len(coord) * 2 + j * 2 + 1] - results[i * len(coord) * 2 + j * 2]) / h
return forces
def calculate_surface(clf, numbers, coords, atom_idx, max_displacement=0.5, steps=25, meta=None):
"""
A function that uses plots the value of the clf as a function of `atom_ix`
displacement.
"""
if meta is None:
meta = [1]
values = numpy.linspace(-max_displacement, max_displacement, steps)
results = numpy.zeros((steps, steps))
for i, x in enumerate(values):
for j, y in enumerate(values):
new_coords = coords.copy()
new_coords[atom_idx, 0] += x
new_coords[atom_idx, 1] += y
mat = get_coulomb_matrix(numbers, new_coords)
mat[mat < 0] = 0
vector = mat[numpy.tril_indices(mat.shape[0])].tolist() + meta
results[i, j] = clf.predict(numpy.matrix(vector))[0]
extent = [-max_displacement, max_displacement, -max_displacement, max_displacement]
get_matrix_plot(results, extent)
print results.max(), results.min(), results.std()
return results
def pack_tril(mat, axis=-1, out=None):
'''flatten the lower triangular part of a matrix.
Given mat, it returns mat[...,numpy.tril_indices(mat.shape[0])]
Examples:
>>> pack_tril(numpy.arange(9).reshape(3,3))
[0 3 4 6 7 8]
'''
if mat.size == 0:
return numpy.zeros(mat.shape+(0,), dtype=mat.dtype)
if mat.ndim == 2:
count, nd = 1, mat.shape[0]
shape = nd*(nd+1)//2
else:
count, nd = mat.shape[:2]
shape = (count, nd*(nd+1)//2)
if mat.ndim == 2 or axis == -1:
mat = numpy.asarray(mat, order='C')
out = numpy.ndarray(shape, mat.dtype, buffer=out)
if mat.dtype == numpy.double:
fn = _np_helper.NPdpack_tril_2d
else:
fn = _np_helper.NPzpack_tril_2d
fn(ctypes.c_int(count), ctypes.c_int(nd),
out.ctypes.data_as(ctypes.c_void_p),
mat.ctypes.data_as(ctypes.c_void_p))
return out
else: # pack the leading two dimension
assert(axis == 0)
out = mat[numpy.tril_indices(nd)]
return out
def test_is_scaled_chisquared(self):
# The 2-dimensional Wishart with an arbitrary scale matrix can be
# transformed to a scaled chi-squared distribution.
# For :math:`S \sim W_p(V,n)` and :math:`\lambda \in \mathbb{R}^p` we have
# :math:`\lambda' S \lambda \sim \lambda' V \lambda \times \chi^2(n)`
np.random.seed(482974)
sn = 500
df = 10
dim = 4
# Construct an arbitrary positive definite matrix
scale = np.diag(np.arange(4)+1)
scale[np.tril_indices(4, k=-1)] = np.arange(6)
scale = np.dot(scale.T, scale)
# Use :math:`\lambda = [1, \dots, 1]'`
lamda = np.ones((dim,1))
sigma_lamda = lamda.T.dot(scale).dot(lamda).squeeze()
w = wishart(df, sigma_lamda)
c = chi2(df, scale=sigma_lamda)
# Statistics
assert_allclose(w.var(), c.var())
assert_allclose(w.mean(), c.mean())
assert_allclose(w.entropy(), c.entropy())
# PDF
X = np.linspace(0.1,10,num=10)
assert_allclose(w.pdf(X), c.pdf(X))
# rvs
rvs = w.rvs(size=sn)
args = (df,0,sigma_lamda)
alpha = 0.01
check_distribution_rvs('chi2', args, alpha, rvs)
def initialize(self, model):
super(GlobalOddsRatio, self).initialize(model)
if self.model.weights is not None:
warnings.warn("weights not implemented for GlobalOddsRatio "
"cov_struct, using unweighted covariance estimate",
NotImplementedWarning)
# Need to restrict to between-subject pairs
cpp = []
for v in model.endog_li:
# Number of subjects in this group
m = int(len(v) / self._ncut)
i1, i2 = np.tril_indices(m, -1)
cpp1 = {}
for k1 in range(self._ncut):
for k2 in range(k1 + 1):
jj = np.zeros((len(i1), 2), dtype=np.int64)
jj[:, 0] = i1 * self._ncut + k1
jj[:, 1] = i2 * self._ncut + k2
cpp1[(k2, k1)] = jj
cpp.append(cpp1)
self.cpp = cpp
# Initialize the dependence parameters
self.crude_or = self.observed_crude_oddsratio()
if self.model.update_dep:
self.dep_params = self.crude_or
def bic(em_fit_result_dict, LL_all):
'''
Compute the Bayesian Information Criterion score
Split it, associating the parameters to the number of datapoint they really take care of.
'''
# Number of parameters:
# - mixt_target_tr: 1
# - mixt_random_tr: 1
# - mixt_nontarget_trk: 1
# - alpha: 1
# - beta: 1
# - gamma: 1
# First count the Loglikelihood
bic_tot = -2. * np.nansum(LL_all[np.tril_indices(LL_all.shape[0])])
# Then count alpha, beta and gamma, for all datapoints appropriately
K = 3
bic_tot += K * np.log(np.nansum(np.isfinite(LL_all)))
# Now do the mixture proportions per condition
for nitems_i, nitems in enumerate(em_fit_result_dict['T_space']):
for trecall_i, trecall in enumerate(em_fit_result_dict['T_space']):
if trecall <= nitems:
K = 3
bic_tot += K * np.log(np.nansum(np.isfinite(LL_all[nitems_i, trecall_i])))
return bic_tot
def symmetrize(m, use_triangle='lower'):
"""Symmetrize a square NumPy array by reflecting one triangular
section across the diagonal to the other.
"""
if use_triangle not in ('lower', 'upper'):
raise ValueError
if not len(m.shape) == 2:
raise ValueError
if not (m.shape[0] == m.shape[1]):
raise ValueError
dim = m.shape[0]
lower_indices = numpy.tril_indices(dim, k=-1)
upper_indices = numpy.triu_indices(dim, k=1)
ms = m.copy()
if use_triangle == 'lower':
ms[upper_indices] = ms[lower_indices]
if use_triangle == 'upper':
ms[lower_indices] = ms[upper_indices]
return ms
def overlap(cibra, ciket, nmo, nocc, s=None):
'''Overlap between two CISD wavefunctions.
Args:
s : 2D array
The overlap matrix of non-orthogonal one-particle basis
'''
if s is None:
return dot(cibra, ciket, nmo, nocc)
DEBUG = True
nvir = nmo - nocc
nov = nocc * nvir
bra0, bra1, bra2 = cisdvec_to_amplitudes(cibra, nmo, nocc)
ket0, ket1, ket2 = cisdvec_to_amplitudes(ciket, nmo, nocc)
# Sort the ket orbitals to make the orbitals in bra one-one mapt to orbitals
# in ket.
if ((not DEBUG) and abs(numpy.linalg.det(s[:nocc, :nocc]) - 1) < 1e-2
and abs(numpy.linalg.det(s[nocc:, nocc:]) - 1) < 1e-2):
ket_orb_idx = numpy.where(abs(s) > 0.9)[1]
s = s[:, ket_orb_idx]
oidx = ket_orb_idx[:nocc]
vidx = ket_orb_idx[nocc:] - nocc
ket1 = ket1[oidx[:, None], vidx]
ket2 = ket2[oidx[:, None, None, None], oidx[:, None, None],
vidx[:, None], vidx]
ooidx = numpy.tril_indices(nocc, -1)
vvidx = numpy.tril_indices(nvir, -1)
bra2aa = bra2 - bra2.transpose(1, 0, 2, 3)
bra2aa = lib.take_2d(bra2aa.reshape(nocc**2,
nvir**2), ooidx[0] * nocc + ooidx[1],
vvidx[0] * nvir + vvidx[1])
ket2aa = ket2 - ket2.transpose(1, 0, 2, 3)
ket2aa = lib.take_2d(ket2aa.reshape(nocc**2,
nvir**2), ooidx[0] * nocc + ooidx[1],
vvidx[0] * nvir + vvidx[1])
occlist0 = numpy.arange(nocc).reshape(1, nocc)
occlists = numpy.repeat(occlist0, 1 + nov + bra2aa.size, axis=0)
occlist0 = occlists[:1]
occlist1 = occlists[1:1 + nov]
occlist2 = occlists[1 + nov:]
ia = 0
for i in range(nocc):
for a in range(nocc, nmo):
occlist1[ia, i] = a
ia += 1
ia = 0
for i in range(nocc):
for j in range(i):
for a in range(nocc, nmo):
for b in range(nocc, a):
occlist2[ia, i] = a
occlist2[ia, j] = b
ia += 1
na = len(occlists)
if DEBUG:
trans = numpy.empty((na, na))
for i, idx in enumerate(occlists):
s_sub = s[idx].T.copy()
minors = s_sub[occlists]
trans[i, :] = numpy.linalg.det(minors)
# Mimic the transformation einsum('ab,ap->pb', FCI, trans).
# The wavefunction FCI has the [excitation_alpha,excitation_beta]
# representation. The zero blocks like FCI[S_alpha,D_beta],
# FCI[D_alpha,D_beta], are explicitly excluded.
bra_mat = numpy.zeros((na, na))
bra_mat[0, 0] = bra0
bra_mat[0, 1:1 + nov] = bra_mat[1:1 + nov, 0] = bra1.ravel()
bra_mat[0, 1 + nov:] = bra_mat[1 + nov:, 0] = bra2aa.ravel()
bra_mat[1:1 + nov, 1:1 + nov] = bra2.transpose(0, 2, 1,
3).reshape(nov, nov)
ket_mat = numpy.zeros((na, na))
ket_mat[0, 0] = ket0
ket_mat[0, 1:1 + nov] = ket_mat[1:1 + nov, 0] = ket1.ravel()
ket_mat[0, 1 + nov:] = ket_mat[1 + nov:, 0] = ket2aa.ravel()
ket_mat[1:1 + nov, 1:1 + nov] = ket2.transpose(0, 2, 1,
3).reshape(nov, nov)
ovlp = lib.einsum('ab,ap,bq,pq->', bra_mat, trans, trans, ket_mat)
else:
nov1 = 1 + nov
noovv = bra2aa.size
bra_SS = numpy.zeros((nov1, nov1))
bra_SS[0, 0] = bra0
bra_SS[0, 1:] = bra_SS[1:, 0] = bra1.ravel()
bra_SS[1:, 1:] = bra2.transpose(0, 2, 1, 3).reshape(nov, nov)
ket_SS = numpy.zeros((nov1, nov1))
ket_SS[0, 0] = ket0
ket_SS[0, 1:] = ket_SS[1:, 0] = ket1.ravel()
ket_SS[1:, 1:] = ket2.transpose(0, 2, 1, 3).reshape(nov, nov)
trans_SS = numpy.empty((nov1, nov1))
trans_SD = numpy.empty((nov1, noovv))
trans_DS = numpy.empty((noovv, nov1))
occlist01 = occlists[:nov1]
for i, idx in enumerate(occlist01):
s_sub = s[idx].T.copy()
minors = s_sub[occlist01]
trans_SS[i, :] = numpy.linalg.det(minors)
minors = s_sub[occlist2]
trans_SD[i, :] = numpy.linalg.det(minors)
s_sub = s[:, idx].copy()
minors = s_sub[occlist2]
trans_DS[:, i] = numpy.linalg.det(minors)
ovlp = lib.einsum('ab,ap,bq,pq->', bra_SS, trans_SS, trans_SS, ket_SS)
ovlp += lib.einsum('ab,a ,bq, q->', bra_SS, trans_SS[:, 0], trans_SD,
ket2aa.ravel())
ovlp += lib.einsum('ab,ap,b ,p ->', bra_SS, trans_SD, trans_SS[:, 0],
ket2aa.ravel())
ovlp += lib.einsum(' b, p,bq,pq->', bra2aa.ravel(), trans_SS[0, :],
trans_DS, ket_SS)
ovlp += lib.einsum(' b, p,b ,p ->', bra2aa.ravel(), trans_SD[0, :],
trans_DS[:, 0], ket2aa.ravel())
ovlp += lib.einsum('a ,ap, q,pq->', bra2aa.ravel(), trans_DS,
trans_SS[0, :], ket_SS)
ovlp += lib.einsum('a ,a , q, q->', bra2aa.ravel(), trans_DS[:, 0],
trans_SD[0, :], ket2aa.ravel())
# FIXME: whether to approximate the overlap between double excitation coefficients
if numpy.linalg.norm(bra2aa) * numpy.linalg.norm(ket2aa) < 1e-4:
# Skip the overlap if coefficients of double excitation are small enough
pass
if (abs(numpy.linalg.det(s[:nocc, :nocc]) - 1) < 1e-2
and abs(numpy.linalg.det(s[nocc:, nocc:]) - 1) < 1e-2):
# If the overlap matrix close to identity enough, use the <D|D'> overlap
# for orthogonal single-particle basis to approximate the overlap
# for non-orthogonal basis.
ovlp += numpy.dot(bra2aa.ravel(), ket2aa.ravel()) * trans_SS[0,
0] * 2
else:
from multiprocessing import sharedctypes, Process
buf_ctypes = sharedctypes.RawArray('d', noovv)
trans_ket = numpy.ndarray(noovv, buffer=buf_ctypes)
def trans_dot_ket(i0, i1):
for i in range(i0, i1):
s_sub = s[occlist2[i]].T.copy()
minors = s_sub[occlist2]
trans_ket[i] = numpy.linalg.det(minors).dot(ket2aa.ravel())
nproc = lib.num_threads()
if nproc > 1:
seg = (noovv + nproc - 1) // nproc
ps = []
for i0, i1 in lib.prange(0, noovv, seg):
p = Process(target=trans_dot_ket, args=(i0, i1))
ps.append(p)
p.start()
[p.join() for p in ps]
else:
trans_dot_ket(0, noovv)
ovlp += numpy.dot(bra2aa.ravel(), trans_ket) * trans_SS[0, 0] * 2
return ovlp
def s2kl_s1(symmetry, eri, norb):
idx = numpy.tril_indices(norb)
eri1 = numpy.empty((norb, norb, norb, norb))
eri1[:, :, idx[0], idx[1]] = eri.reshape(norb, norb, -1)
eri1[:, :, idx[1], idx[0]] = eri.reshape(norb, norb, -1)
return eri1
def main():
usage = '''Usage: python %s [-h] [-s samples] [-k clusters] [-d dims] [-p band positions] fileName\n
spatial and spectral dimensions are lists, e.g., -d [0,0,400,400]''' % sys.argv[
0]
options, args = getopt.getopt(sys.argv[1:], 'hs:k:d:p:')
dims = None
pos = None
K = 8
m = 1000
for option, value in options:
if option == '-h':
print usage
return
elif option == '-d':
dims = eval(value)
elif option == '-p':
pos = eval(value)
elif option == '-k':
K = eval(value)
elif option == '-s':
m = eval(value)
gdal.AllRegister()
infile = args[0]
inDataset = gdal.Open(infile, GA_ReadOnly)
cols = inDataset.RasterXSize
rows = inDataset.RasterYSize
bands = inDataset.RasterCount
if dims:
x0, y0, cols, rows = dims
else:
x0 = 0
y0 = 0
if pos is not None:
bands = len(pos)
else:
pos = range(1, bands + 1)
path = os.path.dirname(infile)
basename = os.path.basename(infile)
root, ext = os.path.splitext(basename)
outfile = path + '/' + root + '_hcl' + ext
print '------- Hierarchical clustering ---------'
print time.asctime()
print 'Input: %s' % infile
print 'Clusters: %i' % K
print 'Samples: %i' % m
start = time.time()
GG = np.zeros((cols * rows, bands))
k = 0
for b in pos:
band = inDataset.GetRasterBand(b)
band = band.ReadAsArray(x0, y0, cols, rows).astype(float)
GG[:, k] = np.ravel(band)
k += 1
# training data
idx = np.random.randint(0, rows * cols, size=m)
G = GG[idx, :]
ones = np.mat(np.ones(m, dtype=np.int))
mults = np.ones(m, dtype=np.int)
Ls = np.array(range(m))
# initial cost array
G2 = np.mat(np.sum(G**2, 1))
Delta = G2.T * ones
Delta = Delta + Delta.T
Delta = Delta - 2 * np.mat(G) * np.mat(G).T
idx = np.tril_indices(m)
Delta[idx] = 10e10
Delta = Delta.A
# begin iteration
cost = 0.0
costarray = []
c = m
while c > K:
bm = best_merge(Delta)
j = bm[0]
i = bm[1]
# j > i
costarray.append(cost + Delta[i, j])
# re-label
idx = np.where(Ls == j)[0]
Ls[idx] = i
idx = np.where(Ls > j)[0]
Ls[idx] -= 1
# pre-merge multiplicities
ni = mults[i]
nj = mults[j]
# update merge-cost array, k = i+1 ... c-1
if c - i - 1 == 0:
k = [i + 1]
else:
k = i + 1 + range(c - i - 1)
nk = mults[k]
Dkj = np.minimum(Delta[k, j].ravel(), Delta[j, k].ravel())
idx = np.where(k == j)[0]
Dkj[idx] = 0
Delta[i, k] = ((ni + nk) * Delta[i, k] +
(nj + nk) * Dkj - nk * Delta[i, j]) / (ni + nj + nk)
# update merge-cost array, k = 0 ... i-1
if i == 0:
k = [0]
else:
k = range(i - 1)
nk = mults[k]
Dkj = np.minimum(Delta[k, j].ravel(), Delta[j, k].ravel())
idx = np.where(k == j)[0]
Dkj[idx] = 0
Delta[k, i] = ((ni + nk) * Delta[k, i] +
(nj + nk) * Dkj - nk * Delta[i, j]) / (ni + nj + nk)
# update multiplicities
mults[i] = mults[i] + mults[j]
# delete the upper cluster
idx = np.ones(c)
idx[j] = 0
idx = np.where(idx == 1)[0]
mults = mults[idx]
Delta = Delta[:, idx]
Delta = Delta[idx, :]
c -= 1
print 'classifying...'
labs = []
for L in Ls:
lab = np.zeros(K)
lab[L] = 1.0
labs.append(lab)
labs = np.array(labs)
classifier = sc.Maxlike(G, labs)
if classifier.train():
driver = gdal.GetDriverByName('GTiff')
outDataset = driver.Create(outfile, cols, rows, 1, GDT_Byte)
projection = inDataset.GetProjection()
geotransform = inDataset.GetGeoTransform()
if geotransform is not None:
gt = list(geotransform)
gt[0] = gt[0] + x0 * gt[1]
gt[3] = gt[3] + y0 * gt[5]
outDataset.SetGeoTransform(tuple(gt))
if projection is not None:
outDataset.SetProjection(projection)
cls, _ = classifier.classify(GG)
outBand = outDataset.GetRasterBand(1)
outBand.WriteArray(np.reshape(cls, (rows, cols)), 0, 0)
outBand.FlushCache()
outDataset = None
inDataset = None
ymax = np.max(costarray)
plt.loglog(range(K, m), list(reversed(costarray)))
p = plt.gca()
p.set_title('Merge cost')
p.set_xlabel('Custers')
p.set_ylim((1, ymax))
plt.show()
print 'result written to: ' + outfile
print 'elapsed time: ' + str(time.time() - start)
else:
print 'classification failed'
def sim_block_study(X, afreq, ldscore, n_study, n_blocks, n_causal_per_block,
block_p, pve, effect_distribution, min_r2, max_r2,
min_ldscore, max_ldscore):
"""
each block has a causal snps, each study assigned to a main block
tissues within a block share the causal snp
tissues out of block have the causal snp with probability block_p
min_r2, max_r2: pairwise r2 values allowed for causal snps
min_lscore, max_ldscore: ldscore range allowed for causal variants
"""
n_variants = X.shape[1]
n_samples = X.shape[0]
n_causal = n_blocks * n_causal_per_block
R2 = np.corrcoef(X.T)**2
active = (ldscore > min_ldscore) & (ldscore < max_ldscore)
causal_snps = select_causal_snps(R2, n_causal, min_r2, max_r2,
active).reshape(n_causal_per_block, -1)
# draw block ids and causal snps
# ensure each block gets at least one tissue
block_id = np.sort(
np.concatenate([
np.arange(n_blocks),
np.random.choice(n_blocks, n_study - n_blocks)
]))
# make block probability matrix
causal_p = np.eye(n_blocks)
causal_p[causal_p == 0] = block_p
results = []
for t in range(n_study):
# sample causal snps for tissue
causal_idx = np.random.binomial(1, causal_p[block_id[t]]) == 1
causal_in_study = np.concatenate(
[cs[causal_idx] for cs in causal_snps])
results.append(
sim_expression_single_study(X, afreq, causal_in_study, pve,
effect_distribution))
expression = np.atleast_2d(np.array([x[0] for x in results]))
true_effects = np.atleast_2d(np.array([x[1] for x in results]))
residual_variance = np.array([x[2] for x in results])
# trim down to the causal snps we actually used
causal_snps = np.arange(n_variants)[np.any(true_effects != 0, 0)]
tril = np.tril_indices(n_study, k=-1)
true_coloc = (true_effects @ true_effects.T != 0)[tril]
return {
'expression': expression,
'true_effects': true_effects,
'true_coloc': true_coloc,
'residual_variance': residual_variance,
'causal_snps': causal_snps,
'n_causal': causal_snps.size,
'K': int(np.ceil(causal_snps.size / 10) * 10),
'ldscore': ldscore
}
def __init__(self,
endog,
exog=None,
order=(1, 0),
trend='c',
error_cov_type='unstructured',
measurement_error=False,
enforce_stationarity=True,
enforce_invertibility=True,
**kwargs):
# Model parameters
self.error_cov_type = error_cov_type
self.measurement_error = measurement_error
self.enforce_stationarity = enforce_stationarity
self.enforce_invertibility = enforce_invertibility
# Save the given orders
self.order = order
self.trend = trend
# Model orders
self.k_ar = int(order[0])
self.k_ma = int(order[1])
self.k_trend = int(self.trend == 'c')
# Check for valid model
if trend not in ['c', 'nc']:
raise ValueError('Invalid trend specification.')
if error_cov_type not in ['diagonal', 'unstructured']:
raise ValueError('Invalid error covariance matrix type'
' specification.')
if self.k_ar == 0 and self.k_ma == 0:
raise ValueError('Invalid VARMAX(p,q) specification; at least one'
' p,q must be greater than zero.')
# Warn for VARMA model
if self.k_ar > 0 and self.k_ma > 0:
warn(
'Estimation of VARMA(p,q) models is not generically robust,'
' due especially to identification issues.', EstimationWarning)
# Exogenous data
self.k_exog = 0
if exog is not None:
exog_is_using_pandas = _is_using_pandas(exog, None)
if not exog_is_using_pandas:
exog = np.asarray(exog)
# Make sure we have 2-dimensional array
if exog.ndim == 1:
if not exog_is_using_pandas:
exog = exog[:, None]
else:
exog = pd.DataFrame(exog)
self.k_exog = exog.shape[1]
# Note: at some point in the future might add state regression, as in
# SARIMAX.
self.mle_regression = self.k_exog > 0
# We need to have an array or pandas at this point
if not _is_using_pandas(endog, None):
endog = np.asanyarray(endog)
# Model order
# Used internally in various places
_min_k_ar = max(self.k_ar, 1)
self._k_order = _min_k_ar + self.k_ma
# Number of states
k_endog = endog.shape[1]
k_posdef = k_endog
k_states = k_endog * self._k_order
# By default, initialize as stationary
kwargs.setdefault('initialization', 'stationary')
# By default, use LU decomposition
kwargs.setdefault('inversion_method', INVERT_UNIVARIATE | SOLVE_LU)
# Initialize the state space model
super(VARMAX, self).__init__(endog,
exog=exog,
k_states=k_states,
k_posdef=k_posdef,
**kwargs)
# Set as time-varying model if we have time-trend or exog
if self.k_exog > 0 or self.k_trend > 1:
self.ssm._time_invariant = False
# Initialize the parameters
self.parameters = OrderedDict()
self.parameters['trend'] = self.k_endog * self.k_trend
self.parameters['ar'] = self.k_endog**2 * self.k_ar
self.parameters['ma'] = self.k_endog**2 * self.k_ma
self.parameters['regression'] = self.k_endog * self.k_exog
if self.error_cov_type == 'diagonal':
self.parameters['state_cov'] = self.k_endog
# These parameters fill in a lower-triangular matrix which is then
# dotted with itself to get a positive definite matrix.
elif self.error_cov_type == 'unstructured':
self.parameters['state_cov'] = (int(self.k_endog *
(self.k_endog + 1) / 2))
self.parameters['obs_cov'] = self.k_endog * self.measurement_error
self.k_params = sum(self.parameters.values())
# Initialize known elements of the state space matrices
# If we have exog effects, then the state intercept needs to be
# time-varying
if self.k_exog > 0:
self.ssm['state_intercept'] = np.zeros((self.k_states, self.nobs))
# The design matrix is just an identity for the first k_endog states
idx = np.diag_indices(self.k_endog)
self.ssm[('design', ) + idx] = 1
# The transition matrix is described in four blocks, where the upper
# left block is in companion form with the autoregressive coefficient
# matrices (so it is shaped k_endog * k_ar x k_endog * k_ar) ...
if self.k_ar > 0:
idx = np.diag_indices((self.k_ar - 1) * self.k_endog)
idx = idx[0] + self.k_endog, idx[1]
self.ssm[('transition', ) + idx] = 1
# ... and the lower right block is in companion form with zeros as the
# coefficient matrices (it is shaped k_endog * k_ma x k_endog * k_ma).
idx = np.diag_indices((self.k_ma - 1) * self.k_endog)
idx = (idx[0] + (_min_k_ar + 1) * self.k_endog,
idx[1] + _min_k_ar * self.k_endog)
self.ssm[('transition', ) + idx] = 1
# The selection matrix is described in two blocks, where the upper
# block selects the all k_posdef errors in the first k_endog rows
# (the upper block is shaped k_endog * k_ar x k) and the lower block
# also selects all k_posdef errors in the first k_endog rows (the lower
# block is shaped k_endog * k_ma x k).
idx = np.diag_indices(self.k_endog)
self.ssm[('selection', ) + idx] = 1
idx = idx[0] + _min_k_ar * self.k_endog, idx[1]
if self.k_ma > 0:
self.ssm[('selection', ) + idx] = 1
# Cache some indices
if self.trend == 'c' and self.k_exog == 0:
self._idx_state_intercept = np.s_['state_intercept', :k_endog]
elif self.k_exog > 0:
self._idx_state_intercept = np.s_['state_intercept', :k_endog, :]
if self.k_ar > 0:
self._idx_transition = np.s_['transition', :k_endog, :]
else:
self._idx_transition = np.s_['transition', :k_endog, k_endog:]
if self.error_cov_type == 'diagonal':
self._idx_state_cov = (('state_cov', ) +
np.diag_indices(self.k_endog))
elif self.error_cov_type == 'unstructured':
self._idx_lower_state_cov = np.tril_indices(self.k_endog)
if self.measurement_error:
self._idx_obs_cov = ('obs_cov', ) + np.diag_indices(self.k_endog)
# Cache some slices
def _slice(key, offset):
length = self.parameters[key]
param_slice = np.s_[offset:offset + length]
offset += length
return param_slice, offset
offset = 0
self._params_trend, offset = _slice('trend', offset)
self._params_ar, offset = _slice('ar', offset)
self._params_ma, offset = _slice('ma', offset)
self._params_regression, offset = _slice('regression', offset)
self._params_state_cov, offset = _slice('state_cov', offset)
self._params_obs_cov, offset = _slice('obs_cov', offset)
def test_gradient():
from brainiak.reprsimil.brsa import BRSA
import brainiak.utils.utils as utils
import scipy.stats
import numpy as np
import os.path
import numdifftools as nd
np.random.seed(100)
file_path = os.path.join(os.path.dirname(__file__), "example_design.1D")
# Load an example design matrix
design = utils.ReadDesign(fname=file_path)
# concatenate it by 4 times, mimicking 4 runs of itenditcal timing
design.design_used = np.tile(design.design_used[:, 0:17], [4, 1])
design.n_TR = design.n_TR * 4
# start simulating some data
n_V = 200
n_C = np.size(design.design_used, axis=1)
n_T = design.n_TR
noise_bot = 0.5
noise_top = 1.5
noise_level = np.random.rand(n_V) * (noise_top - noise_bot) + noise_bot
# noise level is random.
# AR(1) coefficient
rho1_top = 0.8
rho1_bot = -0.2
rho1 = np.random.rand(n_V) * (rho1_top - rho1_bot) + rho1_bot
# generating noise
noise = np.zeros([n_T, n_V])
noise[0, :] = np.random.randn(n_V) * noise_level / np.sqrt(1 - rho1**2)
for i_t in range(1, n_T):
noise[i_t, :] = noise[i_t -
1, :] * rho1 + np.random.randn(n_V) * noise_level
# ideal covariance matrix
ideal_cov = np.zeros([n_C, n_C])
ideal_cov = np.eye(n_C) * 0.6
ideal_cov[0, 0] = 0.2
ideal_cov[5:9, 5:9] = 0.6
for cond in range(5, 9):
ideal_cov[cond, cond] = 1
idx = np.where(np.sum(np.abs(ideal_cov), axis=0) > 0)[0]
L_full = np.linalg.cholesky(ideal_cov)
# generating signal
snr_level = 5.0 # test with high SNR
# snr = np.random.rand(n_V)*(snr_top-snr_bot)+snr_bot
# Notice that accurately speaking this is not snr. the magnitude of signal depends
# not only on beta but also on x.
inten = np.random.randn(n_V) * 20.0
# parameters of Gaussian process to generate pseuso SNR
tau = 0.8
smooth_width = 5.0
inten_kernel = 1.0
coords = np.arange(0, n_V)[:, None]
dist2 = np.square(coords - coords.T)
inten_tile = np.tile(inten, [n_V, 1])
inten_diff2 = (inten_tile - inten_tile.T)**2
K = np.exp(-dist2 / smooth_width**2 / 2.0 - inten_diff2 / inten_kernel**2 /
2.0) * tau**2 + np.eye(n_V) * tau**2 * 0.001
L = np.linalg.cholesky(K)
snr = np.exp(np.dot(L, np.random.randn(n_V))) * snr_level
sqrt_v = noise_level * snr
betas_simulated = np.dot(L_full, np.random.randn(n_C, n_V)) * sqrt_v
signal = np.dot(design.design_used, betas_simulated)
# Adding noise to signal as data
Y = signal + noise
scan_onsets = np.linspace(0, design.n_TR, num=5)
# Test fitting with GP prior.
brsa = BRSA(GP_space=True, GP_inten=True, verbose=False, n_iter=200)
# test if the gradients are correct
XTY, XTDY, XTFY, YTY_diag, YTDY_diag, YTFY_diag, XTX, XTDX, XTFX = brsa._prepare_data(
design.design_used, Y, n_T, n_V, scan_onsets)
l_idx = np.tril_indices(n_C)
n_l = np.size(l_idx[0])
idx_param_sing, idx_param_fitU, idx_param_fitV = brsa._build_index_param(
n_l, n_V, 2)
# Initial parameters are correct parameters with some perturbation
param0_fitU = np.random.randn(n_l + n_V) * 0.1
param0_fitV = np.random.randn(n_V + 1) * 0.1
param0_fitV[:n_V - 1] += np.log(snr[:n_V - 1]) * 2
param0_fitV[n_V - 1] += np.log(smooth_width) * 2
param0_fitV[n_V] += np.log(inten_kernel) * 2
# log likelihood and derivative at the initial parameters
ll0, deriv0 = brsa._loglike_AR1_diagV_fitU(param0_fitU, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, \
XTY, XTDY, XTFY, np.log(snr)*2, l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)
# We test if the numerical and analytical gradient wrt to the first element of Cholesky factor is correct
vec = np.zeros(np.size(param0_fitU))
vec[idx_param_fitU['Cholesky'][0]] = 1
dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\
YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\
l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec)
assert np.isclose(
dd, np.dot(deriv0, vec),
rtol=0.01), 'gradient of fitU wrt Cholesky factor incorrect'
# We test the gradient wrt the reparametrization of AR(1) coefficient of noise.
vec = np.zeros(np.size(param0_fitU))
vec[idx_param_fitU['a1'][0]] = 1
dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\
YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\
l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec)
assert np.isclose(
dd, np.dot(deriv0, vec),
rtol=0.01), 'gradient of fitU wrt to AR(1) coefficient incorrect'
# Test on a random direction
vec = np.random.randn(np.size(param0_fitU))
vec = vec / np.linalg.norm(vec)
dd = nd.directionaldiff(lambda x: brsa._loglike_AR1_diagV_fitU(x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag,\
YTFY_diag, XTY, XTDY, XTFY, np.log(snr)*2,\
l_idx,n_C,n_T,n_V,idx_param_fitU,n_C)[0], param0_fitU, vec)
assert np.isclose(dd, np.dot(deriv0, vec),
rtol=0.01), 'gradient of fitU incorrect'
# We test the gradient of _fitV wrt to log(SNR^2) assuming no GP prior.
ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(
param0_fitV[idx_param_fitV['log_SNR2']], XTX, XTDX, XTFX, YTY_diag,
YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, L_full[l_idx],
np.tan(rho1 * np.pi / 2), l_idx, n_C, n_T, n_V, idx_param_fitV, n_C,
False, False)
vec = np.zeros(np.size(param0_fitV[idx_param_fitV['log_SNR2']]))
vec[idx_param_fitV['log_SNR2'][0]] = 1
dd = nd.directionaldiff(
lambda x: brsa._loglike_AR1_diagV_fitV(
x, XTX, XTDX, XTFX, YTY_diag, YTDY_diag, YTFY_diag, XTY, XTDY,
XTFY, L_full[l_idx], np.tan(rho1 * np.pi / 2), l_idx, n_C, n_T,
n_V, idx_param_fitV, n_C, False, False)[0],
param0_fitV[idx_param_fitV['log_SNR2']], vec)
assert np.isclose(
dd, np.dot(deriv0, vec), rtol=0.01
), 'gradient of fitV wrt log(SNR2) incorrect for model without GP'
# We test the gradient of _fitV wrt to log(SNR^2) assuming GP prior.
ll0, deriv0 = brsa._loglike_AR1_diagV_fitV(param0_fitV, XTX, XTDX, XTFX,
YTY_diag, YTDY_diag, YTFY_diag,
XTY, XTDY, XTFY, L_full[l_idx],
np.tan(rho1 * np.pi / 2), l_idx,
n_C, n_T, n_V, idx_param_fitV,
n_C, True, True, dist2,
inten_diff2, 100, 100)
vec = np.zeros(np.size(param0_fitV))
vec[idx_param_fitV['log_SNR2'][0]] = 1
dd = nd.directionaldiff(
lambda x: brsa._loglike_AR1_diagV_fitV(
x, XTX, XTDX, XTFX, YTY_diag,
YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, L_full[l_idx],
np.tan(rho1 * np.pi / 2), l_idx, n_C, n_T, n_V, idx_param_fitV,
n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV,
vec)
assert np.isclose(
dd, np.dot(deriv0, vec), rtol=0.01
), 'gradient of fitV srt log(SNR2) incorrect for model with GP'
# We test the graident wrt spatial length scale parameter of GP prior
vec = np.zeros(np.size(param0_fitV))
vec[idx_param_fitV['c_space']] = 1
dd = nd.directionaldiff(
lambda x: brsa._loglike_AR1_diagV_fitV(
x, XTX, XTDX, XTFX, YTY_diag,
YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, L_full[l_idx],
np.tan(rho1 * np.pi / 2), l_idx, n_C, n_T, n_V, idx_param_fitV,
n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV,
vec)
assert np.isclose(
dd, np.dot(deriv0, vec),
rtol=0.01), 'gradient of fitV wrt spatial length scale of GP incorrect'
# We test the graident wrt intensity length scale parameter of GP prior
vec = np.zeros(np.size(param0_fitV))
vec[idx_param_fitV['c_inten']] = 1
dd = nd.directionaldiff(
lambda x: brsa._loglike_AR1_diagV_fitV(
x, XTX, XTDX, XTFX, YTY_diag,
YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, L_full[l_idx],
np.tan(rho1 * np.pi / 2), l_idx, n_C, n_T, n_V, idx_param_fitV,
n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV,
vec)
assert np.isclose(
dd, np.dot(deriv0, vec), rtol=0.01
), 'gradient of fitV wrt intensity length scale of GP incorrect'
# We test the graident on a random direction
vec = np.random.randn(np.size(param0_fitV))
vec = vec / np.linalg.norm(vec)
dd = nd.directionaldiff(
lambda x: brsa._loglike_AR1_diagV_fitV(
x, XTX, XTDX, XTFX, YTY_diag,
YTDY_diag, YTFY_diag, XTY, XTDY, XTFY, L_full[l_idx],
np.tan(rho1 * np.pi / 2), l_idx, n_C, n_T, n_V, idx_param_fitV,
n_C, True, True, dist2, inten_diff2, 100, 100)[0], param0_fitV,
vec)
assert np.isclose(dd, np.dot(deriv0, vec),
rtol=0.01), 'gradient of fitV incorrect'
def _make_eris_outcore(mycc, mo_coeff=None):
cput0 = (time.clock(), time.time())
log = logger.Logger(mycc.stdout, mycc.verbose)
eris = _PhysicistsERIs()
eris._common_init_(mycc, mo_coeff)
nocc = eris.nocc
nao, nmo = eris.mo_coeff.shape
nvir = nmo - nocc
assert (eris.mo_coeff.dtype == np.double)
mo_a = eris.mo_coeff[:nao // 2]
mo_b = eris.mo_coeff[nao // 2:]
orbspin = eris.orbspin
feri = eris.feri = lib.H5TmpFile()
dtype = np.result_type(eris.mo_coeff).char
eris.oooo = feri.create_dataset('oooo', (nocc, nocc, nocc, nocc), dtype)
eris.ooov = feri.create_dataset('ooov', (nocc, nocc, nocc, nvir), dtype)
eris.oovv = feri.create_dataset('oovv', (nocc, nocc, nvir, nvir), dtype)
eris.ovov = feri.create_dataset('ovov', (nocc, nvir, nocc, nvir), dtype)
eris.ovvo = feri.create_dataset('ovvo', (nocc, nvir, nvir, nocc), dtype)
eris.ovvv = feri.create_dataset('ovvv', (nocc, nvir, nvir, nvir), dtype)
if orbspin is None:
orbo_a = mo_a[:, :nocc]
orbv_a = mo_a[:, nocc:]
orbo_b = mo_b[:, :nocc]
orbv_b = mo_b[:, nocc:]
max_memory = mycc.max_memory - lib.current_memory()[0]
blksize = min(nocc, max(2, int(max_memory * 1e6 / 8 / (nmo**3 * 2))))
max_memory = max(MEMORYMIN, max_memory)
fswap = lib.H5TmpFile()
ao2mo.kernel(mycc.mol, (orbo_a, mo_a, mo_a, mo_a),
fswap,
'aaaa',
max_memory=max_memory,
verbose=log)
ao2mo.kernel(mycc.mol, (orbo_a, mo_a, mo_b, mo_b),
fswap,
'aabb',
max_memory=max_memory,
verbose=log)
ao2mo.kernel(mycc.mol, (orbo_b, mo_b, mo_a, mo_a),
fswap,
'bbaa',
max_memory=max_memory,
verbose=log)
ao2mo.kernel(mycc.mol, (orbo_b, mo_b, mo_b, mo_b),
fswap,
'bbbb',
max_memory=max_memory,
verbose=log)
for p0, p1 in lib.prange(0, nocc, blksize):
tmp = np.asarray(fswap['aaaa'][p0 * nmo:p1 * nmo])
tmp += np.asarray(fswap['aabb'][p0 * nmo:p1 * nmo])
tmp += np.asarray(fswap['bbaa'][p0 * nmo:p1 * nmo])
tmp += np.asarray(fswap['bbbb'][p0 * nmo:p1 * nmo])
tmp = lib.unpack_tril(tmp).reshape(p1 - p0, nmo, nmo, nmo)
eris.oooo[p0:p1] = (
tmp[:, :nocc, :nocc, :nocc].transpose(0, 2, 1, 3) -
tmp[:, :nocc, :nocc, :nocc].transpose(0, 2, 3, 1))
eris.ooov[p0:p1] = (
tmp[:, :nocc, :nocc, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, :nocc, :nocc].transpose(0, 2, 3, 1))
eris.ovvv[p0:p1] = (
tmp[:, nocc:, nocc:, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, nocc:, nocc:].transpose(0, 2, 3, 1))
eris.oovv[p0:p1] = (
tmp[:, nocc:, :nocc, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, :nocc, nocc:].transpose(0, 2, 3, 1))
eris.ovov[p0:p1] = (
tmp[:, :nocc, nocc:, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, nocc:, :nocc].transpose(0, 2, 3, 1))
eris.ovvo[p0:p1] = (
tmp[:, nocc:, nocc:, :nocc].transpose(0, 2, 1, 3) -
tmp[:, :nocc, nocc:, nocc:].transpose(0, 2, 3, 1))
tmp = None
cput0 = log.timer_debug1('transforming ovvv', *cput0)
eris.vvvv = feri.create_dataset('vvvv', (nvir, nvir, nvir, nvir),
dtype)
tril2sq = lib.square_mat_in_trilu_indices(nvir)
fswap = lib.H5TmpFile()
ao2mo.kernel(mycc.mol, (orbv_a, orbv_a, orbv_a, orbv_a),
fswap,
'aaaa',
max_memory=max_memory,
verbose=log)
ao2mo.kernel(mycc.mol, (orbv_a, orbv_a, orbv_b, orbv_b),
fswap,
'aabb',
max_memory=max_memory,
verbose=log)
ao2mo.kernel(mycc.mol, (orbv_b, orbv_b, orbv_a, orbv_a),
fswap,
'bbaa',
max_memory=max_memory,
verbose=log)
ao2mo.kernel(mycc.mol, (orbv_b, orbv_b, orbv_b, orbv_b),
fswap,
'bbbb',
max_memory=max_memory,
verbose=log)
for p0, p1 in lib.prange(0, nvir, blksize):
off0 = p0 * (p0 + 1) // 2
off1 = p1 * (p1 + 1) // 2
tmp = np.asarray(fswap['aaaa'][off0:off1])
tmp += np.asarray(fswap['aabb'][off0:off1])
tmp += np.asarray(fswap['bbaa'][off0:off1])
tmp += np.asarray(fswap['bbbb'][off0:off1])
if p0 > 0:
c = tmp[tril2sq[p0:p1, :p0] - off0]
c = lib.unpack_tril(c.reshape((p1 - p0) * p0, -1))
eris.vvvv[p0:p1, :p0] = c.reshape(p1 - p0, p0, nvir, nvir)
c = tmp[tril2sq[:p1, p0:p1] - off0]
c = lib.unpack_tril(c.reshape((p1 - p0) * p1, -1))
eris.vvvv[:p1, p0:p1] = c.reshape(p1, p1 - p0, nvir, nvir)
tmp = None
for p0, p1 in lib.prange(0, nvir, blksize):
tmp = np.asarray(eris.vvvv[p0:p1])
eris.vvvv[p0:p1] = tmp.transpose(0, 2, 1, 3) - tmp.transpose(
0, 2, 3, 1)
cput0 = log.timer_debug1('transforming vvvv', *cput0)
else: # with orbspin
mo = mo_a + mo_b
orbo = mo[:, :nocc]
orbv = mo[:, nocc:]
max_memory = mycc.max_memory - lib.current_memory()[0]
blksize = min(nocc, max(2, int(max_memory * 1e6 / 8 / (nmo**3 * 2))))
max_memory = max(MEMORYMIN, max_memory)
fswap = lib.H5TmpFile()
ao2mo.kernel(mycc.mol, (orbo, mo, mo, mo),
fswap,
max_memory=max_memory,
verbose=log)
sym_forbid = orbspin[:, None] != orbspin
for p0, p1 in lib.prange(0, nocc, blksize):
tmp = np.asarray(fswap['eri_mo'][p0 * nmo:p1 * nmo])
tmp = lib.unpack_tril(tmp).reshape(p1 - p0, nmo, nmo, nmo)
tmp[sym_forbid[p0:p1]] = 0
tmp[:, :, sym_forbid] = 0
eris.oooo[p0:p1] = (
tmp[:, :nocc, :nocc, :nocc].transpose(0, 2, 1, 3) -
tmp[:, :nocc, :nocc, :nocc].transpose(0, 2, 3, 1))
eris.ooov[p0:p1] = (
tmp[:, :nocc, :nocc, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, :nocc, :nocc].transpose(0, 2, 3, 1))
eris.ovvv[p0:p1] = (
tmp[:, nocc:, nocc:, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, nocc:, nocc:].transpose(0, 2, 3, 1))
eris.oovv[p0:p1] = (
tmp[:, nocc:, :nocc, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, :nocc, nocc:].transpose(0, 2, 3, 1))
eris.ovov[p0:p1] = (
tmp[:, :nocc, nocc:, nocc:].transpose(0, 2, 1, 3) -
tmp[:, nocc:, nocc:, :nocc].transpose(0, 2, 3, 1))
eris.ovvo[p0:p1] = (
tmp[:, nocc:, nocc:, :nocc].transpose(0, 2, 1, 3) -
tmp[:, :nocc, nocc:, nocc:].transpose(0, 2, 3, 1))
tmp = None
cput0 = log.timer_debug1('transforming ovvv', *cput0)
eris.vvvv = feri.create_dataset('vvvv', (nvir, nvir, nvir, nvir),
dtype)
sym_forbid = (orbspin[nocc:, None] !=
orbspin[nocc:])[np.tril_indices(nvir)]
tril2sq = lib.square_mat_in_trilu_indices(nvir)
fswap = lib.H5TmpFile()
ao2mo.kernel(mycc.mol, orbv, fswap, max_memory=max_memory, verbose=log)
for p0, p1 in lib.prange(0, nvir, blksize):
off0 = p0 * (p0 + 1) // 2
off1 = p1 * (p1 + 1) // 2
tmp = np.asarray(fswap['eri_mo'][off0:off1])
tmp[sym_forbid[off0:off1]] = 0
tmp[:, sym_forbid] = 0
if p0 > 0:
c = tmp[tril2sq[p0:p1, :p0] - off0]
c = lib.unpack_tril(c.reshape((p1 - p0) * p0, -1))
eris.vvvv[p0:p1, :p0] = c.reshape(p1 - p0, p0, nvir, nvir)
c = tmp[tril2sq[:p1, p0:p1] - off0]
c = lib.unpack_tril(c.reshape((p1 - p0) * p1, -1))
eris.vvvv[:p1, p0:p1] = c.reshape(p1, p1 - p0, nvir, nvir)
tmp = None
for p0, p1 in lib.prange(0, nvir, blksize):
tmp = np.asarray(eris.vvvv[p0:p1])
eris.vvvv[p0:p1] = tmp.transpose(0, 2, 1, 3) - tmp.transpose(
0, 2, 3, 1)
cput0 = log.timer_debug1('transforming vvvv', *cput0)
return eris
def tril_indices(self):
return np.tril_indices(self.ddim)
def call(self, x, mask=None):
# TODO: validate input shape
# The input of this layer is [L, mu, a] in concatenated form. We first split
# those up.
idx = 0
if self.mode == 'full':
L_flat = x[:, idx:idx +
(self.nb_actions * self.nb_actions + self.nb_actions) //
2]
idx += (self.nb_actions * self.nb_actions + self.nb_actions) // 2
elif self.mode == 'diag':
L_flat = x[:, idx:idx + self.nb_actions]
idx += self.nb_actions
else:
L_flat = None
assert L_flat is not None
mu = x[:, idx:idx + self.nb_actions]
idx += self.nb_actions
a = x[:, idx:idx + self.nb_actions]
idx += self.nb_actions
if self.mode == 'full':
# Create L and L^T matrix, which we use to construct the positive-definite matrix P.
L = None
LT = None
if K._BACKEND == 'theano':
import theano.tensor as T
import theano
def fn(x, L_acc, LT_acc):
x_ = K.zeros((self.nb_actions, self.nb_actions))
x_ = T.set_subtensor(x_[np.tril_indices(self.nb_actions)],
x)
diag = K.exp(T.diag(x_) + K.epsilon())
x_ = T.set_subtensor(x_[np.diag_indices(self.nb_actions)],
diag)
return x_, x_.T
outputs_info = [
K.zeros((self.nb_actions, self.nb_actions)),
K.zeros((self.nb_actions, self.nb_actions)),
]
results, _ = theano.scan(fn=fn,
sequences=L_flat,
outputs_info=outputs_info)
L, LT = results
elif K._BACKEND == 'tensorflow':
import tensorflow as tf
# Number of elements in a triangular matrix.
nb_elems = (self.nb_actions * self.nb_actions +
self.nb_actions) // 2
# Create mask for the diagonal elements in L_flat. This is used to exponentiate
# only the diagonal elements, which is done before gathering.
diag_indeces = [0]
for row in range(1, self.nb_actions):
diag_indeces.append(diag_indeces[-1] + (row + 1))
diag_mask = np.zeros(1 + nb_elems) # +1 for the leading zero
diag_mask[np.array(diag_indeces) + 1] = 1
diag_mask = K.variable(diag_mask)
# Add leading zero element to each element in the L_flat. We use this zero
# element when gathering L_flat into a lower triangular matrix L.
nb_rows = tf.shape(L_flat)[0]
zeros = tf.expand_dims(tf.tile(K.zeros((1, )), [nb_rows]), 1)
L_flat = tf.concat(1, [zeros, L_flat])
# Create mask that can be used to gather elements from L_flat and put them
# into a lower triangular matrix.
tril_mask = np.zeros((self.nb_actions, self.nb_actions),
dtype='int32')
tril_mask[np.tril_indices(self.nb_actions)] = range(
1, nb_elems + 1)
# Finally, process each element of the batch.
init = [
K.zeros((self.nb_actions, self.nb_actions)),
K.zeros((self.nb_actions, self.nb_actions)),
]
def fn(a, x):
# Exponentiate everything. This is much easier than only exponentiating
# the diagonal elements, and, usually, the action space is relatively low.
x_ = K.exp(x + K.epsilon())
# Only keep the diagonal elements.
x_ *= diag_mask
# Add the original, non-diagonal elements.
x_ += x * (1. - diag_mask)
# Finally, gather everything into a lower triangular matrix.
L_ = tf.gather(x_, tril_mask)
return [L_, tf.transpose(L_)]
tmp = tf.scan(fn, L_flat, initializer=init)
if isinstance(tmp, (list, tuple)):
# TensorFlow 0.10 now returns a tuple of tensors.
L, LT = tmp
else:
# Old TensorFlow < 0.10 returns a shared tensor.
L = tmp[:, 0, :, :]
LT = tmp[:, 1, :, :]
else:
raise RuntimeError('Unknown Keras backend "{}".'.format(
K._BACKEND))
assert L is not None
assert LT is not None
P = K.batch_dot(L, LT)
elif self.mode == 'diag':
if K._BACKEND == 'theano':
import theano.tensor as T
import theano
def fn(x, P_acc):
x_ = K.zeros((self.nb_actions, self.nb_actions))
x_ = T.set_subtensor(x_[np.diag_indices(self.nb_actions)],
x)
return x_
outputs_info = [
K.zeros((self.nb_actions, self.nb_actions)),
]
P, _ = theano.scan(fn=fn,
sequences=L_flat,
outputs_info=outputs_info)
elif K._BACKEND == 'tensorflow':
import tensorflow as tf
# Create mask that can be used to gather elements from L_flat and put them
# into a diagonal matrix.
diag_mask = np.zeros((self.nb_actions, self.nb_actions),
dtype='int32')
diag_mask[np.diag_indices(self.nb_actions)] = range(
1, self.nb_actions + 1)
# Add leading zero element to each element in the L_flat. We use this zero
# element when gathering L_flat into a lower triangular matrix L.
nb_rows = tf.shape(L_flat)[0]
zeros = tf.expand_dims(tf.tile(K.zeros((1, )), [nb_rows]), 1)
L_flat = tf.concat(1, [zeros, L_flat])
# Finally, process each element of the batch.
def fn(a, x):
x_ = tf.gather(x, diag_mask)
return x_
P = tf.scan(fn,
L_flat,
initializer=K.zeros(
(self.nb_actions, self.nb_actions)))
else:
raise RuntimeError('Unknown Keras backend "{}".'.format(
K._BACKEND))
assert P is not None
assert K.ndim(P) == 3
# Combine a, mu and P into a scalar (over the batches). What we compute here is
# -.5 * (a - mu)^T * P * (a - mu), where * denotes the dot-product. Unfortunately
# TensorFlow handles vector * P slightly suboptimal, hence we convert the vectors to
# 1xd/dx1 matrices and finally flatten the resulting 1x1 matrix into a scalar. All
# operations happen over the batch size, which is dimension 0.
prod = K.batch_dot(K.expand_dims(a - mu, dim=1), P)
prod = K.batch_dot(prod, K.expand_dims(a - mu, dim=-1))
A = -.5 * K.batch_flatten(prod)
assert K.ndim(A) == 2
return A
def gradient_marginal_loglikelihood(self, observations, parameters,
forward_message=None, backward_message=None, weights=None,
tqdm=None):
# Forward Pass
forward_messages = self.forward_pass(observations, parameters,
forward_message, include_init_message=True)
# Backward Pass
backward_messages = self.backward_pass(observations, parameters,
backward_message, include_init_message=True)
# Gradients
grad = {var: np.zeros_like(value)
for var, value in parameters.as_dict().items()}
Pi, expanded_pi = parameters.pi, parameters.expanded_pi
D = parameters.D
LRinv, Rinv, R = parameters.LRinv, parameters.Rinv, parameters.R
pbar = enumerate(zip(forward_messages[:-1], backward_messages[1:]))
if tqdm is not None:
pbar = tqdm(pbar)
pbar.set_description("gradient loglike")
for t, (forward_t, backward_t) in pbar:
# r_t is Pr(z_{t-1} | y_{< t})
# s_t is Pr(z_t | y_{< t})
# q_t is Pr(y_{> t} | z_t)
r_t = forward_t['prob_vector']
s_t = np.dot(r_t, Pi)
q_t = backward_t['likelihood_vector']
weight_t = 1.0 if weights is None else weights[t]
# Calculate P_t = Pr(y_t | z_t)
y_cur = observations[t]
P_t, _ = self._likelihoods(
y_cur=y_cur,
parameters=parameters
)
# Marginal + Pairwise Marginal
joint_post = np.diag(r_t).dot(Pi).dot(np.diag(P_t*q_t))
joint_post = joint_post/np.sum(joint_post)
marg_post = np.sum(joint_post, axis=0)
# Grad for pi
if parameters.pi_type == "logit":
# Gradient of logit_pi
grad['logit_pi'] += weight_t * (joint_post - \
np.diag(np.sum(joint_post, axis=1)).dot(Pi))
elif parameters.pi_type == "expanded":
grad['expanded_pi'] += weight_t * np.array([
(expanded_pi[k]**-1)*(
joint_post[k] - np.sum(joint_post[k])*Pi[k])
for k in range(self.num_states)
])
else:
raise RuntimeError()
# grad for mu and LRinv
y_prev = y_cur[1:].flatten()
for k, D_k, LRinv_k, Rinv_k, R_k in zip(
range(self.num_states), D, LRinv, Rinv, R):
diff_k = y_cur[0] - np.dot(D_k, y_prev)
grad['D'][k] += weight_t * (
np.outer(Rinv_k.dot(diff_k), y_prev) * marg_post[k])
grad_LRinv_k = weight_t * (
(R_k - np.outer(diff_k, diff_k)).dot(LRinv_k)
) * marg_post[k]
grad['LRinv_vec'][k] += grad_LRinv_k[np.tril_indices(self.m)]
return grad
def test_ft_aoao(self):
#coords = pdft.gen_grid.gen_uniform_grids(cell)
#aoR = pdft.numint.eval_ao(cell, coords)
#ngrids, nao = aoR.shape
#ref = numpy.asarray([tools.fft(aoR[:,i].conj()*aoR[:,j], cell.mesh)
# for i in range(nao) for j in range(nao)])
#ref = ref.reshape(nao,nao,-1).transpose(2,0,1) * (cell.vol/ngrids)
#dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s1hermi')
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,0]-dat[:,0,0]) , 0, 5)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,1,1]-dat[:,1,1]) , 0.02315483195832373, 4)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,2:]-dat[:,2:,2:]), 0, 9)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,2:]-dat[:,0,2:]) , 0, 9)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,0]-dat[:,2:,0]) , 0, 9)
#idx = numpy.tril_indices(nao)
#ref = dat[:,idx[0],idx[1]]
#dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s2')
#self.assertAlmostEqual(abs(dat-ref).sum(), 0, 9)
coords = pdft.gen_grid.gen_uniform_grids(cell1)
Gv, Gvbase, kws = cell1.get_Gv_weights(cell1.mesh)
b = cell1.reciprocal_vectors()
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s1',
b=b,
gxyz=gxyz,
Gvbase=Gvbase)
self.assertAlmostEqual(lib.fp(dat),
1.5666516306798806 + 1.953555017583245j, 9)
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s2',
b=b,
gxyz=gxyz,
Gvbase=Gvbase)
self.assertAlmostEqual(lib.fp(dat),
-0.85276967757297917 + 1.0378751267506394j, 9)
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s1hermi',
b=b,
gxyz=gxyz,
Gvbase=Gvbase)
self.assertAlmostEqual(lib.fp(dat),
1.5666516306798806 + 1.953555017583245j, 9)
aoR = pdft.numint.eval_ao(cell1, coords)
ngrids, nao = aoR.shape
aoaoR = numpy.einsum('pi,pj->ijp', aoR, aoR)
ref = tools.fft(aoaoR.reshape(nao * nao, -1), cell1.mesh)
ref = ref.reshape(nao, nao, -1).transpose(2, 0,
1) * (cell1.vol / ngrids)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 0, 0] - dat[:, 0, 0]),
0, 7)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 1, 1] - dat[:, 1, 1]),
0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 2:] - dat[:, 2:, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 0, 2:] - dat[:, 0, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 0] - dat[:, 2:, 0]), 0, 7)
idx = numpy.tril_indices(nao)
ref = dat[:, idx[0], idx[1]]
dat = ft_ao.ft_aopair(cell1, cell1.Gv, aosym='s2')
self.assertAlmostEqual(abs(dat - ref).sum(), 0, 9)
def __init__(self, m=None, P=None, U=None, S=None, Pm=None, L=None):
"""Initialize a gaussian pdf given a valid combination of its
parameters. Valid combinations are: m-P, m-U, m-S, Pm-P, Pm-U, Pm-S.
:param m: mean
:param P: precision
:param U: upper triangular precision factor such that U'U = P
:param S: covariance
:param C : upper or lower triangular covariance factor, in any case
S = C'C
:param Pm: precision times mean such that P*m = Pm
:param L: lower triangular covariance factor given as 1D array such that
LL' = S
"""
if m is not None:
m = np.asarray(m)
self.m = m
self.ndim = m.size
if P is not None:
P = np.asarray(P)
L = np.linalg.cholesky(P)
self.P = P
self.C = np.linalg.inv(L)
self.S = np.dot(self.C.T, self.C)
self.Pm = np.dot(P, m)
self.logdetP = 2.0 * np.sum(np.log(np.diagonal(L)))
elif U is not None:
U = np.asarray(U)
self.P = np.dot(U.T, U)
self.C = np.linalg.inv(U.T)
self.S = np.dot(self.C.T, self.C)
self.Pm = np.dot(self.P, m)
self.logdetP = 2.0 * np.sum(np.log(np.diagonal(U)))
elif L is not None:
L = np.asarray(L)
Lm = np.zeros((self.ndim, self.ndim))
idx_l = np.tril_indices(self.ndim, -1)
idx_d = np.diag_indices(self.ndim)
Lm[idx_l] = L[self.ndim:]
Lm[idx_d] = L[0:self.ndim]
self.C = Lm.T
self.S = np.dot(self.C.T, self.C)
self.P = np.linalg.inv(self.S)
self.Pm = np.dot(self.P, m)
self.logdetP = -2.0 * np.sum(np.log(np.diagonal(self.C)))
elif S is not None:
S = np.asarray(S)
self.P = np.linalg.inv(S)
self.C = np.linalg.cholesky(S).T
self.S = S
self.Pm = np.dot(self.P, m)
self.logdetP = -2.0 * np.sum(np.log(np.diagonal(self.C)))
else:
raise ValueError("Precision information missing.")
elif Pm is not None:
Pm = np.asarray(Pm)
self.Pm = Pm
self.ndim = Pm.size
if P is not None:
P = np.asarray(P)
L = np.linalg.cholesky(P)
self.P = P
self.C = np.linalg.inv(L)
self.S = np.dot(self.C.T, self.C)
self.m = np.linalg.solve(P, Pm)
self.logdetP = 2.0 * np.sum(np.log(np.diagonal(L)))
elif U is not None:
U = np.asarray(U)
self.P = np.dot(U.T, U)
self.C = np.linalg.inv(U.T)
self.S = np.dot(self.C.T, self.C)
self.m = np.linalg.solve(self.P, Pm)
self.logdetP = 2.0 * np.sum(np.log(np.diagonal(U)))
elif S is not None:
S = np.asarray(S)
self.P = np.linalg.inv(S)
self.C = np.linalg.cholesky(S).T
self.S = S
self.m = np.dot(S, Pm)
self.logdetP = -2.0 * np.sum(np.log(np.diagonal(self.C)))
else:
raise ValueError("Precision information missing.")
else:
raise ValueError("Mean information missing.")
def s2ij_s1(symmetry, eri, norb):
idx = numpy.tril_indices(norb)
eri1 = numpy.empty((norb, norb, norb, norb))
eri1[idx] = eri.reshape(-1, norb, norb)
eri1[idx[1], idx[0]] = eri.reshape(-1, norb, norb)
return eri1
def get_topologies(self, symbols, saturate=False):
''' Return the possible topologies of a given chemical species.
Parameters
----------
symbols : str
Atomic symbols to construct the topologies from.
saturate : bool
Saturate the molecule with hydrogen based on the
default.radicals set.
Returns
-------
molecules : list (N,)
Gratoms objects with unique connectivity matrix attached.
No 3D positions will be provided for these structures.
'''
num, cnt = Molecule.get_atomic_numbers(symbols, True)
# print(num, cnt)
mcnt = cnt[num != 1]
mnum = num[num != 1]
if cnt[num == 1]:
hcnt = cnt[num == 1][0]
else:
hcnt = 0
elements = np.repeat(mnum, mcnt)
max_degree = defaults.get('radicals')[elements]
n = mcnt.sum()
hmax = int(max_degree.sum() - (n - 1) * 2)
if hcnt > hmax:
hcnt = hmax
if saturate:
hcnt = hmax
if n == 1:
atoms = Gratoms(elements, cell=[1, 1, 1])
hatoms = Molecule.hydrogenate(atoms, np.array([hcnt]))
return [hatoms]
elif n == 0:
hatoms = Gratoms('H{}'.format(hcnt))
if hcnt == 2:
hatoms.graph.add_edge(0, 1, bonds=1)
return [hatoms]
ln = np.arange(n).sum()
il = np.tril_indices(n, -1)
backbones, molecules = [], []
combos = combinations(np.arange(ln), n - 1)
for c in combos:
# Construct the connectivity matrix
ltm = np.zeros(ln)
ltm[np.atleast_2d(c)] = 1
connectivity = np.zeros((n, n))
connectivity[il] = ltm
connectivity = np.maximum(connectivity, connectivity.T)
degree = connectivity.sum(axis=0)
# Not fully connected (subgraph)
if np.any(degree == 0) or not \
is_connected(from_numpy_matrix(connectivity)):
continue
# Overbonded atoms.
remaining_bonds = (max_degree - degree).astype(int)
if np.any(remaining_bonds < 0):
continue
atoms = Gratoms(numbers=elements,
edges=connectivity,
cell=[1, 1, 1])
isomorph = False
for G0 in backbones:
if atoms.is_isomorph(G0):
isomorph = True
break
if not isomorph:
backbones += [atoms]
# The backbone is saturated, do not enumerate
if hcnt == hmax:
hatoms = Molecule.hydrogenate(atoms, remaining_bonds)
molecules += [hatoms]
continue
# Enumerate hydrogens across backbone
for bins in self.bin_hydrogen(hcnt, n):
if not np.all(bins <= remaining_bonds):
continue
hatoms = Molecule.hydrogenate(atoms, bins)
isomorph = False
for G0 in molecules:
if hatoms.is_isomorph(G0):
isomorph = True
break
if not isomorph:
molecules += [hatoms]
return molecules
return np.linalg.norm(A_lamb, 'fro')
###parameters
muTot=200
mu_arr=np.logspace(-10,5.0,muTot)
norm_arr_nonint=np.zeros(muTot)
norm_arr_int=np.zeros(muTot)
hz=5.00#for int Ham
###
t_start_nonint=time.time()
###nonint
H=Ham_nonint(L)
wij, num_lamb_mat=output_gauge_potent(H,L)
###finding minimum and maximum wij
index_lower = np.tril_indices(2**L,-1)
wij_arr=wij[index_lower]
wij_min_nonint= min(wij_arr)
wij_max_nonint=max(wij_arr)
print wij_min_nonint,wij_max_nonint
###running the loop
for i in range(muTot):
mu=mu_arr[i]
A_lamb=gauge_potent_mu(wij, num_lamb_mat,mu)
norm_arr_nonint[i]=norm(A_lamb)
t_end_nonint=time.time()
t_nonint_code=(t_end_nonint-t_start_nonint)/60
#######
def test_outcore(self):
ftmp = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
cderi0 = df.incore.cholesky_eri(mol)
df.outcore.cholesky_eri(mol, ftmp.name)
with h5py.File(ftmp.name, 'r') as feri:
self.assertTrue(numpy.allclose(feri['j3c'], cderi0))
df.outcore.cholesky_eri(mol, ftmp.name, ioblk_size=.05)
with h5py.File(ftmp.name, 'r') as feri:
self.assertTrue(numpy.allclose(feri['j3c'], cderi0))
nao = mol.nao_nr()
naux = cderi0.shape[0]
df.outcore.general(mol, (numpy.eye(nao), ) * 2,
ftmp.name,
max_memory=.05,
ioblk_size=.02)
with h5py.File(ftmp.name, 'r') as feri:
self.assertTrue(numpy.allclose(feri['eri_mo'], cderi0))
####
buf = numpy.zeros((naux, nao, nao))
idx = numpy.tril_indices(nao)
buf[:, idx[0], idx[1]] = cderi0
buf[:, idx[1], idx[0]] = cderi0
cderi0 = buf
df.outcore.cholesky_eri(mol, ftmp.name, aosym='s1', ioblk_size=.05)
with h5py.File(ftmp.name, 'r') as feri:
self.assertTrue(
numpy.allclose(feri['j3c'], cderi0.reshape(naux, -1)))
ftmp = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
numpy.random.seed(1)
co = numpy.random.random((nao, 4))
cv = numpy.random.random((nao, 25))
cderi0 = numpy.einsum('kpq,pi,qj->kij', cderi0, co, cv)
df.outcore.general(mol, (co, cv), ftmp.name, ioblk_size=.05)
with h5py.File(ftmp.name, 'r') as feri:
self.assertTrue(
numpy.allclose(feri['eri_mo'], cderi0.reshape(naux, -1)))
cderi0 = df.incore.aux_e2(mol,
auxmol,
intor='int3c2e_ip1_sph',
aosym='s1',
comp=3).reshape(3, nao**2, -1)
j2c = df.incore.fill_2c2e(mol, auxmol)
low = scipy.linalg.cholesky(j2c, lower=True)
cderi0 = [
scipy.linalg.solve_triangular(low, j3c.T, lower=True)
for j3c in cderi0
]
nao = mol.nao_nr()
df.outcore.general(mol, (numpy.eye(nao), ) * 2,
ftmp.name,
int3c='int3c2e_ip1_sph',
aosym='s1',
int2c='int2c2e_sph',
comp=3,
max_memory=.05,
ioblk_size=.02)
with h5py.File(ftmp.name, 'r') as feri:
self.assertTrue(numpy.allclose(feri['eri_mo'], cderi0))
def test_silhouette_paper_example():
# Explicitly check per-sample results against Rousseeuw (1987)
# Data from Table 1
lower = [
5.58,
7.00,
6.50,
7.08,
7.00,
3.83,
4.83,
5.08,
8.17,
5.83,
2.17,
5.75,
6.67,
6.92,
4.92,
6.42,
5.00,
5.58,
6.00,
4.67,
6.42,
3.42,
5.50,
6.42,
6.42,
5.00,
3.92,
6.17,
2.50,
4.92,
6.25,
7.33,
4.50,
2.25,
6.33,
2.75,
6.08,
6.67,
4.25,
2.67,
6.00,
6.17,
6.17,
6.92,
6.17,
5.25,
6.83,
4.50,
3.75,
5.75,
5.42,
6.08,
5.83,
6.67,
3.67,
4.75,
3.00,
6.08,
6.67,
5.00,
5.58,
4.83,
6.17,
5.67,
6.50,
6.92,
]
D = np.zeros((12, 12))
D[np.tril_indices(12, -1)] = lower
D += D.T
names = [
"BEL",
"BRA",
"CHI",
"CUB",
"EGY",
"FRA",
"IND",
"ISR",
"USA",
"USS",
"YUG",
"ZAI",
]
# Data from Figure 2
labels1 = [1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1]
expected1 = {
"USA": 0.43,
"BEL": 0.39,
"FRA": 0.35,
"ISR": 0.30,
"BRA": 0.22,
"EGY": 0.20,
"ZAI": 0.19,
"CUB": 0.40,
"USS": 0.34,
"CHI": 0.33,
"YUG": 0.26,
"IND": -0.04,
}
score1 = 0.28
# Data from Figure 3
labels2 = [1, 2, 3, 3, 1, 1, 2, 1, 1, 3, 3, 2]
expected2 = {
"USA": 0.47,
"FRA": 0.44,
"BEL": 0.42,
"ISR": 0.37,
"EGY": 0.02,
"ZAI": 0.28,
"BRA": 0.25,
"IND": 0.17,
"CUB": 0.48,
"USS": 0.44,
"YUG": 0.31,
"CHI": 0.31,
}
score2 = 0.33
for labels, expected, score in [
(labels1, expected1, score1),
(labels2, expected2, score2),
]:
expected = [expected[name] for name in names]
# we check to 2dp because that's what's in the paper
pytest.approx(
expected,
silhouette_samples(D, np.array(labels), metric="precomputed"),
abs=1e-2,
)
pytest.approx(
score, silhouette_score(D, np.array(labels), metric="precomputed"), abs=1e-2
)
def fcidump(wfn, fname='INTDUMP', oe_ints=None):
"""Save integrals to file in FCIDUMP format as defined in Comp. Phys. Commun. 54 75 (1989)
Additional one-electron integrals, including orbital energies, can also be saved.
This latter format can be used with the HANDE QMC code but is not standard.
:returns: None
:raises: ValidationError when SCF wavefunction is not RHF
:type wfn: :py:class:`~psi4.core.Wavefunction`
:param wfn: set of molecule, basis, orbitals from which to generate cube files
:param fname: name of the integrals file, defaults to INTDUMP
:param oe_ints: list of additional one-electron integrals to save to file.
So far only EIGENVALUES is a valid option.
:examples:
>>> # [1] Save one- and two-electron integrals to standard FCIDUMP format
>>> E, wfn = energy('scf', return_wfn=True)
>>> fcidump(wfn)
>>> # [2] Save orbital energies, one- and two-electron integrals.
>>> E, wfn = energy('scf', return_wfn=True)
>>> fcidump(wfn, oe_ints=['EIGENVALUES'])
"""
# Get some options
reference = core.get_option('SCF', 'REFERENCE')
ints_tolerance = core.get_global_option('INTS_TOLERANCE')
# Some sanity checks
if reference not in ['RHF', 'UHF']:
raise ValidationError(
'FCIDUMP not implemented for {} references\n'.format(reference))
if oe_ints is None:
oe_ints = []
molecule = wfn.molecule()
docc = wfn.doccpi()
frzcpi = wfn.frzcpi()
frzvpi = wfn.frzvpi()
active_docc = docc - frzcpi
active_socc = wfn.soccpi()
active_mopi = wfn.nmopi() - frzcpi - frzvpi
nbf = active_mopi.sum() if wfn.same_a_b_orbs() else 2 * active_mopi.sum()
nirrep = wfn.nirrep()
nelectron = 2 * active_docc.sum() + active_socc.sum()
irrep_map = _irrep_map(wfn)
wfn_irrep = 0
for h, n_socc in enumerate(active_socc):
if n_socc % 2 == 1:
wfn_irrep ^= h
core.print_out('Writing integrals in FCIDUMP format to ' + fname + '\n')
# Generate FCIDUMP header
header = '&FCI\n'
header += 'NORB={:d},\n'.format(nbf)
header += 'NELEC={:d},\n'.format(nelectron)
header += 'MS2={:d},\n'.format(wfn.nalpha() - wfn.nbeta())
header += 'UHF=.{}.,\n'.format(not wfn.same_a_b_orbs()).upper()
orbsym = ''
for h in range(active_mopi.n()):
for n in range(frzcpi[h], frzcpi[h] + active_mopi[h]):
orbsym += '{:d},'.format(irrep_map[h])
if not wfn.same_a_b_orbs():
orbsym += '{:d},'.format(irrep_map[h])
header += 'ORBSYM={}\n'.format(orbsym)
header += 'ISYM={:d},\n'.format(irrep_map[wfn_irrep])
header += '&END\n'
with open(fname, 'w') as intdump:
intdump.write(header)
# Get an IntegralTransform object
check_iwl_file_from_scf_type(core.get_global_option('SCF_TYPE'), wfn)
spaces = [core.MOSpace.all()]
trans_type = core.IntegralTransform.TransformationType.Restricted
if not wfn.same_a_b_orbs():
trans_type = core.IntegralTransform.TransformationType.Unrestricted
ints = core.IntegralTransform(wfn, spaces, trans_type)
ints.transform_tei(core.MOSpace.all(), core.MOSpace.all(),
core.MOSpace.all(), core.MOSpace.all())
core.print_out('Integral transformation complete!\n')
DPD_info = {
'instance_id': ints.get_dpd_id(),
'alpha_MO': ints.DPD_ID('[A>=A]+'),
'beta_MO': 0
}
if not wfn.same_a_b_orbs():
DPD_info['beta_MO'] = ints.DPD_ID("[a>=a]+")
# Write TEI to fname in FCIDUMP format
core.fcidump_tei_helper(nirrep, wfn.same_a_b_orbs(), DPD_info,
ints_tolerance, fname)
# Read-in OEI and write them to fname in FCIDUMP format
# Indexing functions to translate from zero-based (C and Python) to
# one-based (Fortran)
mo_idx = lambda x: x + 1
alpha_mo_idx = lambda x: 2 * x + 1
beta_mo_idx = lambda x: 2 * (x + 1)
with open(fname, 'a') as intdump:
core.print_out('Writing frozen core operator in FCIDUMP format to ' +
fname + '\n')
if reference == 'RHF':
PSIF_MO_FZC = 'MO-basis Frozen-Core Operator'
moH = core.Matrix(PSIF_MO_FZC, wfn.nmopi(), wfn.nmopi())
moH.load(core.IO.shared_object(), psif.PSIF_OEI)
mo_slice = core.Slice(frzcpi, active_mopi)
MO_FZC = moH.get_block(mo_slice, mo_slice)
offset = 0
for h, block in enumerate(MO_FZC.nph):
il = np.tril_indices(block.shape[0])
for index, x in np.ndenumerate(block[il]):
row = mo_idx(il[0][index] + offset)
col = mo_idx(il[1][index] + offset)
if (abs(x) > ints_tolerance):
intdump.write(
'{:29.20E} {:4d} {:4d} {:4d} {:4d}\n'.format(
x, row, col, 0, 0))
offset += block.shape[0]
# Additional one-electron integrals as requested in oe_ints
# Orbital energies
core.print_out('Writing orbital energies in FCIDUMP format to ' +
fname + '\n')
if 'EIGENVALUES' in oe_ints:
eigs_dump = write_eigenvalues(
wfn.epsilon_a().get_block(mo_slice).to_array(), mo_idx)
intdump.write(eigs_dump)
else:
PSIF_MO_A_FZC = 'MO-basis Alpha Frozen-Core Oper'
moH_A = core.Matrix(PSIF_MO_A_FZC, wfn.nmopi(), wfn.nmopi())
moH_A.load(core.IO.shared_object(), psif.PSIF_OEI)
mo_slice = core.Slice(frzcpi, active_mopi)
MO_FZC_A = moH_A.get_block(mo_slice, mo_slice)
offset = 0
for h, block in enumerate(MO_FZC_A.nph):
il = np.tril_indices(block.shape[0])
for index, x in np.ndenumerate(block[il]):
row = alpha_mo_idx(il[0][index] + offset)
col = alpha_mo_idx(il[1][index] + offset)
if (abs(x) > ints_tolerance):
intdump.write(
'{:29.20E} {:4d} {:4d} {:4d} {:4d}\n'.format(
x, row, col, 0, 0))
offset += block.shape[0]
PSIF_MO_B_FZC = 'MO-basis Beta Frozen-Core Oper'
moH_B = core.Matrix(PSIF_MO_B_FZC, wfn.nmopi(), wfn.nmopi())
moH_B.load(core.IO.shared_object(), psif.PSIF_OEI)
mo_slice = core.Slice(frzcpi, active_mopi)
MO_FZC_B = moH_B.get_block(mo_slice, mo_slice)
offset = 0
for h, block in enumerate(MO_FZC_B.nph):
il = np.tril_indices(block.shape[0])
for index, x in np.ndenumerate(block[il]):
row = beta_mo_idx(il[0][index] + offset)
col = beta_mo_idx(il[1][index] + offset)
if (abs(x) > ints_tolerance):
intdump.write(
'{:29.20E} {:4d} {:4d} {:4d} {:4d}\n'.format(
x, row, col, 0, 0))
offset += block.shape[0]
# Additional one-electron integrals as requested in oe_ints
# Orbital energies
core.print_out('Writing orbital energies in FCIDUMP format to ' +
fname + '\n')
if 'EIGENVALUES' in oe_ints:
alpha_eigs_dump = write_eigenvalues(
wfn.epsilon_a().get_block(mo_slice).to_array(),
alpha_mo_idx)
beta_eigs_dump = write_eigenvalues(
wfn.epsilon_b().get_block(mo_slice).to_array(),
beta_mo_idx)
intdump.write(alpha_eigs_dump + beta_eigs_dump)
# Dipole integrals
#core.print_out('Writing dipole moment OEI in FCIDUMP format to ' + fname + '\n')
# Traceless quadrupole integrals
#core.print_out('Writing traceless quadrupole moment OEI in FCIDUMP format to ' + fname + '\n')
# Frozen core + nuclear repulsion energy
core.print_out(
'Writing frozen core + nuclear repulsion energy in FCIDUMP format to '
+ fname + '\n')
e_fzc = ints.get_frozen_core_energy()
e_nuc = molecule.nuclear_repulsion_energy(
wfn.get_dipole_field_strength())
intdump.write('{: 29.20E} {:4d} {:4d} {:4d} {:4d}\n'.format(
e_fzc + e_nuc, 0, 0, 0, 0))
core.print_out(
'Done generating {} with integrals in FCIDUMP format.\n'.format(fname))
def psthcorr(rec,
nids=None,
ssnids=None,
ssseps=None,
natexps=False,
strange=None,
plot=True):
if nids == None:
nids = sorted(rec.n) # use active neurons
if ssnids == None:
ssnids = nids # use nids as the superset
nn = len(nids)
nnss = len(ssnids)
# note that using norm=True or norm='ntrials' doesn't seem to make a difference to the
# results, probably doesn't matter for calculating corrs:
midbins, psths, spikets = rec.psth(nids=nids,
natexps=natexps,
strange=strange,
plot=False,
binw=0.02,
tres=0.005,
norm=True)
rho = np.corrcoef(psths) # defaults to bias=1
rho[np.diag_indices(
nn)] = np.nan # nan the diagonal, which imshow plots as white
ssrho = np.zeros((nnss, nnss)) # superset rho matrix
ssrho.fill(np.nan) # init with nans
# load up values into appropriate spots in superset rho matrix:
for i in range(nn):
for j in range(nn):
ssi, ssj = ssnids.searchsorted([nids[i], nids[j]])
ssrho[ssi, ssj] = rho[i, j]
if plot == False:
return ssrho
# plot superset rho matrix:
figure(figsize=FIGSIZE)
imshow(ssrho, vmin=-1, vmax=1, cmap='jet') # cmap='gray' is too bland
ssnidticks = np.arange(0, nnss, 10)
xticks(ssnidticks)
yticks(ssnidticks)
if SHOWCOLORBAR:
colorbar()
basetitle = rec.absname
if strange != None:
strange_sec = tuple(np.array(strange) /
1e6) # convert to sec for display
basetitle += '_strange=(%.f, %.f)' % strange_sec
gcfm().window.setWindowTitle(basetitle + '_rho_mat')
tight_layout(pad=0.3)
# plot rho histogram:
lti = np.tril_indices(
nnss, -1) # lower triangle (below diagonal) indices of ssrho
ssrhol = ssrho[lti]
notnanis = np.logical_not(np.isnan(ssrhol)) # indices of non-nan values
fssrhol = ssrhol[notnanis] # ssrhol filtered out for nans
fssrholmean = fssrhol.mean()
t, p = ttest_1samp(fssrhol, 0) # 2-sided ttest relative to 0
print('mean=%g, t=%g, p=%g' % (fssrholmean, t, p))
if p < ALPHA0:
pstring = '$p<%g$' % ceilsigfig(p)
else:
pstring = '$p>%g$' % floorsigfig(p)
figure(figsize=FIGSIZE)
rhobins = np.arange(RHOMIN, RHOMAX + 0.0333,
0.0333) # left edges + rightmost edge
n = hist(fssrhol, bins=rhobins, color='k')[0]
axvline(x=fssrholmean, c='r',
ls='--') # draw vertical red line at mean fssrhol
axvline(x=0, c='e', ls='--') # draw vertical grey line at x=0
xlim(xmin=RHOMIN, xmax=RHOMAX)
ylim(ymax=n.max()) # effectively normalizes the histogram
rhoticks = np.arange(-0.2, 1 + 0.2, 0.2) # excluding the final 1
xticks(rhoticks)
yticks([n.max()]) # turn off y ticks to save space
#yticks([0, n.max()])
text(0.98,
0.98,
'$\mu$=%.2g\n%s' % (fssrholmean, pstring),
color='k',
transform=gca().transAxes,
horizontalalignment='right',
verticalalignment='top')
gcfm().window.setWindowTitle(basetitle + '_rho_hist')
tight_layout(pad=0.3)
# plot rho vs separation:
fssseps = ssseps[notnanis] # ssseps filtered out for nans
figure(figsize=FIGSIZE)
# scatter plot:
pl.plot(fssseps, fssrhol, 'k.')
# bin seps and plot mean rho in each bin:
sepbins = np.arange(0, fssseps.max() + SEPBINW, SEPBINW) # left edges
sepmeans, rhomeans, rhostds = scatterbin(fssseps, fssrhol, sepbins)
#pl.plot(sepmeans, rhomeans, 'r.-', ms=10, lw=2)
errorbar(sepmeans,
rhomeans,
yerr=rhostds,
fmt='r.-',
ms=10,
lw=2,
zorder=9999)
xlim(xmin=0, xmax=SEPMAX)
ylim(ymin=RHOMIN, ymax=RHOMAX)
septicks = np.arange(0, fssseps.max() + 100, 500)
xticks(septicks)
yticks(rhoticks)
gcfm().window.setWindowTitle(basetitle + '_rho_sep')
tight_layout(pad=0.3)
return ssrho
def as_array(self):
"""Return standard numpy array equivalent"""
a = np.zeros((self.size, self.size))
a[np.tril_indices(self.size)] = self._elements
a[np.triu_indices(self.size)] = a.T[np.triu_indices(self.size)]
return a
def __init__(self):
alleles = _AMINO_ACIDS
num_alleles = len(alleles)
root_distribution = [
0.074,
0.052,
0.045,
0.054,
0.025,
0.034,
0.054,
0.074,
0.026,
0.068,
0.099,
0.058,
0.025,
0.047,
0.039,
0.057,
0.051,
0.013,
0.032,
0.073,
]
relative_rates = [
0.735790389698,
0.485391055466,
1.297446705134,
0.543161820899,
0.500964408555,
3.180100048216,
1.459995310470,
0.227826574209,
0.397358949897,
0.240836614802,
1.199705704602,
3.020833610064,
1.839216146992,
1.190945703396,
0.329801504630,
1.170949042800,
1.360574190420,
1.240488508640,
3.761625208368,
0.140748891814,
5.528919177928,
1.955883574960,
0.418763308518,
1.355872344485,
0.798473248968,
0.418203192284,
0.609846305383,
0.423579992176,
0.716241444998,
1.456141166336,
2.414501434208,
0.778142664022,
0.354058109831,
2.435341131140,
1.626891056982,
0.539859124954,
0.605899003687,
0.232036445142,
0.283017326278,
0.418555732462,
0.774894022794,
0.236202451204,
0.186848046932,
0.189296292376,
0.252718447885,
0.800016530518,
0.622711669692,
0.211888159615,
0.218131577594,
0.831842640142,
0.580737093181,
0.372625175087,
0.217721159236,
0.348072209797,
3.890963773304,
1.295201266783,
5.411115141489,
1.593137043457,
1.032447924952,
0.285078800906,
3.945277674515,
2.802427151679,
0.752042440303,
1.022507035889,
0.406193586642,
0.445570274261,
1.253758266664,
0.983692987457,
0.648441278787,
0.222621897958,
0.767688823480,
2.494896077113,
0.555415397470,
0.459436173579,
0.984311525359,
3.364797763104,
6.030559379572,
1.073061184332,
0.492964679748,
0.371644693209,
0.354861249223,
0.281730694207,
0.441337471187,
0.144356959750,
0.291409084165,
0.368166464453,
0.714533703928,
1.517359325954,
2.064839703237,
0.266924750511,
1.773855168830,
1.173275900924,
0.448133661718,
0.494887043702,
0.730628272998,
0.356008498769,
0.858570575674,
0.926563934846,
0.504086599527,
0.527007339151,
0.388355409206,
0.374555687471,
1.047383450722,
0.454123625103,
0.233597909629,
4.325092687057,
1.122783104210,
2.904101656456,
1.582754142065,
1.197188415094,
1.934870924596,
1.769893238937,
1.509326253224,
1.117029762910,
0.357544412460,
0.352969184527,
1.752165917819,
0.918723415746,
0.540027644824,
1.169129577716,
1.729178019485,
0.914665954563,
1.898173634533,
0.934187509431,
1.119831358516,
1.277480294596,
1.071097236007,
0.641436011405,
0.585407090225,
1.179091197260,
0.915259857694,
1.303875200799,
1.488548053722,
0.488206118793,
1.005451683149,
5.151556292270,
0.465839367725,
0.426382310122,
0.191482046247,
0.145345046279,
0.527664418872,
0.758653808642,
0.407635648938,
0.508358924638,
0.301248600780,
0.341985787540,
0.691474634600,
0.332243040634,
0.888101098152,
2.074324893497,
0.252214830027,
0.387925622098,
0.513128126891,
0.718206697586,
0.720517441216,
0.538222519037,
0.261422208965,
0.470237733696,
0.958989742850,
0.596719300346,
0.308055737035,
4.218953969389,
0.674617093228,
0.811245856323,
0.717993486900,
0.951682162246,
6.747260430801,
0.369405319355,
0.796751520761,
0.801010243199,
4.054419006558,
2.187774522005,
0.438388343772,
0.312858797993,
0.258129289418,
1.116352478606,
0.530785790125,
0.524253846338,
0.253340790190,
0.201555971750,
8.311839405458,
2.231405688913,
0.498138475304,
2.575850755315,
0.838119610178,
0.496908410676,
0.561925457442,
2.253074051176,
0.266508731426,
1.000000000000,
]
transition_matrix = np.zeros((num_alleles, num_alleles))
tril = np.tril_indices(num_alleles, k=-1)
transition_matrix[tril] = relative_rates
transition_matrix += np.tril(transition_matrix).T
transition_matrix *= root_distribution
row_sums = transition_matrix.sum(axis=1)
transition_matrix = transition_matrix / max(row_sums)
row_sums = transition_matrix.sum(axis=1, dtype="float64")
np.fill_diagonal(transition_matrix, 1.0 - row_sums)
super().__init__(alleles, root_distribution, transition_matrix)
def psthcorrdiff(rhos, seps, basetitle):
"""Plot difference of a pair of rho matrices (rhos[0] - rhos[1]). seps is the
corresponding distance matrix"""
assert len(rhos) == 2
# calc rho difference matrix:
rhod = rhos[0] - rhos[1]
assert rhod.shape[0] == rhod.shape[1] # square
nn = rhod.shape[0]
# plot rho diff matrix:
figure(figsize=FIGSIZE)
imshow(rhod, vmin=-1, vmax=1, cmap='jet') # cmap='gray' is too bland
ssnidticks = np.arange(0, nn, 10)
xticks(ssnidticks)
yticks(ssnidticks)
if SHOWCOLORBAR:
colorbar()
gcfm().window.setWindowTitle(basetitle + '_rhod_mat')
tight_layout(pad=0.3)
# plot rho difference histogram:
lti = np.tril_indices(nn, -1) # lower triangle (below diagonal) indices
rhol = rhod[lti]
notnanis = np.logical_not(np.isnan(rhol)) # indices of non-nan values
frhol = rhol[notnanis] # rhol filtered out for nans
frholmean = frhol.mean()
t, p = ttest_1samp(frhol, 0) # 2-sided ttest relative to 0
print('mean=%g, t=%g, p=%g' % (frholmean, t, p))
if p < ALPHA0:
pstring = '$p<%g$' % ceilsigfig(p)
else:
pstring = '$p>%g$' % floorsigfig(p)
figure(figsize=FIGSIZE)
rhobins = np.arange(RHODIFFMIN, RHODIFFMAX + 0.0333,
0.0333) # left edges + rightmost edge
n = hist(frhol, bins=rhobins, color='k')[0]
axvline(x=frholmean, c='r',
ls='--') # draw vertical red line at mean frhol
axvline(x=0, c='e', ls='--') # draw vertical grey line at x=0
xlim(xmin=RHODIFFMIN, xmax=RHODIFFMAX)
ylim(ymax=n.max()) # effectively normalizes the histogram
rhoticks = np.arange(-0.6, 0.6 + 0.2, 0.2)
xticks(rhoticks)
yticks([n.max()]) # turn off y ticks to save space
#yticks([0, n.max()])
text(0.98,
0.98,
'$\mu$=%.2g\n%s' % (frholmean, pstring),
color='k',
transform=gca().transAxes,
horizontalalignment='right',
verticalalignment='top')
gcfm().window.setWindowTitle(basetitle + '_rhod_hist')
tight_layout(pad=0.3)
# plot rho difference vs separation:
fseps = seps[notnanis] # seps filtered out for nans
figure(figsize=FIGSIZE)
# scatter plot:
pl.plot(fseps, frhol, 'k.')
# bin seps and plot mean rho in each bin:
sortis = np.argsort(fseps)
seps = fseps[sortis]
rhos = frhol[sortis]
sepbins = np.arange(0, seps.max() + SEPBINW, SEPBINW) # left edges
sepis = seps.searchsorted(sepbins)
sepmeans, rhomeans, rhostds = [], [], []
for sepi0, sepi1 in zip(sepis[:-1], sepis[1:]): # iterate over sepbins
sepmeans.append(
seps[sepi0:sepi1].mean()) # mean sep of all points in this sepbin
rhoslice = rhos[sepi0:sepi1] # rhos in this sepbin
rhomeans.append(
rhoslice.mean()) # mean rho of all points in this sepbin
rhostds.append(rhoslice.std()) # std of rho in this sepbin
#pl.plot(sepmeans, rhomeans, 'r.-', ms=10, lw=2)
errorbar(sepmeans,
rhomeans,
yerr=rhostds,
fmt='r.-',
ms=10,
lw=2,
zorder=9999)
xlim(xmin=0, xmax=SEPMAX)
ylim(ymin=RHODIFFMIN, ymax=RHODIFFMAX)
septicks = np.arange(0, seps.max() + 100, 500)
xticks(septicks)
yticks(rhoticks)
gcfm().window.setWindowTitle(basetitle + '_rhod_sep')
tight_layout(pad=0.3)
def tril_indices(*args, **kwargs):
return tuple(map(torch.from_numpy, _np.tril_indices(*args, **kwargs)))
def to_fcivec(cisdvec, norb, nelec, frozen=None):
'''Convert CISD coefficients to FCI coefficients'''
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
assert (neleca == nelecb)
frozen_mask = numpy.zeros(norb, dtype=bool)
if frozen is None:
nfroz = 0
elif isinstance(frozen, (int, numpy.integer)):
nfroz = frozen
frozen_mask[:frozen] = True
else:
nfroz = len(frozen)
frozen_mask[frozen] = True
nocc = numpy.count_nonzero(~frozen_mask[:neleca])
nmo = norb - nfroz
nvir = nmo - nocc
c0, c1, c2 = cisdvec_to_amplitudes(cisdvec, nmo, nocc)
t1addr, t1sign = tn_addrs_signs(nmo, nocc, 1)
na = cistring.num_strings(nmo, nocc)
fcivec = numpy.zeros((na, na))
fcivec[0, 0] = c0
fcivec[0, t1addr] = fcivec[t1addr, 0] = c1.ravel() * t1sign
c2ab = c2.transpose(0, 2, 1, 3).reshape(nocc * nvir, -1)
c2ab = numpy.einsum('i,j,ij->ij', t1sign, t1sign, c2ab)
fcivec[t1addr[:, None], t1addr] = c2ab
if nocc > 1 and nvir > 1:
c2aa = c2 - c2.transpose(1, 0, 2, 3)
ooidx = numpy.tril_indices(nocc, -1)
vvidx = numpy.tril_indices(nvir, -1)
c2aa = c2aa[ooidx][:, vvidx[0], vvidx[1]]
t2addr, t2sign = tn_addrs_signs(nmo, nocc, 2)
fcivec[0, t2addr] = fcivec[t2addr, 0] = c2aa.ravel() * t2sign
if nfroz == 0:
return fcivec
assert (norb < 63)
strs = cistring.gen_strings4orblist(range(norb), neleca)
na = len(strs)
count = numpy.zeros(na, dtype=int)
parity = numpy.zeros(na, dtype=bool)
core_mask = numpy.ones(na, dtype=bool)
# During the loop, count saves the number of occupied orbitals that
# lower (with small orbital ID) than the present orbital i.
# Moving all the frozen orbitals to the beginning of the orbital list
# (before the occupied orbitals) leads to parity odd (= True, with
# negative sign) or even (= False, with positive sign).
for i in range(norb):
if frozen_mask[i]:
if i < neleca:
# frozen occupied orbital should be occupied
core_mask &= (strs & (1 << i)) != 0
parity ^= (count & 1) == 1
else:
# frozen virtual orbital should not be occupied.
# parity is not needed since it's unoccupied
core_mask &= (strs & (1 << i)) == 0
else:
count += (strs & (1 << i)) != 0
sub_strs = strs[core_mask & (count == nocc)]
addrs = cistring.strs2addr(norb, neleca, sub_strs)
fcivec1 = numpy.zeros((na, na))
fcivec1[addrs[:, None], addrs] = fcivec
fcivec1[parity, :] *= -1
fcivec1[:, parity] *= -1
return fcivec1
def trans_e1_outcore(mol,
mo,
ncore,
ncas,
erifile,
max_memory=None,
level=1,
verbose=logger.WARN):
time0 = (time.clock(), time.time())
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
log.debug1('trans_e1_outcore level %d max_memory %d', level, max_memory)
nao, nmo = mo.shape
nao_pair = nao * (nao + 1) // 2
nocc = ncore + ncas
_tmpfile1 = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
faapp_buf = h5py.File(_tmpfile1.name)
feri = h5py.File(erifile, 'w')
mo_c = numpy.asarray(mo, order='C')
mo = numpy.asarray(mo, order='F')
pashape = (0, nmo, ncore, nocc)
papa_buf = numpy.zeros((nao, ncas, nmo * ncas))
j_pc = numpy.zeros((nmo, ncore))
k_pc = numpy.zeros((nmo, ncore))
mem_words = int(max(2000, max_memory - papa_buf.nbytes / 1e6) * 1e6 / 8)
aobuflen = mem_words // (nao_pair + nocc * nmo) + 1
ao_loc = numpy.array(mol.ao_loc_nr(), dtype=numpy.int32)
shranges = outcore.guess_shell_ranges(mol, True, aobuflen, None, ao_loc)
intor = mol._add_suffix('int2e')
ao2mopt = _ao2mo.AO2MOpt(mol, intor, 'CVHFnr_schwarz_cond',
'CVHFsetnr_direct_scf')
nstep = len(shranges)
paapp = 0
maxbuflen = max([x[2] for x in shranges])
log.debug('mem_words %.8g MB, maxbuflen = %d', mem_words * 8 / 1e6,
maxbuflen)
bufs1 = numpy.empty((maxbuflen, nao_pair))
bufs2 = numpy.empty((maxbuflen, nmo * ncas))
if level == 1:
bufs3 = numpy.empty((maxbuflen, nao * ncore))
log.debug('mem cache %.8g MB',
(bufs1.nbytes + bufs2.nbytes + bufs3.nbytes) / 1e6)
else:
log.debug('mem cache %.8g MB', (bufs1.nbytes + bufs2.nbytes) / 1e6)
ti0 = log.timer('Initializing trans_e1_outcore', *time0)
# fmmm, ftrans, fdrv for level 1
fmmm = libmcscf.AO2MOmmm_ket_nr_s2
ftrans = libmcscf.AO2MOtranse1_nr_s4
fdrv = libmcscf.AO2MOnr_e2_drv
for istep, sh_range in enumerate(shranges):
log.debug('[%d/%d], AO [%d:%d], len(buf) = %d', istep + 1, nstep,
*sh_range)
buf = bufs1[:sh_range[2]]
_ao2mo.nr_e1fill(intor, sh_range, mol._atm, mol._bas, mol._env, 's4',
1, ao2mopt, buf)
if log.verbose >= logger.DEBUG1:
ti1 = log.timer('AO integrals buffer', *ti0)
bufpa = bufs2[:sh_range[2]]
_ao2mo.nr_e1(buf, mo, pashape, 's4', 's1', out=bufpa)
# jc_pp, kc_pp
if level == 1: # ppaa, papa and vhf, jcp, kcp
if log.verbose >= logger.DEBUG1:
ti1 = log.timer('buffer-pa', *ti1)
buf1 = bufs3[:sh_range[2]]
fdrv(ftrans, fmmm, buf1.ctypes.data_as(ctypes.c_void_p),
buf.ctypes.data_as(ctypes.c_void_p),
mo.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(sh_range[2]),
ctypes.c_int(nao), (ctypes.c_int * 4)(0, nao, 0, ncore),
ctypes.POINTER(ctypes.c_void_p)(), ctypes.c_int(0))
p0 = 0
for ij in range(sh_range[0], sh_range[1]):
i, j = lib.index_tril_to_pair(ij)
i0 = ao_loc[i]
j0 = ao_loc[j]
i1 = ao_loc[i + 1]
j1 = ao_loc[j + 1]
di = i1 - i0
dj = j1 - j0
if i == j:
dij = di * (di + 1) // 2
buf = numpy.empty((di, di, nao * ncore))
idx = numpy.tril_indices(di)
buf[idx] = buf1[p0:p0 + dij]
buf[idx[1], idx[0]] = buf1[p0:p0 + dij]
buf = buf.reshape(di, di, nao, ncore)
mo1 = mo_c[i0:i1]
tmp = numpy.einsum('uvpc,pc->uvc', buf, mo[:, :ncore])
tmp = lib.dot(mo1.T, tmp.reshape(di, -1))
j_pc += numpy.einsum('vp,pvc->pc', mo1,
tmp.reshape(nmo, di, ncore))
tmp = numpy.einsum('uvpc,uc->vcp', buf, mo1[:, :ncore])
tmp = lib.dot(tmp.reshape(-1, nmo),
mo).reshape(di, ncore, nmo)
k_pc += numpy.einsum('vp,vcp->pc', mo1, tmp)
else:
dij = di * dj
buf = buf1[p0:p0 + dij].reshape(di, dj, nao, ncore)
mo1 = mo_c[i0:i1]
mo2 = mo_c[j0:j1]
tmp = numpy.einsum('uvpc,pc->uvc', buf, mo[:, :ncore])
tmp = lib.dot(mo1.T, tmp.reshape(di, -1))
j_pc += numpy.einsum('vp,pvc->pc', mo2,
tmp.reshape(nmo, dj, ncore)) * 2
tmp = numpy.einsum('uvpc,uc->vcp', buf, mo1[:, :ncore])
tmp = lib.dot(tmp.reshape(-1, nmo),
mo).reshape(dj, ncore, nmo)
k_pc += numpy.einsum('vp,vcp->pc', mo2, tmp)
tmp = numpy.einsum('uvpc,vc->ucp', buf, mo2[:, :ncore])
tmp = lib.dot(tmp.reshape(-1, nmo),
mo).reshape(di, ncore, nmo)
k_pc += numpy.einsum('up,ucp->pc', mo1, tmp)
p0 += dij
if log.verbose >= logger.DEBUG1:
ti1 = log.timer('j_cp and k_cp', *ti1)
if log.verbose >= logger.DEBUG1:
ti1 = log.timer('half transformation of the buffer', *ti1)
# ppaa, papa
faapp_buf[str(istep)] = \
bufpa.reshape(sh_range[2],nmo,ncas)[:,ncore:nocc].reshape(-1,ncas**2).T
p0 = 0
for ij in range(sh_range[0], sh_range[1]):
i, j = lib.index_tril_to_pair(ij)
i0 = ao_loc[i]
j0 = ao_loc[j]
i1 = ao_loc[i + 1]
j1 = ao_loc[j + 1]
di = i1 - i0
dj = j1 - j0
if i == j:
dij = di * (di + 1) // 2
buf1 = numpy.empty((di, di, nmo * ncas))
idx = numpy.tril_indices(di)
buf1[idx] = bufpa[p0:p0 + dij]
buf1[idx[1], idx[0]] = bufpa[p0:p0 + dij]
else:
dij = di * dj
buf1 = bufpa[p0:p0 + dij].reshape(di, dj, -1)
mo1 = mo[j0:j1, ncore:nocc].copy()
for i in range(di):
lib.dot(mo1.T, buf1[i], 1, papa_buf[i0 + i], 1)
mo1 = mo[i0:i1, ncore:nocc].copy()
buf1 = lib.dot(mo1.T, buf1.reshape(di, -1))
papa_buf[j0:j1] += buf1.reshape(ncas, dj, -1).transpose(1, 0, 2)
p0 += dij
if log.verbose >= logger.DEBUG1:
ti1 = log.timer('ppaa and papa buffer', *ti1)
ti0 = log.timer('gen AO/transform MO [%d/%d]' % (istep + 1, nstep),
*ti0)
buf = buf1 = bufpa = None
bufs1 = bufs2 = bufs3 = None
time1 = log.timer('mc_ao2mo pass 1', *time0)
log.debug1('Half transformation done. Current memory %d',
lib.current_memory()[0])
nblk = int(
max(8,
min(nmo,
(max_memory * 1e6 / 8 - papa_buf.size) / (ncas**2 * nmo))))
log.debug1('nblk for papa = %d', nblk)
dset = feri.create_dataset('papa', (nmo, ncas, nmo, ncas), 'f8')
for i0, i1 in prange(0, nmo, nblk):
tmp = lib.dot(mo[:, i0:i1].T, papa_buf.reshape(nao, -1))
dset[i0:i1] = tmp.reshape(i1 - i0, ncas, nmo, ncas)
papa_buf = tmp = None
time1 = log.timer('papa pass 2', *time1)
tmp = numpy.empty((ncas**2, nao_pair))
p0 = 0
for istep, sh_range in enumerate(shranges):
tmp[:, p0:p0 + sh_range[2]] = faapp_buf[str(istep)]
p0 += sh_range[2]
nblk = int(
max(8, min(nmo,
(max_memory * 1e6 / 8 - tmp.size) / (ncas**2 * nmo) - 1)))
log.debug1('nblk for ppaa = %d', nblk)
dset = feri.create_dataset('ppaa', (nmo, nmo, ncas, ncas), 'f8')
for i0, i1 in prange(0, nmo, nblk):
tmp1 = _ao2mo.nr_e2(tmp,
mo, (i0, i1, 0, nmo),
's4',
's1',
ao_loc=ao_loc)
tmp1 = tmp1.reshape(ncas, ncas, i1 - i0, nmo)
for j in range(i1 - i0):
dset[i0 + j] = tmp1[:, :, j].transpose(2, 0, 1)
tmp = tmp1 = None
time1 = log.timer('ppaa pass 2', *time1)
faapp_buf.close()
feri.close()
_tmpfile1 = None
time0 = log.timer('mc_ao2mo', *time0)
return j_pc, k_pc
cbar=False,
square=True)
plt.title('{} Canonical Angle'.format(['First', 'Second', 'Third'][ii]))
plt.xticks(unique_idx, whisker_unique, rotation=45)
plt.yticks(unique_idx, whisker_unique, rotation=0)
plt.tight_layout()
plt.savefig(os.path.join(p_load,
'canonical_angles_between_neuron_weights.pdf'))
# ===========================================
# plot a histogram of the canonical angles between the weights
# ===========================================
wd = figsize[0] / 1.5
ht = wd
f = plt.figure(figsize=(wd, ht))
x, y = np.tril_indices(canonical_angles.shape[0], -1)
first = canonical_angles[x, y, 0]
second = canonical_angles[x, y, 1]
third = canonical_angles[x, y, 2]
sns.distplot(first, kde=False)
sns.distplot(second, kde=False)
sns.distplot(third, kde=False)
sns.despine()
plt.title('Values of angles between\nsubspaces covered by all neurons')
plt.ylabel('# of pairwise comparisons')
plt.xlabel('$cos(\\theta)$')
plt.legend(
['{} Canonical Angle'.format(x) for x in ['First', 'Second', 'Third']])
plt.tight_layout()
plt.savefig(
def initialize(self, model):
"""
Called on the first call to update
`ilabels` is a list of n_i x n_i matrices containing integer
labels that correspond to specific correlation parameters.
Two elements of ilabels[i] with the same label share identical
variance components.
`designx` is a matrix, with each row containing dummy
variables indicating which variance components are associated
with the corresponding element of QY.
"""
super(Nested, self).initialize(model)
if self.model.weights is not None:
warnings.warn(
"weights not implemented for nested cov_struct, "
"using unweighted covariance estimate", NotImplementedWarning)
# A bit of processing of the nest data
id_matrix = np.asarray(self.model.dep_data)
if id_matrix.ndim == 1:
id_matrix = id_matrix[:, None]
self.id_matrix = id_matrix
endog = self.model.endog_li
designx, ilabels = [], []
# The number of layers of nesting
n_nest = self.id_matrix.shape[1]
for i in range(self.model.num_group):
ngrp = len(endog[i])
glab = self.model.group_labels[i]
rix = self.model.group_indices[glab]
# Determine the number of common variance components
# shared by each pair of observations.
ix1, ix2 = np.tril_indices(ngrp, -1)
ncm = (self.id_matrix[rix[ix1], :] == self.id_matrix[rix[ix2], :]
).sum(1)
# This is used to construct the working correlation
# matrix.
ilabel = np.zeros((ngrp, ngrp), dtype=np.int32)
ilabel[(ix1, ix2)] = ncm + 1
ilabel[(ix2, ix1)] = ncm + 1
ilabels.append(ilabel)
# This is used to estimate the variance components.
dsx = np.zeros((len(ix1), n_nest + 1), dtype=np.float64)
dsx[:, 0] = 1
for k in np.unique(ncm):
ii = np.flatnonzero(ncm == k)
dsx[ii, 1:k + 1] = 1
designx.append(dsx)
self.designx = np.concatenate(designx, axis=0)
self.ilabels = ilabels
svd = np.linalg.svd(self.designx, 0)
self.designx_u = svd[0]
self.designx_s = svd[1]
self.designx_v = svd[2].T
def quadratic_terms(x):
n = len(x)
x = x[np.newaxis] # turn x from 1D to a 2D array
temp = x * x.T - (1 - 1 / np.sqrt(2)) * np.diag(pow(x, 2)[0])
return temp[np.tril_indices(n)]
def _get_transformed_inputs(self,
features: np.ndarray,
edges: np.ndarray,
invalid_prob: float = 1e-9) -> GraphData:
assert edges.shape[0] == edges.shape[1], '{} != {}'.format(
edges.shape[0], edges.shape[1])
assert edges.shape[0] == self._nodes, '{} != {}'.format(
edges.shape[0], self._nodes)
assert features.shape[0] == self._nodes, '{} != {}'.format(
features.shape[0], self._nodes)
assert edges.max() <= self._edge_types, '{} > {}'.format(
edges.max(), self._edge_types)
assert edges.min() == 0, '{} != 0'.format(edges.min())
nn = self._nodes
# lower triangle
idx_lower = np.tril_indices(nn)
row, col = idx_lower
assert row.shape[0] == self._n_adj_flat
# degree[i]: degree of nodes before adding i-th edge
degree = []
for i, (x, y) in enumerate(zip(row, col)):
weight = edges[x, y]
if weight == 0:
continue
if len(degree) == 0:
nc = np.zeros(nn)
else:
nc = degree[-1].copy()
nc[x] += weight
nc[y] += weight
degree.append(nc)
# weight_indicators[i]: binary mask of allowed edge types before
# adding i-th edge
vv = self._valence[features.argmax(axis=-1)]
indicator = np.ones((nn, self._edge_types), dtype=np.float32)
for i, left in enumerate(vv.astype(int)):
indicator[i, left:] = 0
weight_indicators = [indicator]
for deg in degree[:
-1]: # we don't need valence _after_ adding the last edge
indicator = weight_indicators[-1].copy()
d = (vv - deg).astype(int)
for i, left in enumerate(d):
indicator[i, left:] = 0
weight_indicators.append(indicator)
num_edges = len(weight_indicators)
assert np.count_nonzero(edges[idx_lower]) == num_edges
# shape = (num_edges, num_nodes, num_edge_types)
weight_indicators = np.asarray(weight_indicators, dtype=np.float32)
# zero-padding if num_edges < max_edges
null_edges = self._max_edges - num_edges
if null_edges > 0:
null_ind = np.zeros((null_edges, edges.shape[0], self._edge_types),
dtype=np.float32)
weight_indicators = np.row_stack((weight_indicators, null_ind))
# mask zero values
weight_indicators = np.log((1.0 - weight_indicators) * invalid_prob +
weight_indicators)
adj_one_hot = np.zeros((self._edge_types, nn, nn), dtype=np.int32)
# lower triangle of one-hot encoded edges matrix
weight_bin = np.zeros([self._n_adj_flat, self._edge_types],
dtype=np.int32)
# indices of true edges (wrt flat lower triangular matrix)
coord = np.zeros(self._max_edges, dtype=np.int32)
# edge list of true edges (with row, col index)
edge_list = np.zeros((self._max_edges, 2), dtype=np.int32)
cur_edge = 0
for k, (i, j) in enumerate(zip(row, col)):
if edges[i, j] > 0:
ti = edges[i, j] - 1
adj_one_hot[ti, i, j] = 1
adj_one_hot[ti, j, i] = 1
weight_bin[k, ti] = 1
coord[cur_edge] = k
edge_list[cur_edge, :] = i, j
cur_edge += 1
assert cur_edge == num_edges
adj = np.zeros(edges.shape, dtype=np.int32)
adj[edges.nonzero()] = 1
adj_lower = adj[idx_lower][:, np.newaxis]
return GraphData(adj_one_hot, adj_lower, weight_bin, features,
weight_indicators, coord, edge_list, num_edges)
def __init__(self):
alleles = _AMINO_ACIDS
num_alleles = len(alleles)
root_distribution = [
0.087127,
0.040904,
0.040432,
0.046872,
0.033474,
0.038255,
0.049530,
0.088612,
0.033619,
0.036886,
0.085357,
0.080481,
0.014753,
0.039772,
0.050680,
0.069577,
0.058542,
0.010494,
0.029916,
0.064717,
]
relative_rates = [
0.267828,
0.984474,
0.327059,
1.199805,
0.000000,
8.931515,
0.360016,
0.232374,
0.000000,
0.000000,
0.887753,
2.439939,
1.028509,
1.348551,
0.000000,
1.961167,
0.000000,
1.493409,
11.388659,
0.000000,
7.086022,
2.386111,
0.087791,
1.385352,
1.240981,
0.107278,
0.281581,
0.811907,
0.228116,
2.383148,
5.290024,
0.868241,
0.282729,
6.011613,
0.439469,
0.106802,
0.653416,
0.632629,
0.768024,
0.239248,
0.438074,
0.180393,
0.609526,
0.000000,
0.076981,
0.406431,
0.154924,
0.341113,
0.000000,
0.000000,
0.730772,
0.112880,
0.071514,
0.443504,
2.556685,
0.258635,
4.610124,
3.148371,
0.716913,
0.000000,
1.519078,
0.830078,
0.267683,
0.270475,
0.460857,
0.180629,
0.717840,
0.896321,
0.000000,
0.000000,
0.000000,
1.127499,
0.304803,
0.170372,
0.000000,
3.332732,
5.230115,
2.411739,
0.183641,
0.136906,
0.138503,
0.000000,
0.000000,
0.000000,
0.000000,
0.153478,
0.475927,
1.951951,
1.565160,
0.000000,
0.921860,
2.485920,
1.028313,
0.419244,
0.133940,
0.187550,
1.526188,
0.507003,
0.347153,
0.933709,
0.119152,
0.316258,
0.335419,
0.170205,
0.110506,
4.051870,
1.531590,
4.885892,
0.956097,
1.598356,
0.561828,
0.793999,
2.322243,
0.353643,
0.247955,
0.171432,
0.954557,
0.619951,
0.459901,
2.427202,
3.680365,
0.265745,
2.271697,
0.660930,
0.162366,
0.525651,
0.340156,
0.306662,
0.226333,
1.900739,
0.331090,
1.350599,
1.031534,
0.136655,
0.782857,
5.436674,
0.000000,
2.001375,
0.224968,
0.000000,
0.000000,
0.000000,
0.000000,
0.000000,
0.270564,
0.000000,
0.461776,
0.000000,
0.000000,
0.762354,
0.000000,
0.740819,
0.000000,
0.244139,
0.078012,
0.946940,
0.000000,
0.953164,
0.000000,
0.214717,
0.000000,
1.265400,
0.374834,
0.286572,
0.132142,
0.000000,
6.952629,
0.000000,
0.336289,
0.417839,
0.608070,
2.059564,
0.240368,
0.158067,
0.178316,
0.484678,
0.346983,
0.367250,
0.538165,
0.438715,
8.810038,
1.745156,
0.103850,
2.565955,
0.123606,
0.485026,
0.303836,
1.561997,
0.000000,
0.279379,
]
transition_matrix = np.zeros((num_alleles, num_alleles))
tril = np.tril_indices(num_alleles, k=-1)
transition_matrix[tril] = relative_rates
transition_matrix += np.tril(transition_matrix).T
transition_matrix *= root_distribution
row_sums = transition_matrix.sum(axis=1)
transition_matrix = transition_matrix / max(row_sums)
row_sums = transition_matrix.sum(axis=1, dtype="float64")
np.fill_diagonal(transition_matrix, 1.0 - row_sums)
super().__init__(alleles, root_distribution, transition_matrix)