def download(oformat, param, stream, year, month, timestep, back, queue,
urgent):
"""
Download ERA5 variables, to be preferred
if adding a new variable,
if month argument is not passed
then the entire year will be downloaded.
By default downloads hourly data in netcdf format.
\f
Grid and other stream settings are in the era5_<stream>_<timestep>.json files.
"""
if back and stream != 'wfde5' and timestep not in ['mon', 'day']:
print(
'You can the backwards option only with monthly and some daily data'
)
sys.exit()
valid_format = list(
iproduct(['tgz', 'zip'], ['cems_fire', 'agera5', 'wfde5']))
valid_format.extend(
list(
iproduct(['netcdf', 'grib'],
['pressure', 'surface', 'land', 'wave'])))
if (oformat, stream) not in valid_format:
print(f'Download format {oformat} not available for {stream} product')
sys.exit()
if queue:
dump_args(oformat, stream, list(param), list(year), list(month),
timestep, back, urgent)
else:
api_request(oformat, stream, list(param), list(year), list(month),
timestep, back)
def _base(j, k, c):
assert k - j == 1
aajk = subbasis(j, k)
assert all(a.order() in (1, p) for a in aajk)
idxs = [i for i, a in enumerate(aajk) if a.order() == p]
rs = [([0], [0]) for i in range(len(aajk))]
for i in range(len(idxs)):
rs[idxs[i]] = (range(p), [0]) if i % 2 else ([0], range(p))
if len(idxs) % 2:
m = ceil(sqrt(p))
rs[idxs[-1]] = range(0, p, m), range(m)
tab = {}
for x in iproduct(*(r for r, _ in rs)):
key = dotprod(x, aajk)
if hasattr(key, 'set_immutable'):
key.set_immutable()
tab[key] = vector(x)
for y in iproduct(*(r for _, r in rs)):
key = c - dotprod(y, aajk)
if hasattr(key, 'set_immutable'):
key.set_immutable()
if key in tab:
return tab[key] + vector(y)
raise TypeError('Not in group')
def main():
print('case', 'condition', 'temperature')
for i, data in enumerate(iproduct(range(1, 4),
map(lambda x: 0.5*x,
range(-1, 2)))):
print(i + 1, *data)
return 0
def find_interfaces_ntypes(landscape):
'''Determines internal boundaries for landscapes with many habitat types.
Parameters
----------
landscape : 2-d array
Returns
-------
Bx, By : tuple of two dicts
each key is a tuple (i,j) corresponding to the numbers of the habitat
types, and the value corresponds to the indices where a boundary
between them appears, along either the x or y direction
'''
n = np.unique(landscape).astype(int)
A = 2**(landscape.astype(int))
Ax = A[1:, :] - A[:-1, :]
Ay = A[:, 1:] - A[:, :-1]
Bx = {}
By = {}
for i, j in iproduct(n, repeat=2):
if i != j:
Bx[(i, j)] = np.where(Ax == 2**j - 2**i)
By[(i, j)] = np.where(Ay == 2**j - 2**i)
return Bx, By
def run_landscapes(par,
dx,
cover,
frag,
size,
runs=1,
radius=1,
norm='taxicab',
processes=7,
filename=None):
if processes is None or processes > 0:
pool = Pool(processes=processes)
mymap = pool.map
else:
mymap = map
newpars = []
for obj in (par, dx, cover, frag, size):
if not type(obj) is list:
newpars.append([obj])
else:
newpars.append(obj)
newpars += [[radius], [norm]]
works = list(iproduct(*newpars))
# print(works)
solutions = mymap(analyze_random_landscape, works)
if filename:
with open(filename, 'w') as f:
dump([parameters, solutions], f)
return solutions
def encode(dic, degree, num_types):
dic = {k if type(v) in num_types else str(str(k) + "=" + str(v)):
float(v) if type(v) in num_types else 1
for k, v in dic.items()}
#print("dic:", dic)
aux_dic={}
dic_keys = list(dic.keys())
for deg in range(2, degree + 1):
for term_keys in iproduct(dic_keys, repeat=deg):
term_names, term_facts = [], []
for k, n in Counter(term_keys).items():
v = dic[k]
if type(v) is int and n > 1:
break
#term_names.append(k if n == 1 else str(str(k) + "^" + str(n)))
#if (type(v) in num_types):
if (n==1):
term_names.append(k)
else:
aux_str=str(k) + "^" + str(n)
term_names.append(aux_str)
#print("v:", v)
#print("n:", n)
term_facts.append(v**n)
else: # No dummy feature was included more than once
dic['*'.join(sorted(term_names))] = product(term_facts)
output_dic=dict(chain.from_iterable(d.items() for d in (aux_dic,dic)))
return output_dic
def make_diag_figure(self, xnames, ynames):
nobj = len(xnames)
# initialize subplot size
gs, fig = ftools.gen_gridspec_fig(nobj,
add_row=False,
border=(0.6, 0.6, 0.2, 0.4),
space=(0.6, 0.35))
# set up subplot interactions
gs_geo = gs.get_geometry()
fgrid_r, fgrid_c = tuple(list(range(n)) for n in gs_geo)
gs_iter = iproduct(fgrid_r, fgrid_c)
# set up kwargs for matplotlib errorbar
# prefer to change color, then marker
colors_ = ['C{}'.format(cn) for cn in range(10)]
markers_ = ['o', 'v', 's', 'P', 'X', 'D', 'H']
# iterate through rows & columns (rows change fastest)
# which correspond to different quantities
for (i, (ri, ci)) in enumerate(gs_iter):
if i >= len(xnames):
continue
# choose axis
ax = fig.add_subplot(gs[ri, ci])
kwarg_cycler = cycler(marker=markers_) * \
cycler(c=colors_)
xqty = xnames[i]
yqty = ynames[i]
# now iterate through results hdulists
for (j, (result,
kwargs)) in enumerate(zip(self.results, kwarg_cycler)):
kwargs['label'] = result[0].header['PLATEIFU']
ax = self._add_log_offset_plot(j,
xqty=xqty,
yqty=yqty,
ax=ax,
**kwargs)
ax.tick_params(labelsize=5)
if i == 0:
handles_, labels_ = ax.get_legend_handles_labels()
plt.figlegend(handles=handles_,
labels=labels_,
loc='upper right',
prop={'size': 4.})
fig.suptitle('PCA fitting diagnostics', size=8.)
return fig
def _cross_provider_maps(self, lmap, rmap):
result = {}
for lspec, rspec in iproduct(lmap, rmap):
try:
constrained = lspec.constrained(rspec)
except spack.spec.UnsatisfiableSpecError:
continue
# lp and rp are left and right provider specs.
for lp_spec, rp_spec in iproduct(lmap[lspec], rmap[rspec]):
if lp_spec.name == rp_spec.name:
try:
const = lp_spec.constrained(rp_spec, deps=False)
result.setdefault(constrained, set()).add(const)
except spack.spec.UnsatisfiableSpecError:
continue
return result
def _cross_provider_maps(self, lmap, rmap):
result = {}
for lspec, rspec in iproduct(lmap, rmap):
try:
constrained = lspec.constrained(rspec)
except spack.spec.UnsatisfiableSpecError:
continue
# lp and rp are left and right provider specs.
for lp_spec, rp_spec in iproduct(lmap[lspec], rmap[rspec]):
if lp_spec.name == rp_spec.name:
try:
const = lp_spec.constrained(rp_spec, deps=False)
result.setdefault(constrained, set()).add(const)
except spack.spec.UnsatisfiableSpecError:
continue
return result
def rpoints(self):
"""Array with the points in real space in reduced coordinates."""
nx, ny, nz = self.nx, self.ny, self.nz
rpoints = np.empty((self.size,3))
for ifft, p1_fft in enumerate(iproduct(range(nx), range(ny), range(nz))):
rpoints[ifft,:] = p1_fft[0]/nx, p1_fft[1]/ny, p1_fft[2]/nz
return rpoints
def tracetimes(tracer, s, elements, targets, trlist, quiet=True):
'''
For a PathTracer tracer, a 3-D Numpy array s representing a slowness, a
keymap of source coordinates elements, and a list of targets, trace
indicated paths to determine arrival times.
If trlist is True, targets is interpreted as a list of (t, r) indices
into the keymap elements. Otherwise, targets should be a Numpy array
(or compatible sequence) of shape (N, 3) such that targets[i] contains
the world coordinates for the i-th target.
The return value is a Numpy record array of "timetype" records that
each indicate transmit and receive indices and the corresponding path
integral.
Failure to trace a path will cause its time to be NaN.
If quiet is not True, a progress bar will be printed to show tracing
progress.
'''
if trlist:
nrec = len(targets)
itertr = iter(targets)
targc = elements
else:
M, N = len(elements), len(targets)
nrec = M * N
itertr = iproduct(range(M), range(N))
targc = targets
times = np.zeros((nrec, ), dtype=timetype)
tracer.set_slowness(s)
if not quiet: bar = progressbar.ProgressBar(max_value=nrec)
else: bar = None
for i, (t, r) in enumerate(itertr):
src = elements[t]
rcv = targc[r]
record = [t, r]
try:
tm = tracer.trace([src, rcv], intonly=True)
except (ValueError, TraceError):
tm = float('nan')
record.append(tm)
times[i] = tuple(record)
if not quiet: bar.update(i)
if not quiet: bar.update(nrec)
return times
def rpoints(self):
"""Array with the points in real space in reduced coordinates."""
nx, ny, nz = self.nx, self.ny, self.nz
rpoints = np.empty((self.size,3))
for ifft, p1_fft in enumerate(iproduct(range(nx), range(ny), range(nz))):
rpoints[ifft,:] = p1_fft[0]/nx, p1_fft[1]/ny, p1_fft[2]/nz
return rpoints
def get_rpoints(self):
nx, ny, nz = self.nx, self.ny, self.nz
rpoints = np.empty((self.size,3))
for ifft, p1_fft in enumerate(iproduct(range(nx), range(ny), range(nz))):
rpoints[ifft,0] = p1_fft[0] / nx
rpoints[ifft,1] = p1_fft[1] / ny
rpoints[ifft,2] = p1_fft[2] / nz
return rpoints
def make_diag_figure(self, xnames, ynames):
nobj = len(xnames)
# initialize subplot size
gs, fig = ftools.gen_gridspec_fig(
nobj, add_row=False, border=(0.6, 0.6, 0.2, 0.4),
space=(0.6, 0.35))
# set up subplot interactions
gs_geo = gs.get_geometry()
fgrid_r, fgrid_c = tuple(list(range(n)) for n in gs_geo)
gs_iter = iproduct(fgrid_r, fgrid_c)
# set up kwargs for matplotlib errorbar
# prefer to change color, then marker
colors_ = ['C{}'.format(cn) for cn in range(10)]
markers_ = ['o', 'v', 's', 'P', 'X', 'D', 'H']
# iterate through rows & columns (rows change fastest)
# which correspond to different quantities
for (i, (ri, ci)) in enumerate(gs_iter):
if i >= len(xnames):
continue
# choose axis
ax = fig.add_subplot(gs[ri, ci])
kwarg_cycler = cycler(marker=markers_) * \
cycler(c=colors_)
xqty = xnames[i]
yqty = ynames[i]
# now iterate through results hdulists
for (j, (result, kwargs)) in enumerate(
zip(self.results, kwarg_cycler)):
kwargs['label'] = result[0].header['PLATEIFU']
ax = self._add_log_offset_plot(
j, xqty=xqty, yqty=yqty, ax=ax, **kwargs)
ax.tick_params(labelsize=5)
if i == 0:
handles_, labels_ = ax.get_legend_handles_labels()
plt.figlegend(
handles=handles_, labels=labels_,
loc='upper right', prop={'size': 4.})
fig.suptitle('PCA fitting diagnostics', size=8.)
return fig
def match_filenames(self, filenames):
"""Update internal queues with passed filenames. Returns names that match across the head of all queues if
any are found, or an empty list otherwise.
"""
# insert
# we assume that usually we'll just be appending to the end - other options
# include heapq and bisect, but it probably doesn't really matter
for filename in filenames:
qname = self.fname_to_qname_fcn(filename)
if qname is None:
global_logger.get().warn(
"Could not get queue name for file '%s', skipping" %
filename)
continue
tpname = self.fname_to_timepoint_fcn(filename)
if tpname is None:
global_logger.get().warn(
"Could not get timepoint for file '%s', skipping" %
filename)
continue
self.qname_to_queue[qname].append(tpname)
self.keys_to_fullnames[(qname, tpname)] = filename
# maintain sorting and dedup:
for qname, queue in self.qname_to_queue.iteritems():
if not is_sorted(queue):
self.qname_to_queue[qname] = deque(
unique_justseen(sorted(list(queue))))
# all queues are now sorted and unique-ified
# check for matching first entries across queues
matching = self.get_matching_first_entry()
matches = []
dcs = self.do_check_sequence
while matching:
if dcs:
self.check_sequence(matching)
matches.append(matching)
matching = self.get_matching_first_entry()
# convert matches back to full filenames
fullnamekeys = list(iproduct(self.qname_to_queue.iterkeys(), matches))
fullnames = [self.keys_to_fullnames.pop(key) for key in fullnamekeys]
fullnames.sort()
# filter out files that are smaller than the first file to be added to the queue, if requested
# this attempts to check for and work around an error state where some files are incompletely
# transferred
if self.qname_to_expected_size is not None:
fullnames = self.filter_size_mismatch_files(fullnames)
return fullnames
def __str__(self):
message = ''
# header
for var in self.var:
message = message + 'v' + str(var) + '\t'
message = message + 'value\n'
# iterate each
cards = [range(i) for i in self.card]
for comb in iproduct(*cards):
for item in comb:
message = message + str(item) + '\t'
message = message + str(self.val[comb]) + '\n'
return message
def match_filenames(self, filenames):
"""Update internal queues with passed filenames. Returns names that match across the head of all queues if
any are found, or an empty list otherwise.
"""
# insert
# we assume that usually we'll just be appending to the end - other options
# include heapq and bisect, but it probably doesn't really matter
for filename in filenames:
qname = self.fname_to_qname_fcn(filename)
if qname is None:
global_logger.get().warn("Could not get queue name for file '%s', skipping" % filename)
continue
tpname = self.fname_to_timepoint_fcn(filename)
if tpname is None:
global_logger.get().warn("Could not get timepoint for file '%s', skipping" % filename)
continue
self.qname_to_queue[qname].append(tpname)
self.keys_to_fullnames[(qname, tpname)] = filename
# maintain sorting and dedup:
for qname, queue in self.qname_to_queue.iteritems():
if not is_sorted(queue):
self.qname_to_queue[qname] = deque(unique_justseen(sorted(list(queue))))
# all queues are now sorted and unique-ified
# check for matching first entries across queues
matching = self.get_matching_first_entry()
matches = []
dcs = self.do_check_sequence
while matching:
if dcs:
self.check_sequence(matching)
matches.append(matching)
matching = self.get_matching_first_entry()
# convert matches back to full filenames
fullnamekeys = list(iproduct(self.qname_to_queue.iterkeys(), matches))
fullnames = [self.keys_to_fullnames.pop(key) for key in fullnamekeys]
fullnames.sort()
# filter out files that are smaller than the first file to be added to the queue, if requested
# this attempts to check for and work around an error state where some files are incompletely
# transferred
if self.qname_to_expected_size is not None:
fullnames = self.filter_size_mismatch_files(fullnames)
return fullnames
def product(self, other: 'Relation') -> 'Relation':
'''
Cartesian product. Attributes of the relations must differ.
'''
if (not isinstance(other, Relation)):
raise Exception('Operand must be a relation')
if self.header.sharedAttributes(other.header) != 0:
raise Exception(
_('Unable to perform product on relations with colliding attributes'
))
header = Header(self.header + other.header)
content = frozenset(i + j
for i, j in iproduct(self.content, other.content))
return Relation(header, content)
def getFields(src, nm, NL):
"""getFields( src, nm, NL ) -- parse C source src to find
definition of struct nm (all fields must be doubles) and
list the fields.
The legacy form of this function handles arrays only with the
form double foo [NUM_LEGS]. In this case, NL is an integer and
the entry is expanded to a list of fields foo_0 foo_1, foo_(NL-1)
In its newer form, NL is a dictionary mapping names to tuples of
integers. The field double bar [BAR], with NL = {'BAR':(2,3)}
gives fields bar_0_0, bar_0_1, bar_0_2, bar_1_0, bar_1_1, bar_1_2
In addition, integers in the brackets are converted to vector
lengths, i.e. double foo[2] becomes foo_0, foo_1.
"""
# Backward compatible NL format
if type(NL) != dict:
NL = {'NUM_LEGS': (NL, )}
sl = getSlice(src, re.compile('\s*struct\s+%s\s*[{].*' % nm),
re.compile('\s*[}]\s*[;][^E]*ENDS:\s+struct\s+%s.*' % nm))
if not sl:
return None
sl.pop(0)
res = []
rex = re.compile('\s*double\s+(\w+)\s*(?:\[\s*(\w+)\s*\])?.*')
for item in sl:
m = rex.match(item)
if m is None:
raise ValueError, "Line '%s' cannot be parsed" % item
var = m.group(1)
if m.group(2):
# Try to resolve from NL dictionary
sz = NL.get(m.group(2), None)
# If failed --> resolve as integer
if sz is not None:
idx = [
var + "".join(["_%d" % k for k in x])
for x in iproduct(*map(xrange, sz))
]
else:
sz = int(m.group(2))
idx = ["%s_%d" % (var, idx) for idx in xrange(sz)]
res.extend(idx)
else:
res.append(var)
return res
def getFields( src, nm, NL ):
"""getFields( src, nm, NL ) -- parse C source src to find
definition of struct nm (all fields must be doubles) and
list the fields.
The legacy form of this function handles arrays only with the
form double foo [NUM_LEGS]. In this case, NL is an integer and
the entry is expanded to a list of fields foo_0 foo_1, foo_(NL-1)
In its newer form, NL is a dictionary mapping names to tuples of
integers. The field double bar [BAR], with NL = {'BAR':(2,3)}
gives fields bar_0_0, bar_0_1, bar_0_2, bar_1_0, bar_1_1, bar_1_2
In addition, integers in the brackets are converted to vector
lengths, i.e. double foo[2] becomes foo_0, foo_1.
"""
# Backward compatible NL format
if type(NL) != dict:
NL = {'NUM_LEGS' : (NL,) }
sl = getSlice( src,
re.compile('\s*struct\s+%s\s*[{].*' % nm),
re.compile('\s*[}]\s*[;][^E]*ENDS:\s+struct\s+%s.*' % nm) )
if not sl:
return None
sl.pop(0)
res = []
rex = re.compile('\s*double\s+(\w+)\s*(?:\[\s*(\w+)\s*\])?.*')
for item in sl:
m = rex.match(item)
if m is None:
raise ValueError,"Line '%s' cannot be parsed" % item
var = m.group(1)
if m.group(2):
# Try to resolve from NL dictionary
sz = NL.get(m.group(2),None)
# If failed --> resolve as integer
if sz is not None:
idx = [ var+"".join(["_%d" % k for k in x])
for x in iproduct(*map(xrange,sz))]
else:
sz = int(m.group(2))
idx = [ "%s_%d" % (var,idx) for idx in xrange(sz) ]
res.extend(idx)
else:
res.append(var)
return res
def encode(dic, degree, num_types):
dic = {
k if type(v) in num_types else f'{k}={v}':
float(v) if type(v) in num_types else 1
for k, v in dic.items()
}
dic_keys = list(dic.keys())
for deg in range(2, degree + 1):
for term_keys in iproduct(dic_keys, repeat=deg):
term_names, term_facts = [], []
for k, n in Counter(term_keys).items():
v = dic[k]
if type(v) is int and n > 1:
break
term_names.append(k if n == 1 else f'{k}^{n}')
term_facts.append(v**n)
else: # No dummy feature was included more than once
dic['*'.join(sorted(term_names))] = product(term_facts)
return dic
def _distance_2(misorientation, verbose):
if misorientation.size > 1e4: # pragma no cover
confirm = input('Large datasets may crash your RAM.\nAre you sure? (y/n) ')
if confirm != 'y':
raise InterruptedError('Aborted')
from itertools import product as iproduct
S_1, S_2 = misorientation._symmetry
mis2orientation = (~misorientation).outer(S_1).outer(S_1).outer(misorientation)
distance = np.full(misorientation.shape + misorientation.shape, np.infty)
symmetry_pairs = iproduct(S_2, S_2)
if verbose:
from tqdm import tqdm
symmetry_pairs = tqdm(symmetry_pairs, total=S_2.size ** 2)
for s_1, s_2 in symmetry_pairs:
m = s_1 * mis2orientation * s_2
axis = (len(misorientation.shape), len(misorientation.shape) + 1)
angle = m.angle.data.min(axis=axis)
distance = np.minimum(distance, angle)
return distance
def srcint(k, src, obs, cell, ifunc, n = 4, wts = None):
'''
Evaluate source integration, of order n, of the pairwise Green's
function for wave number k from source location src to observer
location obs. The list cell specifies the dimensions of the cell.
The pairwise Green's function function ifunc takes arguments (k, s, o),
where k is the wave number, s is the source location and o is the
observer location. The source position s varies throughout the cell
centered at src according to Gauss-Legendre quadrature rules.
If specified, wts should be an n-by-2 array (or list of lists) in which
the first column contains the quadrature points and the second column
contains the corresponding quadrature weights.
'''
dim = len(src)
if len(obs) != dim: raise ValueError('Dimension of src and obs must agree.')
if len(cell) != dim: raise ValueError('Dimension of src and cell must agree.')
# Compute the node scaling factor
sc = [0.5 * c for c in cell]
# Grab the roots and weights of the Legendre polynomial of order n
if wts is None: wts = spec.legendre(n).weights
# Compute a sparse coordinate grid for sampling within the cell
coords = np.ogrid[[slice(n) for i in range(dim)]]
# Create an iterator factory to loop through coordinate pairs
enum = lambda c: iproduct(*[cv.flat for cv in c])
# Compute the cell-relative quadrature points
qpts = ([o + s * wts[i][0] for i, o, s in zip(c, src, sc)] for c in enum(coords))
# Compute the corresponding quadrature weights
qwts = (cutil.prod(wts[i][1] for i in c) for c in enum(coords))
# Sum all contributions to the integral
ival = np.sum(w * ifunc(k, p, obs) for w, p in zip(qwts, qpts))
return ival * cutil.prod(cell) / 2.**dim
def irottable(self, symmops):
nsym = len(symmops)
nx, ny, nz = self.nx, self.ny, self.nz
red2fft = np.diag([nx, ny, nz])
fft2red = np.diag([1 / nx, 1 / ny, 1 / nz])
# For a fully compatible mesh, each mat in rotsm1_fft should be integer
rotsm1_fft, tnons_fft = np.empty((nsym, 3, 3)), np.empty((nsym, 3))
for isym, symmop in enumerate(symmops):
rotm1_r, tau = symmop.rotm1_r, symmop.tau
rotsm1_fft[isym] = np.dot(np.dot(red2fft, rotm1_r), fft2red)
tnons_fft[isym] = np.dot(red2fft, tau)
# Indeces of $R^{-1}(r-\tau)$ in the FFT box.
irottable = np.empty((nsym, nx * ny * nz), dtype=np.int)
#max_err = 0.0
nxyz = np.array((nx, ny, nz), np.int)
for isym in range(nsym):
rm1_fft = rotsm1_fft[isym]
tau_fft = tnons_fft[isym]
for ifft, p1_fft in enumerate(
iproduct(range(nx), range(ny), range(nz))):
# Form R^-1 (r-\tau) in the FFT basis.
p1_fft = np.array(p1_fft)
prot_fft = np.dot(rm1_fft, p1_fft - tau_fft)
#err = ABS(prot_fft - (ix, iy, iz)) / (nx, ny, nz)
prot_fft = np.round(prot_fft)
jx, jy, jz = prot_fft % nxyz
irottable[isym, ifft] = jz + (jy * nz) + (jx * nx * ny)
# Test
#for isym in range(nsym):
# irottable[isym, ifft]
# rm1_fft = rotsm1_fft[isym]
# tau_fft = tnons_fft[isym]
# for ifft, p1_fft in enumerate(itertools.product(range(nx), range(ny), range(nz))):
# irot_fft == irottable[isym, ifft]
return irottable
def set_symmetry(self, Gl, Gr, verbose=False):
"""Assign symmetries to this misorientation.
Computes equivalent transformations which have the smallest angle of
rotation and assigns these in-place.
Parameters
----------
Gl, Gr : Symmetry
Returns
-------
Misorientation
A new misorientation object with the assigned symmetry.
Examples
--------
>>> from orix.quaternion.symmetry import C4, C2
>>> data = np.array([[0.5, 0.5, 0.5, 0.5], [0, 1, 0, 0]])
>>> m = Misorientation(data).set_symmetry(C4, C2)
>>> m
Misorientation (2,) 4, 2
[[-0.7071 0. -0.7071 0. ]
[ 0. 0.7071 -0.7071 0. ]]
"""
symmetry_pairs = iproduct(Gl, Gr)
if verbose:
import tqdm
symmetry_pairs = tqdm.tqdm(symmetry_pairs, total=Gl.size * Gr.size)
orientation_region = OrientationRegion.from_symmetry(Gl, Gr)
o_inside = self.__class__.identity(self.shape)
outside = np.ones(self.shape, dtype=bool)
for gl, gr in symmetry_pairs:
o_transformed = gl * self[outside] * gr
o_inside[outside] = o_transformed
outside = ~(o_inside < orientation_region)
if not np.any(outside):
break
o_inside._symmetry = (Gl, Gr)
return o_inside
def _run(n, query, stream):
iters = range(n)
hypothesis_sizes = [2, 4, 8, 16, 32]
data = dict(np.load('data/50animals.npz'))
trials = list(iproduct(iters, range(len(hypothesis_sizes))))
np.random.shuffle(trials)
trial_data = np.empty((len(iters), len(hypothesis_sizes)), dtype=int)
for (i, j) in trials:
hyp_size = hypothesis_sizes[j]
animal_choices = np.arange(len(data['animal_names']))
np.random.shuffle(animal_choices)
animal_choices = animal_choices[:hyp_size]
animal_index = animal_choices[np.random.randint(hyp_size)]
animal_name = data['animal_names'][animal_index]
feature_indices = np.nonzero(data['animal_features'][animal_index])[0]
np.random.shuffle(feature_indices)
features = list(data['feature_names'][feature_indices])
animals = list(data['animal_names'][animal_choices])
guessed = False
num_guesses = 0
stream.write("-" * 70 + "\n")
while not guessed:
animal_guess = query(features[:2 + num_guesses], animals)
if animal_guess == animal_name:
stream.write("Correct!\n")
guessed = True
else:
stream.write("Sorry, try again.\n")
stream.write("\n")
num_guesses += 1
trial_data[i, j] = num_guesses
return trial_data
def _run(n, query, stream):
iters = range(n)
hypothesis_sizes = [2, 4, 8, 16, 32]
data = dict(np.load('data/50animals.npz'))
trials = list(iproduct(iters, range(len(hypothesis_sizes))))
np.random.shuffle(trials)
trial_data = np.empty((len(iters), len(hypothesis_sizes)), dtype=int)
for (i, j) in trials:
hyp_size = hypothesis_sizes[j]
animal_choices = np.arange(len(data['animal_names']))
np.random.shuffle(animal_choices)
animal_choices = animal_choices[:hyp_size]
animal_index = animal_choices[np.random.randint(hyp_size)]
animal_name = data['animal_names'][animal_index]
feature_indices = np.nonzero(data['animal_features'][animal_index])[0]
np.random.shuffle(feature_indices)
features = list(data['feature_names'][feature_indices])
animals = list(data['animal_names'][animal_choices])
guessed = False
num_guesses = 0
stream.write("-" * 70 + "\n")
while not guessed:
animal_guess = query(features[:2 + num_guesses], animals)
if animal_guess == animal_name:
stream.write("Correct!\n")
guessed = True
else:
stream.write("Sorry, try again.\n")
stream.write("\n")
num_guesses += 1
trial_data[i, j] = num_guesses
return trial_data
def irottable(self, symmops):
nsym = len(symmops)
nx, ny, nz = self.nx, self.ny, self.nz
red2fft = np.diag([nx, ny, nz])
fft2red = np.diag([1/nx, 1/ny, 1/nz])
# For a fully compatible mesh, each mat in rotsm1_fft should be integer
rotsm1_fft, tnons_fft = np.empty((nsym,3,3)), np.empty((nsym,3))
for isym, symmop in enumerate(symmops):
rotm1_r, tau = symmop.rotm1_r, symmop.tau
rotsm1_fft[isym] = np.dot(np.dot(red2fft, rotm1_r), fft2red)
tnons_fft[isym] = np.dot(red2fft, tau)
# Indeces of $R^{-1}(r-\tau)$ in the FFT box.
irottable = np.empty((nsym, nx*ny*nz), dtype=np.int)
#max_err = 0.0
nxyz = np.array((nx, ny, nz), np.int)
for isym in range(nsym):
rm1_fft = rotsm1_fft[isym]
tau_fft = tnons_fft[isym]
for ifft, p1_fft in enumerate(iproduct(range(nx), range(ny), range(nz))):
# Form R^-1 (r-\tau) in the FFT basis.
p1_fft = np.array(p1_fft)
prot_fft = np.dot(rm1_fft, p1_fft - tau_fft)
#err = ABS(prot_fft - (ix, iy, iz)) / (nx, ny, nz)
prot_fft = np.round(prot_fft)
jx, jy, jz = prot_fft % nxyz
irottable[isym, ifft] = jz + (jy * nz) + (jx * nx * ny)
# Test
#for isym in range(nsym):
# irottable[isym, ifft]
# rm1_fft = rotsm1_fft[isym]
# tau_fft = tnons_fft[isym]
# for ifft, p1_fft in enumerate(itertools.product(range(nx), range(ny), range(nz))):
# irot_fft == irottable[isym, ifft]
return irottable
def make_grid(scale, minx, maxx, miny, maxy, mult=True):
gridx = arange(minx, maxx, scale)
gridy = arange(miny, maxy, scale)
if mult:
pool = multiprocessing.Pool(None)
tasks = list(iproduct(gridx, gridy))
results = []
r = pool.map_async(fmult, tasks, callback=results.append)
r.wait() # Wait on the results
rr = zeros((len(gridx), len(gridy)), dtype='object')
def insert(x):
rr[int((x[0] - minx)/scale)][int((x[1] - miny)/scale)] = x[2]
for x in results[0]:
insert(x)
return rr
else:
return array([ [ F(i + j*1j) for j in gridy ] for i in gridx ])
def get_stable_states(self):
if self.weight is None:
raise Exception("Weight matrix is empty!")
self.text_output.append(
u"<h2>Sinhrono pridobivanje stabilnih stanj</h2>")
if self.function_type == 0:
self.text_output.append(r"$$y = \left\{\begin{matrix} 0 & \mbox {if } v < 0, \\ 1 & \mbox{if } v > 0, \\ \text{enako kot prej} & \mbox{if } v=0\end{matrix}\right.$$")
elif self.function_type == 1:
self.text_output.append(r"$$y = \left\{\begin{matrix} -1 & \mbox {if } v < 0, \\ +1 & \mbox{if } v > 0, \\ \text{enako kot prej} & \mbox{if } v=0\end{matrix}\right.$$")
self.text_output.append(u'<span class="label label-warning">Opozorilo</span>Ta funkcija je še v beta stanju. Nevem namreč kako računat oznake</p>')
self.number_of_weights = len(self.weight)
weights_label = ["\(y_%d\)" % i for i in range(1,
self.number_of_weights + 1)]
header = weights_label + ["Oznaka"] + weights_label + ["Oznaka"]
self.table.append(header)
truth_table = list(
iproduct([0, 1], repeat=int(self.number_of_weights)))
for index, input_row in enumerate(truth_table):
self.text_output.append("<h3>Vrstica %d</h3>" % (index + 1, ))
table_row = []
table_row.extend(input_row)
table_row.append(index)
for i, input_y in enumerate(input_row):
v_i = self.v_i(i, index + 1, input_row)
y_i = self.y_func(v_i, input_y)
table_row.append(y_i)
if self.function_type == 0:
oznaka_bin = "".join(
map(str, table_row[-self.number_of_weights:]))
oznaka = int(oznaka_bin, 2)
if oznaka == index:
oznaka = {'val': oznaka}
else:
oznaka = "??"
table_row.append(oznaka)
self.table.append(table_row)
def gen_mappings(assignments):
from itertools import product as iproduct
I, J = assignments
m = len(unique(I))
M = I.max() + 1
if m == len(I):
mappings = [(I, J)]
else:
pool = [[] for _ in range(M)]
for i, j in zip(I, J):
pool[i].append((i, j))
mappings = []
for mapping in iproduct(*pool):
r = zeros(len(mapping), dtype=int)
c = zeros(len(mapping), dtype=int)
for i, pair in enumerate(mapping):
r[i] = pair[0]
c[i] = pair[1]
mappings.append((r, c))
return mappings
def create(cls, params):
"""Create the tasks dictionary from the parameters."""
sim_root = path(params["sim_root"])
if not sim_root.exists():
sim_root.makedirs_p()
floor_path = CPO_PATH.joinpath(params['floor_path'])
cpo_paths = [CPO_PATH.joinpath(x) for x in params['cpo_paths']]
index_names = params['index_names']
index_levels = params['index_levels']
cpos_rec_names = index_levels['object']
record_intervals = list(np.diff(index_levels['timestep'][1:]))
cond_names = [
'sigma',
'phi',
'kappa',
'stimulus',
'sample',
]
conditions = list(
iproduct(*[
enumerate(index_levels[x]) for x in cond_names
if x != 'stimulus'
]))
n_conditions = len(conditions)
n_chunks = int(np.ceil(n_conditions / float(params['max_chunk_size'])))
chunks = np.array_split(np.arange(n_conditions), n_chunks, axis=0)
base_shape = [
len(index_levels[x]) for x in index_names if x not in cond_names
]
tasks = cls()
completed = cls()
for icpo, cp in enumerate(cpo_paths):
for ichunk, chunk_idx in enumerate(chunks):
sim_name = "%s_%s_%02d" % (cp.namebase, params["tag"], ichunk)
data_path = sim_root.joinpath("%s.npy" % sim_name)
chunk = [conditions[i] for i in chunk_idx]
shape = [len(chunk)] + base_shape
# Make the task dicts for this sample.
tasks[sim_name] = {
"icpo": icpo,
"floor_path": str(floor_path),
"cpo_path": str(cp),
"data_path": str(data_path),
"script_root": params["script_root"],
"task_name": sim_name,
"bodies": cpos_rec_names,
"seed": abs(hash(sim_name)),
"conditions": chunk,
"record_intervals": record_intervals,
"shape": shape,
"num_tries": 0,
}
completed[sim_name] = False
return tasks, completed
HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.
"""
# Observations:
# The product cannot have three or fewer digits (the smallest product containing six digits is 11111 x 1 = 11111, which is greater than any three digit number)
# Also, the product cannot have five or more digits (the largest product containing four digits is 99 x 99 = 9801, which is smaller than any five digit number)
# Thus, the product must have four digits.
from itertools import permutations, combinations, product as iproduct, imap
digits = set([1,2,3,4,5,6,7,8,9])
def digits2num(digits):
return reduce(lambda x, d: x*10 + d, digits)
def num2digits(num):
return set(map(int, str(num)))
pandigital_products = set()
for operand_digits in imap(set, combinations(digits, 5)):
for num_multiplicand_digits in range(3,4+1):
for multiplicand_digits in imap(set, combinations(operand_digits, num_multiplicand_digits)):
multiplier_digits = operand_digits - multiplicand_digits
for multiplicand, multiplier in iproduct(imap(digits2num, permutations(multiplicand_digits)), imap(digits2num, permutations(multiplier_digits))):
product = multiplicand * multiplier
product_digits = num2digits(product)
if len(str(product)) + len(operand_digits) == 9 and 0 not in product_digits and len(product_digits | operand_digits) == 9:
pandigital_products.add(product)
print sum(pandigital_products)
from euler import *
from itertools import product as iproduct
st_digs = [2, 3, 5, 7]
md_digs = [1, 3, 5, 7, 9]
trunc_rl = set(st_digs)
trunc_lr = set(st_digs)
trunc = set()
while len(trunc) < 11:
rl = trunc_rl.copy()
trunc_rl.clear()
for x, d in iproduct(rl, md_digs):
n = x*10 + d
if is_prime(n):
trunc_rl.add(n)
lr = trunc_lr.copy()
trunc_lr.clear()
for x, d in iproduct(lr, xrange(1, 10)):
nd = num_digits(x)
n = (d * 10**nd) + x
if is_prime(n):
trunc_lr.add(n)
if n in trunc_rl:
trunc.add(n)
print sum(trunc)
def solve_landscape_ntypes(landscape,
par,
dx,
f_tol=None,
force_positive=False,
verbose=True,
debug=False):
r"""Find the stationary solution for a landscape with many types of habitat.
Uses a Newton-Krylov solver with LGMRES sparse inverse method to find a
stationary solution (or the solution to the elliptical problem) to the
system of equations in 2 dimensions (x is a 2-d vector):
.. math::
\frac{\partial u_i}{\partial t} = D_i \nabla^2 u_i +
r_i u_i\left(1-\frac{u}{K_i}\right) = 0
Parameters
----------
landscape : 2-d array of ints
describe the landscape, with any number of habitat types
par : dict
parameters (dict keys):
- r : growth rates (can be negative)
- K : carrying capacities (cn be np.Inf)
- mu : mortality rate in the matrix
- D : diffusivities
- g : dict of habitat discontinuities $\gamma_{ij}$ - see interface
conditions below. The keys are tuples (i,j) of the habitat
types indices (optional)
- alpha : dict of habitat preferences, only taken into account if g is
not present. In that case, $\gamma_{ij}$ is calculated as
$\gamma_{ij} = D_j \alpha_{ij} / (D_i*(1-\alpha_{ij}))$ (optional)
- left : (a, b, c): external boundary conditions at left border
- right : (a, b, c): external boundary conditions at right border
- top : (a, b, c): external boundary conditions at top border
- bottom : (a, b, c): external boundary conditions at bottom border
dx : float
lenght of each edge
f_tol : float
tolerance for the residue, passed on to the solver routine. Default is
6e-6
force_positive : bool
make sure the solution is always non-negative - in a hacky way. Default
False
verbose : bool
print residue of the solution and its maximum and minimum values
Returns
-------
solution : 2-d array of the same shape of the landscape input
the solution
.. rubric:: Boundary and interface conditions
External boundaries are of the form
.. math:: a \nabla u \cdot \hat{n} + b u + c = 0
and may be different for left, right, top, bottom. The derivative of u is
taken along the normal to the boundary.
The interfaces between patches and matrix are given by
.. math::
u_i(x) &= \gamma_{ij} u_j(x) \\
D_i \nabla u_i(x) \cdot \hat{n} &= D_j \nabla u_j(x) \cdot \hat{n}
Usually the discontinuity $\gamma_{ij}$ is a result of different
diffusivities and preference at the border (see Ovaskainen and Cornell
2003). In that case, given a preference $\alpha_{ij}$ (between 0 and 1,
exclusive) towards $i$, this parameter should be:
.. math:: \gamma_{ij} = \frac{D_j}{D_i} \frac{\alpha_{ij}}{1-\alpha_{ij}}
This last condition is used in case $\gamma$ is not set. If $\alpha$ isn't
set either, it's assumed $\alpha = 1/2$. Notice that $\alpha_{ij} +
\alpha_{ji} = 1$, and so $\gamma_{ij} = \gamma_{ji}^{-1}$. To ensure this
condition, the key (i,j) is always taken with $i>j$.
These conditions are handled using an asymetric finite difference scheme
for the 2nd derivative:
.. math:: u_{xx}(x) = \frac{4}{3h^2} (u(x-h) - 3 u(x) + 2 u(x+h/2))
At the interface, $u(x+h/2)$ and $v(x+h/2)$ must obey:
.. math::
u(x+h/2) &= \gamma v(x+h/2) \\
D_p (u(x+h/2) - u(x)) &= D_m (v(x+h) - v(x+h/2))
Solving this system, we arrive at the approximation at the interface:
.. math:: u(x+h/2) = \frac{D_m v(x+h)+D_p u(x)}{D_p+D_m / \gamma}
if u(x) is in a patch and v(x+h) is in the matrix, or
.. math:: v(x+h/2) = \frac{D_m v(x)+D_p u(x+h)}{D_p \gamma +D_m}
if v(x) is in the matrix and u(x+h) is in a patch.
Example
-------
>>> # simple patch/matrix
>>> from landscape import *
>>> parn = OrderedDict([
('r', [-0.03, 0.1]),
('K', [np.Inf, 1.0]),
('D', [0.001, 0.0001]),
('left', [1.0, 0.0, 0.0]),
('right', [1.0, 0.0, 0.0]),
('top', [1.0, 0.0, 0.0]),
('bottom', [1.0, 0.0, 0.0])
])
>>> l = np.zeros((100,100), dtype=int)
>>> l[40:60, 40:60] = 1
>>> sol = solve_landscape_ntypes(l, parn, dx)
"""
from scipy.optimize import newton_krylov
n = np.unique(landscape).astype(int)
p = par.copy()
if 'g' not in p.keys():
p['g'] = {}
if 'alpha' not in p.keys():
p['alpha'] = {}
for i, j in iproduct(n, repeat=2):
if i > j:
p['alpha'][(i, j)] = 0.5
for i, j in iproduct(n, repeat=2):
if i > j:
p['g'][(i,j)] = p['D'][j]/p['D'][i] * \
p['alpha'][(i,j)] / (1-p['alpha'][(i,j)])
# this ensures the consistency of the interface discontinuities
# it ignores the values of g_ij with i < j, replacing it by 1/g_ji
for i, j in iproduct(n, repeat=2):
if i < j:
p['g'][(i, j)] = 1 / p['g'][(j, i)]
(al, bl, cl) = p['left']
(ar, br, cr) = p['right']
(at, bt, ct) = p['top']
(ab, bb, cb) = p['bottom']
D = np.zeros_like(landscape, dtype=np.float_)
r = np.zeros_like(landscape, dtype=np.float_)
c = np.zeros_like(landscape, dtype=np.float_)
for i in n:
li = np.where(landscape == i)
D[li] = p['D'][i]
r[li] = p['r'][i]
c[li] = -p['r'][i] / p['K'][i]
Bx, By = find_interfaces_ntypes(landscape)
factor = {}
for i, j in iproduct(n, repeat=2):
if i != j:
factor[(i, j)] = (
# coefficient of term u(x) in u_xx(x)
-2. + 8. / 3 * p['D'][i] /
(p['D'][i] + p['D'][j] / p['g'][(i, j)]),
# coefficient of term u(x+h) in u_xx(x)
-1. + 8. / 3 * p['D'][j] /
(p['D'][i] + p['D'][j] / p['g'][(i, j)]))
shapewb = (landscape.shape[0] + 2, landscape.shape[1] + 2)
Bxleft = np.zeros(shapewb, dtype=np.float_)
Bxcenter = np.zeros(shapewb, dtype=np.float_)
Bxright = np.zeros(shapewb, dtype=np.float_)
Byleft = np.zeros(shapewb, dtype=np.float_)
Bycenter = np.zeros(shapewb, dtype=np.float_)
Byright = np.zeros(shapewb, dtype=np.float_)
for i, j in factor.keys():
## direction x
# patch type i
Bxcenter[:, 1:-1][shifted_index(Bx[i, j], 0, 1)] += factor[i, j][0]
Bxleft[:, 1:-1][shifted_index(Bx[i, j], 0, 0)] += 1. / 3
Bxright[:, 1:-1][shifted_index(Bx[i, j], 0, 2)] += factor[i, j][1]
# patch type j
Bxcenter[:, 1:-1][shifted_index(Bx[i, j], 0, 2)] += factor[j, i][0]
Bxleft[:, 1:-1][shifted_index(Bx[i, j], 0, 1)] += factor[j, i][1]
Bxright[:, 1:-1][shifted_index(Bx[i, j], 0, 3)] += 1. / 3
## direction y
# patch type i
Bycenter[1:-1, :][shifted_index(By[i, j], 1, 1)] += factor[i, j][0]
Byleft[1:-1, :][shifted_index(By[i, j], 1, 0)] += 1. / 3
Byright[1:-1, :][shifted_index(By[i, j], 1, 2)] += factor[i, j][1]
# patch type j
Bycenter[1:-1, :][shifted_index(By[i, j], 1, 2)] += factor[j, i][0]
Byleft[1:-1, :][shifted_index(By[i, j], 1, 1)] += factor[j, i][1]
Byright[1:-1, :][shifted_index(By[i, j], 1, 3)] += 1. / 3
def residual(P):
if force_positive:
P = np.abs(P)
P = np.pad(P, 1, 'constant')
# external boundaries
P[0, :] = (-cl - al / dx * P[0, :]) / (bl - al / dx)
P[-1, :] = (-cr + ar / dx * P[-1, :]) / (br + ar / dx)
P[:, 0] = (-cb - ab / dx * P[:, 0]) / (bb - ab / dx)
P[:, -1] = (-ct + at / dx * P[:, -1]) / (bt + at / dx)
d2x = np.zeros_like(P)
d2x[1:-1, :] = P[2:, :] - 2 * P[1:-1, :] + P[:-2, :]
# interface conditions
d2x[1:-1, :] += (Bxcenter[1:-1, :] * P[1:-1, :] +
Bxleft[:-2, :] * P[:-2, :] +
Bxright[2:, :] * P[2:, :])
d2y = np.zeros_like(P)
d2y[:, 1:-1] = P[:, 2:] - 2 * P[:, 1:-1] + P[:, :-2]
# interface conditions
d2y[:,
1:-1] += (Bycenter[:, 1:-1] * P[:, 1:-1] +
Byleft[:, :-2] * P[:, :-2] + Byright[:, 2:] * P[:, 2:])
return D*(d2x[1:-1,1:-1] + d2y[1:-1,1:-1])/dx/dx + r*P[1:-1,1:-1] \
+ c*P[1:-1,1:-1]**2
# solve
guess = r.copy()
guess[guess > 0] = 1 / ((-c / r)[guess > 0])
guess[guess <= 0] = 1e-6
if debug:
return guess, residual
sol = newton_krylov(residual, guess, method='lgmres', f_tol=f_tol)
if force_positive:
sol = np.abs(sol)
if verbose:
print('Residual: %e' % abs(residual(sol)).max())
print('max. pop.: %f' % sol.max())
print('min. pop.: %f' % sol.min())
return sol
def go(n):
# order to calculate up to
#n = 4
# dimension of the states base
d = n + 2
# number of time scales
T = 1 + n//2
z = S.Symbol('z', real=True) # perturbation \epsilon << 1
s = S.Symbol('s', real=True) # parameter \sigma ~ ord(1)
g = S.Symbol('g', real=True) # forcing oscilattion parameter
# time variables
ts = [ S.Symbol('t%i' % i, real=True) for i in range(T) ]
# coefficients array
# not including the ones we know are zero
c = N.array([S.Symbol("c_%i%i" % (i, j), complex=True) if j <= i+1 and j % 2 == (i+1) % 2 else S.sympify(0) for (i, j) in iproduct(range(n+1), range(d))]).reshape(n+1, d)
# the amplitude at order zero is a "free" parameter, depending on t1, t2 etc. (but *not* t0)
A = S.Function('A')(*ts[1:])
c[0][1] = A
# the solution ansatz
u = N.sum([ z**i * c[i,:] for i in range(n+1) ], axis = 0)
one = N.zeros_like(u)
one[0] = 1/2
cosine = N.zeros_like(u)
cosine[1] = 1/2
# finally the equation
E = N.vectorize(S.simplify)( D(u, ts, z, 1) + prod(delay_taylor(u, ts, z, param=s*z**2, order=n, tau=S.pi/2), one + z * u + g * z**2 * prod(u, cosine)) )
E = N.vectorize(lambda x: S.Poly(x, z))(E)
# cross your fingers
sols = {}
diffs = {}
M = S.sympify(0)
for o in range(1, n+1):
eq1 = N.vectorize(lambda x: x.coeff(o))(E)
eq = N.vectorize(S.simplify) (subs(subs(eq1, sols), diffs))
# keep firt position out
coeffs = [ c[o][i] for i in range(d) if c[o][i] ]
# as well as the equation for it
solution = apply(S.solvers.solve, [[eq[0]] + eq[2:].tolist()] + coeffs)
if solution:
sols.update(solution)
# zero frequency coefficients can be taken to be real
sols[c[o][0]] = S.simplify(sols[c[o][0]].as_real_imag()[0])
if o is not 0:
# homogeneous solution appears only in order zero
sols[c[o][1]] = S.sympify(0)
if o % 2 == 0:
ss = S.solve(E[1].subs(sols).coeff(o).subs(diffs), A.diff(ts[o//2]))
if ss:
diffs[A.diff(ts[o//2])] = ss[0]
M += z ** (o) * ss[0]
else:
print 'Solution not found at order %i.' % o
return { 'success': False, 'eq': eq }
x, y = S.symbols('xy', real=True)
rmsubs = {S.re(A): x, S.im(A): y}
Q = list((M.subs(diffs)/z**2).expand().as_real_imag())
Q[0] = S.collect(S.simplify(Q[0].subs(rmsubs)), z)
Q[1] = S.collect(S.simplify(Q[1].subs(rmsubs)), z)
return { 'success': True,
'M': M,
'Q': Q,
'E': E,
'diffs': diffs,
'sols': sols,
'ts': ts, 'c': c, 'A': A, 'z': z, 'g': g, 's': s, 'x': x, 'y': y
}
def test_meters_of_seawater(self):
dbars = [5e2, 1e3, 2e3, 3e3, 4e3, 5e3, 6e3, 7e3, 8e3, 9e3, 10e3]
lats = [0, 30, 45, 60, 90]
expected = [
496.65,
496.00,
495.34,
494.69,
494.03,
992.12,
990.81,
989.50,
988.19,
986.88,
1979.55,
1976.94,
1974.33,
1971.72,
1969.11,
2962.43,
2958.52,
2954.61,
2950.71,
2946.81,
3940.88,
3935.68,
3930.49,
3925.30,
3920.10,
4915.04,
4908.56,
4902.08,
4895.60,
4889.13,
5885.03,
5877.27,
5869.51,
5861.76,
5854.01,
6850.95,
6841.92,
6832.89,
6823.86,
6814.84,
7812.93,
7802.63,
7792.33,
7782.04,
7771.76,
8771.07,
8759.51,
8747.95,
8736.40,
8724.85,
9725.47,
9712.65,
9699.84,
9687.03,
9674.23,
]
for inputs, output in zip(iproduct(dbars, lats), expected):
kw = dict(dbar=inputs[0], latitude=inputs[1])
p = Pressure(**kw)
kw['expected_output'] = output
with self.subTest(**kw):
self.assertAlmostEqual(p.m_seawater, output, 2)
self.assertRaises(NotImplementedError, meters_of_seawater_to_dbar, 1,
0)
self.assertRaises(AttributeError, Pressure, **dict(m_seawater=100))
def _build(self, **kwargs):
"""Finds all the direct parents for the clusters in partitions. This is the first
step of weave(). Subclasses can override this function to achieve different results.
Parameters
----------
cutoff : keyword argument (0.5 ~ 1.0, default=0.8)
containment index cutoff for claiming parenthood.
Returns
-------
G : networkx.DiGraph
"""
cutoff = kwargs.pop('cutoff', 0.8)
assume_levels = self.assume_levels
terminals = self.terminals
n_nodes = self.n_terminals
L = self._assignment
labels = self._labels
levels = self._levels
n_sets = len(L)
rng = range(n_sets)
if assume_levels:
gen = ((i, j) for i, j in iproduct(rng, rng)
if levels[i] > levels[j])
else:
gen = ((i, j) for i, j in iproduct(rng, rng) if i != j)
# find all potential parents
LOGGER.timeit('_init')
LOGGER.info('initializing the graph...')
# calculate containment indices
CI = containment_indices_boolean(L, L)
G = nx.DiGraph()
for i, j in gen:
C = CI[i, j]
na = (i, 0)
nb = (j, 0)
if not G.has_node(na):
G.add_node(na, index=i, level=levels[i], label=labels[i])
if not G.has_node(nb):
G.add_node(nb, index=j, level=levels[j], label=labels[j])
if C >= cutoff:
if G.has_edge(na, nb):
C0 = G[na][nb]['weight']
if C > C0:
G.remove_edge(na, nb)
else:
continue
#if not nx.has_path(G, nb, na):
G.add_edge(nb, na, weight=C)
LOGGER.report('graph initialized in %.2fs', '_init')
# add a root node to the graph
roots = []
for node, indeg in G.in_degree():
if indeg == 0:
roots.append(node)
if len(roots) > 1:
root = (-1, 0) # (-1, 0) will be changed to (0, 0) later
G.add_node(root, index=-1, level=-1, label=True)
for node in roots:
G.add_edge(root, node, weight=1.)
else:
root = roots[0]
# remove grandparents (redundant edges)
LOGGER.timeit('_redundancy')
LOGGER.info('removing redudant edges...')
redundant = []
for node in G.nodes():
parents = [_ for _ in G.predecessors(node)]
ancestors = [_ for _ in nx.ancestors(G, node)]
for a in parents:
for b in ancestors:
if neq(a, b) and G.has_edge(a, b):
# a is a grandparent
redundant.append((a, node))
break
# rcl = getrecursionlimit()
# if rcl < RECURSION_MAX_DEPTH:
# setrecursionlimit(RECURSION_MAX_DEPTH)
# for u, v in G.edges():
# if n_simple_paths(G, u, v) > 1:
# redundant.append((u, v))
# setrecursionlimit(rcl)
#nx.write_edgelist(G, 'sample_granny_network.txt')
G.remove_edges_from(redundant)
LOGGER.report('redundant edges removed in %.2fs', '_redundancy')
# attach graph nodes to nodes in G
# for efficiency purposes, this is done after redundant edges are
# removed. So we need to make sure we don't introduce new redundancy
LOGGER.timeit('_attach')
LOGGER.info('attaching terminal nodes to the graph...')
X = np.arange(n_nodes)
nodes = [node for node in G.nodes]
attached_record = defaultdict(list)
for node in nodes:
n = node[0]
if n == -1:
continue
x = X[L[n]]
for i in x:
ter = denumpize(terminals[i])
attached = attached_record[ter]
skip = False
if attached:
for other in reversed(attached):
if nx.has_path(
G, node,
other): # other is a descendant of node, skip
skip = True
break
elif nx.has_path(
G, other, node
): # node is a descendant of other, remove other
attached.remove(other)
G.remove_edge(other, ter)
if not skip:
G.add_edge(node, ter, weight=1.)
attached.append(node)
LOGGER.report('terminal nodes attached in %.2fs', '_attach')
self._full = G
# find secondary edges
def node_size(node):
if istuple(node):
i = node[0]
return np.count_nonzero(L[i])
else:
return 1
LOGGER.timeit('_sec')
LOGGER.info('finding secondary edges...')
secondary_edges = []
secondary_terminal_edges = []
for node in G.nodes():
parents = [_ for _ in G.predecessors(node)]
if len(parents) > 1:
nsize = node_size(node)
if istuple(node):
pref = []
for p in parents:
w = G.edges()[p, node]['weight']
psize = node_size(p)
usize = w * nsize
j = usize / (nsize + psize - usize)
pref.append(j)
# weight (CI) * node_size gives the size of the union between the node and the parent
ranked_edges = [((x[0], node), x[1]) for x in sorted(
zip(parents, pref), key=lambda x: x[1], reverse=True)]
secondary_edges.extend(ranked_edges[1:])
else:
edges = []
for p in parents:
#psize = node_size(p)
n_steps = nx.shortest_path_length(G, root, p)
edges.append(((p, node), n_steps))
edges = sorted(edges, key=lambda x: x[1], reverse=True)
secondary_terminal_edges.extend(edges[1:])
secondary_edges.sort(key=lambda x: x[1], reverse=True)
secondary_terminal_edges.sort(key=lambda x: x[1], reverse=True)
self._secondary_edges = secondary_edges
self._secondary_terminal_edges = secondary_terminal_edges
LOGGER.report('secondary edges found in %.2fs', '_sec')
return G
def _build(self, **kwargs):
"""Finds all the direct parents for the clusters in partitions. This is the first
step of weave(). Subclasses can override this function to achieve different results.
Parameters
----------
cutoff : keyword argument (0.5 ~ 1.0, default=0.75)
containment index cutoff for claiming parenthood.
merge : bool
Returns
-------
G : networkx.DiGraph
"""
cutoff = kwargs.pop('cutoff', 0.75)
merge = kwargs.pop('merge', False)
assume_levels = self.assume_levels
terminals = self.terminals
n_nodes = self.n_terminals
L = self._assignment
labels = self._labels
levels = self._levels
n_sets = len(L)
rng = range(n_sets)
if assume_levels:
gen = ((i, j) for i, j in iproduct(rng, rng)
if levels[i] > levels[j])
else:
gen = ((i, j) for i, j in iproduct(rng, rng) if i != j)
# find all potential parents
LOGGER.timeit('_init')
LOGGER.info('initializing the graph...')
# calculate containment indices
CI = containment_indices_boolean(L, L)
G = nx.DiGraph()
for i, j in gen:
C = CI[i, j]
na = (i, 0)
nb = (j, 0)
if not G.has_node(na):
G.add_node(na, index=i, level=levels[i], label=labels[i])
if not G.has_node(nb):
G.add_node(nb, index=j, level=levels[j], label=labels[j])
if C >= cutoff:
if not merge:
if G.has_edge(na, nb):
C0 = G[na][nb]['weight']
if C > C0:
G.remove_edge(na, nb)
else:
continue
G.add_edge(nb, na, weight=C)
LOGGER.report('graph initialized in %.2fs', '_init')
# remove loops
if merge:
def _collapse_nodes(G, vs):
all_in_nodes, all_out_nodes = [], []
vs = list(vs)
vs = sorted(vs, key=lambda x: G.nodes[x]['index'])
# add merge record
new_index = []
for v in vs:
new_index.append(G.nodes[v]['index'])
all_in_nodes.extend([w for w in G.predecessors(v)])
all_out_nodes.extend([w for w in G.successors(v)])
all_in_nodes = list(set(all_in_nodes).difference(vs))
all_out_nodes = list(set(all_out_nodes).difference(vs))
dict_in_weights = {u: 0 for u in all_in_nodes}
dict_out_weights = {u: 0 for u in all_out_nodes}
for v in vs:
for w in G.predecessors(v):
if not w in all_in_nodes:
continue
if G[w][v]['weight'] > dict_in_weights[w]:
dict_in_weights[w] = G[w][v]['weight']
for v in vs:
for w in G.successors(v):
if not w in all_out_nodes:
continue
if G[v][w]['weight'] > dict_out_weights[w]:
dict_out_weights[w] = G[v][w]['weight']
G.remove_nodes_from(vs[1:])
G.nodes[vs[0]]['index'] = tuple(
new_index) # TODO: why does this has to be a tuple?
for u in all_in_nodes:
if not G.has_predecessor(vs[0], u):
G.add_edge(u, vs[0], weight=dict_in_weights[u])
for u in all_out_nodes:
if not G.has_successor(vs[0], u):
G.add_edge(vs[0], u, weight=dict_out_weights[u])
return G
LOGGER.timeit('_cluster_redundancy')
LOGGER.info(
'"merge" parameter set to true, so merging redundant clusters...'
)
try:
cycles = list(nx.simple_cycles(G))
# LOGGER.info('Merge {} redundant groups ...'.format(len(cycles)))
except:
LOGGER.info('No redundant groups has been found ...')
cycles = []
if len(cycles) > 0:
Gcyc = nx.Graph()
for i in range(len(cycles)):
for v, w in itertools.combinations(cycles[i], 2):
Gcyc.add_edge(v, w)
components = list(nx.connected_components(Gcyc))
LOGGER.info('Merge {} redundant groups ...'.format(
len(components)))
for vs in components:
G = _collapse_nodes(
G,
vs,
)
LOGGER.report('redundant nodes removed in %.2fs',
'_cluster_redundancy')
# add a root node to the graph
roots = []
for node, indeg in G.in_degree():
if indeg == 0:
roots.append(node)
# TODO: right now needs a cluster full of 1, otherwise report an error; figure out why and fix it
if len(roots) > 1:
root = (-1, 0) # (-1, 0) will be changed to (0, 0) later
G.add_node(root, index=-1, level=-1, label=True)
for node in roots:
G.add_edge(root, node, weight=1.)
else:
root = roots[0]
# remove grandparents (redundant edges)
LOGGER.timeit('_redundancy')
LOGGER.info('removing redudant edges...')
redundant = []
for node in G.nodes():
parents = [_ for _ in G.predecessors(node)]
ancestors = [_ for _ in nx.ancestors(G, node)]
for a in parents:
for b in ancestors:
if neq(a, b) and G.has_edge(a, b):
# a is a grandparent
redundant.append((a, node))
break
G.remove_edges_from(redundant)
LOGGER.report('redundant edges removed in %.2fs', '_redundancy')
# attach graph nodes to nodes in G (this part can be skipped)
LOGGER.timeit('_attach')
LOGGER.info('attaching terminal nodes to the graph...')
X = np.arange(n_nodes)
nodes = [node for node in G.nodes]
attached_record = defaultdict(list)
for node in nodes:
n = node[0]
if n == -1:
continue
x = X[L[n]]
for i in x:
ter = denumpize(terminals[i])
attached = attached_record[ter]
skip = False
if attached:
for other in reversed(attached):
if nx.has_path(
G, node,
other): # other is a descendant of node, skip
skip = True
break
elif nx.has_path(
G, other, node
): # node is a descendant of other, remove other
attached.remove(other)
G.remove_edge(other, ter)
if not skip:
G.add_edge(node, ter, weight=1.)
attached.append(node)
LOGGER.report('terminal nodes attached in %.2fs', '_attach')
# update node assignments
LOGGER.timeit('_update')
LOGGER.info(
'propagate terminal node assignments upward in the hierarchy'
) # TODO: this can be iterated until there's no change
L_sp = sp.sparse.csr_matrix(L.T)
## construct a community connectivity matrix
row, col = [], []
for v in nodes:
row.append(v[0])
col.append(v[0])
for v, w in itertools.combinations(nodes, 2):
if nx.has_path(G, v, w): # w is a descendant of v
row.append(w[0])
col.append(v[0])
data = np.ones_like(row, dtype=int)
cc_mat = sp.sparse.coo_matrix((data, (row, col)),
shape=(L.shape[0], L.shape[0]))
cc_mat = cc_mat.tocsr()
L_sp_new = L_sp.dot(cc_mat) > 0
self._assignment = L_sp_new.toarray().T
LOGGER.report('terminal nodes propagated in %.2fs', '_update')
in_degrees = np.array([deg for (_, deg) in G.in_degree()])
if np.where(in_degrees == 0)[0] > 1:
G.add_node('root') # add root
# print('root added')
for node in G.nodes():
if G.in_degree(node) == 0:
G.add_edge('root', node)
self._full = G
# find secondary edges
def node_size(node):
if istuple(node):
i = node[0]
return np.count_nonzero(L[i])
else:
return 1
LOGGER.timeit('_sec')
LOGGER.info('finding secondary edges...')
secondary = []
for node in G.nodes():
parents = [_ for _ in G.predecessors(node)]
if len(parents) > 1:
nsize = node_size(node)
pref = []
for p in parents:
w = G.edges()[p, node]['weight']
psize = node_size(p)
usize = w * nsize
j = usize / (nsize + psize - usize)
pref.append(j)
# weight (CI) * node_size gives the size of the union between the node and the parent
ranked_edges = [((x[0], node), x[1]) for x in sorted(
zip(parents, pref), key=lambda x: x[1], reverse=True)]
secondary.extend(ranked_edges[1:])
secondary.sort(key=lambda x: x[1], reverse=True)
self._secondary = secondary
LOGGER.report('secondary edges found in %.2fs', '_sec')
return G
def __init__(self, voxmap, s):
'''
Initialize a PiecewiseSlowness instance. The map voxmap should
map keys to 3-D array of shape (L, M, N) such that, if
keys = sorted(voxmap.keys()),
a slowness image for a perturbation x is given by
slowness = s + sum(voxmap[keys[i]] * x[i]
for i in range(len(x))).
A special class of keys, starting with 'unconstrained', will
behave differently. Each nonzero voxel in the image at
voxmap['unconstrained'] will effectively get its own key,
allowing each nonzero pixel in the 'unconstrained'
voxmap to take a distinct value.
Additional 'unconstrained' keys are allowed to take the form
'unconstrained_<d>x', where '<d>' is an arbitrary base-10
integer. Each nonzero voxel in I = voxmap['unconstrained_Dx']
for an integer D represents a unique value corresponding to a
cluster of DxDxD ordinary voxels; i.e., each voxel (i,j,k) in I
corresponds to an effective map M_ijk with
M_ijk[D*i:D*(i+1),D*j:D*(j+1),D*k:D*(k+1)] = I[i,j,k]
and M_ijk = 0 everywhere else.
The 'unconstrained' class of keys is case sensitive.
'''
# Build a sparse matrix representation from the voxmap
self._shape = None
data, rows, cols = [], [], []
M, N = 0, 0
# Match unconstrained keys with optional scales
unre = re.compile('^unconstrained(_([0-9]+)x)?')
# Note that voxmap may not be a proper dictionary (e.g., NpzFile)
for key in sorted(voxmap.keys()):
# Check if the key is a scaled or unconstrained key
m = unre.match(key)
if m: scale = int(m.groups(1)[1])
else: scale = 1
v = np.asarray(voxmap[key]).astype(np.float64)
if v.ndim != 3:
raise ValueError('All voxmaps must have three dimensions')
# Scale the shape of the grid if appropriate
shape = v.shape
if scale != 1: shape = tuple(scale * sv for sv in shape)
if not self._shape:
self._shape = shape
M = np.product(self._shape)
elif self._shape != shape:
raise ValueError('All voxmap shapes must be compatible')
if not m or scale == 1:
# Process constrained or scale-1 unconstrained maps
v = v.ravel('C')
ri = np.nonzero(v)[0]
data.extend(v[ri])
rows.extend(ri)
if not m:
# Constrained voxels share a column
cols.extend(N for sv in range(len(ri)))
N += 1
else:
# Unconstrained voxels get their own columns
cols.extend(range(N, N + len(ri)))
N += len(ri)
continue
# List of neighbor offsets for scaled voxels
nbrs = list(iproduct(*(range(scale) for sv in range(v.ndim))))
# Process each scaled voxel as a separate column
for i, j, k in np.transpose(np.nonzero(v)):
# Explode each voxel in a scaled unconstrained image
# np.ravel_multi_index requires the transposed form
vxi = np.transpose(
[[scale * i + ii, scale * j + jj, scale * k + kk]
for ii, jj, kk in nbrs])
# Map the exploded voxels to C-raveled indices
ri = np.ravel_multi_index(vxi, shape, order='C')
# Build the next block of the matrix
# All voxels in the block get the same weight
rows.extend(ri)
cols.extend(N for sv in range(len(ri)))
data.extend(v[i, j, k] for sv in range(len(ri)))
N += 1
# Confirm that the background has the right form
self._s = np.array(s, dtype=np.float64)
if self._s.shape and self._s.shape != self._shape:
raise ValueError(
'Background slowness s must be scalar or match voxmap shapes')
# Convert the representation to CSR for efficiency
self._voxmap = coo_matrix((data, (rows, cols)), shape=(M, N)).tocsr()
def solve_landscape_ntypes_nspecies(landscape,
par,
dx,
f_tol=None,
force_positive=False,
skip_refine=False,
return_residual=False,
verbose=True):
'''Find the stationary solution for a given landscape and set of parameters.
Uses a Newton-Krylov solver with LGMRES sparse inverse method to find a
stationary solution (or the solution to the elliptical problem) to the
system of 2n equations in 2 dimensions (x is a 2-d vector):
.. math::
\\frac{\partial u_{ik}}{\partial t} &= D_k \\nabla^2 u_{ik} + r_{ik} u_{ik} (1-\sum_{j=1}^n \\alpha_j u_{jk}) = 0
where i runs over the n species and k over the patch types.
Parameters
----------
landscape : 2-d array of ints
describe the landscape, with any number of habitat types
par : list
the first element is the matrix (or dict with tuple keys) of
competition coefficients, including the inverse of carrying capacities,
and the following elements are dicts with parameters as in the
`solve_landscape_ntypes()` function, except for the carrying capacity.
dx : float
length of each edge
f_tol : float
tolerance for the residue, passed on to the solver routine. Default is
6e-6
force_positive : bool
make sure the solution is always non-negative - in a hacky way. Default
False
skip_refine : bool
do not refine the grid to calculate the residual. This can greatly
improve speed, but will generate errors (even silent wrong results) if
the landscape has contiguous interfaces
return_residual : bool
returns only the residual function, without calculating the solution
verbose : bool
print residue of the solution and its maximum and minimum values
Returns
-------
solution : 2-d array of the same shape of the landscape input containing
the solution
Boundary and interface conditions
---------------------------------
External boundaries are of the form
.. math::
a \\nabla u \cdot \hat{n} + b u + c = 0
and may be different for left, right, top, bottom. The derivative of u is
taken along the normal to the boundary.
The interfaces between patches and matrix are given by
.. math::
u(x) &= \gamma v(x) \\\\
D_p \\nabla u(x) \cdot \hat{n} &= D_m \\nabla v(x) \cdot \hat{n}
where u is a patch and v is the solution in the matrix.
Example
-------
>>> from landscape import *
>>> lA = loadtxt('landA.txt')
>>> par = [
[
[[0, 0],
[0.1, 0.1]],
[[0.1, 0],
[0.1, 0.1]]
],
{'r': [-0.03, 0.1],
'D': [0.001, 0.0001],
'left': [1.0, 0.0, 0.0],
'right': [1.0, 0.0, 0.0],
'top': [1.0, 0.0, 0.0],
'bottom': [1.0, 0.0, 0.0]},
{'r': [0.05, 0.05],
'D': [0.001, 0.001],
'left': [1.0, 0.0, 0.0],
'right': [1.0, 0.0, 0.0],
'top': [1.0, 0.0, 0.0],
'bottom': [1.0, 0.0, 0.0]}
]
>>> sol = solve_landscape_ntypes_nspecies(lA, par, dx)
'''
from scipy.optimize import newton_krylov
if not skip_refine:
# refine the grid to avoid contiguous interfaces
landscape = refine_grid(landscape)
dx /= 2
N = len(par) - 1
n = np.unique(landscape).astype(int)
resi = [
solve_landscape_ntypes(landscape,
dict(p, K=np.Inf * np.ones(len(n))),
dx,
skip_refine=True,
return_residual=True) for p in par[1:]
]
sec_term = np.zeros((N, N, landscape.shape[0], landscape.shape[1]))
for i, j in iproduct(range(N), range(N)):
for k in n:
lk = np.where(landscape == k)
sec_term[i, j][lk] = par[0][k][i][j]
def residual(P):
if force_positive:
P = np.abs(P)
res = np.zeros_like(P)
# loops are for lazy people
for i, Pi in enumerate(P):
res[i, :, :] = resi[i](Pi) - Pi * (sec_term[i, :, :] *
P).sum(axis=0)
return res
if return_residual:
return residual
# build guess based on where growth is positive
guess = np.zeros((N, landscape.shape[0], landscape.shape[1]))
for i in range(N):
for k in n:
lk = np.where(landscape == k)
rik = par[i + 1]['r'][k]
if rik <= 0:
guess[i, :, :][lk] = 1e-6
else:
guess[i, :, :][lk] = rik / par[0][k][i][i]
# solve
sol = newton_krylov(residual, guess, method='lgmres', f_tol=f_tol)
if force_positive:
sol = np.abs(sol)
if verbose:
print('Residuals:',
*['%e' % i for i in np.abs(residual(sol)).max(axis=(1, 2))])
print('max. pops.:', *['%f' % i for i in sol.max(axis=(1, 2))])
print('min. pops.:', *['%f' % i for i in sol.min(axis=(1, 2))])
if not skip_refine:
sol = coarse_grid(sol)
return sol
def main():
print('case', 'condition', 'temperature')
for i, data in enumerate(
iproduct(range(1, 4), map(lambda x: 0.5 * x, range(-1, 2)))):
print(i + 1, *data)
return 0
def main(argv):
try:
opts, args = getopt.getopt(argv, "f:i:r:s:otv", [
"field=", "species=", "infile=", "radius=", "output_csv", "total",
"ion_velocity"
])
except getopt.GetoptError:
print(getopt.GetoptError)
print('error')
return
out_csv, total, ion_velocity = False, False, False
for opt, arg in opts:
if opt in ("-f", "--field"):
if arg == "all":
fields_suffix = ['flux', 'number_density']
elif arg == 'mag':
fields_suffix = [
'magnetic_field_normal', 'magnetic_field_total',
'magnetic_field_x', 'magnetic_field_y', 'magnetic_field_z'
]
else:
fields_suffix = [arg]
elif opt in ("-s", "--species"):
if arg == 'all': ions = ['O2_p1_', 'O_p1_'] #'CO2_p1',
elif arg == 'None': ions = ['']
else: ions = [arg + "_"]
elif opt in ("-i", "--infile"):
dsk = arg.split('/')[-1].split('.')[0]
ds_names = {dsk: arg}
if 'batsrus' in dsk: ds_types = {'batsrus': [dsk]}
else: ds_types = {'rhybrid': [dsk]}
elif opt in ("-r", "--radius"):
if arg == 'all': radii = np.arange(1.0, 3.0, 0.2)
else: radii = ast.literal_eval(arg)
if type(radii) == float: radii = [radii]
elif opt in ("-o", "-output_csv"):
out_csv = True
elif opt in ("-t", "-total"):
total = True
elif opt in ("-v", "-ion_velocity"):
ion_velocity = True
fields = [ion + suff for ion, suff in iproduct(ions, fields_suffix)]
if total: fields.append('total_flux')
if out_csv: df = pd.DataFrame(columns=ions, index=radii)
for ds_type in ds_names.keys():
for r in radii:
field_dat = run_sphere_flux(ds_names,
ds_types,
r,
fields,
ion_velocity=ion_velocity)
if out_csv:
for ion in ions:
total_ions = np.sum(np.nan_to_num(field_dat['area']*\
field_dat[ion+'flux'][ds_type]))
df.loc[r, ion] = total_ions
if out_csv: df.to_csv('Output/sphere_flux_{0}.csv'.format(ds_type))
def group_cavity_solve(
S=(100, 100),
mu=1,
sigma=.0,
gamma=0,
mean_k=1.,
sigma_k=0,
sigma_d=0,
tau=1,
x0=None,
NTRIALS=3,
EPS=10**-15,
logmode=0,
ftol=0.003,
SIGMA_THRESH=0.01, #Threshold for recursing
varmode=1,
sigrow=None,
**kwargs):
USE_RECURS = kwargs.get('USE_RECURS', 1)
USE_ROOT_HELPER = kwargs.get('USE_ROOT_HELPER', 1)
#tau = ratio of typical timescales (e.g. for metabolic)
levels = len(S)
S, mean_k, sigma_k = [
np.array(x).astype('float')
if np.array(x).shape else np.array([float(x) for nb in range(levels)])
for x in S, mean_k, sigma_k
]
s = S / np.mean(S)
#Making matrices
if len(mu.shape) < 2:
MU = (np.ones((levels, levels)) * mu).T
else:
MU = mu
if len(sigma.shape) < 2:
SIGMA2 = (np.ones((levels, levels)) * sigma**2).T
else:
SIGMA2 = sigma**2
if len(gamma.shape) < 2:
GAMMA = (np.ones((levels, levels)) * gamma).T
else:
GAMMA = gamma #sigma**2
if not sigrow is None:
SIGROW2 = sigrow**2
else:
SIGROW2 = 0
if 0 and (MU < 0).any():
test = -(s * MU.T)
import numpy.linalg as la
if np.max(np.abs(la.eigvals(test))) > 1:
return np.zeros((4, levels)) + EPS
CALC_INTEGRAL = kwargs.get('CALC_INTEGRAL', 0)
traceback = []
def eqs(vec, calc=CALC_INTEGRAL, logmode=logmode):
if logmode:
logvec = vec
vec = np.exp(np.clip(vec, None, 30))
N1, N2, V, Phi = vec.reshape((4, levels))
if varmode:
N2 = N2 * N1**2
if logmode:
# Phi=np.clip(Phi,0,1)
pass
else:
zerocond = np.min(
np.concatenate([N1.ravel(),
Phi.ravel(),
N2.ravel()
])) # Things that should be positive!
if 0:
traceback.append(vec)
#N2=np.clip(N2,0,None)
#N1=np.clip(N1,0,None)
#Phi=np.clip(Phi,0,None)
mean0, var0, Veq = group_cavity_calc(S,
MU,
SIGMA2,
GAMMA,
mean_k,
sigma_k,
sigma_d,
N1,
N2,
V,
Phi,
tau,
SIGROW2=SIGROW2)
#print N1,mean0,var0,erfmom(1,mean0,var0)
eq4 = 1 - Veq
if calc:
raise Exception(
"TODO: explicit calculation in group_cavity_solve not done yet"
)
else:
#Equivalent with directly computed moments of erf
if logmode:
flor = EPS
else:
flor = 0
roof = np.max(np.sqrt(mean_k**2 + sigma_k**2)) * 10**7
theophi = np.clip(erfmom(0, mean0, var0), flor, 1)
theoN1 = np.clip(erfmom(1, mean0, var0), flor, roof)
theoN2 = np.clip(erfmom(2, mean0, var0), flor, roof**2)
#ref[theophi<10**-5]=0
def refscale(x):
if 0:
return 1
else:
return np.mean(x)
if not logmode:
#Putting all the equations on the same scale, while regularizing zero denominators
# tmp=refscale(Phi)
# eq1=1 -(Phi+tmp)/(theophi+tmp)
eq1 = Phi - theophi
phi = np.clip(theophi, 0.001, None)
tmp = refscale(theoN1)
# eq2=1-(np.abs(Phi)*N1 +tmp)/(theoN1+tmp)
eq2 = (phi * N1 - theoN1) / tmp
tmp = refscale(theoN2)
# eq3=1-(np.abs(Phi)*N2 +tmp)/(theoN2+tmp)
eq3 = (phi * N2 - theoN2) / tmp
else:
if 0:
eq1 = (Phi - theophi) / max(theophi)
eq2 = (Phi * N1 - theoN1) / max(theoN1)
eq3 = (Phi * N2 - theoN2) / max(theoN2)
else:
logN1, logN2, logV, logPhi = logvec.reshape((4, levels))
tmp = refscale(theophi)
eq1 = 1 - (Phi + tmp) / (theophi + tmp)
tmp = refscale(np.log(theoN1))
eq2 = 1 - (logN1 + tmp) / (np.log(theoN1) -
np.log(theophi) + tmp)
tmp = refscale(np.log(theoN2))
eq3 = 1 - (logN2 + tmp) / (np.log(theoN2) -
np.log(theophi) + tmp)
res = np.concatenate((eq2, eq3, eq4, eq1))
# if logmode:
# res*=max(1,1+np.max(vec)/20.)
return res
#root=sopt.newton_krylov
#root=sopt.anderson
tries = 0
class Tmp():
success = False
fun = 1000
res = Tmp()
trials_left = kwargs.pop('trials_left', NTRIALS)
recurs_depth = kwargs.pop('recurs_depth', 0)
X0 = None
XMF = None
while not res.success and np.max(np.abs(
res.fun)) > ftol and trials_left - tries > 0:
newx0 = 0
if (recurs_depth > 5
or tries > 1) and np.max(sigma) > SIGMA_THRESH and USE_RECURS:
kw = {}
kw.update(kwargs)
#print 'SIGMA', sigma
#print kwargs.get('trials_left')
factor = max(1.03, np.exp(np.log(np.max(sigma) / 0.01) / 10.))
print '====> RECURSE FROM', np.max(
sigma**
2), 'TRIES LEFT', trials_left - tries, 'DEPTH', recurs_depth
x0 = np.concatenate(
group_cavity_solve(S=S,
mu=mu,
sigma=sigma / factor,
mean_k=mean_k,
gamma=gamma,
sigma_k=sigma_k,
sigma_d=sigma_d,
x0=None,
logmode=False,
NTRIALS=2,
recurs_depth=recurs_depth + 1,
**kwargs)[:4])
tries = trials_left
newx0 = 1
elif x0 is None:
#Starting from Mean Field solution
XMF = np.ones((4, levels))
Phi = erfmom(0, mean_k, sigma_k**2)
Phi[Phi == 0] = 1
if not kwargs.get('N0', None) is None:
print 'INITIALIZING WITH EMPIRICAL Ns'
XMF[0], XMF[3] = group_meanfield(s,
MU,
mean_k,
sigma_k=sigma_k,
Ninit=kwargs.get('N0', None))
if ((XMF[0], XMF[3]) <= 10**-14 + np.zeros((2, levels))).all():
print "ZEROS FROM MEANFIELD"
return np.zeros((4, levels)) + EPS
XMF[1] = XMF[0]**2
XMF[2] = 1
#XMF[3]=np.clip(Phi,0.01,1)
mean0, var0, Veq = group_cavity_calc(S,
MU,
SIGMA2,
GAMMA,
mean_k,
sigma_k,
sigma_d,
XMF[0],
XMF[1],
XMF[2],
Phi,
tau,
SIGROW2=SIGROW2)
XMF[3] = np.clip(np.minimum(XMF[3], erfmom(0, mean0, var0)), 0.01,
1)
x0 = XMF
x0 = x0.ravel()
newx0 = 1
if varmode and newx0:
x0[levels:2 * levels] = np.clip(
x0[levels:2 * levels] / x0[:levels]**2, 0, 100)
x0[levels:2 * levels][x0[:levels] == 0] = 1
if logmode:
X0 = np.log(x0 + EPS)
else:
X0 = x0
funinit = np.abs(eqs(X0))
if np.max(np.abs(funinit)) < ftol / 10:
res.x = x0
res.success = True
res.fun = funinit
if XMF is None:
print " x0:", np.sum(funinit), "maxerr", np.max(funinit)
root = sopt.root
if logmode:
bounds = None
else:
bounds = [(0, None)
for i in range(3 * levels)] + [(0, 1)
for i in range(levels)]
methods = ['hybr']
if np.max(sigma) < SIGMA_THRESH:
#Last chance, no recursion, so better try methods
if logmode:
methods = ['Krylov', 'df-sane', 'hybr']
else:
methods = [
'hybr', 'Krylov', 'df-sane'
] #df-sane never seems to work better than hybr; Krylov rarely (but very slow)
if (tries > 0 or recurs_depth > 0) and USE_ROOT_HELPER:
print ' Using root helper'
X1 = root_helper(eqs, X0, bounds=bounds, tol=ftol)
import numpy.linalg as la
nm = la.norm(X1 - X0)
mx = np.argmax(np.abs(X1 - X0))
print ' Root helper pushed', nm, [
'{}_{}'.format(i, j) for i, j in iproduct(
['N1', 'N2', 'V', 'Phi'], [str(z) for z in range(levels)])
][mx], X0[mx], '->', X1[mx]
X0 = X1
while not res.success and methods:
method = methods.pop(0)
try:
res = root(eqs, X0, method=method, tol=ftol)
except Exception as e:
print e
if not res.success:
print ' Root finding failure:', method
# if not methods and not logmode:
# methods=['Krylov']
# logmode=1
tries += 1
print MU, SIGMA2, GAMMA, SIGROW2
if not res.success:
code_debugger()
result = np.clip(res.x, EPS, None)
if logmode:
result = np.exp(np.clip(result, np.log(EPS), 42))
#print eqs(XMF.ravel()),res.fun
success = 1
error = np.max(np.abs(res.fun))
if res.success and error > ftol:
res.success = False
print ' WARNING: groups.py claims success but error={}>ftol, REJECTED!'.format(
error)
if not res.success and error > ftol:
success = 0
DEBUG = kwargs.get('DEBUG', False)
if DEBUG:
print '\nERROR: {}'.format(
res.message
) #,list(kwargs.get('best_fun',res.fun).reshape((4,levels))) )
x0error = eqs(X0)
x0better = (np.abs(res.fun) > np.abs(x0error))
labels = [
'{}_{}'.format(i, j) for i, j in iproduct(
['N1', 'N2', 'V', 'Phi'], [str(z) for z in range(levels)])
]
ERRORS = [
'{}: {} ({}) -- prev {} ({})'.format(*i)
for i in zip(labels, result, res.fun, x0, x0error)
if np.abs(i[2]) > ftol
]
nberr = 15
print ERRORS[:nberr],
if len(ERRORS) > nberr:
print 'and {} others'.format(len(ERRORS) - nberr)
else:
print ''
print 'RECURSION DEPTH', recurs_depth, 'NTRIALS', trials_left, "SIGMA2", np.max(
sigma**2)
result[x0better] = x0[x0better]
error = min(error, np.max(np.abs(x0error)))
handled = not DEBUG
while not handled:
N1, N2, V, Phi = result.reshape((4, levels))
if varmode:
N2 = N2 * N1**2
handled = 1
# code_debugger()
else:
if tries > 1:
print ' Root finding: finally, success'
#mean0,var0,Veq=group_cavity_calc(s,MU,SIGMA2,GAMMA,mean_k,sigma_k,
#sigma_d,XMF[0],XMF[1],XMF[2],XMF[3],tau)
#print mean0
#print np.sqrt(var0)
#print np.clip(erfmom(0,mean0,var0),0,1)
#print Veq
#Veff=np.dot(np.sqrt(SIGMA2*SIGMA2.T),s*Phi*V)
#print 1-Veff
#else:
#print res.fun
N1, N2, V, Phi = result.reshape((4, levels))
N1[Phi < EPS] = EPS
N2[Phi < EPS] = EPS
if varmode:
N2 = N2 * N1**2
return N1, N2, V, Phi, success / error
