def __init__(self,
X,
ntrees,
sample_size,
limit=None,
ExtensionLevel=0,
seed=None,
n_jobs=1):
""" iForest(X, ntrees, sample_size, limit=None, ExtensionLevel=0)
Initialize a forest by passing in training data, number of trees to be
used and the subsample size.
Parameters
----------
X : list of list of floats
Training data. List of [x1,x2,...,xn] coordinate points.
ntrees : int
Number of trees to be used.
sample_size : int
The size of the subsample to be used in creation of each tree.
Must be smaller than |X|.
limit : int
The maximum allowed tree depth. This is by default set to average
length of unsucessful search in a binary tree.
ExtensionLevel : int
Specifies degree of freedom in choosing the hyperplanes for
dividing up data. Must be smaller than the dimension n of the
dataset.
"""
self.ntrees = ntrees
self.X = X
self.nobjs = len(X)
self.sample = sample_size
self.limit = limit
self.exlevel = ExtensionLevel
# Extension Level check. See def for explanation.
self._checkExtensionLevel()
if limit is None:
# Set limit to the default as specified by the paper (average depth
# of unsuccesful search through a binary tree).
self.limit = int(_np.ceil(_np.log2(self.sample)))
self.c = c_factor(self.sample)
# This loop builds an ensemble of iTrees (the forest).
sp = _split_n(ntrees, _effective_n_jobs(n_jobs))
_rn.seed(seed)
_np.random.seed(seed)
tr = _Parallel(backend='multiprocessing',
n_jobs=n_jobs)(_delayed(_create_tree)(
X, sp[i], self.sample, self.limit, self.exlevel)
for i in range(len(sp)))
self.Trees = [j for i in tr for j in i]
def compute_paths(self, X_in=None, n_jobs=1):
"""
compute_paths(X_in = None)
Compute anomaly scores for all data points in a dataset X_in
Parameters ---------- X_in : list of list of floats Data to be scored.
iForest.Trees are used for computing the depth reached in each tree by
each data point.
Returns
-------
float
Anomaly score for a given data point.
"""
if X_in is None:
X_in = self.X
sp = _np.array_split(X_in, _effective_n_jobs(n_jobs))
S = _Parallel(backend='multiprocessing', n_jobs=n_jobs)(
_delayed(_get_anom_score)(sp[i], self.ntrees, self.c, self.Trees)
for i in range(len(sp)))
return _np.array([j for i in S for j in i])
def expm(self,
psi_0,
H_time_eval=0.0,
iterate=False,
n_jobs=1,
block_diag=False,
a=-1j,
start=None,
stop=None,
endpoint=None,
num=None,
shift=None):
"""Creates symmetry blocks of the Hamiltonian and then uses them to run `_expm_multiply()` in parallel.
**Arguments NOT described below can be found in the documentation for the `exp_op` class.**
Examples
--------
The example below builds on the code snippet shown in the description of the `block_ops` class.
.. literalinclude:: ../../doc_examples/block_ops-example.py
:linenos:
:language: python
:lines: 60-67
Parameters
-----------
psi_0 : numpy.ndarray, list, tuple
Quantum state which defined on the full Hilbert space of the problem.
Does not need to obey and sort of symmetry.
t0 : float
Inistial time to start the evolution at.
H_time_eval : numpy.ndarray, list
Times to evaluate the Hamiltonians at when doing the matrix exponentiation.
iterate : bool, optional
Flag to return generator when set to `True`. Otherwise the output is an array of states.
Default is 'False'.
n_jobs : int, optional
Number of processes requested for the computation time evolution dynamics.
NOTE: one of those processes is used to gather results. For best performance, all blocks
should be approximately the same size and `n_jobs-1` must be a common devisor of the number of
blocks, such that there is roughly an equal workload for each process. Otherwise the computation
will be as slow as the slowest process.
block_diag : bool, optional
When set to `True`, this flag puts the Hamiltonian matrices for the separate symemtri blocks
into a list and then loops over it to do time evolution. When set to `False`, it puts all
blocks in a single giant sparse block diagonal matrix. Default is `False`.
This flag is useful if there are a lot of smaller-sized blocks.
Returns
--------
obj
if `iterate = True`, returns generator which generates the time dependent state in the
full H-space basis.
if `iterate = False`, returns `numpy.ndarray` which has the time-dependent states in the
full H-space basis in the rows.
Raises
------
ValueError
Various `ValueError`s of `exp_op` class.
RuntimeError
Terminates when initial state has no projection onto the specified symmetry blocks.
"""
from ..operators import hamiltonian
if iterate:
if start is None and stop is None:
raise ValueError(
"'iterate' can only be True with time discretization. must specify 'start' and 'stop' points."
)
if num is not None:
if type(num) is not int:
raise ValueError("expecting integer for 'num'.")
else:
num = 50
if endpoint is not None:
if type(endpoint) is not bool:
raise ValueError("expecting bool for 'endpoint'.")
else:
endpoint = True
else:
if start is None and stop is None:
if num != None:
raise ValueError("unexpected argument 'num'.")
if endpoint != None:
raise ValueError("unexpected argument 'endpoint'.")
else:
if not (_np.isscalar(start) and _np.isscalar(stop)):
raise ValueError(
"expecting scalar values for 'start' and 'stop'")
if not (_np.isreal(start) and _np.isreal(stop)):
raise ValueError(
"expecting real values for 'start' and 'stop'")
if num is not None:
if type(num) is not int:
raise ValueError("expecting integer for 'num'.")
else:
num = 50
if endpoint is not None:
if type(endpoint) is not bool:
raise ValueError("expecting bool for 'endpoint'.")
else:
endpoint = True
P = []
H_list = []
psi_blocks = []
for key, b in _iteritems(self._basis_dict):
p = self._get_P(key)
if _sp.issparse(psi_0):
psi = p.H.dot(psi_0).toarray()
else:
psi = p.H.dot(psi_0)
psi = psi.ravel()
if _np.linalg.norm(psi) > 1000 * _np.finfo(self.dtype).eps:
psi_blocks.append(psi)
P.append(p.tocoo())
H = self._get_H(key)
H = H(H_time_eval) * a
if shift is not None:
H += a * shift * _sp.identity(b.Ns, dtype=self.dtype)
H_list.append(H)
if block_diag and H_list:
N_H = len(H_list)
n_pp = N_H // n_jobs
n_left = n_pp + N_H % n_jobs
H_list_prime = []
psi_blocks_prime = []
psi_block = _np.hstack(psi_blocks[:n_left])
H_block = _sp.block_diag(H_list[:n_left], format="csr")
H_list_prime.append(H_block)
psi_blocks_prime.append(psi_block)
for i in range(n_jobs - 1):
i1 = n_left + i * n_pp
i2 = n_left + (i + 1) * n_pp
psi_block = _np.hstack(psi_blocks[i1:i2])
H_block = _sp.block_diag(H_list[i1:i2], format="csr")
H_list_prime.append(H_block)
psi_blocks_prime.append(psi_block)
H_list = H_list_prime
psi_blocks = psi_blocks_prime
H_is_complex = _np.iscomplexobj(
[_np.float32(1.0).astype(H.dtype) for H in H_list])
if H_list:
P = _sp.hstack(P, format="csr")
if iterate:
return _block_expm_iter(psi_blocks, H_list, P, start, stop,
num, endpoint, n_jobs)
else:
ver = [int(v) for v in _scipy.__version__.split(".")]
if H_is_complex and (start, stop, num, endpoint) != (
None, None, None, None) and ver[1] < 19:
mats = _block_expm_iter(psi_blocks, H_list, P, start, stop,
num, endpoint, n_jobs)
return _np.array([mat for mat in mats]).T
else:
psi_t = _Parallel(n_jobs=n_jobs)(
_delayed(_expm_multiply)(H,
psi,
start=start,
stop=stop,
num=num,
endpoint=endpoint)
for psi, H in _izip(psi_blocks, H_list))
psi_t = _np.hstack(psi_t).T
psi_t = P.dot(psi_t)
return psi_t
else:
raise RuntimeError(
"initial state has no projection on to specified blocks.")
def evolve(self,
psi_0,
t0,
times,
iterate=False,
n_jobs=1,
block_diag=False,
stack_state=False,
imag_time=False,
solver_name="dop853",
**solver_args):
"""Creates symmetry blocks of the Hamiltonian and then uses them to run `hamiltonian.evolve()` in parallel.
**Arguments NOT described below can be found in the documentation for the `hamiltonian.evolve()` method.**
Examples
--------
The example below builds on the code snippet shown in the description of the `block_ops` class.
.. literalinclude:: ../../doc_examples/block_ops-example.py
:linenos:
:language: python
:lines: 69-
Parameters
-----------
psi_0 : numpy.ndarray, list, tuple
Quantum state which defined on the full Hilbert space of the problem.
Does not need to obey and sort of symmetry.
t0 : float
Inistial time to start the evolution at.
times : numpy.ndarray, list
Contains the times to compute the solution at. Must be some an iterable object.
iterate : bool, optional
Flag to return generator when set to `True`. Otherwise the output is an array of states.
Default is 'False'.
n_jobs : int, optional
Number of processes requested for the computation time evolution dynamics.
NOTE: one of those processes is used to gather results. For best performance, all blocks
should be approximately the same size and `n_jobs-1` must be a common devisor of the number of
blocks, such that there is roughly an equal workload for each process. Otherwise the computation
will be as slow as the slowest process.
block_diag : bool, optional
When set to `True`, this flag puts the Hamiltonian matrices for the separate symemtry blocks
into a list and then loops over it to do time evolution. When set to `False`, it puts all
blocks in a single giant sparse block diagonal matrix. Default is `False`.
This flag is useful if there are a lot of smaller-sized blocks.
Returns
--------
obj
if `iterate = True`, returns generator which generates the time dependent state in the
full H-space basis.
if `iterate = False`, returns `numpy.ndarray` which has the time-dependent states in the
full H-space basis in the rows.
Raises
------
ValueError
Variable `imag_time=True` option on `hamiltonian.evolve()` method not supported.
ValueError
`iterate=True` requires `times` to be an array or a list.
RuntimeError
Terminates when initial state has no projection onto the specified symmetry blocks.
"""
if imag_time:
raise ValueError(
"imaginary time not supported for block evolution.")
P = []
H_list = []
psi_blocks = []
for key, b in _iteritems(self._basis_dict):
p = self._get_P(key)
if _sp.issparse(psi_0):
psi = p.H.dot(psi_0).toarray()
else:
psi = p.H.dot(psi_0)
psi = _np.asarray(psi).ravel()
if _np.linalg.norm(psi) > 1000 * _np.finfo(self.dtype).eps:
psi_blocks.append(psi)
P.append(p.tocoo())
H_list.append(self._get_H(key))
if block_diag and H_list:
N_H = len(H_list)
n_pp = N_H // n_jobs
n_left = n_pp + N_H % n_jobs
H_list_prime = []
psi_blocks_prime = []
if n_left != 0:
H_list_prime.append(
block_diag_hamiltonian(H_list[:n_left],
None,
None,
None,
None,
self._dtype,
get_proj=False,
**self._no_checks))
psi_list_prime.append(_np.hstack(psi_blocks[:n_left]))
for i in range(n_jobs - 1):
i1 = n_left + i * n_pp
i2 = n_left + (i + 1) * n_pp
H_list_prime.append(
block_diag_hamiltonian(H_list[i1:i2],
None,
None,
None,
None,
self._dtype,
get_proj=False,
**self._no_checks))
psi_list_prime.append(_np.hstack(psi_blocks[i1:i2]))
H_list = H_list_prime
psi_blocks = psi_blocks_prime
if len(H_list) > 0:
P = _sp.hstack(P, format="csr")
if iterate:
if _np.isscalar(times):
raise ValueError(
"If iterate=True times must be a list/array.")
return _block_evolve_iter(psi_blocks, H_list, P, t0, times,
stack_state, imag_time, solver_name,
solver_args, n_jobs)
else:
psi_t = _Parallel(n_jobs=n_jobs)(
_delayed(_block_evolve_helper)(
H, psi, t0, times, stack_state, imag_time, solver_name,
solver_args) for psi, H in _izip(psi_blocks, H_list))
psi_t = _np.vstack(psi_t)
psi_t = P.dot(psi_t)
return psi_t
else:
raise RuntimeError(
"initial state has no projection on to specified blocks.")