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# -*- coding: utf-8 -*-
# Authors: Eric Larson <larson.eric.d@gmail.com>
# License: BSD-3-Clause
import numpy as np
from .utils import _ensure_int, verbose, logger
###############################################################################
# Class for interpolation between adjacent points
class _Interp2(object):
r"""Interpolate between two points.
Parameters
----------
control_points : array, shape (n_changes,)
The control points (indices) to use.
values : callable | array, shape (n_changes, ...)
Callable that takes the control point and returns a list of
arrays that must be interpolated.
interp : str
Can be 'zero', 'linear', 'hann', or 'cos2' (same as hann).
Notes
-----
This will process data using overlapping windows of potentially
different sizes to achieve a constant output value using different
2-point interpolation schemes. For example, for linear interpolation,
and window sizes of 6 and 17, this would look like::
1 _ _
|\ / '-. .-'
| \ / '-. .-'
| x |-.-|
| / \ .-' '-.
|/ \_.-' '-.
0 +----|----|----|----|---
0 5 10 15 20 25
"""
def __init__(self, control_points, values, interp='hann'):
# set up interpolation
self.control_points = np.array(control_points, int).ravel()
if not np.array_equal(np.unique(self.control_points),
self.control_points):
raise ValueError('Control points must be sorted and unique')
if len(self.control_points) == 0:
raise ValueError('Must be at least one control point')
if not (self.control_points >= 0).all():
raise ValueError('All control points must be positive (got %s)'
% (self.control_points[:3],))
if isinstance(values, np.ndarray):
values = [values]
if isinstance(values, (list, tuple)):
for v in values:
if not (v is None or isinstance(v, np.ndarray)):
raise TypeError('All entries in "values" must be ndarray '
'or None, got %s' % (type(v),))
if v is not None and v.shape[0] != len(self.control_points):
raise ValueError('Values, if provided, must be the same '
'length as the number of control points '
'(%s), got %s'
% (len(self.control_points), v.shape[0]))
use_values = values
def val(pt):
idx = np.where(control_points == pt)[0][0]
return [v[idx] if v is not None else None for v in use_values]
values = val
self.values = values
self.n_last = None
self._position = 0 # start at zero
self._left_idx = 0
self._left = self._right = self._use_interp = None
known_types = ('cos2', 'linear', 'zero', 'hann')
if interp not in known_types:
raise ValueError('interp must be one of %s, got "%s"'
% (known_types, interp))
self._interp = interp
def feed_generator(self, n_pts):
"""Feed data and get interpolators as a generator."""
self.n_last = 0
n_pts = _ensure_int(n_pts, 'n_pts')
original_position = self._position
stop = self._position + n_pts
logger.debug('Feed %s (%s-%s)' % (n_pts, self._position, stop))
used = np.zeros(n_pts, bool)
if self._left is None: # first one
logger.debug(' Eval @ %s (%s)' % (0, self.control_points[0]))
self._left = self.values(self.control_points[0])
if len(self.control_points) == 1:
self._right = self._left
n_used = 0
# Left zero-order hold condition
if self._position < self.control_points[self._left_idx]:
n_use = min(self.control_points[self._left_idx] - self._position,
n_pts)
logger.debug(' Left ZOH %s' % n_use)
this_sl = slice(None, n_use)
assert used[this_sl].size == n_use
assert not used[this_sl].any()
used[this_sl] = True
yield [this_sl, self._left, None, None]
self._position += n_use
n_used += n_use
self.n_last += 1
# Standard interpolation condition
stop_right_idx = np.where(self.control_points >= stop)[0]
if len(stop_right_idx) == 0:
stop_right_idx = [len(self.control_points) - 1]
stop_right_idx = stop_right_idx[0]
left_idxs = np.arange(self._left_idx, stop_right_idx)
self.n_last += max(len(left_idxs) - 1, 0)
for bi, left_idx in enumerate(left_idxs):
if left_idx != self._left_idx or self._right is None:
if self._right is not None:
assert left_idx == self._left_idx + 1
self._left = self._right
self._left_idx += 1
self._use_interp = None # need to recreate it
eval_pt = self.control_points[self._left_idx + 1]
logger.debug(' Eval @ %s (%s)'
% (self._left_idx + 1, eval_pt))
self._right = self.values(eval_pt)
assert self._right is not None
left_point = self.control_points[self._left_idx]
right_point = self.control_points[self._left_idx + 1]
if self._use_interp is None:
interp_span = right_point - left_point
if self._interp == 'zero':
self._use_interp = None
elif self._interp == 'linear':
self._use_interp = np.linspace(1., 0., interp_span,
endpoint=False)
else: # self._interp in ('cos2', 'hann'):
self._use_interp = np.cos(
np.linspace(0, np.pi / 2., interp_span,
endpoint=False))
self._use_interp *= self._use_interp
n_use = min(stop, right_point) - self._position
if n_use > 0:
logger.debug(' Interp %s %s (%s-%s)' % (self._interp, n_use,
left_point, right_point))
interp_start = self._position - left_point
assert interp_start >= 0
if self._use_interp is None:
this_interp = None
else:
this_interp = \
self._use_interp[interp_start:interp_start + n_use]
assert this_interp.size == n_use
this_sl = slice(n_used, n_used + n_use)
assert used[this_sl].size == n_use
assert not used[this_sl].any()
used[this_sl] = True
yield [this_sl, self._left, self._right, this_interp]
self._position += n_use
n_used += n_use
# Right zero-order hold condition
if self.control_points[self._left_idx] <= self._position:
n_use = stop - self._position
if n_use > 0:
logger.debug(' Right ZOH %s' % n_use)
this_sl = slice(n_pts - n_use, None)
assert not used[this_sl].any()
used[this_sl] = True
assert self._right is not None
yield [this_sl, self._right, None, None]
self._position += n_use
n_used += n_use
self.n_last += 1
assert self._position == stop
assert n_used == n_pts
assert used.all()
assert self._position == original_position + n_pts
def feed(self, n_pts):
"""Feed data and get interpolated values."""
# Convenience function for assembly
out_arrays = None
for o in self.feed_generator(n_pts):
if out_arrays is None:
out_arrays = [np.empty(v.shape + (n_pts,))
if v is not None else None for v in o[1]]
for ai, arr in enumerate(out_arrays):
if arr is not None:
if o[3] is None:
arr[..., o[0]] = o[1][ai][..., np.newaxis]
else:
arr[..., o[0]] = (
o[1][ai][..., np.newaxis] * o[3] +
o[2][ai][..., np.newaxis] * (1. - o[3]))
assert out_arrays is not None
return out_arrays
###############################################################################
# Constant overlap-add processing class
def _check_store(store):
if isinstance(store, np.ndarray):
store = [store]
if isinstance(store, (list, tuple)) and all(isinstance(s, np.ndarray)
for s in store):
store = _Storer(*store)
if not callable(store):
raise TypeError('store must be callable, got type %s'
% (type(store),))
return store
class _COLA:
r"""Constant overlap-add processing helper.
Parameters
----------
process : callable
A function that takes a chunk of input data with shape
``(n_channels, n_samples)`` and processes it.
store : callable | ndarray
A function that takes a completed chunk of output data.
Can also be an ``ndarray``, in which case it is treated as the
output data in which to store the results.
n_total : int
The total number of samples.
n_samples : int
The number of samples per window.
n_overlap : int
The overlap between windows.
window : str
The window to use. Default is "hann".
tol : float
The tolerance for COLA checking.
Notes
-----
This will process data using overlapping windows to achieve a constant
output value. For example, for ``n_total=27``, ``n_samples=10``,
``n_overlap=5`` and ``window='triang'``::
1 _____ _______
| \ /\ /\ /
| \ / \ / \ /
| x x x
| / \ / \ / \
| / \/ \/ \
0 +----|----|----|----|----|-
0 5 10 15 20 25
This produces four windows: the first three are the requested length
(10 samples) and the last one is longer (12 samples). The first and last
window are asymmetric.
"""
@verbose
def __init__(self, process, store, n_total, n_samples, n_overlap,
sfreq, window='hann', tol=1e-10, *, verbose=None):
from scipy.signal import get_window
n_samples = _ensure_int(n_samples, 'n_samples')
n_overlap = _ensure_int(n_overlap, 'n_overlap')
n_total = _ensure_int(n_total, 'n_total')
if n_samples <= 0:
raise ValueError('n_samples must be > 0, got %s' % (n_samples,))
if n_overlap < 0:
raise ValueError('n_overlap must be >= 0, got %s' % (n_overlap,))
if n_total < 0:
raise ValueError('n_total must be >= 0, got %s' % (n_total,))
self._n_samples = int(n_samples)
self._n_overlap = int(n_overlap)
del n_samples, n_overlap
if n_total < self._n_samples:
raise ValueError('Number of samples per window (%d) must be at '
'most the total number of samples (%s)'
% (self._n_samples, n_total))
if not callable(process):
raise TypeError('process must be callable, got type %s'
% (type(process),))
self._process = process
self._step = self._n_samples - self._n_overlap
self._store = _check_store(store)
self._idx = 0
self._in_buffers = self._out_buffers = None
# Create our window boundaries
window_name = window if isinstance(window, str) else 'custom'
self._window = get_window(window, self._n_samples,
fftbins=(self._n_samples - 1) % 2)
self._window /= _check_cola(self._window, self._n_samples, self._step,
window_name, tol=tol)
self.starts = np.arange(0, n_total - self._n_samples + 1, self._step)
self.stops = self.starts + self._n_samples
delta = n_total - self.stops[-1]
self.stops[-1] = n_total
sfreq = float(sfreq)
pl = 's' if len(self.starts) != 1 else ''
logger.info(' Processing %4d data chunk%s of (at least) %0.1f sec '
'with %0.1f sec overlap and %s windowing'
% (len(self.starts), pl, self._n_samples / sfreq,
self._n_overlap / sfreq, window_name))
del window, window_name
if delta > 0:
logger.info(' The final %0.3f sec will be lumped into the '
'final window' % (delta / sfreq,))
@property
def _in_offset(self):
"""Compute from current processing window start and buffer len."""
return self.starts[self._idx] + self._in_buffers[0].shape[-1]
@verbose
def feed(self, *datas, verbose=None, **kwargs):
"""Pass in a chunk of data."""
# Append to our input buffer
if self._in_buffers is None:
self._in_buffers = [None] * len(datas)
if len(datas) != len(self._in_buffers):
raise ValueError('Got %d array(s), needed %d'
% (len(datas), len(self._in_buffers)))
for di, data in enumerate(datas):
if not isinstance(data, np.ndarray) or data.ndim < 1:
raise TypeError('data entry %d must be an 2D ndarray, got %s'
% (di, type(data),))
if self._in_buffers[di] is None:
# In practice, users can give large chunks, so we use
# dynamic allocation of the in buffer. We could save some
# memory allocation by only ever processing max_len at once,
# but this would increase code complexity.
self._in_buffers[di] = np.empty(
data.shape[:-1] + (0,), data.dtype)
if data.shape[:-1] != self._in_buffers[di].shape[:-1] or \
self._in_buffers[di].dtype != data.dtype:
raise TypeError('data must dtype %s and shape[:-1]==%s, '
'got dtype %s shape[:-1]=%s'
% (self._in_buffers[di].dtype,
self._in_buffers[di].shape[:-1],
data.dtype, data.shape[:-1]))
logger.debug(' + Appending %d->%d'
% (self._in_offset, self._in_offset + data.shape[-1]))
self._in_buffers[di] = np.concatenate(
[self._in_buffers[di], data], -1)
if self._in_offset > self.stops[-1]:
raise ValueError('data (shape %s) exceeded expected total '
'buffer size (%s > %s)'
% (data.shape, self._in_offset,
self.stops[-1]))
# Check to see if we can process the next chunk and dump outputs
while self._idx < len(self.starts) and \
self._in_offset >= self.stops[self._idx]:
start, stop = self.starts[self._idx], self.stops[self._idx]
this_len = stop - start
this_window = self._window.copy()
if self._idx == len(self.starts) - 1:
this_window = np.pad(
self._window, (0, this_len - len(this_window)), 'constant')
for offset in range(self._step, len(this_window), self._step):
n_use = len(this_window) - offset
this_window[offset:] += self._window[:n_use]
if self._idx == 0:
for offset in range(self._n_samples - self._step, 0,
-self._step):
this_window[:offset] += self._window[-offset:]
logger.debug(' * Processing %d->%d' % (start, stop))
this_proc = [in_[..., :this_len].copy()
for in_ in self._in_buffers]
if not all(proc.shape[-1] == this_len == this_window.size
for proc in this_proc):
raise RuntimeError('internal indexing error')
outs = self._process(*this_proc, **kwargs)
if self._out_buffers is None:
max_len = np.max(self.stops - self.starts)
self._out_buffers = [np.zeros(o.shape[:-1] + (max_len,),
o.dtype) for o in outs]
for oi, out in enumerate(outs):
out *= this_window
self._out_buffers[oi][..., :stop - start] += out
self._idx += 1
if self._idx < len(self.starts):
next_start = self.starts[self._idx]
else:
next_start = self.stops[-1]
delta = next_start - self.starts[self._idx - 1]
for di in range(len(self._in_buffers)):
self._in_buffers[di] = self._in_buffers[di][..., delta:]
logger.debug(' - Shifting input/output buffers by %d samples'
% (delta,))
self._store(*[o[..., :delta] for o in self._out_buffers])
for ob in self._out_buffers:
ob[..., :-delta] = ob[..., delta:]
ob[..., -delta:] = 0.
def _check_cola(win, nperseg, step, window_name, tol=1e-10):
"""Check whether the Constant OverLap Add (COLA) constraint is met."""
# adapted from SciPy
binsums = np.sum([win[ii * step:(ii + 1) * step]
for ii in range(nperseg // step)], axis=0)
if nperseg % step != 0:
binsums[:nperseg % step] += win[-(nperseg % step):]
const = np.median(binsums)
deviation = np.max(np.abs(binsums - const))
if deviation > tol:
raise ValueError('segment length %d with step %d for %s window '
'type does not provide a constant output '
'(%g%% deviation)'
% (nperseg, step, window_name,
100 * deviation / const))
return const
class _Storer(object):
"""Store data in chunks."""
def __init__(self, *outs, picks=None):
for oi, out in enumerate(outs):
if not isinstance(out, np.ndarray) or out.ndim < 1:
raise TypeError('outs[oi] must be >= 1D ndarray, got %s'
% (out,))
self.outs = outs
self.idx = 0
self.picks = picks
def __call__(self, *outs):
if (len(outs) != len(self.outs) or
not all(out.shape[-1] == outs[0].shape[-1] for out in outs)):
raise ValueError('Bad outs')
idx = (Ellipsis,)
if self.picks is not None:
idx += (self.picks,)
stop = self.idx + outs[0].shape[-1]
idx += (slice(self.idx, stop),)
for o1, o2 in zip(self.outs, outs):
o1[idx] = o2
self.idx = stop
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