698 lines
20 KiB
Python
698 lines
20 KiB
Python
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"""
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Numpy encode/decode/utility implementations for run length encodings.
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# Run Length Encoded Features
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Encoding/decoding functions for run length encoded data.
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We include code for two variations:
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* run length encoding (RLE)
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* binary run length encdoing (BRLE)
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RLE stores sequences of repeated values as the value followed by its count, e.g.
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```python
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dense_to_rle([5, 5, 3, 2, 2, 2, 2, 6]) == [5, 2, 3, 1, 2, 4, 6, 1]
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```
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i.e. the value `5` is repeated `2` times, then `3` is repeated `1` time, `2` is
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repeated `4` times and `6` is repeated `1` time.
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BRLE is an optimized form for when the stored values can only be `0` or `1`.
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This means we only need to save the counts, and assume the values alternate
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(starting at `0`).
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```python
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dense_to_brle([1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]) == \
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[0, 2, 4, 7, 2]
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```
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i.e. the value zero occurs `0` times, followed by `2` ones, `4` zeros, `7` ones
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and `2` zeros.
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Sequences with counts exceeding the data type's maximum value have to be
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handled carefully. For example, the `uint8` encoding of 300 zeros
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(`uint8` has a max value of 255) is:
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* RLE: `[0, 255, 0, 45]` (`0` repeated `255` times + `0` repeated `45` times)
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* BRLE: `[255, 0, 45, 0]` (`255` zeros + `0` ones + `45` zeros + `0` ones)
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This module contains implementations of various RLE/BRLE operations.
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"""
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import functools
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import numpy as np
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def brle_length(brle):
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"""Optimized implementation of `len(brle_to_dense(brle))`"""
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return np.sum(brle)
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def rle_length(rle):
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"""Optimized implementation of `len(rle_to_dense(rle_to_brle(rle)))`"""
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return np.sum(rle[1::2])
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def rle_to_brle(rle, dtype=None):
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"""
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Convert run length encoded (RLE) value/counts to BRLE.
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RLE data is stored in a rank 1 array with each pair giving:
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(value, count)
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e.g. the RLE encoding of [4, 4, 4, 1, 1, 6] is [4, 3, 1, 2, 6, 1].
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Parameters
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----------
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rle : (n,) int
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Run length encoded data
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Returns
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----------
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equivalent binary run length encoding. a list if dtype is None,
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otherwise brle_to_brle is called on that list before returning.
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Raises
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----------
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ValueError
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If any of the even counts of `rle` are not zero or 1.
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"""
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curr_val = 0
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out = [0]
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acc = 0
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for value, count in np.reshape(rle, (-1, 2)):
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acc += count
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if value not in (0, 1):
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raise ValueError(
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"Invalid run length encoding for conversion to BRLE")
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if value == curr_val:
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out[-1] += count
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else:
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out.append(int(count))
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curr_val = value
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if len(out) % 2:
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out.append(0)
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if dtype is not None:
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out = brle_to_brle(out, dtype=dtype)
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return out
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def brle_logical_not(brle):
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"""
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Get the BRLE encoding of the `logical_not`ed dense form of `brle`.
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Equivalent to `dense_to_brle(np.logical_not(brle_to_dense(brle)))` but
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highly optimized - just pads brle with a 0 on each end (or strips is
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existing endpoints are both zero).
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Parameters
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----------
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brle: rank 1 int array of binary run length encoded data
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Returns
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----------
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rank 1 int array of binary run length encoded data corresponding to
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element-wise not of the input.
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"""
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if brle[0] or brle[-1]:
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return np.pad(brle, [1, 1], mode='constant')
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else:
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return brle[1:-1]
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def merge_brle_lengths(lengths):
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"""Inverse of split_long_brle_lengths."""
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if len(lengths) == 0:
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return []
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out = [int(lengths[0])]
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accumulating = False
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for length in lengths[1:]:
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if accumulating:
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out[-1] += length
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accumulating = False
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else:
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if length == 0:
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accumulating = True
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else:
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out.append(int(length))
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return out
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def split_long_brle_lengths(lengths, dtype=np.int64):
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"""
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Split lengths that exceed max dtype value.
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Lengths `l` are converted into [max_val, 0] * l // max_val + [l % max_val]
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e.g. for dtype=np.uint8 (max_value == 255)
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```
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split_long_brle_lengths([600, 300, 2, 6], np.uint8) == \
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[255, 0, 255, 0, 90, 255, 0, 45, 2, 6]
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```
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"""
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lengths = np.asarray(lengths)
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max_val = np.iinfo(dtype).max
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bad_length_mask = lengths > max_val
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if np.any(bad_length_mask):
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# there are some bad lengths
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nl = len(lengths)
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repeats = np.asarray(lengths) // max_val
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remainders = (lengths % max_val).astype(dtype)
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lengths = np.concatenate(
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[np.array([max_val, 0] * repeat + [remainder], dtype=dtype)
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for repeat, remainder in zip(repeats, remainders)])
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lengths = lengths.reshape((np.sum(repeats) * 2 + nl,)).astype(dtype)
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return lengths
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elif lengths.dtype != dtype:
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return lengths.astype(dtype)
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else:
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return lengths
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def dense_to_brle(dense_data, dtype=np.int64):
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"""
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Get the binary run length encoding of `dense_data`.
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Parameters
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----------
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dense_data: rank 1 bool array of data to encode.
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dtype: numpy int type.
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Returns
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----------
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Binary run length encoded rank 1 array of dtype `dtype`.
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Raises
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----------
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ValuError if dense_data is not a rank 1 bool array.
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"""
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if dense_data.dtype != np.bool:
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raise ValueError("`dense_data` must be bool")
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if len(dense_data.shape) != 1:
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raise ValueError("`dense_data` must be rank 1.")
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n = len(dense_data)
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starts = np.r_[0, np.flatnonzero(dense_data[1:] != dense_data[:-1]) + 1]
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lengths = np.diff(np.r_[starts, n])
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lengths = split_long_brle_lengths(lengths, dtype=dtype)
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if dense_data[0]:
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lengths = np.pad(lengths, [1, 0], mode='constant')
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return lengths
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_ft = np.array([False, True], dtype=np.bool)
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def brle_to_dense(brle_data, vals=None):
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"""Decode binary run length encoded data to dense.
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Parameters
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----------
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brle_data: BRLE counts of False/True values
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vals: if not `None`, a length 2 array/list/tuple with False/True substitute
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values, e.g. brle_to_dense([2, 3, 1, 0], [7, 9]) == [7, 7, 9, 9, 9, 7]
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Returns
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----------
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rank 1 dense data of dtype `bool if vals is None else vals.dtype`
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Raises
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----------
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ValueError if vals it not None and shape is not (2,)
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"""
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if vals is None:
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vals = _ft
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else:
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vals = np.asarray(vals)
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if vals.shape != (2,):
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raise ValueError("vals.shape must be (2,), got %s" % (vals.shape))
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ft = np.repeat(
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_ft[np.newaxis, :], (len(brle_data) + 1) // 2, axis=0).flatten()
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return np.repeat(ft[:len(brle_data)], brle_data).flatten()
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def rle_to_dense(rle_data, dtype=np.int64):
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"""Get the dense decoding of the associated run length encoded data."""
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values, counts = np.split(np.reshape(rle_data, (-1, 2)), 2, axis=-1)
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if dtype is not None:
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values = np.asanyarray(values, dtype=dtype)
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try:
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result = np.repeat(np.squeeze(values, axis=-1),
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np.squeeze(counts, axis=-1))
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except TypeError:
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# on windows it sometimes fails to cast data type
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result = np.repeat(np.squeeze(values.astype(np.int64), axis=-1),
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np.squeeze(counts.astype(np.int64), axis=-1))
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return result
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def dense_to_rle(dense_data, dtype=np.int64):
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"""Get run length encoding of the provided dense data."""
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n = len(dense_data)
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starts = np.r_[0, np.flatnonzero(dense_data[1:] != dense_data[:-1]) + 1]
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lengths = np.diff(np.r_[starts, n])
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values = dense_data[starts]
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values, lengths = split_long_rle_lengths(values, lengths, dtype=dtype)
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out = np.stack((values, lengths), axis=1)
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return out.flatten()
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def split_long_rle_lengths(values, lengths, dtype=np.int64):
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"""
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Split long lengths in the associated run length encoding.
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e.g.
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```python
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split_long_rle_lengths([5, 300, 2, 12], np.uint8) == [5, 255, 5, 45, 2, 12]
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```
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Parameters
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----------
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values: values column of run length encoding, or `rle[::2]`
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lengths: counts in run length encoding, or `rle[1::2]`
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dtype: numpy data type indicating the maximum value.
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Returns
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----------
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values, lengths associated with the appropriate splits. `lengths` will be
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of type `dtype`, while `values` will be the same as the value passed in.
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"""
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max_length = np.iinfo(dtype).max
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lengths = np.asarray(lengths)
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repeats = lengths // max_length
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if np.any(repeats):
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repeats += 1
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remainder = lengths % max_length
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values = np.repeat(values, repeats)
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lengths = np.empty(len(repeats), dtype=dtype)
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lengths.fill(max_length)
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lengths = np.repeat(lengths, repeats)
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lengths[np.cumsum(repeats) - 1] = remainder
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elif lengths.dtype != dtype:
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lengths = lengths.astype(dtype)
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return values, lengths
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def merge_rle_lengths(values, lengths):
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"""Inverse of split_long_rle_lengths except returns normal python lists."""
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ret_values = []
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ret_lengths = []
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curr = None
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for value, length in zip(values, lengths):
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if length == 0:
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continue
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if value == curr:
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ret_lengths[-1] += length
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else:
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curr = value
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ret_lengths.append(int(length))
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ret_values.append(value)
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return ret_values, ret_lengths
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def brle_to_rle(brle, dtype=np.int64):
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if len(brle) % 2 == 1:
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brle = np.concatenate([brle, [0]])
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lengths = brle
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values = np.tile(_ft, len(brle) // 2)
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return rle_to_rle(
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np.stack((values, lengths), axis=1).flatten(), dtype=dtype)
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def brle_to_brle(brle, dtype=np.int64):
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"""
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Almost the identity function.
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Checks for possible merges and required splits.
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"""
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return split_long_brle_lengths(merge_brle_lengths(brle), dtype=dtype)
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def rle_to_rle(rle, dtype=np.int64):
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"""
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Almost the identity function.
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Checks for possible merges and required splits.
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"""
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values, lengths = np.reshape(rle, (-1, 2)).T
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values, lengths = merge_rle_lengths(values, lengths)
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values, lengths = split_long_rle_lengths(values, lengths, dtype=dtype)
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return np.stack((values, lengths), axis=1).flatten()
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def _unsorted_gatherer(indices, sorted_gather_fn):
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if not isinstance(indices, np.ndarray):
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indices = np.array(indices, copy=False)
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order = np.argsort(indices)
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ordered_indices = indices[order]
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def f(data, dtype=None):
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result = np.empty(len(order), dtype=dtype or getattr(data, 'dtype', None))
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result[order] = tuple(sorted_gather_fn(data, ordered_indices))
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return result
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return f
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def sorted_rle_gather_1d(rle_data, ordered_indices):
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"""
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Gather brle_data at ordered_indices.
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This is equivalent to `rle_to_dense(brle_data)[ordered_indices]` but avoids
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the decoding.
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Parameters
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----------
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brle_data: iterable of run-length-encoded data.
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ordered_indices: iterable of ints in ascending order.
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Returns
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|
----------
|
||
|
|
`brle_data` iterable of values at the dense indices, same length as
|
||
|
|
ordered indices.
|
||
|
|
"""
|
||
|
|
data_iter = iter(rle_data)
|
||
|
|
index_iter = iter(ordered_indices)
|
||
|
|
index = next(index_iter)
|
||
|
|
start = 0
|
||
|
|
while True:
|
||
|
|
while start <= index:
|
||
|
|
try:
|
||
|
|
value = next(data_iter)
|
||
|
|
start += next(data_iter)
|
||
|
|
except StopIteration:
|
||
|
|
raise IndexError(
|
||
|
|
'Index %d out of range of raw_values length %d'
|
||
|
|
% (index, start))
|
||
|
|
try:
|
||
|
|
while index < start:
|
||
|
|
yield value
|
||
|
|
index = next(index_iter)
|
||
|
|
except StopIteration:
|
||
|
|
break
|
||
|
|
|
||
|
|
|
||
|
|
def rle_mask(rle_data, mask):
|
||
|
|
"""
|
||
|
|
Perform masking of the input run-length data.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
rle_data: iterable of run length encoded data
|
||
|
|
mask: iterable of bools corresponding to the dense mask.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
iterable of dense values of rle_data wherever mask is True.
|
||
|
|
"""
|
||
|
|
data_iter = iter(rle_data)
|
||
|
|
mask_iter = iter(mask)
|
||
|
|
while True:
|
||
|
|
try:
|
||
|
|
value = next(data_iter)
|
||
|
|
count = next(data_iter)
|
||
|
|
except StopIteration:
|
||
|
|
break
|
||
|
|
for _ in range(count):
|
||
|
|
m = next(mask_iter)
|
||
|
|
if m:
|
||
|
|
yield value
|
||
|
|
|
||
|
|
|
||
|
|
def brle_mask(rle_data, mask):
|
||
|
|
"""
|
||
|
|
Perform masking of the input binary run-length data.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
brle_data: iterable of binary run length encoded data
|
||
|
|
mask: iterable of bools corresponding to the dense mask.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
iterable dense values of brle_data wherever mask is True.
|
||
|
|
"""
|
||
|
|
data_iter = iter(rle_data)
|
||
|
|
mask_iter = iter(mask)
|
||
|
|
value = True
|
||
|
|
while True:
|
||
|
|
try:
|
||
|
|
value = not value
|
||
|
|
count = next(data_iter)
|
||
|
|
except StopIteration:
|
||
|
|
break
|
||
|
|
for _ in range(count):
|
||
|
|
m = next(mask_iter)
|
||
|
|
if m:
|
||
|
|
yield value
|
||
|
|
|
||
|
|
|
||
|
|
def rle_gatherer_1d(indices):
|
||
|
|
"""
|
||
|
|
Get a gather function at the given indices.
|
||
|
|
|
||
|
|
Because gathering on RLE data requires sorting, for instances where
|
||
|
|
gathering at the same indices on different RLE data this can save the
|
||
|
|
sorting process.
|
||
|
|
|
||
|
|
If only gathering on a single RLE iterable, use `rle_gather_1d`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
indices: iterable of integers
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
gather function, mapping `(rle_data, dtype=None) -> values`.
|
||
|
|
`values` will have the same length as `indices` and dtype provided,
|
||
|
|
or rle_data.dtype if no dtype is provided.
|
||
|
|
"""
|
||
|
|
return _unsorted_gatherer(indices, sorted_rle_gather_1d)
|
||
|
|
|
||
|
|
|
||
|
|
def rle_gather_1d(rle_data, indices, dtype=None):
|
||
|
|
"""
|
||
|
|
Gather RLE data values at the provided dense indices.
|
||
|
|
|
||
|
|
This is equivalent to `rle_to_dense(rle_data)[indices]` but the
|
||
|
|
implementation does not require the construction of the dense array.
|
||
|
|
|
||
|
|
If indices is known to be in order, use `sorted_gather_1d`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
rle_data: run length encoded data
|
||
|
|
indices: dense indices
|
||
|
|
dtype: numpy dtype. If not provided, uses rle_data.dtype
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
numpy array, dense data at indices, same length as indices and dtype as
|
||
|
|
rle_data
|
||
|
|
"""
|
||
|
|
return rle_gatherer_1d(indices)(rle_data, dtype=dtype)
|
||
|
|
|
||
|
|
|
||
|
|
def sorted_brle_gather_1d(brle_data, ordered_indices):
|
||
|
|
"""
|
||
|
|
Gather brle_data at ordered_indices.
|
||
|
|
|
||
|
|
This is equivalent to `brle_to_dense(brle_data)[ordered_indices]` but
|
||
|
|
avoids the decoding.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
raw_data: iterable of run-length-encoded data.
|
||
|
|
ordered_indices: iterable of ints in ascending order.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
`raw_data` iterable of values at the dense indices, same length as
|
||
|
|
ordered indices.
|
||
|
|
"""
|
||
|
|
data_iter = iter(brle_data)
|
||
|
|
index_iter = iter(ordered_indices)
|
||
|
|
index = next(index_iter)
|
||
|
|
start = 0
|
||
|
|
value = True
|
||
|
|
while True:
|
||
|
|
while start <= index:
|
||
|
|
try:
|
||
|
|
value = not value
|
||
|
|
start += next(data_iter)
|
||
|
|
except StopIteration:
|
||
|
|
raise IndexError(
|
||
|
|
'Index %d out of range of raw_values length %d'
|
||
|
|
% (index, start))
|
||
|
|
try:
|
||
|
|
while index < start:
|
||
|
|
yield value
|
||
|
|
index = next(index_iter)
|
||
|
|
except StopIteration:
|
||
|
|
break
|
||
|
|
|
||
|
|
|
||
|
|
def brle_gatherer_1d(indices):
|
||
|
|
"""
|
||
|
|
Get a gather function at the given indices.
|
||
|
|
|
||
|
|
Because gathering on BRLE data requires sorting, for instances where
|
||
|
|
gathering at the same indices on different RLE data this can save the
|
||
|
|
sorting process.
|
||
|
|
|
||
|
|
If only gathering on a single RLE iterable, use `brle_gather_1d`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
indices: iterable of integers
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
gather function, mapping `(rle_data, dtype=None) -> values`.
|
||
|
|
`values` will have the same length as `indices` and dtype provided,
|
||
|
|
or rle_data.dtype if no dtype is provided.
|
||
|
|
"""
|
||
|
|
return functools.partial(
|
||
|
|
_unsorted_gatherer(indices, sorted_brle_gather_1d), dtype=np.bool)
|
||
|
|
|
||
|
|
|
||
|
|
def brle_gather_1d(brle_data, indices):
|
||
|
|
"""
|
||
|
|
Gather BRLE data values at the provided dense indices.
|
||
|
|
|
||
|
|
This is equivalent to `rle_to_dense(rle_data)[indices]` but the
|
||
|
|
implementation does not require the construction of the dense array.
|
||
|
|
|
||
|
|
If indices is known to be in order, use `sorted_brle_gather_1d`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
rle_data: run length encoded data
|
||
|
|
indices: dense indices
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
numpy array, dense data at indices, same length as indices and dtype as
|
||
|
|
rle_data
|
||
|
|
"""
|
||
|
|
return brle_gatherer_1d(indices)(brle_data)
|
||
|
|
|
||
|
|
|
||
|
|
def brle_reverse(brle_data):
|
||
|
|
"""Equivalent to dense_to_brle(brle_to_dense(brle_data)[-1::-1])."""
|
||
|
|
if len(brle_data) % 2 == 0:
|
||
|
|
brle_data = np.concatenate([brle_data, [0]], axis=0)
|
||
|
|
end = -1 if brle_data[-1] == 0 else None
|
||
|
|
return brle_data[-1:end:-1]
|
||
|
|
|
||
|
|
|
||
|
|
def rle_reverse(rle_data):
|
||
|
|
"""Get the rle encoding of the reversed dense array."""
|
||
|
|
if not isinstance(rle_data, np.ndarray):
|
||
|
|
rle_data = np.array(rle_data, copy=False)
|
||
|
|
rle_data = np.reshape(rle_data, (-1, 2))
|
||
|
|
rle_data = rle_data[-1::-1]
|
||
|
|
return np.reshape(rle_data, (-1,))
|
||
|
|
|
||
|
|
|
||
|
|
def rle_to_sparse(rle_data):
|
||
|
|
"""Get dense indices associated with non-zeros."""
|
||
|
|
indices = []
|
||
|
|
values = []
|
||
|
|
it = iter(rle_data)
|
||
|
|
index = 0
|
||
|
|
try:
|
||
|
|
while True:
|
||
|
|
value = next(it)
|
||
|
|
counts = next(it)
|
||
|
|
end = index + counts
|
||
|
|
if value:
|
||
|
|
indices.append(np.arange(index, end, dtype=np.int64))
|
||
|
|
values.append(np.repeat(value, counts))
|
||
|
|
index = end
|
||
|
|
except StopIteration:
|
||
|
|
pass
|
||
|
|
if len(indices) == 0:
|
||
|
|
assert(len(values)) == 0
|
||
|
|
return indices, values
|
||
|
|
|
||
|
|
indices = np.concatenate(indices)
|
||
|
|
values = np.concatenate(values)
|
||
|
|
return indices, values
|
||
|
|
|
||
|
|
|
||
|
|
def brle_to_sparse(brle_data, dtype=np.int64):
|
||
|
|
ends = np.cumsum(brle_data)
|
||
|
|
indices = [np.arange(s, e, dtype=dtype) for s, e in
|
||
|
|
zip(ends[::2], ends[1::2])]
|
||
|
|
return np.concatenate(indices)
|
||
|
|
|
||
|
|
|
||
|
|
def rle_strip(rle_data):
|
||
|
|
"""
|
||
|
|
Remove leading and trailing zeros.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
rle_data: run length encoded data
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
(stripped_rle_data, padding)
|
||
|
|
stripped_rle_data: rle data without any leading or trailing zeros
|
||
|
|
padding: 2-element dense padding
|
||
|
|
"""
|
||
|
|
rle_data = np.reshape(rle_data, (-1, 2))
|
||
|
|
start = 0
|
||
|
|
for i, (val, count) in enumerate(rle_data):
|
||
|
|
if val and count > 0:
|
||
|
|
break
|
||
|
|
else:
|
||
|
|
start += count
|
||
|
|
|
||
|
|
end = 0
|
||
|
|
for j, (val, count) in enumerate(rle_data[::-1]):
|
||
|
|
if val and count > 0:
|
||
|
|
break
|
||
|
|
else:
|
||
|
|
end += count
|
||
|
|
rle_data = rle_data[i:None if j == 0 else -j].reshape((-1,))
|
||
|
|
return rle_data, (start, end)
|
||
|
|
|
||
|
|
|
||
|
|
def brle_strip(brle_data):
|
||
|
|
"""
|
||
|
|
Remove leading and trailing zeros.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
brle_data: binary run length encoded data.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
----------
|
||
|
|
(stripped_brle_data, padding)
|
||
|
|
stripped_brle_data: rle data without any leading or trailing zeros
|
||
|
|
padding: 2-element dense padding
|
||
|
|
"""
|
||
|
|
start = 0
|
||
|
|
val = True
|
||
|
|
for i, count in enumerate(brle_data):
|
||
|
|
val = not val
|
||
|
|
if val and count > 0:
|
||
|
|
break
|
||
|
|
else:
|
||
|
|
start += count
|
||
|
|
end = 0
|
||
|
|
val = bool(len(brle_data) % 2)
|
||
|
|
for j, count in enumerate(brle_data[::-1]):
|
||
|
|
val = not val
|
||
|
|
if val and count > 0:
|
||
|
|
break
|
||
|
|
else:
|
||
|
|
end += count
|
||
|
|
brle_data = brle_data[i:None if j == 0 else -j]
|
||
|
|
brle_data = np.concatenate([[0], brle_data])
|
||
|
|
return brle_data, (start, end)
|