826 lines
25 KiB
Python
826 lines
25 KiB
Python
"""
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grouping.py
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-------------
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Functions for grouping values and rows.
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"""
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import numpy as np
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from . import util
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from .constants import log, tol
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try:
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from scipy.spatial import cKDTree
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except BaseException as E:
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# wrapping just ImportError fails in some cases
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# will raise the error when someone tries to use KDtree
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from . import exceptions
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cKDTree = exceptions.closure(E)
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def merge_vertices(mesh,
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merge_tex=False,
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merge_norm=False,
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digits_vertex=None,
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digits_norm=2,
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digits_uv=4,
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**kwargs):
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"""
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Removes duplicate vertices. By default, based on integer hashes of
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each row.
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Parameters
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-------------
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mesh : Trimesh object
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Mesh to merge vertices on
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merge_tex : bool
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If True textured meshes with UV coordinates will
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have vertices merged regardless of UV coordinates
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merge_norm : bool
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If True, meshes with vertex normals will have
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vertices merged ignoring different normals
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digits_vertex : None or int
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Number of digits to consider for vertex position
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digits_norm : int
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Number of digits to consider for unit normals
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digits_uv : int
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Number of digits to consider for UV coordinates
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"""
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# use tol.merge if digit precision not passed
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if not isinstance(digits_vertex, int):
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digits_vertex = util.decimal_to_digits(tol.merge)
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# if we have a ton of unreferenced vertices it will
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# make the unique_rows call super slow so cull first
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if hasattr(mesh, 'faces') and len(mesh.faces) > 0:
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referenced = np.zeros(len(mesh.vertices), dtype=np.bool)
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referenced[mesh.faces] = True
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else:
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# this is used for geometry without faces
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referenced = np.ones(len(mesh.vertices), dtype=np.bool)
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# collect vertex attributes into sequence we can stack
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stacked = [mesh.vertices * (10 ** digits_vertex)]
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# UV texture visuals require us to update the
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# vertices and normals differently
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if (not merge_tex and
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mesh.visual.defined and
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mesh.visual.kind == 'texture' and
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mesh.visual.uv is not None and
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len(mesh.visual.uv) == len(mesh.vertices)):
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# get an array with vertices and UV coordinates
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# converted to integers at requested precision
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stacked.append(mesh.visual.uv * (10 ** digits_uv))
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# check to see if we have vertex normals
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normals = mesh._cache['vertex_normals']
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if not merge_norm and np.shape(normals) == mesh.vertices.shape:
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stacked.append(normals * (10 ** digits_norm))
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# stack collected vertex properties and round to integer
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stacked = np.column_stack(stacked).round().astype(np.int64)
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# check unique rows of referenced vertices
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u, i = unique_rows(stacked[referenced])
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# construct an inverse using the subset
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inverse = np.zeros(len(mesh.vertices), dtype=np.int64)
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inverse[referenced] = i
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# get the vertex mask
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mask = np.nonzero(referenced)[0][u]
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# run the update including normals and UV coordinates
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mesh.update_vertices(mask=mask, inverse=inverse)
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def group(values, min_len=0, max_len=np.inf):
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"""
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Return the indices of values that are identical
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Parameters
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----------
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values : (n,) int
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Values to group
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min_len : int
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The shortest group allowed
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All groups will have len >= min_length
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max_len : int
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The longest group allowed
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All groups will have len <= max_length
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Returns
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----------
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groups : sequence
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Contains indices to form groups
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IE [0,1,0,1] returns [[0,2], [1,3]]
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"""
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original = np.asanyarray(values)
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# save the sorted order and then apply it
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order = original.argsort()
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values = original[order]
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# find the indexes which are duplicates
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if values.dtype.kind == 'f':
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# for floats in a sorted array, neighbors are not duplicates
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# if the difference between them is greater than approximate zero
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nondupe = np.greater(np.abs(np.diff(values)), tol.zero)
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else:
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# for ints and strings we can check exact non- equality
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# for all other types this will only work if they defined
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# an __eq__
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nondupe = values[1:] != values[:-1]
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dupe_idx = np.append(0, np.nonzero(nondupe)[0] + 1)
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dupe_len = np.diff(np.concatenate((dupe_idx, [len(values)])))
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dupe_ok = np.logical_and(np.greater_equal(dupe_len, min_len),
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np.less_equal(dupe_len, max_len))
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groups = [order[i:(i + j)]
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for i, j in zip(dupe_idx[dupe_ok],
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dupe_len[dupe_ok])]
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groups = np.array(groups)
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return groups
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def hashable_rows(data, digits=None):
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"""
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We turn our array into integers based on the precision
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given by digits and then put them in a hashable format.
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Parameters
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---------
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data : (n, m) array
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Input data
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digits : int or None
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How many digits to add to hash if data is floating point
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If None, tol.merge will be used
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Returns
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---------
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hashable : (n,) array
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Custom data type which can be sorted
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or used as hash keys
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"""
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# if there is no data return immediately
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if len(data) == 0:
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return np.array([])
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# get array as integer to precision we care about
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as_int = float_to_int(data, digits=digits)
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# if it is flat integers already, return
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if len(as_int.shape) == 1:
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return as_int
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# if array is 2D and smallish, we can try bitbanging
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# this is significantly faster than the custom dtype
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if len(as_int.shape) == 2 and as_int.shape[1] <= 4:
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# time for some righteous bitbanging
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# can we pack the whole row into a single 64 bit integer
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precision = int(np.floor(64 / as_int.shape[1]))
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# if the max value is less than precision we can do this
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if np.abs(as_int).max() < 2**(precision - 1):
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# the resulting package
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hashable = np.zeros(len(as_int), dtype=np.int64)
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# loop through each column and bitwise xor to combine
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# make sure as_int is int64 otherwise bit offset won't work
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for offset, column in enumerate(as_int.astype(np.int64).T):
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# will modify hashable in place
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np.bitwise_xor(hashable,
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column << (offset * precision),
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out=hashable)
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return hashable
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# reshape array into magical data type that is weird but hashable
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dtype = np.dtype((np.void, as_int.dtype.itemsize * as_int.shape[1]))
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# make sure result is contiguous and flat
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hashable = np.ascontiguousarray(as_int).view(dtype).reshape(-1)
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return hashable
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def float_to_int(data, digits=None, dtype=np.int32):
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"""
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Given a numpy array of float/bool/int, return as integers.
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Parameters
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-------------
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data : (n, d) float, int, or bool
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Input data
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digits : float or int
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Precision for float conversion
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dtype : numpy.dtype
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What datatype should result be returned as
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Returns
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-------------
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as_int : (n, d) int
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Data as integers
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"""
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# convert to any numpy array
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data = np.asanyarray(data)
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# if data is already an integer or boolean we're done
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# if the data is empty we are also done
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if data.dtype.kind in 'ib' or data.size == 0:
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return data.astype(dtype)
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# populate digits from kwargs
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if digits is None:
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digits = util.decimal_to_digits(tol.merge)
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elif isinstance(digits, float) or isinstance(digits, np.float):
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digits = util.decimal_to_digits(digits)
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elif not (isinstance(digits, int) or isinstance(digits, np.integer)):
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log.warning('Digits were passed as %s!', digits.__class__.__name__)
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raise ValueError('Digits must be None, int, or float!')
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# data is float so convert to large integers
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data_max = np.abs(data).max() * 10**digits
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# ignore passed dtype if we have something large
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dtype = [np.int32, np.int64][int(data_max > 2**31)]
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# multiply by requested power of ten
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# then subtract small epsilon to avoid "go either way" rounding
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# then do the rounding and convert to integer
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as_int = np.round((data * 10 ** digits) - 1e-6).astype(dtype)
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return as_int
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def unique_ordered(data):
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"""
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Returns the same as np.unique, but ordered as per the
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first occurrence of the unique value in data.
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Examples
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---------
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In [1]: a = [0, 3, 3, 4, 1, 3, 0, 3, 2, 1]
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In [2]: np.unique(a)
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Out[2]: array([0, 1, 2, 3, 4])
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In [3]: trimesh.grouping.unique_ordered(a)
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Out[3]: array([0, 3, 4, 1, 2])
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"""
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data = np.asanyarray(data)
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order = np.sort(np.unique(data, return_index=True)[1])
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result = data[order]
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return result
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def unique_bincount(values,
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minlength=0,
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return_inverse=False,
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return_counts=False):
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"""
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For arrays of integers find unique values using bin counting.
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Roughly 10x faster for correct input than np.unique
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Parameters
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--------------
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values : (n,) int
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Values to find unique members of
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minlength : int
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Maximum value that will occur in values (values.max())
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return_inverse : bool
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If True, return an inverse such that unique[inverse] == values
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return_counts : bool
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If True, also return the number of times each
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unique item appears in values
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Returns
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------------
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unique : (m,) int
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Unique values in original array
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inverse : (n,) int, optional
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An array such that unique[inverse] == values
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Only returned if return_inverse is True
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counts : (m,) int, optional
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An array holding the counts of each unique item in values
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Only returned if return_counts is True
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"""
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values = np.asanyarray(values)
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if len(values.shape) != 1 or values.dtype.kind != 'i':
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raise ValueError('input must be 1D integers!')
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try:
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# count the number of occurrences of each value
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counts = np.bincount(values, minlength=minlength)
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except TypeError:
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# casting failed on 32 bit windows
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log.warning('casting failed, falling back!')
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# fall back to numpy unique
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return np.unique(values,
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return_inverse=return_inverse,
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return_counts=return_counts)
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# which bins are occupied at all
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# counts are integers so this works
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unique_bin = counts.astype(np.bool)
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# which values are unique
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# indexes correspond to original values
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unique = np.where(unique_bin)[0]
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ret = (unique,)
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if return_inverse:
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# find the inverse to reconstruct original
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inverse = (np.cumsum(unique_bin) - 1)[values]
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ret += (inverse,)
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if return_counts:
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unique_counts = counts[unique]
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ret += (unique_counts,)
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if len(ret) == 1:
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return ret[0]
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return ret
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def merge_runs(data, digits=None):
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"""
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Merge duplicate sequential values. This differs from unique_ordered
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in that values can occur in multiple places in the sequence, but
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only consecutive repeats are removed
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Parameters
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-----------
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data: (n,) float or int
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Returns
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--------
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merged: (m,) float or int
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Examples
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---------
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In [1]: a
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Out[1]:
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array([-1, -1, -1, 0, 0, 1, 1, 2, 0,
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3, 3, 4, 4, 5, 5, 6, 6, 7,
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7, 8, 8, 9, 9, 9])
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In [2]: trimesh.grouping.merge_runs(a)
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Out[2]: array([-1, 0, 1, 2, 0, 3, 4, 5, 6, 7, 8, 9])
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"""
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data = np.asanyarray(data)
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mask = np.abs(np.diff(data)) > tol.merge
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mask = np.concatenate((np.array([True]), mask))
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return data[mask]
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def unique_float(data,
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return_index=False,
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return_inverse=False,
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digits=None):
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"""
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Identical to the numpy.unique command, except evaluates floating point
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numbers, using a specified number of digits.
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If digits isn't specified, the library default TOL_MERGE will be used.
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"""
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data = np.asanyarray(data)
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as_int = float_to_int(data, digits)
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_junk, unique, inverse = np.unique(as_int,
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return_index=True,
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return_inverse=True)
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if (not return_index) and (not return_inverse):
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return data[unique]
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result = [data[unique]]
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if return_index:
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result.append(unique)
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if return_inverse:
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result.append(inverse)
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return tuple(result)
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def unique_rows(data, digits=None):
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"""
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Returns indices of unique rows. It will return the
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first occurrence of a row that is duplicated:
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[[1,2], [3,4], [1,2]] will return [0,1]
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Parameters
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---------
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data : (n, m) array
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Floating point data
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digits : int or None
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How many digits to consider
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Returns
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--------
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unique : (j,) int
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Index in data which is a unique row
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inverse : (n,) int
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Array to reconstruct original
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Example: unique[inverse] == data
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"""
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hashes = hashable_rows(data, digits=digits)
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garbage, unique, inverse = np.unique(
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hashes,
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return_index=True,
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return_inverse=True)
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return unique, inverse
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def unique_value_in_row(data, unique=None):
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"""
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For a 2D array of integers find the position of a
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value in each row which only occurs once.
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If there are more than one value per row which
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occur once, the last one is returned.
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Parameters
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----------
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data : (n, d) int
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Data to check values
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unique : (m,) int
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List of unique values contained in data.
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Generated from np.unique if not passed
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Returns
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---------
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result : (n, d) bool
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With one or zero True values per row.
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|
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Examples
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-------------------------------------
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In [0]: r = np.array([[-1, 1, 1],
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[-1, 1, -1],
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[-1, 1, 1],
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[-1, 1, -1],
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[-1, 1, -1]], dtype=np.int8)
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In [1]: unique_value_in_row(r)
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Out[1]:
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array([[ True, False, False],
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[False, True, False],
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[ True, False, False],
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[False, True, False],
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[False, True, False]], dtype=bool)
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In [2]: unique_value_in_row(r).sum(axis=1)
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Out[2]: array([1, 1, 1, 1, 1])
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In [3]: r[unique_value_in_row(r)]
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Out[3]: array([-1, 1, -1, 1, 1], dtype=int8)
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"""
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if unique is None:
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unique = np.unique(data)
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data = np.asanyarray(data)
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result = np.zeros_like(data, dtype=np.bool, subok=False)
|
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for value in unique:
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test = np.equal(data, value)
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test_ok = test.sum(axis=1) == 1
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result[test_ok] = test[test_ok]
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return result
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|
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|
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def group_rows(data, require_count=None, digits=None):
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"""
|
|
Returns index groups of duplicate rows, for example:
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[[1,2], [3,4], [1,2]] will return [[0,2], [1]]
|
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|
|
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|
Note that using require_count allows numpy advanced
|
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indexing to be used in place of looping and
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checking hashes and is ~10x faster.
|
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|
|
|
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Parameters
|
|
----------
|
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data : (n, m) array
|
|
Data to group
|
|
require_count : None or int
|
|
Only return groups of a specified length, eg:
|
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require_count = 2
|
|
[[1,2], [3,4], [1,2]] will return [[0,2]]
|
|
digits : None or int
|
|
If data is floating point how many decimals
|
|
to consider, or calculated from tol.merge
|
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|
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Returns
|
|
----------
|
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groups : sequence (*,) int
|
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Indices from in indicating identical rows.
|
|
"""
|
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|
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def group_dict():
|
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"""
|
|
Simple hash table based grouping.
|
|
The loop and appends make this rather slow on
|
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large arrays but it works on irregular groups.
|
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"""
|
|
observed = dict()
|
|
hashable = hashable_rows(data, digits=digits)
|
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for index, key in enumerate(hashable):
|
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key_string = key.tostring()
|
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if key_string in observed:
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observed[key_string].append(index)
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else:
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observed[key_string] = [index]
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return np.array(list(observed.values()))
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|
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def group_slice():
|
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# create a representation of the rows that can be sorted
|
|
hashable = hashable_rows(data, digits=digits)
|
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# record the order of the rows so we can get the original indices back
|
|
# later
|
|
order = np.argsort(hashable)
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|
# but for now, we want our hashes sorted
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|
hashable = hashable[order]
|
|
# this is checking each neighbour for equality, example:
|
|
# example: hashable = [1, 1, 1]; dupe = [0, 0]
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dupe = hashable[1:] != hashable[:-1]
|
|
# we want the first index of a group, so we can slice from that location
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|
# example: hashable = [0 1 1]; dupe = [1,0]; dupe_idx = [0,1]
|
|
dupe_idx = np.append(0, np.nonzero(dupe)[0] + 1)
|
|
# if you wanted to use this one function to deal with non- regular groups
|
|
# you could use: np.array_split(dupe_idx)
|
|
# this is roughly 3x slower than using the group_dict method above.
|
|
start_ok = np.diff(
|
|
np.concatenate((dupe_idx, [len(hashable)]))) == require_count
|
|
groups = np.tile(dupe_idx[start_ok].reshape((-1, 1)),
|
|
require_count) + np.arange(require_count)
|
|
groups_idx = order[groups]
|
|
if require_count == 1:
|
|
return groups_idx.reshape(-1)
|
|
return groups_idx
|
|
|
|
if require_count is None:
|
|
return group_dict()
|
|
else:
|
|
return group_slice()
|
|
|
|
|
|
def boolean_rows(a, b, operation=np.intersect1d):
|
|
"""
|
|
Find the rows in two arrays which occur in both rows.
|
|
|
|
Parameters
|
|
---------
|
|
a: (n, d) int
|
|
Array with row vectors
|
|
b: (m, d) int
|
|
Array with row vectors
|
|
operation : function
|
|
Numpy boolean set operation function:
|
|
-np.intersect1d
|
|
-np.setdiff1d
|
|
|
|
Returns
|
|
--------
|
|
shared: (p, d) array containing rows in both a and b
|
|
"""
|
|
a = np.asanyarray(a, dtype=np.int64)
|
|
b = np.asanyarray(b, dtype=np.int64)
|
|
|
|
av = a.view([('', a.dtype)] * a.shape[1]).ravel()
|
|
bv = b.view([('', b.dtype)] * b.shape[1]).ravel()
|
|
shared = operation(av, bv).view(a.dtype).reshape(-1, a.shape[1])
|
|
|
|
return shared
|
|
|
|
|
|
def group_vectors(vectors,
|
|
angle=1e-4,
|
|
include_negative=False):
|
|
"""
|
|
Group vectors based on an angle tolerance, with the option to
|
|
include negative vectors.
|
|
|
|
Parameters
|
|
-----------
|
|
vectors : (n,3) float
|
|
Direction vector
|
|
angle : float
|
|
Group vectors closer than this angle in radians
|
|
include_negative : bool
|
|
If True consider the same:
|
|
[0,0,1] and [0,0,-1]
|
|
|
|
Returns
|
|
------------
|
|
new_vectors : (m,3) float
|
|
Direction vector
|
|
groups : (m,) sequence of int
|
|
Indices of source vectors
|
|
"""
|
|
|
|
vectors = np.asanyarray(vectors, dtype=np.float64)
|
|
angle = float(angle)
|
|
|
|
if include_negative:
|
|
vectors = util.vector_hemisphere(vectors)
|
|
|
|
spherical = util.vector_to_spherical(vectors)
|
|
angles, groups = group_distance(spherical, angle)
|
|
new_vectors = util.spherical_to_vector(angles)
|
|
return new_vectors, groups
|
|
|
|
|
|
def group_distance(values, distance):
|
|
"""
|
|
Find groups of points which have neighbours closer than radius,
|
|
where no two points in a group are farther than distance apart.
|
|
|
|
Parameters
|
|
---------
|
|
points : (n, d) float
|
|
Points of dimension d
|
|
distance : float
|
|
Max distance between points in a cluster
|
|
|
|
Returns
|
|
----------
|
|
unique : (m, d) float
|
|
Median value of each group
|
|
groups : (m) sequence of int
|
|
Indexes of points that make up a group
|
|
|
|
"""
|
|
values = np.asanyarray(values,
|
|
dtype=np.float64)
|
|
|
|
consumed = np.zeros(len(values),
|
|
dtype=np.bool)
|
|
tree = cKDTree(values)
|
|
|
|
# (n, d) set of values that are unique
|
|
unique = []
|
|
# (n) sequence of indices in values
|
|
groups = []
|
|
|
|
for index, value in enumerate(values):
|
|
if consumed[index]:
|
|
continue
|
|
group = np.array(tree.query_ball_point(value, distance),
|
|
dtype=np.int)
|
|
consumed[group] = True
|
|
unique.append(np.median(values[group], axis=0))
|
|
groups.append(group)
|
|
return np.array(unique), np.array(groups)
|
|
|
|
|
|
def clusters(points, radius):
|
|
"""
|
|
Find clusters of points which have neighbours closer than radius
|
|
|
|
Parameters
|
|
---------
|
|
points : (n, d) float
|
|
Points of dimension d
|
|
radius : float
|
|
Max distance between points in a cluster
|
|
|
|
Returns
|
|
----------
|
|
groups : (m,) sequence of int
|
|
Indices of points in a cluster
|
|
|
|
"""
|
|
from . import graph
|
|
tree = cKDTree(points)
|
|
|
|
# some versions return pairs as a set of tuples
|
|
pairs = tree.query_pairs(r=radius, output_type='ndarray')
|
|
# group connected components
|
|
groups = graph.connected_components(pairs)
|
|
|
|
return groups
|
|
|
|
|
|
def blocks(data,
|
|
min_len=2,
|
|
max_len=np.inf,
|
|
wrap=False,
|
|
digits=None,
|
|
only_nonzero=False):
|
|
"""
|
|
Find the indices in an array of contiguous blocks
|
|
of equal values.
|
|
|
|
Parameters
|
|
------------
|
|
data : (n,) array
|
|
Data to find blocks on
|
|
min_len : int
|
|
The minimum length group to be returned
|
|
max_len : int
|
|
The maximum length group to be retuurned
|
|
wrap : bool
|
|
Combine blocks on both ends of 1D array
|
|
digits : None or int
|
|
If dealing with floats how many digits to consider
|
|
only_nonzero : bool
|
|
Only return blocks of non- zero values
|
|
|
|
Returns
|
|
---------
|
|
blocks : (m) sequence of (*,) int
|
|
Indices referencing data
|
|
"""
|
|
data = float_to_int(data, digits=digits)
|
|
|
|
# find the inflection points
|
|
# AKA locations where the array goes from True to False.
|
|
infl = np.concatenate(([0],
|
|
np.nonzero(np.diff(data))[0] + 1,
|
|
[len(data)]))
|
|
infl_len = np.diff(infl)
|
|
# check the length of each group
|
|
infl_ok = np.logical_and(infl_len >= min_len,
|
|
infl_len <= max_len)
|
|
|
|
if only_nonzero:
|
|
# check to make sure the values of each contiguous block
|
|
# are True by checking the first value of each block
|
|
infl_ok = np.logical_and(
|
|
infl_ok, data[infl[:-1]])
|
|
|
|
# inflate start/end indexes into full ranges of values
|
|
blocks = [np.arange(infl[i], infl[i + 1])
|
|
for i, ok in enumerate(infl_ok) if ok]
|
|
|
|
if wrap:
|
|
# wrap only matters if first and last points are the same
|
|
if data[0] != data[-1]:
|
|
return blocks
|
|
# if we are only grouping nonzero things and
|
|
# the first and last point are zero we can exit
|
|
if only_nonzero and not bool(data[0]):
|
|
return blocks
|
|
|
|
# so now first point equals last point, so the cases are:
|
|
# - first and last point are in a block: combine two blocks
|
|
# - first OR last point are in block: add other point to block
|
|
# - neither are in a block: check if combined is eligible block
|
|
|
|
# first point is in a block
|
|
first = len(blocks) > 0 and blocks[0][0] == 0
|
|
# last point is in a block
|
|
last = len(blocks) > 0 and blocks[-1][-1] == (len(data) - 1)
|
|
|
|
# CASE: first and last point are BOTH in block: combine blocks
|
|
if first and last:
|
|
blocks[0] = np.append(blocks[-1], blocks[0])
|
|
blocks.pop()
|
|
else:
|
|
# combined length
|
|
combined = infl_len[0] + infl_len[-1]
|
|
# exit if lengths aren't OK
|
|
if combined < min_len or combined > max_len:
|
|
return blocks
|
|
# new block combines both ends
|
|
new_block = np.append(np.arange(infl[-2], infl[-1]),
|
|
np.arange(infl[0], infl[1]))
|
|
# we are in a first OR last situation now
|
|
if first:
|
|
# first was already in a block so replace it with combined
|
|
blocks[0] = new_block
|
|
elif last:
|
|
# last was already in a block so replace with superset
|
|
blocks[-1] = new_block
|
|
else:
|
|
# both are false
|
|
# combined length generated new block
|
|
blocks.append(new_block)
|
|
|
|
return blocks
|
|
|
|
|
|
def group_min(groups, data):
|
|
"""
|
|
Given a list of groups find the minimum element of data
|
|
within each group
|
|
|
|
Parameters
|
|
-----------
|
|
groups : (n,) sequence of (q,) int
|
|
Indexes of each group corresponding to each element in data
|
|
data : (m,)
|
|
The data that groups indexes reference
|
|
|
|
Returns
|
|
-----------
|
|
minimums : (n,)
|
|
Minimum value of data per group
|
|
|
|
"""
|
|
# sort with major key groups, minor key data
|
|
order = np.lexsort((data, groups))
|
|
groups = groups[order] # this is only needed if groups is unsorted
|
|
data = data[order]
|
|
# construct an index which marks borders between groups
|
|
index = np.empty(len(groups), 'bool')
|
|
index[0] = True
|
|
index[1:] = groups[1:] != groups[:-1]
|
|
return data[index]
|