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# Author: Leland McInnes <leland.mcinnes@gmail.com>
#
# License: BSD 3 clause
import time
from warnings import warn
import numpy as np
import numba
from sklearn.utils.validation import check_is_fitted
import scipy.sparse
@numba.njit(parallel=True)
def fast_knn_indices(X, n_neighbors):
"""A fast computation of knn indices.
Parameters
----------
X: array of shape (n_samples, n_features)
The input data to compute the k-neighbor indices of.
n_neighbors: int
The number of nearest neighbors to compute for each sample in ``X``.
Returns
-------
knn_indices: array of shape (n_samples, n_neighbors)
The indices on the ``n_neighbors`` closest points in the dataset.
"""
knn_indices = np.empty((X.shape[0], n_neighbors), dtype=np.int32)
for row in numba.prange(X.shape[0]):
# v = np.argsort(X[row]) # Need to call argsort this way for numba
v = X[row].argsort(kind="quicksort")
v = v[:n_neighbors]
knn_indices[row] = v
return knn_indices
@numba.njit("i4(i8[:])")
def tau_rand_int(state):
"""A fast (pseudo)-random number generator.
Parameters
----------
state: array of int64, shape (3,)
The internal state of the rng
Returns
-------
A (pseudo)-random int32 value
"""
state[0] = (((state[0] & 4294967294) << 12) & 0xFFFFFFFF) ^ (
(((state[0] << 13) & 0xFFFFFFFF) ^ state[0]) >> 19
)
state[1] = (((state[1] & 4294967288) << 4) & 0xFFFFFFFF) ^ (
(((state[1] << 2) & 0xFFFFFFFF) ^ state[1]) >> 25
)
state[2] = (((state[2] & 4294967280) << 17) & 0xFFFFFFFF) ^ (
(((state[2] << 3) & 0xFFFFFFFF) ^ state[2]) >> 11
)
return state[0] ^ state[1] ^ state[2]
@numba.njit("f4(i8[:])")
def tau_rand(state):
"""A fast (pseudo)-random number generator for floats in the range [0,1]
Parameters
----------
state: array of int64, shape (3,)
The internal state of the rng
Returns
-------
A (pseudo)-random float32 in the interval [0, 1]
"""
integer = tau_rand_int(state)
return abs(float(integer) / 0x7FFFFFFF)
@numba.njit()
def norm(vec):
"""Compute the (standard l2) norm of a vector.
Parameters
----------
vec: array of shape (dim,)
Returns
-------
The l2 norm of vec.
"""
result = 0.0
for i in range(vec.shape[0]):
result += vec[i] ** 2
return np.sqrt(result)
@numba.njit(parallel=True)
def submatrix(dmat, indices_col, n_neighbors):
"""Return a submatrix given an orginal matrix and the indices to keep.
Parameters
----------
dmat: array, shape (n_samples, n_samples)
Original matrix.
indices_col: array, shape (n_samples, n_neighbors)
Indices to keep. Each row consists of the indices of the columns.
n_neighbors: int
Number of neighbors.
Returns
-------
submat: array, shape (n_samples, n_neighbors)
The corresponding submatrix.
"""
n_samples_transform, n_samples_fit = dmat.shape
submat = np.zeros((n_samples_transform, n_neighbors), dtype=dmat.dtype)
for i in numba.prange(n_samples_transform):
for j in numba.prange(n_neighbors):
submat[i, j] = dmat[i, indices_col[i, j]]
return submat
# Generates a timestamp for use in logging messages when verbose=True
def ts():
return time.ctime(time.time())
# I'm not enough of a numba ninja to numba this successfully.
# np.arrays of lists, which are objects...
def csr_unique(matrix, return_index=True, return_inverse=True, return_counts=True):
"""Find the unique elements of a sparse csr matrix.
We don't explicitly construct the unique matrix leaving that to the user
who may not want to duplicate a massive array in memory.
Returns the indices of the input array that give the unique values.
Returns the indices of the unique array that reconstructs the input array.
Returns the number of times each unique row appears in the input matrix.
matrix: a csr matrix
return_index = bool, optional
If true, return the row indices of 'matrix'
return_inverse: bool, optional
If true, return the the indices of the unique array that can be
used to reconstruct 'matrix'.
return_counts = bool, optional
If true, returns the number of times each unique item appears in 'matrix'
The unique matrix can computed via
unique_matrix = matrix[index]
and the original matrix reconstructed via
unique_matrix[inverse]
"""
lil_matrix = matrix.tolil()
rows = np.asarray([tuple(x + y) for x, y in zip(lil_matrix.rows, lil_matrix.data)], dtype=object)
return_values = return_counts + return_inverse + return_index
return np.unique(
rows,
return_index=return_index,
return_inverse=return_inverse,
return_counts=return_counts,
)[1 : (return_values + 1)]
def disconnected_vertices(model):
"""
Returns a boolean vector indicating which vertices are disconnected from the umap graph.
These vertices will often be scattered across the space and make it difficult to focus on the main
manifold. They can either be filtered and have UMAP re-run or simply filtered from the interactive plotting tool
via the subset_points parameter.
Use ~disconnected_vertices(model) to only plot the connected points.
Parameters
----------
model: a trained UMAP model
Returns
-------
A boolean vector indicating which points are disconnected
"""
check_is_fitted(model, "graph_")
if model.unique:
vertices_disconnected = (
np.array(model.graph_[model._unique_inverse_].sum(axis=1)).flatten() == 0
)
else:
vertices_disconnected = np.array(model.graph_.sum(axis=1)).flatten() == 0
return vertices_disconnected
def average_nn_distance(dist_matrix):
"""Calculate the average distance to each points nearest neighbors.
Parameters
----------
dist_matrix: a csr_matrix
A distance matrix (usually umap_model.graph_)
Returns
-------
An array with the average distance to each points nearest neighbors
"""
(row_idx, col_idx, val) = scipy.sparse.find(dist_matrix)
# Count/sum is done per row
count_non_zero_elems = np.bincount(row_idx)
sum_non_zero_elems = np.bincount(row_idx, weights=val)
averages = sum_non_zero_elems / count_non_zero_elems
if any(np.isnan(averages)):
warn(
"Embedding contains disconnected vertices which will be ignored."
"Use umap.utils.disconnected_vertices() to identify them."
)
return averages
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