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"""Utilities to work with sparse matrices and arrays written in Cython."""
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
from libc.math cimport fabs, sqrt, isnan
from libc.stdint cimport intptr_t
import numpy as np
from cython cimport floating
from ..utils._typedefs cimport float64_t, int32_t, int64_t, intp_t, uint64_t
ctypedef fused integral:
int32_t
int64_t
def csr_row_norms(X):
"""Squared L2 norm of each row in CSR matrix X."""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
return _sqeuclidean_row_norms_sparse(X.data, X.indptr)
def _sqeuclidean_row_norms_sparse(
const floating[::1] X_data,
const integral[::1] X_indptr,
):
cdef:
integral n_samples = X_indptr.shape[0] - 1
integral i, j
dtype = np.float32 if floating is float else np.float64
cdef floating[::1] squared_row_norms = np.zeros(n_samples, dtype=dtype)
with nogil:
for i in range(n_samples):
for j in range(X_indptr[i], X_indptr[i + 1]):
squared_row_norms[i] += X_data[j] * X_data[j]
return np.asarray(squared_row_norms)
def csr_mean_variance_axis0(X, weights=None, return_sum_weights=False):
"""Compute mean and variance along axis 0 on a CSR matrix
Uses a np.float64 accumulator.
Parameters
----------
X : CSR sparse matrix, shape (n_samples, n_features)
Input data.
weights : ndarray of shape (n_samples,), dtype=floating, default=None
If it is set to None samples will be equally weighted.
.. versionadded:: 0.24
return_sum_weights : bool, default=False
If True, returns the sum of weights seen for each feature.
.. versionadded:: 0.24
Returns
-------
means : float array with shape (n_features,)
Feature-wise means
variances : float array with shape (n_features,)
Feature-wise variances
sum_weights : ndarray of shape (n_features,), dtype=floating
Returned if return_sum_weights is True.
"""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
if weights is None:
weights = np.ones(X.shape[0], dtype=X.dtype)
means, variances, sum_weights = _csr_mean_variance_axis0(
X.data, X.shape[0], X.shape[1], X.indices, X.indptr, weights)
if return_sum_weights:
return means, variances, sum_weights
return means, variances
def _csr_mean_variance_axis0(
const floating[::1] X_data,
uint64_t n_samples,
uint64_t n_features,
const integral[:] X_indices,
const integral[:] X_indptr,
const floating[:] weights,
):
# Implement the function here since variables using fused types
# cannot be declared directly and can only be passed as function arguments
cdef:
intp_t row_ind
uint64_t feature_idx
integral i, col_ind
float64_t diff
# means[j] contains the mean of feature j
float64_t[::1] means = np.zeros(n_features)
# variances[j] contains the variance of feature j
float64_t[::1] variances = np.zeros(n_features)
float64_t[::1] sum_weights = np.full(
fill_value=np.sum(weights, dtype=np.float64), shape=n_features
)
float64_t[::1] sum_weights_nz = np.zeros(shape=n_features)
float64_t[::1] correction = np.zeros(shape=n_features)
uint64_t[::1] counts = np.full(
fill_value=weights.shape[0], shape=n_features, dtype=np.uint64
)
uint64_t[::1] counts_nz = np.zeros(shape=n_features, dtype=np.uint64)
for row_ind in range(len(X_indptr) - 1):
for i in range(X_indptr[row_ind], X_indptr[row_ind + 1]):
col_ind = X_indices[i]
if not isnan(X_data[i]):
means[col_ind] += <float64_t>(X_data[i]) * weights[row_ind]
# sum of weights where X[:, col_ind] is non-zero
sum_weights_nz[col_ind] += weights[row_ind]
# number of non-zero elements of X[:, col_ind]
counts_nz[col_ind] += 1
else:
# sum of weights where X[:, col_ind] is not nan
sum_weights[col_ind] -= weights[row_ind]
# number of non nan elements of X[:, col_ind]
counts[col_ind] -= 1
for feature_idx in range(n_features):
means[feature_idx] /= sum_weights[feature_idx]
for row_ind in range(len(X_indptr) - 1):
for i in range(X_indptr[row_ind], X_indptr[row_ind + 1]):
col_ind = X_indices[i]
if not isnan(X_data[i]):
diff = X_data[i] - means[col_ind]
# correction term of the corrected 2 pass algorithm.
# See "Algorithms for computing the sample variance: analysis
# and recommendations", by Chan, Golub, and LeVeque.
correction[col_ind] += diff * weights[row_ind]
variances[col_ind] += diff * diff * weights[row_ind]
for feature_idx in range(n_features):
if counts[feature_idx] != counts_nz[feature_idx]:
correction[feature_idx] -= (
sum_weights[feature_idx] - sum_weights_nz[feature_idx]
) * means[feature_idx]
correction[feature_idx] = correction[feature_idx]**2 / sum_weights[feature_idx]
if counts[feature_idx] != counts_nz[feature_idx]:
# only compute it when it's guaranteed to be non-zero to avoid
# catastrophic cancellation.
variances[feature_idx] += (
sum_weights[feature_idx] - sum_weights_nz[feature_idx]
) * means[feature_idx]**2
variances[feature_idx] = (
(variances[feature_idx] - correction[feature_idx]) /
sum_weights[feature_idx]
)
if floating is float:
return (
np.array(means, dtype=np.float32),
np.array(variances, dtype=np.float32),
np.array(sum_weights, dtype=np.float32),
)
else:
return (
np.asarray(means), np.asarray(variances), np.asarray(sum_weights)
)
def csc_mean_variance_axis0(X, weights=None, return_sum_weights=False):
"""Compute mean and variance along axis 0 on a CSC matrix
Uses a np.float64 accumulator.
Parameters
----------
X : CSC sparse matrix, shape (n_samples, n_features)
Input data.
weights : ndarray of shape (n_samples,), dtype=floating, default=None
If it is set to None samples will be equally weighted.
.. versionadded:: 0.24
return_sum_weights : bool, default=False
If True, returns the sum of weights seen for each feature.
.. versionadded:: 0.24
Returns
-------
means : float array with shape (n_features,)
Feature-wise means
variances : float array with shape (n_features,)
Feature-wise variances
sum_weights : ndarray of shape (n_features,), dtype=floating
Returned if return_sum_weights is True.
"""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
if weights is None:
weights = np.ones(X.shape[0], dtype=X.dtype)
means, variances, sum_weights = _csc_mean_variance_axis0(
X.data, X.shape[0], X.shape[1], X.indices, X.indptr, weights)
if return_sum_weights:
return means, variances, sum_weights
return means, variances
def _csc_mean_variance_axis0(
const floating[::1] X_data,
uint64_t n_samples,
uint64_t n_features,
const integral[:] X_indices,
const integral[:] X_indptr,
const floating[:] weights,
):
# Implement the function here since variables using fused types
# cannot be declared directly and can only be passed as function arguments
cdef:
integral i, row_ind
uint64_t feature_idx, col_ind
float64_t diff
# means[j] contains the mean of feature j
float64_t[::1] means = np.zeros(n_features)
# variances[j] contains the variance of feature j
float64_t[::1] variances = np.zeros(n_features)
float64_t[::1] sum_weights = np.full(
fill_value=np.sum(weights, dtype=np.float64), shape=n_features
)
float64_t[::1] sum_weights_nz = np.zeros(shape=n_features)
float64_t[::1] correction = np.zeros(shape=n_features)
uint64_t[::1] counts = np.full(
fill_value=weights.shape[0], shape=n_features, dtype=np.uint64
)
uint64_t[::1] counts_nz = np.zeros(shape=n_features, dtype=np.uint64)
for col_ind in range(n_features):
for i in range(X_indptr[col_ind], X_indptr[col_ind + 1]):
row_ind = X_indices[i]
if not isnan(X_data[i]):
means[col_ind] += <float64_t>(X_data[i]) * weights[row_ind]
# sum of weights where X[:, col_ind] is non-zero
sum_weights_nz[col_ind] += weights[row_ind]
# number of non-zero elements of X[:, col_ind]
counts_nz[col_ind] += 1
else:
# sum of weights where X[:, col_ind] is not nan
sum_weights[col_ind] -= weights[row_ind]
# number of non nan elements of X[:, col_ind]
counts[col_ind] -= 1
for feature_idx in range(n_features):
means[feature_idx] /= sum_weights[feature_idx]
for col_ind in range(n_features):
for i in range(X_indptr[col_ind], X_indptr[col_ind + 1]):
row_ind = X_indices[i]
if not isnan(X_data[i]):
diff = X_data[i] - means[col_ind]
# correction term of the corrected 2 pass algorithm.
# See "Algorithms for computing the sample variance: analysis
# and recommendations", by Chan, Golub, and LeVeque.
correction[col_ind] += diff * weights[row_ind]
variances[col_ind] += diff * diff * weights[row_ind]
for feature_idx in range(n_features):
if counts[feature_idx] != counts_nz[feature_idx]:
correction[feature_idx] -= (
sum_weights[feature_idx] - sum_weights_nz[feature_idx]
) * means[feature_idx]
correction[feature_idx] = correction[feature_idx]**2 / sum_weights[feature_idx]
if counts[feature_idx] != counts_nz[feature_idx]:
# only compute it when it's guaranteed to be non-zero to avoid
# catastrophic cancellation.
variances[feature_idx] += (
sum_weights[feature_idx] - sum_weights_nz[feature_idx]
) * means[feature_idx]**2
variances[feature_idx] = (
(variances[feature_idx] - correction[feature_idx])
) / sum_weights[feature_idx]
if floating is float:
return (np.array(means, dtype=np.float32),
np.array(variances, dtype=np.float32),
np.array(sum_weights, dtype=np.float32))
else:
return (
np.asarray(means), np.asarray(variances), np.asarray(sum_weights)
)
def incr_mean_variance_axis0(X, last_mean, last_var, last_n, weights=None):
"""Compute mean and variance along axis 0 on a CSR or CSC matrix.
last_mean, last_var are the statistics computed at the last step by this
function. Both must be initialized to 0.0. last_n is the
number of samples encountered until now and is initialized at 0.
Parameters
----------
X : CSR or CSC sparse matrix, shape (n_samples, n_features)
Input data.
last_mean : float array with shape (n_features,)
Array of feature-wise means to update with the new data X.
last_var : float array with shape (n_features,)
Array of feature-wise var to update with the new data X.
last_n : float array with shape (n_features,)
Sum of the weights seen so far (if weights are all set to 1
this will be the same as number of samples seen so far, before X).
weights : float array with shape (n_samples,) or None. If it is set
to None samples will be equally weighted.
Returns
-------
updated_mean : float array with shape (n_features,)
Feature-wise means
updated_variance : float array with shape (n_features,)
Feature-wise variances
updated_n : int array with shape (n_features,)
Updated number of samples seen
Notes
-----
NaNs are ignored during the computation.
References
----------
T. Chan, G. Golub, R. LeVeque. Algorithms for computing the sample
variance: recommendations, The American Statistician, Vol. 37, No. 3,
pp. 242-247
Also, see the non-sparse implementation of this in
`utils.extmath._batch_mean_variance_update`.
"""
if X.dtype not in [np.float32, np.float64]:
X = X.astype(np.float64)
X_dtype = X.dtype
if weights is None:
weights = np.ones(X.shape[0], dtype=X_dtype)
elif weights.dtype not in [np.float32, np.float64]:
weights = weights.astype(np.float64, copy=False)
if last_n.dtype not in [np.float32, np.float64]:
last_n = last_n.astype(np.float64, copy=False)
return _incr_mean_variance_axis0(X.data,
np.sum(weights),
X.shape[1],
X.indices,
X.indptr,
X.format,
last_mean.astype(X_dtype, copy=False),
last_var.astype(X_dtype, copy=False),
last_n.astype(X_dtype, copy=False),
weights.astype(X_dtype, copy=False))
def _incr_mean_variance_axis0(
const floating[:] X_data,
floating n_samples,
uint64_t n_features,
const int[:] X_indices,
# X_indptr might be either int32 or int64
const integral[:] X_indptr,
str X_format,
floating[:] last_mean,
floating[:] last_var,
floating[:] last_n,
# previous sum of the weights (ie float)
const floating[:] weights,
):
# Implement the function here since variables using fused types
# cannot be declared directly and can only be passed as function arguments
cdef:
uint64_t i
# last = stats until now
# new = the current increment
# updated = the aggregated stats
# when arrays, they are indexed by i per-feature
floating[::1] new_mean
floating[::1] new_var
floating[::1] updated_mean
floating[::1] updated_var
if floating is float:
dtype = np.float32
else:
dtype = np.float64
new_mean = np.zeros(n_features, dtype=dtype)
new_var = np.zeros_like(new_mean, dtype=dtype)
updated_mean = np.zeros_like(new_mean, dtype=dtype)
updated_var = np.zeros_like(new_mean, dtype=dtype)
cdef:
floating[::1] new_n
floating[::1] updated_n
floating[::1] last_over_new_n
# Obtain new stats first
updated_n = np.zeros(shape=n_features, dtype=dtype)
last_over_new_n = np.zeros_like(updated_n, dtype=dtype)
# X can be a CSR or CSC matrix
if X_format == 'csr':
new_mean, new_var, new_n = _csr_mean_variance_axis0(
X_data, n_samples, n_features, X_indices, X_indptr, weights)
else: # X_format == 'csc'
new_mean, new_var, new_n = _csc_mean_variance_axis0(
X_data, n_samples, n_features, X_indices, X_indptr, weights)
# First pass
cdef bint is_first_pass = True
for i in range(n_features):
if last_n[i] > 0:
is_first_pass = False
break
if is_first_pass:
return np.asarray(new_mean), np.asarray(new_var), np.asarray(new_n)
for i in range(n_features):
updated_n[i] = last_n[i] + new_n[i]
# Next passes
for i in range(n_features):
if new_n[i] > 0:
last_over_new_n[i] = dtype(last_n[i]) / dtype(new_n[i])
# Unnormalized stats
last_mean[i] *= last_n[i]
last_var[i] *= last_n[i]
new_mean[i] *= new_n[i]
new_var[i] *= new_n[i]
# Update stats
updated_var[i] = (
last_var[i] + new_var[i] +
last_over_new_n[i] / updated_n[i] *
(last_mean[i] / last_over_new_n[i] - new_mean[i])**2
)
updated_mean[i] = (last_mean[i] + new_mean[i]) / updated_n[i]
updated_var[i] /= updated_n[i]
else:
updated_var[i] = last_var[i]
updated_mean[i] = last_mean[i]
updated_n[i] = last_n[i]
return (
np.asarray(updated_mean),
np.asarray(updated_var),
np.asarray(updated_n),
)
def inplace_csr_row_normalize_l1(X):
"""Normalize inplace the rows of a CSR matrix or array by their L1 norm.
Parameters
----------
X : scipy.sparse.csr_matrix and scipy.sparse.csr_array, \
shape=(n_samples, n_features)
The input matrix or array to be modified inplace.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from sklearn.utils.sparsefuncs_fast import inplace_csr_row_normalize_l1
>>> import numpy as np
>>> indptr = np.array([0, 2, 3, 4])
>>> indices = np.array([0, 1, 2, 3])
>>> data = np.array([1.0, 2.0, 3.0, 4.0])
>>> X = csr_matrix((data, indices, indptr), shape=(3, 4))
>>> X.toarray()
array([[1., 2., 0., 0.],
[0., 0., 3., 0.],
[0., 0., 0., 4.]])
>>> inplace_csr_row_normalize_l1(X)
>>> X.toarray()
array([[0.33... , 0.66... , 0. , 0. ],
[0. , 0. , 1. , 0. ],
[0. , 0. , 0. , 1. ]])
"""
_inplace_csr_row_normalize_l1(X.data, X.shape, X.indices, X.indptr)
def _inplace_csr_row_normalize_l1(
floating[:] X_data,
shape,
const integral[:] X_indices,
const integral[:] X_indptr,
):
cdef:
uint64_t n_samples = shape[0]
# the column indices for row i are stored in:
# indices[indptr[i]:indices[i+1]]
# and their corresponding values are stored in:
# data[indptr[i]:indptr[i+1]]
uint64_t i
integral j
double sum_
for i in range(n_samples):
sum_ = 0.0
for j in range(X_indptr[i], X_indptr[i + 1]):
sum_ += fabs(X_data[j])
if sum_ == 0.0:
# do not normalize empty rows (can happen if CSR is not pruned
# correctly)
continue
for j in range(X_indptr[i], X_indptr[i + 1]):
X_data[j] /= sum_
def inplace_csr_row_normalize_l2(X):
"""Normalize inplace the rows of a CSR matrix or array by their L2 norm.
Parameters
----------
X : scipy.sparse.csr_matrix, shape=(n_samples, n_features)
The input matrix or array to be modified inplace.
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> from sklearn.utils.sparsefuncs_fast import inplace_csr_row_normalize_l2
>>> import numpy as np
>>> indptr = np.array([0, 2, 3, 4])
>>> indices = np.array([0, 1, 2, 3])
>>> data = np.array([1.0, 2.0, 3.0, 4.0])
>>> X = csr_matrix((data, indices, indptr), shape=(3, 4))
>>> X.toarray()
array([[1., 2., 0., 0.],
[0., 0., 3., 0.],
[0., 0., 0., 4.]])
>>> inplace_csr_row_normalize_l2(X)
>>> X.toarray()
array([[0.44... , 0.89... , 0. , 0. ],
[0. , 0. , 1. , 0. ],
[0. , 0. , 0. , 1. ]])
"""
_inplace_csr_row_normalize_l2(X.data, X.shape, X.indices, X.indptr)
def _inplace_csr_row_normalize_l2(
floating[:] X_data,
shape,
const integral[:] X_indices,
const integral[:] X_indptr,
):
cdef:
uint64_t n_samples = shape[0]
uint64_t i
integral j
double sum_
for i in range(n_samples):
sum_ = 0.0
for j in range(X_indptr[i], X_indptr[i + 1]):
sum_ += (X_data[j] * X_data[j])
if sum_ == 0.0:
# do not normalize empty rows (can happen if CSR is not pruned
# correctly)
continue
sum_ = sqrt(sum_)
for j in range(X_indptr[i], X_indptr[i + 1]):
X_data[j] /= sum_
def assign_rows_csr(
X,
const intptr_t[:] X_rows,
const intptr_t[:] out_rows,
floating[:, ::1] out,
):
"""Densify selected rows of a CSR matrix into a preallocated array.
Like out[out_rows] = X[X_rows].toarray() but without copying.
No-copy supported for both dtype=np.float32 and dtype=np.float64.
Parameters
----------
X : scipy.sparse.csr_matrix, shape=(n_samples, n_features)
X_rows : array, dtype=np.intp, shape=n_rows
out_rows : array, dtype=np.intp, shape=n_rows
out : array, shape=(arbitrary, n_features)
"""
cdef:
# intptr_t (npy_intp, np.intp in Python) is what np.where returns,
# but int is what scipy.sparse uses.
intp_t i, ind, j, k
intptr_t rX
const floating[:] data = X.data
const int32_t[:] indices = X.indices
const int32_t[:] indptr = X.indptr
if X_rows.shape[0] != out_rows.shape[0]:
raise ValueError("cannot assign %d rows to %d"
% (X_rows.shape[0], out_rows.shape[0]))
with nogil:
for k in range(out_rows.shape[0]):
out[out_rows[k]] = 0.0
for i in range(X_rows.shape[0]):
rX = X_rows[i]
for ind in range(indptr[rX], indptr[rX + 1]):
j = indices[ind]
out[out_rows[i], j] = data[ind]
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