def d_TSV(mat):
dif_c = 2*cp.diff(mat,axis=1)
dif_1 = cp.pad(dif_c, [(0,0),(1,0)], mode = 'constant')
dif_2 = cp.pad(-dif_c, [(0,0),(0,1)], mode = 'constant')
dif_c= 2*cp.diff(mat,axis=0)
dif_3 = cp.pad(dif_c, [(1,0),(0,0)], mode = 'constant')
dif_4 = cp.pad(-dif_c, [(0,1),(0,0)], mode = 'constant')
return dif_1 + dif_2 + dif_3 + dif_4
def TSV(mat):
# TSV terms from left to right
dif_c = cp.diff(mat,axis=1)
sum_tsv1 = cp.sum(dif_c*dif_c)
# TSV terms from bottom to top
dif_c= cp.diff(mat,axis=0)
sum_tsv2 = cp.sum(dif_c*dif_c)
#Return all TSV terms
return sum_tsv1+sum_tsv2
def count_nonzero(X, axis=None, sample_weight=None):
"""A variant of X.getnnz() with extension to weighting on axis 0
Useful in efficiently calculating multilabel metrics.
Parameters
----------
X : CSR sparse matrix of shape (n_samples, n_labels)
Input data.
axis : None, 0 or 1
The axis on which the data is aggregated.
sample_weight : array-like of shape (n_samples,), default=None
Weight for each row of X.
"""
if axis == -1:
axis = 1
elif axis == -2:
axis = 0
elif X.format != 'csr':
raise TypeError('Expected CSR sparse format, got {0}'.format(X.format))
# We rely here on the fact that np.diff(Y.indptr) for a CSR
# will return the number of nonzero entries in each row.
# A bincount over Y.indices will return the number of nonzeros
# in each column. See ``csr_matrix.getnnz`` in scipy >= 0.14.
if axis is None:
if sample_weight is None:
return X.nnz
else:
return np.dot(np.diff(X.indptr), sample_weight)
elif axis == 1:
out = np.diff(X.indptr)
if sample_weight is None:
# astype here is for consistency with axis=0 dtype
return out.astype('intp')
return out * sample_weight
elif axis == 0:
if sample_weight is None:
return np.bincount(X.indices, minlength=X.shape[1])
else:
weights = np.repeat(sample_weight, np.diff(X.indptr))
return np.bincount(X.indices,
minlength=X.shape[1],
weights=weights)
else:
raise ValueError('Unsupported axis: {0}'.format(axis))
def average_precision_score(y_true, y_score):
"""
Compute average precision score using precision and recall computed from cuml.
"""
precision, recall, _ = precision_recall_curve(y_true, y_score)
# return step function integral
return -cp.sum(cp.diff(recall) * cp.array(precision)[:-1])
def _sparse_fit(self, X, strategy, missing_values, fill_value):
"""Fit the transformer on sparse data."""
mask_data = _get_mask(X.data, missing_values)
n_implicit_zeros = X.shape[0] - np.diff(X.indptr)
statistics = np.empty(X.shape[1])
if strategy == "constant":
# for constant strategy, self.statistcs_ is used to store
# fill_value in each column
statistics.fill(fill_value)
else:
for i in range(X.shape[1]):
column = X.data[X.indptr[i]:X.indptr[i + 1]]
mask_column = mask_data[X.indptr[i]:X.indptr[i + 1]]
column = column[~mask_column]
# combine explicit and implicit zeros
mask_zeros = _get_mask(column, 0)
column = column[~mask_zeros]
n_explicit_zeros = mask_zeros.sum()
n_zeros = n_implicit_zeros[i] + n_explicit_zeros
if strategy == "mean":
s = column.size + n_zeros
statistics[i] = np.nan if s == 0 else column.sum() / s
elif strategy == "median":
statistics[i] = _get_median(column, n_zeros)
elif strategy == "most_frequent":
statistics[i] = _most_frequent(column, 0, n_zeros)
return statistics
def transform(self, X) -> SparseCumlArray:
"""Impute all missing values in X.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data to complete.
"""
check_is_fitted(self)
X = self._validate_input(X, in_fit=False)
X_indicator = super()._transform_indicator(X)
statistics = self.statistics_
if X.shape[1] != statistics.shape[0]:
raise ValueError("X has %d features per sample, expected %d" %
(X.shape[1], self.statistics_.shape[0]))
# Delete the invalid columns if strategy is not constant
if self.strategy == "constant":
valid_statistics = statistics
else:
# same as np.isnan but also works for object dtypes
invalid_mask = _get_mask(statistics, np.nan)
valid_mask = np.logical_not(invalid_mask)
valid_statistics = statistics[valid_mask]
valid_statistics_indexes = np.flatnonzero(valid_mask)
if invalid_mask.any():
missing = np.arange(X.shape[1])[invalid_mask]
if self.verbose:
warnings.warn("Deleting features without "
"observed values: %s" % missing)
X = X[:, valid_statistics_indexes]
# Do actual imputation
if sparse.issparse(X):
if self.missing_values == 0:
raise ValueError("Imputation not possible when missing_values "
"== 0 and input is sparse. Provide a dense "
"array instead.")
else:
mask = _get_mask(X.data, self.missing_values)
indexes = np.repeat(np.arange(len(X.indptr) - 1, dtype=np.int),
np.diff(X.indptr).tolist())[mask]
X.data[mask] = valid_statistics[indexes].astype(X.dtype,
copy=False)
else:
mask = _get_mask(X, self.missing_values)
if self.strategy == "constant":
X[mask] = valid_statistics[0]
else:
for i, vi in enumerate(valid_statistics_indexes):
feature_idxs = np.flatnonzero(mask[:, vi])
X[feature_idxs, vi] = valid_statistics[i]
X = super()._concatenate_indicator(X, X_indicator)
return X
def _major_slice(self, idx, copy=False):
"""Index along the major axis where idx is a slice object.
"""
if idx == slice(None):
return self.copy() if copy else self
M, N = self._swap(*self.shape)
start, stop, step = idx.indices(M)
M = len(range(start, stop, step))
new_shape = self._swap(M, N)
if M == 0:
return self.__class__(new_shape)
row_nnz = cupy.diff(self.indptr)
idx_dtype = self.indices.dtype
res_indptr = cupy.zeros(M + 1, dtype=idx_dtype)
cupy.cumsum(row_nnz[idx], out=res_indptr[1:])
if step == 1:
idx_start = self.indptr[start]
idx_stop = self.indptr[stop]
res_indices = cupy.array(self.indices[idx_start:idx_stop],
copy=copy)
res_data = cupy.array(self.data[idx_start:idx_stop], copy=copy)
else:
res_indices, res_data = _index._csr_row_slice(
start, step, self.indptr, self.indices, self.data, res_indptr)
return self.__class__((res_data, res_indices, res_indptr),
shape=new_shape,
copy=False)
def _csr_row_index(rows, Ap, Aj, Ax):
"""Populate indices and data arrays from the given row index
Args:
rows (cupy.ndarray): index array of rows to populate
Ap (cupy.ndarray): indptr array from input sparse matrix
Aj (cupy.ndarray): indices array from input sparse matrix
Ax (cupy.ndarray): data array from input sparse matrix
Returns:
Bp (cupy.ndarray): indptr array for output sparse matrix
Bj (cupy.ndarray): indices array of output sparse matrix
Bx (cupy.ndarray): data array of output sparse matrix
"""
row_nnz = cupy.diff(Ap)
Bp = cupy.empty(rows.size + 1, dtype=Ap.dtype)
Bp[0] = 0
cupy.cumsum(row_nnz[rows], out=Bp[1:])
nnz = int(Bp[-1])
out_rows = cupy.empty(nnz, dtype=numpy.int32)
# Build a COO row array from output CSR indptr.
# Calling backend cusparse API directly to avoid
# constructing a whole COO object.
handle = device.get_cusparse_handle()
cusparse.xcsr2coo(handle, Bp.data.ptr, nnz, Bp.size - 1, out_rows.data.ptr,
cusparse.CUSPARSE_INDEX_BASE_ZERO)
Bj, Bx = _csr_row_index_ker(out_rows, rows, Ap, Aj, Ax, Bp)
return Bp, Bj, Bx
def _basic_simps(y, start, stop, x, dx, axis):
import cupy
nd = len(y.shape)
if start is None:
start = 0
step = 2
slice_all = (slice(None), ) * nd
slice0 = tupleset(slice_all, axis, slice(start, stop, step))
slice1 = tupleset(slice_all, axis, slice(start + 1, stop + 1, step))
slice2 = tupleset(slice_all, axis, slice(start + 2, stop + 2, step))
if x is None: # Even spaced Simpson's rule.
result = cupy.sum(dx / 3.0 * (y[slice0] + 4 * y[slice1] + y[slice2]),
axis=axis)
else:
# Account for possibly different spacings.
# Simpson's rule changes a bit.
h = cupy.diff(x, axis=axis)
sl0 = tupleset(slice_all, axis, slice(start, stop, step))
sl1 = tupleset(slice_all, axis, slice(start + 1, stop + 1, step))
h0 = h[sl0]
h1 = h[sl1]
hsum = h0 + h1
hprod = h0 * h1
h0divh1 = h0 / h1
tmp = hsum / 6.0 * (y[slice0] * (2 - 1.0 / h0divh1) +
y[slice1] * hsum * hsum / hprod + y[slice2] *
(2 - h0divh1))
result = cupy.sum(tmp, axis=axis)
return result
def _min_or_max_axis(X, axis, min_or_max):
N = X.shape[axis]
if N == 0:
raise ValueError("zero-size array to reduction operation")
M = X.shape[1 - axis]
mat = X.tocsc() if axis == 0 else X.tocsr()
mat.sum_duplicates()
major_index, value = _minor_reduce(mat, min_or_max)
not_full = np.diff(mat.indptr)[major_index] < N
if min_or_max == 'min':
min_or_max = np.fmin
else:
min_or_max = np.fmax
value[not_full] = min_or_max(value[not_full], 0)
mask = value != 0
major_index = np.compress(mask, major_index)
value = np.compress(mask, value)
if axis == 0:
res = gpu_sp.coo_matrix((value, (np.zeros(len(value)), major_index)),
dtype=X.dtype,
shape=(1, M))
else:
res = gpu_sp.coo_matrix((value, (major_index, np.zeros(len(value)))),
dtype=X.dtype,
shape=(M, 1))
return res.A.ravel()
def wint(n, t):
N = len(t)
s = cp.linspace(1e-40, 1, n)
# Inverse vandermonde matrix
tmp1 = cp.arange(n)
tmp2 = cp.arange(1, n + 2)
iv = cp.linalg.inv(cp.exp(cp.outer(tmp1, cp.log(s))))
u = cp.diff(
cp.exp(cp.outer(tmp2, cp.log(s))) *
cp.tile(1.0 / tmp2[..., cp.newaxis],
[1, n])) # integration over short intervals
W1 = cp.matmul(iv, u[1:n + 1, :]) # x*pn(x) term
W2 = cp.matmul(iv, u[0:n, :]) # const*pn(x) term
# Compensate for overlapping short intervals
tmp1 = cp.arange(1, n)
tmp2 = (n - 1) * cp.ones((N - 2 * (n - 1) - 1))
tmp3 = cp.arange(n - 1, 0, -1)
p = 1 / cp.concatenate((tmp1, tmp2, tmp3))
w = cp.zeros(N)
for j in range(N - n + 1):
# Change coordinates, and constant and linear parts
W = ((t[j + n - 1] - t[j])**2) * W1 + (t[j + n - 1] - t[j]) * t[j] * W2
for k in range(n - 1):
w[j:j + n] = w[j:j + n] + p[j + k] * W[:, k]
wn = w
wn[-40:] = (w[-40]) / (N - 40) * cp.arange(N - 40, N)
return wn
def _perform_insert(self, indices_inserts, data_inserts,
rows, row_counts, idx_dtype):
"""Insert new elements into current sparse matrix in sorted order"""
indptr_diff = cupy.diff(self.indptr)
indptr_diff[rows] += row_counts
new_indptr = cupy.empty(self.indptr.shape, dtype=idx_dtype)
new_indptr[0] = idx_dtype(0)
new_indptr[1:] = indptr_diff
# Build output arrays
cupy.cumsum(new_indptr, out=new_indptr)
out_nnz = int(new_indptr[-1])
new_indices = cupy.empty(out_nnz, dtype=idx_dtype)
new_data = cupy.empty(out_nnz, dtype=self.data.dtype)
# Build an indexed indptr that contains the offsets for each
# row but only for in i, j, and x.
new_indptr_lookup = cupy.zeros(new_indptr.size, dtype=idx_dtype)
new_indptr_lookup[1:][rows] = row_counts
cupy.cumsum(new_indptr_lookup, out=new_indptr_lookup)
_index._insert_many_populate_arrays(
indices_inserts, data_inserts, new_indptr_lookup,
self.indptr, self.indices, self.data, new_indptr, new_indices,
new_data, size=self.indptr.size-1)
self.indptr = new_indptr
self.indices = new_indices
self.data = new_data
def run_bootstrap(v, number_samples=2, block_size=60, number_of_threads=256):
"""
@v, stock price matrix. [time, stocks]
@number_samples, number of samples
@block_size, sample block size
"""
length, assets = v.shape # get the time length and the number of assets,
init_prices = v[0, :].reshape(1, -1, 1) # initial prices for all assets
v = cupy.log(v)
# compute the price difference, dimension of [length -1, assets]
ref = cupy.diff(v, axis=0)
# output results
output = cupy.zeros((number_samples, assets, length))
# sample starting position, exclusive
sample_range = length - block_size
# number of positions to sample to cover the whole seq length
num_positions = (length - 2) // block_size + 1
sample_positions = cupy.random.randint(
0, sample_range,
num_positions * number_samples) # compute random starting posistion
number_of_blocks = len(sample_positions)
boot_strap[(number_of_blocks, ),
(number_of_threads, )](output, ref.T, block_size, num_positions,
sample_positions)
# reshape the results [number_samples, number assets, time]
# output = output.reshape(number_samples, assets, length)
# convert it into prices
return (cupy.exp(output.cumsum(axis=2)) * init_prices)
def cumulative_trapezoid(y, x=None, dx=1.0, axis=-1, initial=None):
if _GPU_ENABLED:
y = cp.asarray(y)
if x is None:
d = dx
else:
x = cp.asarray(x)
if x.ndim == 1:
d = cp.diff(x)
shape = [1] * y.ndim
shape[axis] = -1
d = d.reshape(shape)
elif len(x.shape) != len(y.shape):
raise ValueError("If given, shape of x must be 1-D or the "
"same as y.")
else:
d = cp.diff(x, axis=axis)
if d.shape[axis] != y.shape[axis] - 1:
raise ValueError("If given, length of x along axis must be the "
"same as y.")
def tupleset(t, i, value):
l = list(t)
l[i] = value
return tuple(l)
nd = len(y.shape)
slice1 = tupleset((slice(None), ) * nd, axis, slice(1, None))
slice2 = tupleset((slice(None), ) * nd, axis, slice(None, -1))
res = cp.cumsum(d * (y[slice1] + y[slice2]) / 2.0, axis=axis)
if initial is not None:
if not np.isscalar(initial):
raise ValueError("`initial` parameter should be a scalar.")
shape = list(res.shape)
shape[axis] = 1
res = cp.concatenate(
[cp.full(shape, initial, dtype=res.dtype), res], axis=axis)
return res
else:
try:
from scipy.integrate import cumulative_trapezoid as ctz
except ImportError:
from scipy.integrate import cumtrapz as ctz
return ctz(y=y, x=x, dx=dx, axis=axis, initial=initial)
def _filter_cells(sparse_gpu_array, min_genes, max_genes, barcodes=None):
degrees = cp.diff(sparse_gpu_array.indptr)
query = ((min_genes <= degrees) & (degrees <= max_genes))
query = query.get()
if barcodes is None:
return sparse_gpu_array.get()[query]
else:
return sparse_gpu_array.get()[query], barcodes[query]
def euler(func, x0, t, args=None):
solution = cp.empty(shape=(len(t), len(x0), len(x0[0])))
solution[0] = x0
x = x0
for i, dt in enumerate(cp.diff(t)):
x = cp.add(x, cp.multiply(dt, func(x, t[i], *args)))
solution[i + 1] = x
return solution
def csr_polynomial_expansion(X, interaction_only, degree):
"""Apply polynomial expansion on CSR matrix
Parameters
----------
X : sparse CSR matrix
Input array
Returns
-------
New expansed matrix
"""
assert degree in (2, 3)
interaction_only = 1 if interaction_only else 0
d = X.shape[1]
if degree == 2:
expanded_dimensionality = int((d**2 + d) / 2 - interaction_only * d)
else:
expanded_dimensionality = int((d**3 + 3 * d**2 + 2 * d) / 6 -
interaction_only * d**2)
if expanded_dimensionality == 0:
return None
assert expanded_dimensionality > 0
nnz = cp.diff(X.indptr)
if degree == 2:
total_nnz = (nnz**2 + nnz) / 2 - interaction_only * nnz
else:
total_nnz = ((nnz**3 + 3 * nnz**2 + 2 * nnz) / 6 -
interaction_only * nnz**2)
del nnz
nnz_cumsum = total_nnz.cumsum(dtype=cp.int64)
total_nnz_max = int(total_nnz.max())
total_nnz = int(total_nnz.sum())
num_rows = X.indptr.shape[0] - 1
expanded_data = cp.empty(shape=total_nnz, dtype=X.data.dtype)
expanded_indices = cp.empty(shape=total_nnz, dtype=X.indices.dtype)
expanded_indptr = cp.empty(shape=num_rows + 1, dtype=X.indptr.dtype)
expanded_indptr[0] = X.indptr[0]
expanded_indptr[1:] = nnz_cumsum
tpb = (32, 32)
bpg_x = ceil(X.indptr.shape[0] / tpb[0])
bpg_y = ceil(total_nnz_max / tpb[1])
bpg = (bpg_x, bpg_y)
perform_expansion[bpg, tpb](X.indptr, X.indices, X.data, expanded_data,
expanded_indices, d, interaction_only, degree,
expanded_indptr)
return cp.sparse.csr_matrix(
(expanded_data, expanded_indices, expanded_indptr),
shape=(num_rows, expanded_dimensionality))
def _minor_reduce(X, min_or_max):
fminmax = ufunc_dic[min_or_max]
major_index = np.flatnonzero(np.diff(X.indptr))
values = cpu_np.zeros(major_index.shape[0], dtype=X.dtype)
ptrs = X.indptr[major_index]
start = ptrs[0]
for i, end in enumerate(ptrs[1:]):
values[i] = fminmax(X.data[start:end])
start = end
values[-1] = fminmax(X.data[end:])
return major_index, np.array(values)
def _compute_weights_3d(data, spacing, beta, eps, multichannel):
# Weight calculation is main difference in multispectral version
# Original gradient**2 replaced with sum of gradients ** 2
gradients = cp.concatenate(
[cp.diff(data[..., 0], axis=ax).ravel() / spacing[ax]
for ax in [2, 1, 0] if data.shape[ax] > 1], axis=0)
gradients *= gradients
for channel in range(1, data.shape[-1]):
grad = cp.concatenate(
[cp.diff(data[..., channel], axis=ax).ravel() / spacing[ax]
for ax in [2, 1, 0] if data.shape[ax] > 1], axis=0)
grad *= grad
gradients += grad
# All channels considered together in this standard deviation
scale_factor = -beta / (10 * data.std())
if multichannel:
# New final term in beta to give == results in trivial case where
# multiple identical spectra are passed.
scale_factor /= math.sqrt(data.shape[-1])
weights = cp.exp(scale_factor * gradients)
weights += eps
return -weights
def inplace_csr_row_scale(X, scale):
""" Inplace row scaling of a CSR matrix.
Scale each sample of the data matrix by multiplying with specific scale
provided by the caller assuming a (n_samples, n_features) shape.
Parameters
----------
X : CSR sparse matrix, shape (n_samples, n_features)
Matrix to be scaled.
scale : float array with shape (n_samples,)
Array of precomputed sample-wise values to use for scaling.
"""
assert scale.shape[0] == X.shape[0]
X.data *= np.repeat(scale, np.diff(X.indptr).tolist())
def average_precision_score(y_true, y_score):
"""
Compute average precision (AP) from prediction scores.
.. note:: this implementation can only be used with binary classification.
Parameters
----------
y_true : array-like of shape (n_samples,)
True labels. The binary cases
expect labels with shape (n_samples,)
y_score : array-like of shape (n_samples,)
Target scores. In the binary cases, these can be either
probability estimates or non-thresholded decision values (as returned
by `decision_function` on some classifiers). The binary
case expects a shape (n_samples,), and the scores must be the scores of
the class with the greater label.
Returns
-------
average_precision : float
Examples
--------
>>> import numpy as np
>>> from cuml.metrics import average_precision_score
>>> y_true = np.array([0, 0, 1, 1])
>>> y_scores = np.array([0.1, 0.4, 0.35, 0.8])
>>> print(average_precision_score(y_true, y_scores))
0.83
"""
# y_true, n_rows, n_cols, ytype = \
# input_to_cupy_array(y_true, check_dtype=[np.int32, np.int64,
# np.float32, np.float64])
# y_score, _, _, _ = \
# input_to_cupy_array(y_score, check_dtype=[np.int32, np.int64,
# np.float32, np.float64],
# check_rows=n_rows, check_cols=n_cols)
if cp.unique(y_true).shape[0] == 1:
raise ValueError("average_precision_score cannot be used when "
"only one class present in y_true. Average precision "
"score is not defined in that case.")
precision, recall, thresholds = precision_recall_curve(y_true, y_score)
return -cp.sum(cp.diff(recall) * cp.array(precision)[:-1])
def __init__(
self,
points,
values,
method="linear",
bounds_error=True,
fill_value=cp.nan,
):
if method not in ["linear", "nearest"]:
raise ValueError("Method '%s' is not defined" % method)
self.method = method
self.bounds_error = bounds_error
# allow reasonable duck-typed values
values = cp.asarray(values)
if len(points) > values.ndim:
raise ValueError("There are %d point arrays, but values has %d "
"dimensions" % (len(points), values.ndim))
if hasattr(values, "dtype") and hasattr(values, "astype"):
if not cp.issubdtype(values.dtype, cp.inexact):
values = values.astype(float)
self.fill_value = fill_value
if fill_value is not None:
fill_value_dtype = cp.asarray(fill_value).dtype
if hasattr(values, "dtype") and not cp.can_cast(
fill_value_dtype, values.dtype, casting="same_kind"):
raise ValueError("fill_value must be either 'None' or "
"of a type compatible with values")
for i, p in enumerate(points):
if not cp.all(cp.diff(p) > 0.0):
raise ValueError("The points in dimension %d must be strictly "
"ascending" % i)
if not cp.asarray(p).ndim == 1:
raise ValueError("The points in dimension %d must be "
"1-dimensional" % i)
if not values.shape[i] == len(p):
raise ValueError("There are %d points and %d values in "
"dimension %d" % (len(p), values.shape[i], i))
self.grid = tuple([cp.asarray(p) for p in points])
self.values = values
def _major_index_fancy(self, idx):
"""Index along the major axis where idx is an array of ints.
"""
_, N = self._swap(*self.shape)
M = len(idx)
new_shape = self._swap(M, N)
if M == 0:
return self.__class__(new_shape)
row_nnz = cupy.diff(self.indptr)
idx_dtype = self.indices.dtype
res_indptr = cupy.zeros(M + 1, dtype=idx_dtype)
cupy.cumsum(row_nnz[idx], out=res_indptr[1:])
res_indices, res_data = _index._csr_row_index(idx, self.indptr,
self.indices, self.data,
res_indptr)
return self.__class__((res_data, res_indices, res_indptr),
shape=new_shape,
copy=False)
def _csr_row_index(Ax, Aj, Ap, rows):
"""Populate indices and data arrays from the given row index
Args:
Ax (cupy.ndarray): data array from input sparse matrix
Aj (cupy.ndarray): indices array from input sparse matrix
Ap (cupy.ndarray): indptr array from input sparse matrix
rows (cupy.ndarray): index array of rows to populate
Returns:
Bx (cupy.ndarray): data array of output sparse matrix
Bj (cupy.ndarray): indices array of output sparse matrix
Bp (cupy.ndarray): indptr array for output sparse matrix
"""
row_nnz = cupy.diff(Ap)
Bp = cupy.empty(rows.size + 1, dtype=Ap.dtype)
Bp[0] = 0
cupy.cumsum(row_nnz[rows], out=Bp[1:])
nnz = int(Bp[-1])
out_rows = _csr_indptr_to_coo_rows(nnz, Bp)
Bj, Bx = _csr_row_index_ker(out_rows, rows, Ap, Aj, Ax, Bp)
return Bx, Bj, Bp
def inplace_csr_row_normalize_l1(X):
"""Normalize CSR matrix inplace with L1 norm
Parameters
----------
X : sparse CSR matrix
Input array
Returns
-------
Normalized matrix
"""
n_rows = X.indptr.shape[0]
max_nnz = cp.diff(X.indptr).max()
tpb = (32, 32)
bpg_x = ceil(n_rows / tpb[0])
bpg_y = ceil(max_nnz / tpb[1])
bpg = (bpg_x, bpg_y)
norm = cp.zeros(n_rows - 1, dtype=X.dtype)
l1_step1_k[bpg, tpb](X.indptr, X.data, norm)
norm_step2_k[bpg, tpb](X.indptr, X.data, norm)
def _minor_reduce(X, min_or_max):
if min_or_max == 'min':
min_or_max = np.min
else:
min_or_max = np.max
major_index = np.flatnonzero(np.diff(X.indptr))
# reduceat tries casts X.indptr to intp, which errors
# if it is int64 on a 32 bit system.
# Reinitializing prevents this where possible, see #13737
X = type(X)((X.data, X.indices, X.indptr), shape=X.shape)
value = cpu_np.zeros(len(X.indptr) - 1, dtype=X.dtype)
start = X.indptr[0]
for i, end in enumerate(X.indptr[1:]):
value[i] = min_or_max(X.data[start:end])
start = end
value = np.array(value)
return major_index, value
def diag_indices_from(arr):
"""
Return the indices to access the main diagonal of an n-dimensional array.
See `diag_indices` for full details.
Args:
arr (cupy.ndarray): At least 2-D.
.. seealso:: :func:`numpy.diag_indices_from`
"""
if not isinstance(arr, cupy.ndarray):
raise TypeError("Argument must be cupy.ndarray")
if not arr.ndim >= 2:
raise ValueError("input array must be at least 2-d")
# For more than d=2, the strided formula is only valid for arrays with
# all dimensions equal, so we check first.
if not cupy.all(cupy.diff(arr.shape) == 0):
raise ValueError("All dimensions of input must be of equal length")
return diag_indices(arr.shape[0], arr.ndim)
def cumsum(x, Kahan=0):
"""
Wrapper for exclusive prefix sum computation with an optional
refinement step using a approach similar to Kahan summation.
This function is not exposed to the user.
Arguments:
-------
x: cupy.core.core.ndarray
the input array of length n to be scanned with operation +
Kahan: int
non-negative number of Kahan summation adjustment rounds
Returns
-------
cupy.core.core.ndarray
the computed exclusive prefix scan of length n+1
"""
assert(isinstance(Kahan, int) and Kahan >= 0)
# allocate an empty array with leading 0
y = cp.empty(len(x)+1, dtype=x.dtype)
y[0] = 0
# compute the inclusive prefix sum starting at entry 1
cp.cumsum(x, out=y[1:])
# basically exploit that (d/dt int f(t) dt) - f(t) = r = 0 forall f(t)
# in case delta is non-vanishing due to numeric inaccuracies, we add
# the prefix scan of r to the final result (inaccuracies might add up)
if Kahan:
r = x-cp.diff(y)
if(cp.max(cp.abs(r))):
y += cumsum(r, Kahan-1)
return y
def trapz(y, x=None, dx=1.0, axis=-1):
"""
Lifted from `numpy <https://github.com/numpy/numpy/blob/v1.15.1/numpy/lib/function_base.py#L3804-L3891>`_.
Integrate along the given axis using the composite trapezoidal rule.
Integrate `y` (`x`) along given axis.
Parameters
==========
y : array_like
Input array to integrate.
x : array_like, optional
The sample points corresponding to the `y` values. If `x` is None,
the sample points are assumed to be evenly spaced `dx` apart. The
default is None.
dx : scalar, optional
The spacing between sample points when `x` is None. The default is 1.
axis : int, optional
The axis along which to integrate.
Returns
=======
trapz : float
Definite integral as approximated by trapezoidal rule.
References
==========
.. [1] Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule
Examples
========
>>> trapz([1,2,3])
4.0
>>> trapz([1,2,3], x=[4,6,8])
8.0
>>> trapz([1,2,3], dx=2)
8.0
>>> a = xp.arange(6).reshape(2, 3)
>>> a
array([[0, 1, 2],
[3, 4, 5]])
>>> trapz(a, axis=0)
array([ 1.5, 2.5, 3.5])
>>> trapz(a, axis=1)
array([ 2., 8.])
"""
y = xp.asanyarray(y)
if x is None:
d = dx
else:
x = xp.asanyarray(x)
if x.ndim == 1:
d = xp.diff(x)
# reshape to correct shape
shape = [1] * y.ndim
shape[axis] = d.shape[0]
d = d.reshape(shape)
else:
d = xp.diff(x, axis=axis)
ndim = y.ndim
slice1 = [slice(None)] * ndim
slice2 = [slice(None)] * ndim
slice1[axis] = slice(1, None)
slice2[axis] = slice(None, -1)
product = d * (y[tuple(slice1)] + y[tuple(slice2)]) / 2.0
try:
ret = product.sum(axis)
except ValueError:
ret = xp.add.reduce(product, axis)
return ret
def _sparse_document_frequency(X):
"""Count the number of non-zero values for each feature in sparse X."""
if cupyx.scipy.sparse.isspmatrix_csr(X):
return cp.bincount(X.indices, minlength=X.shape[1])
else:
return cp.diff(X.indptr)
