mindspore/tests/vm_impl/vm_me.py

873 lines
25 KiB
Python

# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""VM implementations based on numpy."""
import numpy as np
from mindspore._checkparam import Validator as validator
def avg_pooling(x, pool_h, pool_w, stride):
"""
Applies average pooling over an input array.
Args:
x (numpy.ndarray): The input array to be average pooled.
pool_h (int): Height of the pooling window.
pool_w (int): Width of the pooling window.
stride (int): The stride of the sliding window.
Returns:
numpy.ndarray, an output array after applying average pooling on input array.
"""
validator.check_positive_int(stride, "stride")
num, channel, height, width = x.shape
out_h = (height - pool_h) // stride + 1
out_w = (width - pool_w) // stride + 1
col = im2col(x, pool_h, pool_w, stride)
col = col.reshape(-1, pool_h * pool_w)
out = np.mean(col, axis=1)
out = out.reshape((num, out_h, out_w, channel)).transpose(0, 3, 1, 2)
return out
def avg_pool_grad(dout, origin_shape, pool_h, pool_w, stride):
"""
Gets grad of average pooling.
Args:
x (numpy.ndarray): The input array to be average pooled.
dout (numpy.ndarray): The grad of pre-layer.
pool_h (int): Height of the pooling window.
pool_w (int): Width of the pooling window.
stride (int): The stride of the sliding window.
Returns:
numpy.ndarray, grad of avgerage pooling.
"""
# pylint: disable=unused-argument
_, _, height, width = dout.shape
dx = np.zeros(origin_shape)
for i in range(height):
for j in range(width):
dx[:, :, i:(i + pool_h), j:(j + pool_w)] += np.ones((pool_h, pool_w))
return dx
def _batch_norm(x, scale, shift, running_mean=None, running_var=None,
eps=1e-05, momentum=0.1, is_training=True):
"""Batch normalization over an array."""
_, c_h_w = x.shape
# Handle running_mean and running_var are not None
# if running_mean is None:
# running_mean = np.zeros(c_h_w)
# running_var = np.zeros(c_h_w)
running_mean = np.zeros(c_h_w)
running_var = np.zeros(c_h_w)
if np.ndim(scale) > 0:
scale = scale.mean()
if np.ndim(shift) > 0:
shift = shift.mean()
if is_training:
x_mean = np.mean(x, axis=0)
x_var = np.var(x, axis=0)
# Normalization followed by Affine transformation
x_norm = (x - x_mean) / np.sqrt(x_var + eps)
# Estimate running average of mean and variance to use at test time
running_mean = momentum * running_mean + (1 - momentum) * x_mean
running_var = momentum * running_var + (1 - momentum) * x_var
else:
# normalize using running average
x_norm = (x - running_mean) / np.sqrt(running_var + eps)
x_mean = running_mean
x_var = running_var
out = scale * x_norm + shift
return out, x_mean, x_var, running_mean, running_var
def batch_norm(x, scale=1, shift=0, mean=None, variance=None,
eps=1e-05, momentum=0.1, is_training=True):
"""Batch normalization over an array."""
input_shape = x.shape
if x.ndim != 2:
batch_num = x.shape[0]
x = x.reshape(batch_num, -1)
out, _, _, running_mean, running_var = _batch_norm(x, scale, shift, mean, variance, \
eps, momentum, is_training)
return out.reshape(*input_shape), np.array(scale), np.array(shift), running_mean, running_var
def _batch_norm_grad(dout, x, scale, save_mean, save_inv_variance, \
eps=1e-05, momentum=0.1, is_training=True):
"""Batch normalization over an array."""
if x.ndim != 2:
batch_num = x.shape[0]
x = x.reshape(batch_num, -1)
if np.ndim(scale) > 0:
scale = scale.mean()
x_norm, x_mean, x_var, _, _ = _batch_norm(x, scale, shift=0, running_mean=save_mean, \
running_var=save_inv_variance, \
eps=eps, momentum=momentum, is_training=is_training)
batch_size = x.shape[0]
dx_norm = scale * dout
dvar = np.sum(dx_norm * (x - x_mean) * ((x_var + eps) ** (-3.0 / 2)) * (-1.0 / 2), axis=0)
dmean = np.sum(dx_norm * (-1.0 / np.sqrt(x_var + eps)), axis=0) \
+ dvar * (np.sum(-2 * (x - x_mean), axis=0) * (1.0 / batch_size))
dx = dx_norm * (1.0 / np.sqrt(x_var + eps)) + dvar * (2.0 * (x - x_mean) / batch_size) + dmean * (1.0 / batch_size)
dgamma = np.sum(dout * x_norm, axis=0)
dbeta = np.sum(dout, axis=0)
return dx, dgamma, dbeta
def batch_norm_grad(dy, x, scale, save_mean, save_inv_variance):
"""Batch normalization over an array."""
if dy.ndim != 2:
batch_size = dy.shape[0]
dy = dy.reshape(batch_size, -1)
dx, dgamma, dbeta = _batch_norm_grad(dy, x, scale, save_mean, save_inv_variance)
input_shape = x.shape
dx = dx.reshape(*input_shape)
return dx, dgamma, dbeta
def col2im(col, input_shape, filter_h, filter_w, stride=1, pad=0):
"""Rearranges a row vector to an image."""
if isinstance(stride, int):
stride_h = stride
stride_w = stride
elif isinstance(stride, tuple) and len(stride) == 2:
stride_h = stride[0]
stride_w = stride[1]
elif isinstance(stride, tuple) and len(stride) == 4:
stride_h = stride[2]
stride_w = stride[3]
else:
raise ValueError(f"The \'stride\' should be an int number or "
f"a tuple of two or four int numbers, but got {stride}")
if isinstance(pad, int):
pad_top = pad
pad_bottom = pad
pad_left = pad
pad_right = pad
elif isinstance(pad, tuple) and len(pad) == 2:
pad_top = pad[0]
pad_bottom = pad[0]
pad_left = pad[1]
pad_right = pad[1]
elif isinstance(pad, tuple) and len(pad) == 4:
pad_top, pad_bottom, pad_left, pad_right = pad
else:
raise ValueError(f"The \'pad\' should be an int number or "
f"a tuple of two or four int numbers, but got {pad}")
batch_num, channel, height, width = input_shape
out_h = (height + pad_top + pad_bottom - filter_h) // stride_h + 1
out_w = (width + pad_left + pad_right - filter_w) // stride_w + 1
col = col.reshape(batch_num, out_h, out_w, channel, filter_h, filter_w) \
.transpose(0, 3, 4, 5, 1, 2)
img = np.zeros((batch_num,
channel,
height + pad_top + pad_bottom + stride_h - 1,
width + pad_left + pad_right + stride_w - 1)) \
.astype(col.dtype)
for y in range(filter_h):
y_max = y + stride_h * out_h
for x in range(filter_w):
x_max = x + stride_h * out_w
img[:, :, y:y_max:stride_h, x:x_max:stride_h] += col[:, :, y, x, :, :]
return img[:, :, pad_top:height + pad_bottom, pad_left:width + pad_right]
def convolve(x, w, b=None, pad_mode="valid"):
"""
Gets the discrete, linear convolution of two one-dimensional sequences.
Args:
x (numpy.ndarray): One-dimensional input array.
w (numpy.ndarray): One-dimensional input array.
b (numpy.ndarray): One-dimensional input array. Default: None.
pad_mode (str): Padding mode which can be: "full" means returns the
convolution at each point of overlap, with an output shape
of (N+M-1,); "same" means returns output of length max(M, N);
Amd "valid" means returns output of length max(M, N) - min(M, N)
+ 1. Default: "valid".
Returns:
numpy.ndarray, discrete, linear convolution of x and w, then plus b.
"""
if pad_mode not in {"same", "valid"}:
pad_mode = "full"
y = np.convolve(x, w, pad_mode)
if b:
y += b
return y
def conv2d(x, weight, bias=None, stride=1, pad=0,
dilation=1, groups=1, padding_mode='zeros'):
"""Convolution 2D."""
# pylint: disable=unused-argument
validator.check_value_type('stride', stride, (int, tuple))
if isinstance(stride, int):
stride = (stride, stride)
elif len(stride) == 4:
stride = (stride[2], stride[3])
if len(stride) != 2 or (not isinstance(stride[0], int)) or \
(not isinstance(stride[1], int)) or \
stride[0] < 1 or stride[1] < 1:
raise ValueError(f"The \'stride\' of \'conv2d\' should be an positive int number or "
f"a tuple of two positive int numbers, but got {stride}")
stride_h = stride[0]
stride_w = stride[1]
validator.check_value_type('dilation', dilation, (int, tuple))
if isinstance(dilation, int):
dilation = (dilation, dilation)
elif len(dilation) == 4:
dilation = (dilation[2], dilation[3])
if len(dilation) != 2 or (not isinstance(dilation[0], int)) or \
(not isinstance(dilation[1], int)) or \
dilation[0] < 1 or dilation[1] < 1:
raise ValueError(f"The \'dilation\' of \'conv2d\' should be an positive int number or "
f"a tuple of two positive int numbers, but got {dilation}")
dilation_h = dilation[0]
dilation_w = dilation[1]
if isinstance(pad, int):
pad_top = pad
pad_bottom = pad
pad_left = pad
pad_right = pad
elif isinstance(pad, tuple) and len(pad) == 4:
pad_top, pad_bottom, pad_left, pad_right = pad
else:
raise ValueError(f"The \'pad\' should be an int number or "
f"a tuple of two or four int numbers, but got {pad}")
batch_num, _, x_h, x_w = x.shape
filter_num, _, filter_h, filter_w = weight.shape
out_h = 1 + int((x_h + pad_top + pad_bottom - filter_h - (filter_h - 1) * (dilation_h - 1)) / stride_h)
out_w = 1 + int((x_w + pad_left + pad_right - filter_w - (filter_w - 1) * (dilation_w - 1)) / stride_w)
col = im2col(x, filter_h, filter_w, stride, pad, dilation)
col_w = np.reshape(weight, (filter_num, -1)).T
out = np.dot(col, col_w)
out = out.reshape(batch_num, out_h, out_w, -1).transpose(0, 3, 1, 2)
if bias is not None:
out += bias
return out
def conv2d_backprop_filter(dout, x, w_size, stride=1, pad=0):
"""Backpropagation filter for conv2d."""
filter_num, channel, filter_height, filter_width = w_size
dout = dout.transpose(0, 2, 3, 1).reshape(-1, filter_num)
col = im2col(x, filter_height, filter_width, stride, pad)
dw = np.dot(col.T, dout)
dw = dw.transpose(1, 0).reshape(filter_num, channel, filter_height, filter_width)
return dw
def conv2d_backprop_input(dout, x_size, weight, stride=1, pad=0):
"""Backpropagation input for conv2d."""
filter_num, _, filter_h, filter_w = weight.shape
dout = dout.transpose(0, 2, 3, 1).reshape(-1, filter_num)
col_w = weight.reshape(filter_num, -1).T
dcol = np.dot(dout, col_w.T)
dx = col2im(dcol, x_size, filter_h, filter_w, stride, pad)
return dx
def flatten(x):
"""
Flattens an array to one dimension.
Args:
x (numpy.ndarray): An array to be flattened.
Returns:
numpy.ndarray, a flattened array in one dimension.
"""
return x.flatten()
def flatten2(x):
"""
Flattens an array to one dimension by reshape.
Args:
x (numpy.ndarray): An array to be flattened.
Returns:
numpy.ndarray, a flattened array in one dimension.
"""
return x.reshape(1, -1)
def flatten_batch(x):
"""
Flattens a batch of arrays to one dimension.
Args:
x (numpy.ndarray): A batch of arrays to be flattened.
Returns:
numpy.ndarray, a flattened one dimension array.
"""
return x.reshape(x.shape[0], -1)
def flatten_grad(dout, x):
"""Grad of flatten."""
dout = np.reshape(dout, x)
return dout
def im2col(img, filter_h, filter_w, stride=1, pad=0, dilation=1):
"""Rearranges an image to row vector."""
if isinstance(stride, int):
stride_h = stride
stride_w = stride
elif isinstance(stride, tuple) and len(stride) == 2:
stride_h = stride[0]
stride_w = stride[1]
elif isinstance(stride, tuple) and len(stride) == 4:
stride_h = stride[2]
stride_w = stride[3]
else:
raise ValueError(f"The \'stride\' should be an int number or "
f"a tuple of two or four int numbers, but got {stride}")
if isinstance(dilation, int):
dilation_h = dilation
dilation_w = dilation
elif isinstance(dilation, tuple) and len(dilation) == 2:
dilation_h = dilation[0]
dilation_w = dilation[1]
elif isinstance(dilation, tuple) and len(dilation) == 4:
dilation_h = dilation[2]
dilation_w = dilation[3]
else:
raise ValueError(f"The \'dilation\' should be an int number or "
f"a tuple of two or four int numbers, but got {dilation}")
if isinstance(pad, int):
pad_top = pad
pad_bottom = pad
pad_left = pad
pad_right = pad
elif isinstance(pad, tuple) and len(pad) == 4:
pad_top, pad_bottom, pad_left, pad_right = pad
else:
raise ValueError(f"The \'pad\' should be an int number or "
f"a tuple of two or four int numbers, but got {pad}")
batch_num, channel, height, width = img.shape
out_h = (height + pad_top + pad_bottom - filter_h - (filter_h - 1) * (dilation_h - 1)) // stride_h + 1
out_w = (width + pad_left + pad_right - filter_w - (filter_w - 1) * (dilation_w - 1)) // stride_w + 1
img = np.pad(img, [(0, 0), (0, 0), (pad_top, pad_bottom), (pad_left, pad_right)], 'constant')
col = np.zeros((batch_num, channel, filter_h, filter_w, out_h, out_w)).astype(img.dtype)
for y in range(filter_h):
y_max = y + stride_h * out_h
for x in range(filter_w):
x_max = x + stride_h * out_w
col[:, :, y, x, :, :] = img[:, :, y:y_max:stride_h, x:x_max:stride_h]
col = col.transpose(0, 4, 5, 1, 2, 3).reshape(batch_num * out_h * out_w, -1)
return col
def matmul(x, w, b=None):
"""
Dot product of array x and w, then plus array b if b is not None.
Args:
x (numpy.ndarray): Represents the input array.
w (numpy.ndarray): Represents weights array.
b (numpy.ndarray): Represents bias array which has the same shape as x. Default: None.
Returns:
numpy.ndarray, the result of (x*w + b).
"""
y = np.dot(x, w)
if b:
y += b
return y
def max_pooling(x, pool_h, pool_w, stride):
"""Max pooling."""
validator.check_positive_int(stride, "stride")
num, channel, height, width = x.shape
out_h = (height - pool_h) // stride + 1
out_w = (width - pool_w) // stride + 1
col = im2col(x, pool_h, pool_w, stride)
col = col.reshape(-1, pool_h * pool_w)
out = np.max(col, axis=1)
out = out.reshape((num, out_h, out_w, channel)).transpose(0, 3, 1, 2)
return out
def max_pool_grad(x, dout, pool_h, pool_w, stride):
"""Grad of max pooling."""
dout = dout.transpose(0, 2, 3, 1)
pool_size = pool_h * pool_w
dmax = np.zeros((dout.size, pool_size), dout.dtype)
col = im2col(x, pool_h, pool_w, stride)
col = col.reshape(-1, pool_h * pool_w)
arg_max = np.argmax(col, axis=1)
dmax[np.arange(arg_max.size), arg_max.flatten()] = dout.flatten()
dmax = dmax.reshape(dout.shape + (pool_size,))
dcol = dmax.reshape(dmax.shape[0] * dmax.shape[1] * dmax.shape[2], -1)
dx = col2im(dcol, x.shape, pool_h, pool_w, stride)
return dx
def max_pool_grad_with_argmax(x, dout, arg_max, pool_h, pool_w, stride):
"""Grad of max pooling with argmax."""
dout = dout.transpose(0, 2, 3, 1)
pool_size = pool_h * pool_w
dmax = np.zeros((dout.size, pool_size), dout.dtype)
dmax[np.arange(arg_max.size), arg_max.flatten()] = dout.flatten()
dmax = dmax.reshape(dout.shape + (pool_size,))
dcol = dmax.reshape(dmax.shape[0] * dmax.shape[1] * dmax.shape[2], -1)
dx = col2im(dcol, x.shape, pool_h, pool_w, stride)
return dx
def max_pool_with_argmax(x, pool_h, pool_w, stride):
"""Max pooling with argmax."""
validator.check_positive_int(stride, "stride")
num, channel, height, width = x.shape
out_h = (height - pool_h) // stride + 1
out_w = (width - pool_w) // stride + 1
col = im2col(x, pool_h, pool_w, stride)
col = col.reshape(-1, pool_h * pool_w)
out = np.max(col, axis=1)
out_argmax = np.argmax(col, axis=1)
out = out.reshape((num, out_h, out_w, channel)).transpose(0, 3, 1, 2)
out_argmax = out_argmax.reshape((num, out_h, out_w, channel)).transpose(0, 3, 1, 2)
return out, out_argmax
def relu(x):
"""
Rectified linear unit.
Args:
x (numpy.ndarray): The input array.
Returns:
numpy.ndarray, the array applied relu.
"""
return x * (x > 0)
def relu_grad(y):
"""
Grad of relu.
Args:
y (numpy.ndarray): The input array.
Returns:
numpy.ndarray, the array applied grad of relu.
"""
y[y <= 0] = 0
y[y > 0] = 1
return y
def sigmoid(x):
"""
Sigmoid activation function.
Args:
x (numpy.ndarray): The input array.
Returns:
numpy.ndarray, the array applied sigmoid.
"""
return 1 / (1 + np.exp(x * -1))
def tanh(x):
"""
Computes hyperbolic tangent element-wise.
Args:
x (numpy.ndarray): The input array.
Returns:
numpy.ndarray, the array applied tanh.
"""
a = np.exp(x) - np.exp(x * -1)
b = np.exp(x) + np.exp(x * -1)
return a / b
def softmax(x, axis=None):
"""
Softmax function which is `softmax(x) = np.exp(x)/sum(np.exp(x))`.
Args:
x (numpy.ndarray): Input array.
axis (Union[int, tuple[int]]): Axis to compute values along. Default: None.
Returns:
numpy.ndarray, has the same shape as x.
"""
from scipy.special import softmax as scipy_softmax
return scipy_softmax(x, axis)
def softmax_cross_entropy_with_logits(logits, labels):
sample_num = labels.shape[0]
prob = softmax(logits)
log_likelihood = -np.log(prob[range(sample_num)]) * labels
loss = np.sum(log_likelihood)
dx = prob.copy()
dx[range(sample_num)] -= labels
return loss, dx
def shape(x):
"""
Gets the array's dimensions.
Args:
x (numpy.ndarray): Input array.
Returns:
tuple, the shape/dimensions of the input array.
"""
return np.array(np.shape(x))
def expand_dims(x, axis):
"""
Expands the shape of an array.
Args:
x (numpy.ndarray): Input array.
axis (int): Position in the expanded axes where the new axis is placed.
Returns:
numpy.ndarray, view of input array with the number of dimensions increased by one.
"""
return np.expand_dims(x, axis)
def squeeze(x, axis):
"""
Removes single-dimensional entries from the shape of an array.
Args:
x (numpy.ndarray): Input array.
axis (Union[int, tuple[int]]): Selected subset of the single-dimensional entries in the shape.
Returns:
numpy.ndarray, the input numpy.ndarray, but with all or a subset of the dimensions of length
1 removed.
"""
return np.squeeze(x, tuple(axis))
def reshape(x, shp):
"""
Applies a new shape to an array without changing its data.
Args:
x (numpy.ndarray): Input array.
shp (tuple[int]): New shape to apply to x.
Returns:
numpy.ndarray, a new view object or a copy of input array.
"""
return np.reshape(x, tuple(shp))
def rank(x):
"""
Gets number of array dimensions.
Args:
x (numpy.ndarray): Input array.
Returns:
int, number of input array dimensions.
"""
return np.array(np.ndim(x))
def logsoftmax(x):
"""
Log softmax function.
Args:
x (numpy.ndarray): Input array.
Returns:
numpy.ndarray, the result of applying log softmax on the input array.
"""
return np.array(np.log(softmax(x)))
def transpose(x, axes=None):
"""
Transposes an input array according to axes.
Args:
x (numpy.ndarray): Input array.
axes (list): The axes to be transposed. Default: None.
Returns:
numpy.ndarray, transposed array.
"""
return np.transpose(x, axes)
def invert_permutation(x):
"""
Gets the inverse permutation of an array.
Args:
x (numpy.ndarray): Input array.
Returns:
tuple, the inverse permutation of the input array.
"""
x = np.array(x)
y = np.argsort(x)
return tuple(y)
def select(cond, x, y):
"""
Gets elements from x or y depending on cond.
Args:
cond (bool): Where True, yield x, otherwise yield y.
x (numpy.ndarray): Values from which to choose.
y (numpy.ndarray): Values from which to choose.
Returns:
numpy.ndarray, elements from x where condition is True, and elements from y elsewhere.
"""
return np.where(cond, x, y)
def sum_by_axis(x, axis):
"""
Sum of array elements over a given axis.
Args:
x (numpy.ndarray): Input array.
axis (Union[int, tuple[int]]): Axis or axes along which a sum is performed.
Returns:
numpy.ndarray, has the same shape as input array with the specified axis removed.
"""
return np.sum(x, axis)
def equal(x, y):
"""
Gets (x == y) element-wise.
Args:
x (numpy.ndarray): Input array.
y (numpy.ndarray): Input array.
Returns:
numpy.ndarray, element-wise comparison of x and y.
"""
return np.equal(x, y)
def not_equal(x, y):
"""
Gets (x != y) element-wise.
Args:
x (numpy.ndarray): Input array.
y (numpy.ndarray): Input array.
Returns:
numpy.ndarray, element-wise comparison of x and y.
"""
return np.not_equal(x, y)
def greater(x, y):
"""
Get the truth value of (x > y) element-wise.
Args:
x (numpy.ndarray): Input array.
y (numpy.ndarray): Input array.
Returns:
numpy.ndarray, element-wise comparison of x and y.
"""
return np.greater(x, y)
def less(x, y):
"""
Get the truth value of (x < y) element-wise.
Args:
x (numpy.ndarray): Input array.
y (numpy.ndarray): Input array.
Returns:
Array, element-wise comparison of x and y.
"""
return np.less(x, y)
def logical_not(x):
"""
Gets the truth value of NOT x element-wise.
Args:
x (numpy.ndarray): Input array.
Returns:
bool, have the same shape as x of the NOT operation on elements of x.
"""
return np.logical_not(x)
def sqrt(x):
"""
Gets the non-negative square-root of an numpy.ndarray, element-wise.
Args:
x (numpy.ndarray): Input array.
Returns:
numpy.ndarray, has the same shape as x, containing the positive square-root of each
element in x.
"""
return np.sqrt(x)
def power(x, y):
"""
First array elements raised to powers from second numpy.ndarray, element-wise.
Args:
x (numpy.ndarray): The bases array.
y (numpy.ndarray): The exponents array.
Returns:
numpy.ndarray, the bases in x raised to the exponents in y.
"""
return np.power(x, y)
def exp(x):
"""
Gets the exponential of all elements in the input array.
Args:
x (numpy.ndarray): Input array.
Returns:
numpy.ndarray, element-wise exponential of x.
"""
return np.exp(x)
def maximum(x, y):
"""
Gets the max of x and y element-wise.
If x > y, return x. Otherwise, return y.
Args:
x (numpy.ndarray): First input array.
y (numpy.ndarray): Second input array ave the same type as x.
Returns:
numpy.ndarray, has the same type as x.
"""
return np.maximum(x, y)
def minimum(x, y):
"""
Gets the min of x and y element-wise.
If x < y, return x. Otherwise, return y.
Args:
x (numpy.ndarray): First input array.
y (numpy.ndarray): Second input array have the same type as x.
Returns:
numpy.ndarray, has the same type as x.
"""
return np.minimum(x, y)
def all_(x, axis=(), keep_dims=False):
"""
Check all array elements along a given axis evaluate to True.
Args:
x (numpy.ndarray): An array to be reduced.
axis (Union[None, int, tuple(int)): Dimensions of reduction.
keep_dims (bool): Whether to keep the reduced dimensions.
Returns:
numpy.ndarray, has the same type as x.
"""
axis = None if axis == () else axis
return np.all(x, axis, keepdims=keep_dims)
def any_(x, axis=(), keep_dims=False):
"""
Check any array element along a given axis evaluate to True.
Args:
x (numpy.ndarray): An array to be reduced.
axis (Union[None, int, tuple(int)): Dimensions of reduction.
keep_dims (bool): Whether to keep the reduced dimensions.
Returns:
numpy.ndarray, has the same type as x.
"""
axis = None if axis == () else axis
return np.any(x, axis, keepdims=keep_dims)