amax

paddle. amax ( x, axis=None, keepdim=False, name=None ) [source]

Computes the maximum of tensor elements over the given axis.

Note

The difference between max and amax is: If there are multiple maximum elements, amax evenly distributes gradient between these equal values, while max propagates gradient to all of them.

Parameters
  • x (Tensor) – A tensor, the data type is float32, float64, int32, int64, the dimension is no more than 4.

  • axis (int|list|tuple, optional) – The axis along which the maximum is computed. If None, compute the maximum over all elements of x and return a Tensor with a single element, otherwise must be in the range \([-x.ndim(x), x.ndim(x))\). If \(axis[i] < 0\), the axis to reduce is \(x.ndim + axis[i]\).

  • keepdim (bool, optional) – Whether to reserve the reduced dimension in the output Tensor. The result tensor will have one fewer dimension than the x unless keepdim is true, default value is False.

  • name (str, optional) – The default value is None. Normally there is no need for user to set this property. For more information, please refer to Name

Returns

Tensor, results of maximum on the specified axis of input tensor, it’s data type is the same as x.

Examples

import paddle
# data_x is a Tensor with shape [2, 4] with multiple maximum elements
# the axis is a int element

x = paddle.to_tensor([[0.1, 0.9, 0.9, 0.9],
                      [0.9, 0.9, 0.6, 0.7]],
                     dtype='float64', stop_gradient=False)
# There are 5 maximum elements:
# 1) amax evenly distributes gradient between these equal values,
#    thus the corresponding gradients are 1/5=0.2;
# 2) while max propagates gradient to all of them,
#    thus the corresponding gradient are 1.
result1 = paddle.amax(x)
result1.backward()
print(result1, x.grad)
#[0.9], [[0., 0.2, 0.2, 0.2], [0.2, 0.2, 0., 0.]]

x.clear_grad()
result1_max = paddle.max(x)
result1_max.backward()
print(result1_max, x.grad)
#[0.9], [[0., 1.0, 1.0, 1.0], [1.0, 1.0, 0., 0.]]

###############################

x.clear_grad()
result2 = paddle.amax(x, axis=0)
result2.backward()
print(result2, x.grad)
#[0.9, 0.9, 0.9, 0.9], [[0., 0.5, 1., 1.], [1., 0.5, 0., 0.]]

x.clear_grad()
result3 = paddle.amax(x, axis=-1)
result3.backward()
print(result3, x.grad)
#[0.9, 0.9], [[0., 0.3333, 0.3333, 0.3333], [0.5, 0.5, 0., 0.]]

x.clear_grad()
result4 = paddle.amax(x, axis=1, keepdim=True)
result4.backward()
print(result4, x.grad)
#[[0.9], [0.9]], [[0., 0.3333, 0.3333, 0.3333.], [0.5, 0.5, 0., 0.]]

# data_y is a Tensor with shape [2, 2, 2]
# the axis is list
y = paddle.to_tensor([[[0.1, 0.9], [0.9, 0.9]],
                      [[0.9, 0.9], [0.6, 0.7]]],
                     dtype='float64', stop_gradient=False)
result5 = paddle.amax(y, axis=[1, 2])
result5.backward()
print(result5, y.grad)
#[0.9., 0.9], [[[0., 0.3333], [0.3333, 0.3333]], [[0.5, 0.5], [0., 1.]]]

y.clear_grad()
result6 = paddle.amax(y, axis=[0, 1])
result6.backward()
print(result6, y.grad)
#[0.9., 0.9], [[[0., 0.3333], [0.5, 0.3333]], [[0.5, 0.3333], [1., 1.]]]