einophotoshop库rearrange，reduce和repeat的

用法介绍

 einops是一个简洁优雅操作张量的库，并且支持对numpy，pytorch，tensorflow中的张量进行操作，该库最大的优点是函数的使用逻辑清晰明了，其中中常用的三个函数分别是rearrange，repeat，reduce。

• rearrange: 用于对张量的维度进行重新变换排序，可用于替换pytorch中的reshape，view，transpose和permute等操作
• repeat: 用于对张量的某一个维度进行复制，可用于替换pytorch中的repeat
• reduce: 类似于tensorflow中的reduce操作，可以用于求平均值，最大最小值的同时压缩张量维度

 einops中rearrange，repeat，reduce的函数细节介绍如下所示

def rearrange(inputs, pattern, **axes_lengths)$⟶$ transform_inputs

• inputs (tensor): 表示输入的张量
• pattern (str): 表示张量维度变换的映射关系
• **axes_lengths: 表示按照指定的规格形式进行变换

def repeat(inputs, pattern, **axes_lengths)$⟶$ transform_inputs

• inputs (tensor): 表示输入的张量
• pattern (str): 表示张量按照某个维度复制的映射关系
• **axes_lengths: 表示按照指定的规格形式进行复制

def reduce(inputs, pattern, reduction, **axes_lengths)$⟶$ transform_inputs

• inputs (tensor): 表示输入的张量
• pattern (str): 表示张量执行某种运算做操作后维度变换的映射关系
• reduction (str): 表示运算操作的类型，分别有’max’，‘min’，‘sum’，‘mean’，‘prod’
• **axes_lengths: 表示按照指定的规格形式进行运算操作

代码示例

 einops库中rearrange函数的代码示例如下所示

# suppose we have a set of 32 images in "h w c" format (height-width-channel)
>>> images = [np.random.randn(30, 40, 3) for _ in range(32)]
# stack along first (batch) axis, output is a single array
>>> rearrange(images, 'b h w c -> b h w c').shape
(32, 30, 40, 3)
# concatenate images along height (vertical axis), 960 = 32 * 30
>>> rearrange(images, 'b h w c -> (b h) w c').shape
(960, 40, 3)
# concatenated images along horizontal axis, 1280 = 32 * 40
>>> rearrange(images, 'b h w c -> h (b w) c').shape
(30, 1280, 3)
# reordered axes to "b c h w" format for deep learning
>>> rearrange(images, 'b h w c -> b c h w').shape
(32, 3, 30, 40)
# flattened each image into a vector, 3600 = 30 * 40 * 3
>>> rearrange(images, 'b h w c -> b (c h w)').shape
(32, 3600)
# split each image into 4 smaller (top-left, top-right, bottom-left, bottom-right), 128 = 32 * 2 * 2
>>> rearrange(images, 'b (h1 h) (w1 w) c -> (b h1 w1) h w c', h1=2, w1=2).shape
(128, 15, 20, 3)
# space-to-depth operation
>>> rearrange(images, 'b (h h1) (w w1) c -> b h w (c h1 w1)', h1=2, w1=2).shape
(32, 15, 20, 12)

 einops库中repeat函数的代码示例如下所示

# a grayscale image (of shape height x width)
>>> image = np.random.randn(30, 40)
# change it to RGB format by repeating in each channel
>>> repeat(image, 'h w -> h w c', c=3).shape
(30, 40, 3)
# repeat image 2 times along height (vertical axis)
>>> repeat(image, 'h w -> (repeat h) w', repeat=2).shape
(60, 40)
# repeat image 2 time along height and 3 times along width
>>> repeat(image, 'h w -> h (repeat w)', repeat=3).shape
(30, 120)
# convert each pixel to a small square 2x2. Upsample image by 2x
>>> repeat(image, 'h w -> (h h2) (w w2)', h2=2, w2=2).shape
(60, 80)
# pixelate image first by downsampling by 2x, then upsampling
>>> downsampled = reduce(image, '(h h2) (w w2) -> h w', 'mean', h2=2, w2=2)
>>> repeat(downsampled, 'h w -> (h h2) (w w2)', h2=2, w2=2).shape
(30, 40)

 einops库中reduce函数的代码示例如下所示

>>> x = np.random.randn(100, 32, 64)
# perform max-reduction on the first axis
>>> y = reduce(x, 't b c -> b c', 'max')
# same as previous, but with clearer axes meaning
>>> y = reduce(x, 'time batch channel -> batch channel', 'max')
>>> x = np.random.randn(10, 20, 30, 40)
# 2d max-pooling with kernel size = 2 * 2 for image processing
>>> y1 = reduce(x, 'b c (h1 h2) (w1 w2) -> b c h1 w1', 'max', h2=2, w2=2)
# if one wants to go back to the original height and width, depth-to-space trick can be applied
>>> y2 = rearrange(y1, 'b (c h2 w2) h1 w1 -> b c (h1 h2) (w1 w2)', h2=2, w2=2)
>>> assert parse_shape(x, 'b _ h w') == parse_shape(y2, 'b _ h w')
# Adaptive 2d max-pooling to 3 * 4 grid
>>> reduce(x, 'b c (h1 h2) (w1 w2) -> b c h1 w1', 'max', h1=3, w1=4).shape
(10, 20, 3, 4)
# Global average pooling
>>> reduce(x, 'b c h w -> b c', 'mean').shape
(10, 20)
# Subtracting mean over batch for each channel
>>> y = x - reduce(x, 'b c h w -> () c () ()', 'mean')
# Subtracting per-image mean for each channel
>>> y = x - reduce(x, 'b c h w -> b c () ()', 'mean')

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