可视化NumPy、Torch和Tensorflow的基本操作

深度学习

在深入学习的基本单位上实施初级到高级操作。

> Excerpts

我习惯于为不同的问题创建新的深度学习架构，但选择哪个框架（Keras、Pytorch、TensorFlow）通常比较困难。

由于其中存在不确定性，因此了解这些框架的基本单元（NumPy、Torch、Tensor）的基本操作是件好事。

在这篇文章中，我跨 3 个框架执行了几个相同的操作，也尝试了大多数框架的可视化操作。

这是一个初学者友好的帖子，所以让我们开始。

1. 安装

pip install numpypip install tensorflowpip install torch

2. 版本检查

import numpy as npimport tensorflow as tfimport torchprint(np.__version__)print(tf.__version__)print(torch.__version__)### OUTPUT ###2.3.0 1.18.5 1.6.0+cu101view raw

3. 阵列初始化 = 1-D、2-D、3-D

标量和一维阵列

> Scalar, 1-D, 2-D arrays

Numpy

# Numpya = np.array(10)print(a)print(a.shape, a.dtype) #shape of the array and type of the elementsa = np.array([10])print(a)print(a.shape, a.dtype) #shape of the array and type of the elementsa = np.array([10], dtype=np.float32)print(a)print(a.shape, a.dtype) #shape of the array and type of the elements############################# OUTPUT ##############################10 () int64[10] (1,) int64[10.] (1,) float32

TensorFlow

# TensorFlowb = tf.constant(10) # As Scalarprint(b)b = tf.constant(10, shape=(1,1)) # As 1-D Vectorprint(b)b = tf.constant(10, shape=(1,1), dtype=tf.float32) # with Data-typeprint(b)############################# OUTPUT ##############################tf.Tensor(10, shape=(), dtype=int32)tf.Tensor([[10]], shape=(1, 1), dtype=int32)tf.Tensor([[10.]], shape=(1, 1), dtype=float32)

Torch

# Torchc = torch.tensor(10, ) # As Scalarprint(c)c = torch.tensor([10]) # As 1-D Vectorprint(c, c.shape, c.dtype)c = torch.tensor([10], dtype=torch.float32) # With Data-typeprint(c)############################# OUTPUT ##############################tensor(10) tensor([10])torch.Size([1]) torch.int64tensor([10.])

二维矢量阵列

> 2-D Array

Numpy

# Numpya = np.array([[1,2,3], [4,5,6]])print(a)print(a.shape, a.dtype)############################# OUTPUT ##############################[[1 2 3]   [4 5 6]] (2, 3) int64

TensorFlow

# TensorFlowb = tf.constant([[1,2,3], [4,5,6]])print(b)print(b.shape)############################# OUTPUT ##############################tf.Tensor([[1 2 3] [4 5 6]], shape=(2, 3), dtype=int32)(2, 3)

Torch

# Torchc = torch.tensor([[1,2,3], [4,5,6]])print(c)print(c.shape)############################# OUTPUT ##############################tensor([[1, 2, 3],        [4, 5, 6]])torch.Size([2, 3])

4. 生成数据

> Zeros and Ones

> Diagonal & Same element fill

Numpy

# Numpya = np.zeros((3,3))print(a, a.shape, a.dtype)a = np.ones((3,3))print(a, a.shape, a.dtype)a = np.eye(3)print(a, a.shape, a.dtype)a = np.full((3,3),10.0)print(a, a.shape, a.dtype)############################# OUTPUT ##############################[[0. 0. 0.] [0. 0. 0.] [0. 0. 0.]] (3, 3) float64[[1. 1. 1.] [1. 1. 1.] [1. 1. 1.]] (3, 3) float64[[1. 0. 0.] [0. 1. 0.] [0. 0. 1.]] (3, 3) float64[[10. 10. 10.] [10. 10. 10.] [10. 10. 10.]] (3, 3) float64

Tensorflow

# TensorFlowb = tf.zeros((3,3))print(b)b = tf.ones((3,3))print(b)b = tf.eye(3)print(b)b = tf.fill([3,3], 10)print(b)############################# OUTPUT ##############################tf.Tensor( [[0. 0. 0.]            [0. 0. 0.]            [0. 0. 0.]], shape=(3, 3), dtype=float32)tf.Tensor( [[1. 1. 1.]            [1. 1. 1.]            [1. 1. 1.]], shape=(3, 3), dtype=float32)tf.Tensor( [[1. 0. 0.]            [0. 1. 0.]            [0. 0. 1.]], shape=(3, 3), dtype=float32)tf.Tensor( [[10 10 10]            [10 10 10]            [10 10 10]], shape=(3, 3), dtype=int32)

Torch

# Torchc = torch.zeros((3,3))print(c)c = torch.ones((3,3))print(c)c = torch.eye(3)print(c)c = c.new_full([3,3], 10)print(c)############################# OUTPUT ##############################tensor([[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]])tensor([[1., 1., 1.], [1., 1., 1.], [1., 1., 1.]])tensor([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])tensor([[10., 10., 10.], [10., 10., 10.], [10., 10., 10.]])

从正态分布绘制随机样本

> Normal Dist'n Bell Curve

> Samples were drawn from Normal Dist'n

Numpy

# Numpya = np.random.randn(3,3)print(a, a.shape, a.dtype)print(a.mean(), a.std())############################# OUTPUT ##############################[[ 0.41406362 -1.51382214  0.55400531] [-0.95226975 -0.50038461  1.29014057] [ 0.90320426 -1.65923581 -1.03100388]] (3, 3) float64-0.27725582657643905 1.0291132313341855

Tensorflow

# TensorFlowb = tf.random.normal((3,3),mean=0, stddev=1)print(b)print(tf.reduce_mean(b), tf.math.reduce_std(b))############################# OUTPUT ##############################tf.Tensor([[0.04017716 -2.2840774 -0.3615016 ] [-1.9259684 1.2054121 0.02211744] [0.96204025 0.07906733 -2.2352242 ]], shape=(3, 3), dtype=float32)tf.Tensor(-0.49977303, shape=(), dtype=float32) tf.Tensor(1.2557517, shape=(), dtype=float32)

Torch

# Torchc = torch.normal(mean=0, std=1, size=(3, 3))print(c)print(torch.mean(c), torch.std(c))############################# OUTPUT ##############################tensor([[-0.1682,  0.9610,  1.1005],        [-1.0462,  0.4431,  0.6005],         [-1.2714, -1.1894,  0.7221]])tensor(0.0169) tensor(0.9595)

从均匀分布中抽取样本

> Uniform Dist'n Curve

> Samples were drawn from Uniform Dist'n

Numpy

# Numpya = np.random.uniform(low=0, high=1, size=(3,3))print(a, a.shape, a.dtype)print(a.mean(), a.std())############################# OUTPUT ##############################[[0.00738313 0.56734768 0.92893306] [0.36580515 0.91986967 0.70643149] [0.72854485 0.73961837 0.88049091]] (3, 3) float640.6493804787345917 0.28317558657389263

Tensorflow

# TensorFlowb = tf.random.uniform((3,3),minval=0,maxval=1)#Values are always > 1print(b)print(tf.reduce_mean(b), tf.math.reduce_std(b))############################# OUTPUT ##############################tf.Tensor( [[0.11186028 0.04624796 0.59104955]           [0.5344571  0.1144793  0.8468257 ]           [0.5247066  0.61488223 0.7592212 ]], shape=(3, 3), dtype=float32)tf.Tensor(0.4604144, shape=(), dtype=float32)tf.Tensor(0.2792521, shape=(), dtype=float32)

Torch

# Torchnum_samples = 3Dim = 3c = torch.distributions.Uniform(0, +1).sample((num_samples, Dim))print(c)print(torch.mean(c), torch.std(c))############################# OUTPUT ##############################tensor([[0.5842, 0.5787, 0.3526], [0.2647, 0.6233, 0.4482], [0.3495, 0.0562, 0.0495]])tensor(0.3674) tensor(0.2158)

向量排列

Numpy

# Numpya = np.arange(0,9)print(a)a = np.arange(start=1, stop=20, step=2, dtype=np.float32)print(a, a.dtype)############################# OUTPUT ##############################[0 1 2 3 4 5 6 7 8][ 1.  3.  5.  7.  9. 11. 13. 15. 17. 19.] float32

Tensorflow

# TensorFlowb = tf.range(9)print(b)b = tf.range(start=1, limit=20, delta=2, dtype=tf.float64)print(b)############################# OUTPUT ##############################tf.Tensor([0 1 2 3 4 5 6 7 8], shape=(9,), dtype=int32)tf.Tensor([ 1. 3. 5. 7. 9. 11. 13. 15. 17. 19.], shape=(10,), dtype=float64)

Torch

# Torchc = torch.arange(start=0, end=9)print(c)c = torch.arange(start=1, end=20, step=2, dtype=torch.float64)print(c)############################# OUTPUT ##############################tensor([0, 1, 2, 3, 4, 5, 6, 7, 8])tensor([ 1.,  3.,  5.,  7.,  9., 11., 13., 15., 17., 19.], dtype=torch.float64)

7. 数据类型 + 转换

uint8/16/32/64 ← →浮子8/16/32/64

Numpy

# Numpya = a.astype(np.uint8)print(a, a.dtype)############################# OUTPUT ##############################[ 1 3 5 7 9 11 13 15 17 19] uint8

Tensorflow

# TensorFlowb = tf.cast(b, dtype=tf.uint8)print(b)############################# OUTPUT ##############################tf.Tensor([ 1  3  5  7  9 11 13 15 17 19], shape=(10,), dtype=uint8)

Torch

# Torchc = torch.tensor(c)c = c.type(torch.int64)print(c)############################# OUTPUT ##############################tensor([ 1, 3, 5, 7, 9, 11, 13, 15, 17, 19])

8. 数学运算

> Sum and Subtract operations

> multiply and divide operations

Numpy

# Numpya = np.array([1,2,3,4,5])b = np.array([6,7,8,9,10])c = np.add(a, b)print(c, c.dtype)c = np.subtract(b,a)print(c, c.dtype)c = np.divide(b,a)print(c, c.dtype)c = np.multiply(b,a)print(c, c.dtype)c = (a**2)print(c)############################# OUTPUT ##############################[ 7  9 11 13 15] int64  [5 5 5 5 5] int64[6.         3.5        2.66666667 2.25       2.        ] float64[ 6 14 24 36 50] int64[ 1  4  9 16 25]

Tensorflow

# TensorFlowx = tf.constant([1,2,3,4,5])y = tf.constant([6,7,8,9,10])z = tf.add(x,y)print(z)z = tf.subtract(y,x)print(z)z = tf.divide(y,x)print(z)z = tf.multiply(y,x)print(z)z = (x **2)print(z)############################# OUTPUT ##############################tf.Tensor([ 7 9 11 13 15], shape=(5,), dtype=int32)tf.Tensor([5 5 5 5 5], shape=(5,), dtype=int32)tf.Tensor([6. 3.5 2.66666667 2.25 2. ], shape=(5,), dtype=float64)tf.Tensor([ 6 14 24 36 50], shape=(5,), dtype=int32)tf.Tensor([ 1 4 9 16 25], shape=(5,), dtype=int32)

Torch

# Torcht = torch.tensor([1,2,3,4,5])u = torch.tensor([6,7,8,9,10])v = torch.add(t, u) print(v)v = torch.sub(u,t)print(v)v = torch.true_divide (u, t)print(v)v = torch.mul(u,t)print(v)v = (t **2)print(v)############################# OUTPUT ##############################tensor([ 7,  9, 11, 13, 15])tensor([5, 5, 5, 5, 5])tensor([6.0000, 3.5000, 2.6667, 2.2500, 2.0000])tensor([ 6, 14, 24, 36, 50])tensor([ 1,  4,  9, 16, 25])

9. 点积

> Dot Product

Numpy

# Numpya = np.array([1,2,3,4,5])b = np.array([6,7,8,9,10])c = np.dot(a, b)print(c, c.dtype)############################# OUTPUT ##############################130 int64

Tensorflow

# TensorFlowx = tf.constant([1,2,3,4,5])y = tf.constant([6,7,8,9,10])z = tf.tensordot(x,y, axes=1)print(z)############################# OUTPUT ##############################tf.Tensor(130, shape=(), dtype=int32)

Torch

# Torcht = torch.tensor([1,2,3,4,5])u = torch.tensor([6,7,8,9,10])v = torch.dot(t,u)print(v)############################# OUTPUT ##############################tensor(130)

10. 矩阵乘法

> Matrix Multiplication

Numpy

# Numpya = np.array([[1,2,3], [4,5,6]])b = np.array([[1,2,3], [4,5,6], [7,8,9]])c = np.matmul(a,b) # (2,3) @ (3,3) --> (2,3) output shapeprint(c)############################# OUTPUT ##############################[[30 36 42] [66 81 96]]

Tensorflow

# TensorFlowx = tf.constant([[1,2,3], [4,5,6]])y = tf.constant([[1,2,3], [4,5,6], [7,8,9]])z = tf.matmul(x,y) # (2,3) @ (3,3) --> (2,3) output shapeprint(z)############################# OUTPUT ##############################tf.Tensor([[30 36 42] [66 81 96]], shape=(2, 3), dtype=int32)

Torch

# Torcht = torch.tensor([[1,2,3], [4,5,6]])u = torch.tensor([[1,2,3], [4,5,6], [7,8,9]])v = torch.matmul(t,u) # (2,3) @ (3,3) --> (2,3) output shapeprint(v)############################# OUTPUT ##############################tensor([[30, 36, 42],        [66, 81, 96]])

11. 索引和切片（2D）

> Indexing and Slicing

Numpy

# Numpya = np.array([1,2,3,4,5,6,7,8])print(a[:])print(a[2:-3])print(a[3:-1])print(a[::2])indices = np.array([0,3,5])x_indices = a[indices]print(x_indices)############################# OUTPUT ##############################[1 2 3 4 5 6 7 8][3 4 5][4 5 6 7][1 3 5 7][1 4 6]

Tensorflow

# TensorFlowb = tf.constant([1,2,3,4,5,6,7,8])print(b[:])print(b[2:-3])print(b[3:-1])print(b[::2])indices = tf.constant([0,3,5])x_indices = tf.gather(b, indices)print(x_indices)############################# OUTPUT ##############################tf.Tensor([1 2 3 4 5 6 7 8], shape=(8,), dtype=int32)tf.Tensor([3 4 5], shape=(3,), dtype=int32) tf.Tensor([4 5 6 7], shape=(4,), dtype=int32) tf.Tensor([1 3 5 7], shape=(4,), dtype=int32)tf.Tensor([1 4 6], shape=(3,), dtype=int32)

Torch

# Torchc = torch.tensor([1,2,3,4,5,6,7,8])print(c[:])print(c[2:-3])print(c[3:-1])print(c[::2])indices = torch.tensor([0,3,5])x_indices = c[indices]print(x_indices)############################# OUTPUT ##############################tensor([1, 2, 3, 4, 5, 6, 7, 8]) tensor([3, 4, 5]) tensor([4, 5, 6, 7]) tensor([1, 3, 5, 7])tensor([1, 4, 6])

12. 索引和切片（2D + 矩阵）

> Matrix Slicing

Numpy

# Numpya = np.array([[1,2,3],[4,5,6],[7,8,9]])# Matrix Indexing# Print all individual Rows and Columnsprint('Row-1',a[0, :])print('Row-2',a[1, :])print('Row-3',a[2, :])print('Col-1',a[:, 0])print('Col-2',a[:, 1])print('Col-3',a[:, 2])# Print the sub-diagonal matrixprint('Upper-Left',a[0:2,0:2])print('Upper-Right',a[0:2,1:3])print('Bottom-Left',a[1:3,0:2])print('Bottom-Right',a[1:3,1:3])############################# OUTPUT ##############################Row-1 [1 2 3]Row-2 [4 5 6] Row-3 [7 8 9]Col-1 [1 4 7] Col-2 [2 5 8] Col-3 [3 6 9]Upper-Left [[1 2]            [4 5]]Upper-Right [[2 3]             [5 6]]Bottom-Left [[4 5]             [7 8]]Bottom-Right [[5 6]              [8 9]]

Tensorflow

# TensorFlowb = tf.constant([[1,2,3],[4,5,6],[7,8,9]])# Matrix Indexing# Print all individual Rows and Columnsprint('Row-1',b[0, :])print('Row-2',b[1, :])print('Row-3',b[2, :])print('Col-1',b[:, 0])print('Col-2',b[:, 1])print('Col-3',b[:, 2])# Print the sub-diagonal matrixprint('Upper-Left',b[0:2,0:2])print('Upper-Right',b[0:2,1:3])print('Bottom-Left',b[1:3,0:2])print('Bottom-Right',b[1:3,1:3])############################# OUTPUT ##############################Row-1 tf.Tensor([1 2 3], shape=(3,), dtype=int32)Row-2 tf.Tensor([4 5 6], shape=(3,), dtype=int32)Row-3 tf.Tensor([7 8 9], shape=(3,), dtype=int32)Col-1 tf.Tensor([1 4 7], shape=(3,), dtype=int32) Col-2 tf.Tensor([2 5 8], shape=(3,), dtype=int32) Col-3 tf.Tensor([3 6 9], shape=(3,), dtype=int32)Upper-Left tf.Tensor( [[1 2] [4 5]], shape=(2, 2), dtype=int32) Upper-Right tf.Tensor( [[2 3] [5 6]], shape=(2, 2), dtype=int32) Bottom-Left tf.Tensor( [[4 5] [7 8]], shape=(2, 2), dtype=int32) Bottom-Right tf.Tensor( [[5 6] [8 9]], shape=(2, 2), dtype=int32)

Torch

# Torchc = torch.tensor([[1,2,3],[4,5,6],[7,8,9]])# Matrix Indexing# Print all individual Rows and Columnsprint('Row-1',c[0, :])print('Row-2',c[1, :])print('Row-3',c[2, :])print('Col-1',c[:, 0])print('Col-2',c[:, 1])print('Col-3',c[:, 2])# Print the sub-diagonal matrixprint('Upper-Left',c[0:2,0:2])print('Upper-Right',c[0:2,1:3])print('Bottom-Left',c[1:3,0:2])print('Bottom-Right',c[1:3,1:3])############################# OUTPUT ##############################Row-1 tensor([1, 2, 3]) Row-2 tensor([4, 5, 6]) Row-3 tensor([7, 8, 9])Col-1 tensor([1, 4, 7]) Col-2 tensor([2, 5, 8]) Col-3 tensor([3, 6, 9])Upper-Left tensor([[1, 2],[4, 5]]) Upper-Right tensor([[2, 3],[5, 6]])  Bottom-Left tensor([[4, 5],[7, 8]]) Bottom-Right tensor([[5, 6],[8, 9]])

13. 轴的重塑和转置

> Reshape & Transpose

Numpy

# Numpya = np.arange(9)print(a)a = np.reshape(a, (3,3))print(a)a = np.transpose(a, (1,0)) # Swap axes (1,0)print(a)############################# OUTPUT ##############################[0 1 2 3 4 5 6 7 8][[0 1 2] [3 4 5] [6 7 8]][[0 3 6] [1 4 7] [2 5 8]]

Tensorflow

# TensorFlowb = tf.range(9)print(b)b = tf.reshape(b, (3,3))print(b)b = tf.transpose(b, perm=[1,0]) # Swap axes in perm (1,0)print(b)############################# OUTPUT ##############################tf.Tensor([0 1 2 3 4 5 6 7 8], shape=(9,), dtype=int32)tf.Tensor( [[0 1 2]  [3 4 5]  [6 7 8]], shape=(3, 3), dtype=int32) tf.Tensor( [[0 3 6]  [1 4 7]  [2 5 8]], shape=(3, 3), dtype=int32)

Torch

# Torchc = torch.arange(9)print(c)c = torch.reshape(c, (3,3))print(c)c = c.permute(1,0) # Swap axes in perm (1,0)############################# OUTPUT ##############################tensor([0, 1, 2, 3, 4, 5, 6, 7, 8]) tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) tensor([[0, 3, 6], [1, 4, 7], [2, 5, 8]])

14. 串联

> Matrix Concatenation

Numpy

# Numpya = np.array([[1, 2], [3, 4]])print('a',a)b = np.array([[5, 6]])print('b',b)d = np.concatenate((a, b), axis=0)print('Concat (axis=0 - Row)')print(d)e = np.concatenate((a, b.T), axis=1)print('Concat (axis=1 - Column)')print(e)############################# OUTPUT ##############################a [[1 2]  [3 4]] b [[5 6]]Concat (axis=0 - Row) [[1 2]   [3 4]   [5 6]]Concat (axis=1 - Column) [[1 2 5]   [3 4 6]]

Tensorflow

# TensorFlowx = tf.constant([[1, 2], [3, 4]])print('x',x)y = tf.constant([[5, 6]])print('y',y)z = tf.concat((x, y), axis=0)print('Concat (axis=0 - Row)')print(z)z = tf.concat((x, tf.transpose(y)), axis=1)print('Concat (axis=1 - Column)')print(z)############################# OUTPUT ##############################x tf.Tensor( [[1 2] [3 4]], shape=(2, 2), dtype=int32) y tf.Tensor([[5 6]], shape=(1, 2), dtype=int32)Concat (axis=0 - Row) tf.Tensor( [[1 2] [3 4] [5 6]], shape=(3, 2), dtype=int32)Concat (axis=1 - Column) tf.Tensor( [[1 2 5] [3 4 6]], shape=(2, 3), dtype=int32)

Torch

# Torcht = torch.tensor([[1, 2], [3, 4]])print('x',t)u = torch.tensor([[5, 6]])print('y',u)v = torch.cat((t , u), axis=0)print('Concat (axis=0 - Row)')print(v)v = torch.cat((t , u.T), axis=1)print('Concat (axis=1 - Column)')print(v)############################# OUTPUT ##############################x tensor([[1, 2], [3, 4]]) y tensor([[5, 6]])Concat (axis=0 - Row) tensor([[1, 2],        [3, 4],                 [5, 6]])Concat (axis=1 - Column) tensor([[1, 2, 5],        [3, 4, 6]])

15. 跨轴求和

> Axes — Sum

Numpy

# Numpya = np.array([[1,2,3,4,5], [10,10,10,10,10]])print(a)print('Overall flattened Sum', a.sum())print('Sum across Columns',a.sum(axis=0))print('Sum across Rows',a.sum(axis=1))############################# OUTPUT ##############################[[ 1 2 3 4 5] [10 10 10 10 10]]Overall flattened Sum 65 Sum across Columns [11 12 13 14 15]Sum across Rows [15 50]

Tensorflow

# TensorFlowb = tf.constant([[1,2,3,4,5], [10,10,10,10,10]])print(b)print('Overall flattened Sum',tf.math.reduce_sum(b))print('Sum across Columns',tf.math.reduce_sum(b, axis=0))print('Sum across Rows',tf.math.reduce_sum(b, axis=1))############################# OUTPUT ##############################tf.Tensor([[ 1  2  3  4  5]  [10 10 10 10 10]], shape=(2, 5), dtype=int32)Overall flattened Sum tf.Tensor(65, shape=(), dtype=int32) Sum across Columns tf.Tensor([11 12 13 14 15], shape=(5,), dtype=int32) Sum across Rows tf.Tensor([15 50], shape=(2,), dtype=int32)

Torch

# Torchc = torch.tensor([[1,2,3,4,5], [10,10,10,10,10]])#print(c)print('Overall flattened Sum',torch.sum(c))print('Sum across Columns',torch.sum(c, axis=0))print('Sum across Rows',torch.sum(c, axis=1))############################# OUTPUT ##############################Overall flattened Sum tensor(65) Sum across Columns tensor([11, 12, 13, 14, 15]) Sum across Rows tensor([15, 50])

16. 轴的均值

Numpy

# Numpya = np.array([[1,2,3,4,5],                [10,10,10,10,10]])print(a)print('Overall flattened mean', a.mean())print('Sum across Columns',a.mean(axis=0))print('Sum across Rows',a.mean(axis=1))############################# OUTPUT ##############################[[ 1  2  3  4  5]  [10 10 10 10 10]]Overall flattened mean 6.5 Sum across Columns [5.5 6.  6.5 7.  7.5] Sum across Rows [ 3. 10.]

Tensorflow

# TensorFlowb = tf.constant([[1,2,3,4,5], [10,10,10,10,10]])print(b)print('Overall flattened mean',tf.math.reduce_mean(b))print('Sum across Columns',tf.math.reduce_mean(b, axis=0))print('Sum across Rows',tf.math.reduce_mean(b, axis=1))############################# OUTPUT ##############################tf.Tensor( [[ 1 2 3 4 5] [10 10 10 10 10]], shape=(2, 5), dtype=int32)Overall flattened mean tf.Tensor(6, shape=(), dtype=int32) Sum across Columns tf.Tensor([5 6 6 7 7], shape=(5,), dtype=int32) Sum across Rows tf.Tensor([ 3 10], shape=(2,), dtype=int32)

Torch

# Torchc = torch.tensor([[1,2,3,4,5], [10,10,10,10,10]], dtype=torch.float32)print(c)print('Overall flattened mean',torch.mean(c))print('Sum across Columns',torch.mean(c, axis=0))print('Sum across Rows',torch.mean(c, axis=1))############################# OUTPUT ##############################tensor([[ 1.,  2.,  3.,  4.,  5.],        [10., 10., 10., 10., 10.]])  Overall flattened mean tensor(6.5000) Sum across Columns tensor([5.5000, 6.0000, 6.5000, 7.0000, 7.5000])Sum across Rows tensor([ 3., 10.])

17. 尺寸扩展和移动轴

> Concat and move axes

Numpy

# Numpya = np.full((3,3),10.0)print(a)print(a.shape)a = np.expand_dims(a, axis=0)print(a)print(a.shape)b = np.full((3,3),20.0)print(b)b = np.expand_dims(b, axis=0)print(b.shape)c = np.concatenate((a,b), axis=0)c = np.moveaxis(c,2,0) # Move 2nd dimension to 0th positionprint(c)print(c.shape)############################# OUTPUT ##############################[[10. 10. 10.] [10. 10. 10.] [10. 10. 10.]] (3, 3)[[[10. 10. 10.] [10. 10. 10.] [10. 10. 10.]]] (1, 3, 3)[[20. 20. 20.] [20. 20. 20.] [20. 20. 20.]] (1, 3, 3)[[[10. 10. 10.] [20. 20. 20.]] [[10. 10. 10.] [20. 20. 20.]] [[10. 10. 10.] [20. 20. 20.]]](3, 2, 3)

Tensorflow

# TensorFlowx = tf.fill((3,3),10.0)print(x)print(x.shape)x = tf.expand_dims(x, axis=0)print(x.shape)y = tf.fill((3,3),20.0)print(y)print(y.shape)y = tf.expand_dims(y, axis=0)print(y.shape)z = tf.concat((x,y), axis=0)z = tf.transpose(z, [1, 0, 2])print(z.shape)############################# OUTPUT ##############################tf.Tensor( [[10. 10. 10.]              [10. 10. 10.]              [10. 10. 10.]], shape=(3, 3), dtype=float32) (3, 3) (1, 3, 3) tf.Tensor( [[20. 20. 20.]              [20. 20. 20.]              [20. 20. 20.]], shape=(3, 3), dtype=float32) (3, 3)(1, 3, 3)(3, 2, 3)

Torch

# Torchm1 = torch.ones((2,), dtype=torch.int32)m1 = m1.new_full((3, 3), 10)m1 = torch.unsqueeze(m1, axis=0)print(m1)print(m1.shape)m2 = torch.ones((2,), dtype=torch.int32)m2 = m2.new_full((3, 3), 20)print(m2)m2 = torch.unsqueeze(m2, axis=0)print(m2.shape)m = torch.cat((m1,m2), axis=0)m = m.permute([1,0,2])print(m)print(m.shape)############################# OUTPUT ##############################tensor([[[10, 10, 10], [10, 10, 10], [10, 10, 10]]], dtype=torch.int32)torch.Size([1, 3, 3])tensor([[20, 20, 20], [20, 20, 20], [20, 20, 20]], dtype=torch.int32)torch.Size([1, 3, 3])tensor([[[10, 10, 10], [20, 20, 20]], [[10, 10, 10], [20, 20, 20]], [[10, 10, 10], [20, 20, 20]]], dtype=torch.int32)torch.Size([3, 2, 3])

最大最小值

> Max for axis=0

> Max for axis=1

Numpy

# Numpya = np.array([[5,10,15],              [20,25,30]])b = np.array([[6,69,35],              [70,10,82]])c = np.array([[25,45,48],              [4,100,89]])print(a)final = np.zeros((3,2,3))print(final.shape)final[0, :, :] = afinal[1, :, :] = bfinal[2, :, :] = cprint(final)print('Overall flattened max', final.max())print('max across Columns',final.max(axis=0))print('max across Rows',final.max(axis=1))print('Index of max value across the flattened max', final.argmax())print('Index of max value across Columns',final.argmax(axis=0))print('Index of max value across Rows',final.argmax(axis=1))############################# OUTPUT ##############################[[ 5 10 15]   [20 25 30]](3, 2, 3)[[[  5.  10.  15.]  [ 20.  25.  30.]][[  6.  69.  35.] [ 70.  10.  82.]][[ 25.  45.  48.] [  4. 100.  89.]]]Overall flattened max 100.0max across Columns [[ 25.  69.  48.]   [ 70. 100.  89.]]max across Rows [[ 20.  25.  30.]   [ 70.  69.  82.]   [ 25. 100.  89.]]Index of max value across the flattened max 16 Index of max value across Columns [[2 1 2]  [1 2 2]]Index of max value across Rows [[1 1 1]   [1 0 1] [0 1 1]]

Tensorflow

# Tensorflowfinal = tf.constant([[[5,10,15], [20,25,30]], [[6,69,35], [70,10,82]], [[25,45,48], [4,100,89]]])print(final)print('Overall flattened max', tf.math.reduce_max(final))print('max across Columns',tf.math.reduce_max(final,axis=0))print('max across Rows',tf.math.reduce_max(final, axis=1))print('Index of max value across the flattened max', tf.math.argmax(final))print('Index of max value across Columns',tf.math.argmax(final, axis=0))print('Index of max value across Rows',tf.math.argmax(final, axis=1))############################# OUTPUT ##############################tf.Tensor( [[[ 5 10 15] [ 20 25 30]] [[ 6 69 35] [ 70 10 82]] [[ 25 45 48] [ 4 100 89]]], shape=(3, 2, 3), dtype=int32)Overall flattened max tf.Tensor(100, shape=(), dtype=int32) max across Columns tf.Tensor( [[ 25 69 48] [ 70 100 89]], shape=(2, 3), dtype=int32)max across Rows tf.Tensor( [[ 20 25 30] [ 70 69 82] [ 25 100 89]], shape=(3, 3), dtype=int32)Index of max value across the flattened max tf.Tensor( [[2 1 2] [1 2 2]], shape=(2, 3), dtype=int64)Index of max value across Columns tf.Tensor( [[2 1 2] [1 2 2]], shape=(2, 3), dtype=int64)Index of max value across Rows tf.Tensor( [[1 1 1] [1 0 1] [0 1 1]], shape=(3, 3), dtype=int64)

Torch

# Torchfinal = torch.tensor([[[5,10,15],                      [20,25,30]],                     [[6,69,35],                      [70,10,82]],                     [[25,45,48],                      [4,100,89]]])print(final)print('Overall flattened max', torch.max(final))print('max across Columns',torch.max(final,axis=0))print('max across Rows',torch.max(final, axis=1))print('Index of max value across the flattened max', torch.argmax(final))print('Index of max value across Columns',torch.argmax(final, axis=0))print('Index of max value across Rows',torch.argmax(final, axis=1))############################# OUTPUT ##############################tensor([[[  5,  10,  15],         [ 20,  25,  30]],                  [[  6,  69,  35],              [ 70,  10,  82]],            [[ 25,  45,  48],                [  4, 100,  89]]])Overall flattened max tensor(100) max across Columns torch.return_types.max( values=tensor([[ 25,  69,  48],        [ 70, 100,  89]]), indices=tensor([[2, 1, 2],               [1, 2, 2]]))max across Rows torch.return_types.max( values=tensor([[ 20,  25,  30],                 [ 70,  69,  82],                 [ 25, 100,  89]]), indices=tensor([[1, 1, 1],                         [1, 0, 1],                         [0, 1, 1]]))Index of max value across the flattened max tensor(16) Index of max value across Columns tensor([[2, 1, 2],         [1, 2, 2]])Index of max value across Rows tensor([[1, 1, 1],        [1, 0, 1],                [0, 1, 1]])

19. 切片和索引（3D矩阵）

> 3x3 Matrix and its indices

> Upper-Left & Lower-Right

> Middle Elements & Inverse Middle Element

Numpy

# Numpya = np.array([[10,10,10],[10,10,10], [10,10,10],[10,10,10]])b = np.array([[20,20,20],[20,20,20], [20,20,20],[20,20,20]])c = np.array([[30,30,30],[30,30,30], [30,30,30],[30,30,30]])final = np.zeros((3,4,3))final[0, :, :] = afinal[1, :, :] = bfinal[2, :, :] = cprint('Upper-Left',final[:, 0:2, 0:2])print('Lower-Right',final[:, 2:, 1:])print('Middle Elements',final[:,1:3, 1])# Ignore Middle Elementsa = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])b = np.array([[13,14,15],[16,17,18],[19,20,21],[22,23,24]])c = np.array([[25,26,27],[28,29,30],[31,32,33],[34,35,36]])final = np.zeros((3,4,3))print(final.shape)final[0, :, :] = afinal[1, :, :] = bfinal[2, :, :] = c# Though may work,but not efficientprint('Ignore Middle',final[:,[0,0,0,1,1,2,2,3,3,3], [0,1,2,0,2,0,2,0,1,2]]) ############################# OUTPUT ##############################Upper-Left [[[10. 10.] [10. 10.]] [[20. 20.] [20. 20.]] [[30. 30.] [30. 30.]]]Lower-Right [[[10. 10.] [10. 10.]] [[20. 20.] [20. 20.]] [[30. 30.] [30. 30.]]]Middle Elements [[10. 10.] [20. 20.] [30. 30.]](3, 4, 3)Ignore Middle [[ 1. 2. 3. 4. 6. 7. 9. 10. 11. 12.] [13. 14. 15. 16. 18. 19. 21. 22. 23. 24.] [25. 26. 27. 28. 30. 31. 33. 34. 35. 36.]]

Tensorflow

# Tensorflowfinal = tf.constant([[[10,10,10],[10,10,10],                  [10,10,10],[10,10,10]],                  [[20,20,20],[20,20,20],                  [20,20,20],[20,20,20]],                  [[30,30,30],[30,30,30],                  [30,30,30],[30,30,30]]])print('Upper-Left',final[:, 0:2, 0:2])print('Lower-Right',final[:, 2:, 1:])print('Middle Elements',final[:,1:3, 1])############################# OUTPUT ##############################Upper-Left tf.Tensor([[[10 10]  [10 10]] [[20 20]  [20 20]] [[30 30]  [30 30]]], shape=(3, 2, 2), dtype=int32)Lower-Right tf.Tensor([[[10 10]  [10 10]] [[20 20]  [20 20]] [[30 30]  [30 30]]], shape=(3, 2, 2), dtype=int32)Middle Elements tf.Tensor([[10 10] [20 20] [30 30]], shape=(3, 2), dtype=int32)

Torch

# Torcha = torch.Tensor([[10,10,10],[10,10,10], [10,10,10],[10,10,10]])b = torch.Tensor([[20,20,20],[20,20,20], [20,20,20],[20,20,20]])c = torch.Tensor([[30,30,30],[30,30,30], [30,30,30],[30,30,30]])final = np.zeros((3,4,3))final[0, :, :] = afinal[1, :, :] = bfinal[2, :, :] = cprint('Upper-Left',final[:, 0:2, 0:2])print('Lower-Right',final[:, 2:, 1:])print('Middle Elements',final[:,1:3, 1])# Ignore Middle Elementsa = torch.Tensor([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])b = torch.Tensor([[13,14,15],[16,17,18],[19,20,21],[22,23,24]])c = torch.Tensor([[25,26,27],[28,29,30],[31,32,33],[34,35,36]])final = np.zeros((3,4,3))print(final.shape)final[0, :, :] = afinal[1, :, :] = bfinal[2, :, :] = c# Though may work,but not efficientprint('Ignore Middle',final[:,[0,0,0,1,1,2,2,3,3,3], [0,1,2,0,2,0,2,0,1,2]])############################# OUTPUT ##############################Upper-Left [[[10. 10.] [10. 10.]] [[20. 20.] [20. 20.]] [[30. 30.] [30. 30.]]]Lower-Right [[[10. 10.] [10. 10.]] [[20. 20.] [20. 20.]] [[30. 30.] [30. 30.]]]Middle Elements [[10. 10.] [20. 20.] [30. 30.]](3, 4, 3)Ignore Middle [[ 1. 2. 3. 4. 6. 7. 9. 10. 11. 12.] [13. 14. 15. 16. 18. 19. 21. 22. 23. 24.] [25. 26. 27. 28. 30. 31. 33. 34. 35. 36.]]

由于可视化约束，我跳过了对较高维度零件的操作。

我希望我能够提供一些视觉理解的一些基本操作，以及您选择的深度学习框架，我将很快添加更详细的操作。

查看谷歌科拉布的笔记本→实验室。

（或）

看看卡格尔的笔记本在这里→

在那之前，下次见。

文章通过：

巴拉克里什纳库马尔五世

联合创始人 – 深度光学（基于人工智能的医学成像初创公司）

与我联系→ LinkedIn， Github， 推特， 媒体

(本文翻译自Piotr Janusz的文章《Visual Representation of Matrix and Vector Operations and implementations in NumPy, Torch, and TensorFlow.》，参考：
https://medium.com/towards-artificial-intelligence/visual-representation-of-matrix-and-vector-operations-and-implementation-in-numpy-torch-and-tensor-6a94d14913c6)

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