List, Numpy, Tensor operation basics

Everything is a matrix in computer vision:

• Image: 3D data (color), 2D data (black and white)
• Video: 4-dimensional data (T,3,H,W)

$$If\; you\; want\; to\; write\; code\; smoothly,youmustbe\; familiar\; with\; the\; operations\; oflist,numpy,andtensor$$

1. list list

1.1 list creation

list is the most basic data structure in Python. Each element in a sequence is assigned a number (its position index), and like string indices, list indices start at 0. Lists can be indexed, sliced, added, multiplied, checked for membership, truncated, combined, etc. Use commas to separate any type of value in [] to achieve index access.

• Create directly :

l = [1,2,3,4,5]
l[0] = 10
print(l[0])

10

• List generation :

l = [e for e in range(10)]
print(l)

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

• Random generation : random.random()used to generate a random floating point number between 0 and 1

l = [random.random() for i in range(10)]
print(l)

[0.9941637112357136, 0.7179263215012058, 0.41440567906139236, 0.5241162283103614, 0.6378630095667321, 0.11731480610659373, 0.9410968887798861, 0.8591094876738674, 0.9812292614236708, 0.1962255254167019]

1.1 list built-in method

• Slicing [start (start), stop (stop), step (step size)] : The direction of list slicing depends on the start index, end index and step size. When the start index is on the right side of the end index, it is taken from right to left value, and vice versa. 当步长为负数时, 从start开始索引至stop, the start point must be greater than the end point.

a[:]           # a copy of the whole array
a[start:]      # items start through the rest of the array
a[:stop]       # items from the beginning through stop-1
a[start:stop]  # items start through stop-1
a[start:stop:step] # start through not past stop, by step

a[-1]    # last item in the array
a[-2:]   # last two items in the array
a[:-2]   # every items except the last two items

a[::-1]    # all items in the array, reversed
a[1::-1]   # the first two items, reversed
a[:-3:-1]  # the last two items, reversed
a[-3::-1]  # every items except the last two items, reversed

• Index access [idx] : 正向取值+反向取值, which can be stored or withdrawn list[idx].

L = ['Google', 'Runoob', 'Taobao']
print(L[0], L[-1])  # 读取列表第一个和倒数第一个元素

Google Taobao

• Splice+ : +号Used to splice lists.

l = [1,2,3] + [4,5,6]
print(l)

[1, 2, 3, 4, 5, 6]

• repeat *: *号for repeating a list.

l2 = [1]*5
print(l2)

[1, 1, 1, 1, 1]

• Length len() : the number of list elementslen(list)

l = [1,2,3,4,5,6]
print(len(l))

• Membership operations in and not in : determine whether an element is in the list,e in list

l = [1,2,3,4,5,6]
print(3 in l)
print(6 not in l)

True
False

• Delete by subscript del : Use the del statement to delete the elements of the list according to the subscript idx,del list[idx]

l = [1,2,3,4,5,6]
del l[0]
print(l)

[2, 3, 4, 5, 6]

• Insert insert() : Insert an element at any position idxlist.insert(idx,e)

l = [1,2,4]
l.insert(2,3)
print(l)

[1, 2, 3, 4]

• Append value append() : add a new object at the end of the list,list.append(e)

l = [1,2,3,4,5,6]
l.append(7)
print(l)

[1, 2, 3, 4, 5, 6, 7]

• Pop stack pop() : list.pop()delete the last element by default

l = [1,2,3,4]
l.pop()
print(l)

[1, 2, 3]

• Remove by value remove() : Traverse sequentially from left to right, delete the first found element corresponding to the valuelist.remove(e)

l = [1,2,3,3,3]
l.remove(3)
print(l)

[1, 2, 3, 3]

• Empty clear() : Clear all elements in the list,list.clear()

l = [1,2,3,3,3]
l.clear()
print(l)

[]

• reverse reverse() : reverse the listlist.reverse()

l = [1,2,3,4,5]
l.reverse()
print(l)

[5, 4, 3, 2, 1]

• Sort sort() : can be sorted in descending or ascending order,list.sort(reverse=Ture/False)

l = [1,2,3,4,5]
l.sort(reverse=True)
print(l)

[5, 4, 3, 2, 1]

• Find index() : Find the subscript of the corresponding element (find the first one in order),list.index(e)

l = [1,2,3,3,3]
print(l.index(3))

2

• Count count() : Count the number of occurrences of the corresponding elementlist.count(e)

l = [1,2,3,3,3]
print(l.count(3))

3

Two, numpy matrix

2.1 Create numpy.ndarray

One of the most important features of NumPy is its N-dimensional array object ndarray, which is a collection of a series of data of the same type, starting with subscript 0 to index the elements in the collection. nd array represents numbers in n dimensions.

• Create numpy.array(list) with list : objectit is a list object, dtype(optional) the data class of the array elements, copy(optional) whether the object needs to be copied, order(default A) the style of creating the array, C is the row direction, F is the column Direction, A is any direction, subokreturns an array consistent with the base class type by default, and ndminspecifies the minimum dimension of the generated array

numpy.array(object, dtype = None, copy = True, order = None, subok = False, ndmin = 0)

n = np.array([[1,2,3],[4,5,6]])
print(n)

[[1 2 3]
[4 5 6]]

• Created using the np function : shape can be a tuple or a list, and dtype indicates the element type (default numpy.float64).

np.random.random(size=(3,4))  # 生成size维度的多维矩阵，元素是0-1间的随机数
np.random.random(d1,d2...dn)  # 生成d1xd2xd3..xdn维度的矩阵，元素是0-1间的随机数，如random(3，4)生成3行4列数组

np.random.randn(d1,d2...dn)  # 生成d1xd2xd3..xdn维度的矩阵，元素服从标准正态分布~N(0,1)，如randn(3，4)生成3行4列数组
np.random.normal(loc,scale,size=(3,4))  # 生成size形状的矩阵，元素服从整体分布~N(loc均值,scale标准差)

np.random.randint(low=0,high=255,size=[3,64,64])  # 生成形状size的多维数组，整数元素在[low,high]之间随机取值，size默认是1个整数

np.arange(start,end,stop)  # 创建[start,end)步长step的序列，start默认为0，step默认为1，和list的range相同
np.linspace(start,end,num)  # 从start到end共1xnum个元素的等差数列

np.ones(shape, dtype)  # 全1矩阵
np.zeros(shape, dtype)  # 全0矩阵
np.full(shape, full_value, dtype)  # 全full_value矩阵
np.eyes(N, dtype)  # N阶单位方阵

2.2 Common properties of ndarray

• ndim: dimension
• shape:shape
• size: number of elements
• dtype: element type

img = plt.imread('1.jpg')
print(img.ndim)
print(img.shape)
print(img.size)
print(img.dtype)

3
(1630, 1080, 3)
5281200
uint8

2.2 ndarray built-in methods

• Index operation [idx] : exactly the same as the list list,

l = np.random.randint(1,10,[3,5])
print(l[0])

[2 3 3 4 6]

• Slicing [start (start), stop (stop), step (step)] : Same as list slice operation, 当步长为负数时, 从start开始索引至stop, the starting point must be greater than the end point.

a[:]           # a copy of the whole array
a[start:]      # items start through the rest of the array
a[:stop]       # items from the beginning through stop-1
a[start:stop]  # items start through stop-1
a[start:stop:step] # start through not past stop, by step

a[-1]    # last item in the array
a[-2:]   # last two items in the array
a[:-2]   # every items except the last two items

a[::-1]    # all items in the array, reversed
a[1::-1]   # the first two items, reversed
a[:-3:-1]  # the last two items, reversed
a[-3::-1]  # every items except the last two items, reversed

l = np.random.randint(1,10,[3,4])
print(l[1:8:2,:])

[[5 2 3 8]]

For example, perform row inversion (up and down inversion), column inversion (left and right inversion), and color inversion (RGB-BGR) on the original image

# 读取图像
img = cv2.imread('test.jpg')
print(img.shape)  # (64, 64, 3)
img = img[::-1,::-1,::-1]
# 显示图像
cv2.imshow('Image', img)
cv2.waitKey(0)
cv2.destroyAllWindows()

• Deformation reshape() : n.reshape(new_shape), directly transform the np array with reshape, the new shape new_shape can be a list or a tuple, to be sure old_shape所有维度乘积==new_shape所有维度乘积, -1 means to automatically calculate the remaining dimensions.

img = cv2.imread('test.jpg')
print(img.shape)  # (64, 64, 3)
img = np.reshape(img, (4,4,-1)) 
print(img.shape)  # (4, 4, 768)

• Splicing concatenate() : The dimensions of the spliced ​​arrays must be the same, and the splicing direction can be changed through the axis parameter np.concatenate((n1,n1), axis=dim_idx), which indicates the number of dimensions to merge

n1 = np.random.randint(1,100,[3,4])  # 3行4列
n2 = np.random.randint(1,100,[3,4])
print(np.concatenate((n1,n1),axis=0).shape) # 上下合并(行合并)合并第一个维度axis=0
print(np.concatenate((n1,n1),axis=1).shape) # 左右合并(列合并)合并第二个维度axis=1

print(np.hstack((n1,n2)).shape)  # 垂直合并
print(np.vstack((n1,n2)).shape)  # 水平合并

(6, 4)
(3, 8)
(3, 8)
(6, 4)

• Split split() : np.split(n, (1,2,1), axis=1)Specify axis=1 to split in the second dimension, and specify the split ratio (1,2,1)

n = np.array([[71,44,92,63],[1,19,70,23],[19,73,24,79]])
print(np.vsplit(n, 3))  # 垂直拆分，均匀按行拆分3份
print(np.hsplit(n, 4))  # 水平拆分，均匀按列拆分4份
print(np.split(n,(1,2,1),axis=1))  # 指定axis维度拆分，指定拆分比例

[array([[71, 44, 92, 63]]), array([[ 1, 19, 70, 23]]), array([[19, 73, 24, 79]])]
[array([[71],
[ 1],
[19]]), array([[44],
[19],
[73]]), array([[92],
[70],
[24]]), array([[63],
[23],
[79]])]
[array([[71],
[ 1],
[19]]), array([[44],
[19],
[73]]), array([], shape=(3, 0), dtype=int32), array([[44, 92, 63],
[19, 70, 23],
[73, 24, 79]])]

For example, splitting a grayscale image of a certain channel of an RGB image

# 读取图像
img = cv2.imread("test.jpg")
img, _, _ = np.split(img,3,axis=2)
# 显示图像
img = cv2.convertScaleAbs(img)
cv2.imshow('Image', img)
cv2.waitKey(0)
cv2.destroyAllWindows()

• Assignment = and copy copy() : assignment: use the same memory, deep copy: create a new copy.

n1 = np.array([1,2,3,4])
n2 = n1  # 赋值:用的是同一个内存
n3 = np.copy(n1)  # 深拷贝:新建副本
n1[0] = 0
print(n2)
print(n3)

[0, 2, 3, 4]
[1 2 3 4]

• Statistical operations : pay attention to the axis here 不是对该维度求统计值, but 对其他维度求多个该维度的统计值. For example, axis=0 means that multiple rows of each column are used to find the median

n = np.array([[1,2,3],[4,5,6],[7,8,9]])
print(np.sum(n, axis=0))  # axis=0表示每一列的多行求和
print(np.min(n,axis=0))  # axis=0表示每一列的多行求最小值
print(np.max(n,axis=0))  # axis=0表示每一列的多行求最大值
print(np.mean(n,axis=0))  # axis=0表示每一列的多行求平均值
print(np.average(n,axis=0))  # axis=0表示每一列的多行求平均值
print(np.median(n,axis=0))  # axis=0表示每一列的多行求中位数
print(np.argmin(n,axis=0))  # axis=0表示每一列的多行求最小值下标
print(np.argmax(n,axis=0))  # axis=0表示每一列的多行求最小值下标
print(np.std(n,axis=0))  # axis=0表示每一列的多行求标准差
print(np.var(n,axis=0))  # axis=0表示每一列的多行求方差

[12 15 18]
[1 2 3]
[7 8 9]
[4. 5. 6.]
[4. 5. 6.]
[4. 5. 6.]
[0 0 0]
[2 2 2]
[2.44948974 2.44948974 2.44948974]
[6. 6. 6.]

• Matrix operations : operations on all elements of the matrix, addition/subtraction/multiplication between matrices (multiplication requires mxn, nxk), matrix transposition/inversion

n1 = np.array([[1,2,3],[4,5,6],[7,8,9]])
print(n1+10) # 加
print(n1-10) # 减
print(n1*10) # 乘
print(n1/10) # 除
print(n1//2) # 整除
print(n1**2) # 平方
print(n1%2) # 取余

[[11 12 13]
[14 15 16]
[17 18 19]]
[[-9 -8 -7]
[-6 -5 -4]
[-3 -2 -1]]
[[10 20 30]
[40 50 60]
[70 80 90]]
[[0.1 0.2 0.3]
[0.4 0.5 0.6]
[0.7 0.8 0.9]]
[[0 1 1]
[2 2 3]
[3 4 4]]
[[ 1 4 9]
[16 25 36]
[49 64 81]]
[[1 0 1]
[0 1 0]
[1 0 1]]

n1 = np.array([[1,2,3],[4,5,6],[7,8,9]])
n2 = np.array([[1,2,3],[4,5,6],[7,8,9]])
print(n1+n2)  # 矩阵加法
print(n1-n2)  # 矩阵减法
print(n1.dot(n2))  # 矩阵乘法
print(n1 @ n2)  # 矩阵乘法
print(n1.T)  # 矩阵转置

[[ 2 4 6]
[ 8 10 12]
[14 16 18]]
[[0 0 0]
[0 0 0]
[0 0 0]]
[[ 30 36 42]
[ 66 81 96]
[102 126 150]]
[[ 30 36 42]
[ 66 81 96]
[102 126 150]]

n1 = np.array([[1,2],[-1,-3]])
print(n1.T)  # 矩阵转置
print(np.linalg.inv(n1))  # 矩阵逆
print(np.linalg.det(n1))  # 矩阵行列式

[[ 1 -1]
[ 2 -3]]
[[ 3. 2.]
[-1. -1.]]
-1.0

• Broadcast mechanism : try to provide the possibility of operation for matrices of different dimensions ( 补充缺失的维度, 用已有值填充缺失元素)

 n1 = np.array([[1,1,1],[2,2,2]])
n2 = np.array([3,3,3])  # 第二列补全为[3,3,3]
print(n1+n2)

[[4 4 4]
[5 5 5]]

• Math operations :
  

• save : np.save("name", n)save ndarry as .npy file

np1 = np.array([[1,1,1],[2,2,2]])
np.save('np1',np1)

Three, tensor tensor

3.1 create tensor

• Create with list :

DEVICE = "cuda" if torch.cuda.is_available() else "cpu"
x = torch.tensor([[1, 2, 3], [4, 5, 6]], dtype=torch.float32, device=DEVICE, requires_grad=True)
print(x)

tensor([[1., 2., 3.],
[4., 5., 6.]], device=‘cuda:0’, requires_grad=True)

• Create with numpy : tensor and numpy conversion

# 从numpy创建tensor
x = torch.from_numpy(np.array([1, 2]))
print(x)
# 将tensor转换为numpy
x = x.numpy()
print(x)

tensor([1, 2], dtype=torch.int32)
[1 2]

• Normal/uniform distribution creation :

# 标准正态分布 形状为[2, 3]
print(torch.randn(2, 3))

# 0-1均匀分布 形状为[2, 3]
x = torch.rand(2, 3)
print(x)

# low-high的整数的均匀分布 形状为[2, 3]
print(torch.randint(low=0, high=1, [2, 3]))

# 0-1均匀分布 和x形状相同的矩阵
y = torch.rand_like(x)
print(y)

tensor([[-0.8816, 0.6829, 0.2136],
[ 0.3556, -0.7659, -0.5187]])
tensor([[0.7780, 0.6701, 0.7642],
[0.2193, 0.4377, 0.5646]])
tensor([[5, 9, 2],
[9, 5, 4]])

• Padding created :

#全1填充
print(torch.ones(2, 3))
#全0填充
print(torch.zeros(2, 3))
#full填充
print(torch.full([2, 3], 7))
#对角矩阵
print(torch.eye(3, 3))
#创建但不初始化 0
print(torch.empty(2, 3))

tensor([[1., 1., 1.],
[1., 1., 1.]])
tensor([[0., 0., 0.],
[0., 0., 0.]])
tensor([[7, 7, 7],
[7, 7, 7]])
tensor([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
tensor([[0.0000, 1.8750, 0.0000],
[1.8750, 0.0000, 1.8750]])

• Increment/decrement sequence :

#自增数列,0到9,步长是2
print(torch.arange(start=0, end=10, step=2))
#等差数列,0到10,4个数
print(torch.linspace(start=0, end=10, steps=4))

tensor([0, 2, 4, 6, 8])
tensor([ 0.0000, 3.3333, 6.6667, 10.0000])

• Specified type creation :

#指定类型的创建
print(torch.FloatTensor([1, 2]))
print(torch.LongTensor([1, 2]))
#获取数据类型
print(torch.randn(2, 3).dtype)
#转换数据类型
print(torch.randn(2, 3).to(torch.float64).dtype)

tensor([1., 2.])
tensor([1, 2])
torch.float32
torch.float64

3.2 tensor built-in method

tensor index

#创建测试数据
#4张图片,3通道,28*28像素
a = torch.randn(4, 3, 28, 28)
a.shape

#直接索引
#查看第0张图片
print(a[0].shape)
#查看第0张图片的第0个通道
print(a[0, 0].shape)
#查看第0张图片的第0个通道的第2行
print(a[0, 0, 2].shape)
#查看第0张图片的第0个通道的第2行第4列
print(a[0, 0, 2, 4].shape)

#切片
#查看0-1张图片
print(a[:2].shape)
#查看0-1张图片的0-1通道
print(a[:2, :2].shape)
#查看0-1张图片的所有通道的倒数5-正数24行
print(a[:2, :, -5:25].shape)
#有间隔的索引
print(a[:, :, :, ::2].shape)
#用...表示多个被省略的:
#取所有图片的第0-2列
print(a[..., :2].shape)
#取所有图片的第0-2行
print(a[..., :2, :].shape)
#取第2张图片
print(a[2, ...].shape)

torch.Size([3, 28, 28])
torch.Size([28, 28])
torch.Size([28])
torch.Size([])
torch.Size([2, 3, 28, 28])
torch.Size([2, 2, 28, 28])
torch.Size([2, 3, 2, 28])
torch.Size([4, 3, 28, 14])
torch.Size([4, 3, 28, 2])
torch.Size([4, 3, 2, 28])
torch.Size([3, 28, 28])

Tensor dimension transformation

view, reshape dimension transformation, unsqueeze insert dimension, squeeze delete dimension, can only delete dimension of 1, repeat copy dimension, dimension exchange transpose and permute

#view,reshape维度变换
#4张图片,单通道,28*28像素
a = torch.randn(4, 1, 28, 28)
print(a.shape)
#转换为4,784维度,相当于打平了
print(a.reshape(4, 784).shape)
#转换为4,28,28维度,相当于重新展开
print((a.reshape(4, 784)).reshape(4, 28, 28).shape)
#view的用法和reshape是完全一样的')
print(a.view(4, 784).shape)

torch.Size([4, 1, 28, 28])
torch.Size([4, 784])
torch.Size([4, 28, 28])
torch.Size([4, 784])

#unsqueeze插入维度
#2*2的tensor
a = torch.randn(2, 2)
print(a.shape)
#插入维度在第0维
print(a.unsqueeze(0).shape)
#插入维度在倒数第1维
print(a.unsqueeze(-1).shape)

torch.Size([2, 2])
torch.Size([1, 2, 2])
torch.Size([2, 2, 1])

#squeeze删除维度,只能删除为1的维度
#1*2*2*1的tensor
a = torch.randn(1, 2, 2, 1)
print(a.shape)
#删除第0维
print(a.squeeze(0).shape)
#删除倒数第1维
print(a.squeeze(-1).shape)
#删除所有为1的维度
print(a.squeeze().shape)

torch.Size([1, 2, 2, 1])
torch.Size([2, 2, 1])
torch.Size([1, 2, 2])
torch.Size([2, 2])

#repeat复制维度
#分别复制2次和3次
print(torch.randn(2, 2).repeat(2, 3).shape)

torch.Size([4, 6])

#维度交换
#t转置,只能操作2维tensor
print(torch.randn(1, 2).t().shape)
#transpose维度交换,指定要转换的维度,只能两两交换
print(torch.randn(1, 2, 3).transpose(0, 1).shape)
#permute维度交换,输入维度的顺序
print(torch.rand(1, 2, 3).permute(2, 1, 0).shape)

torch.Size([2, 1])
torch.Size([2, 1, 3])
torch.Size([3, 2, 1])

broadcast broadcasting mechanism

#broadcast
a = torch.randn(2, 3)
b = torch.randn(1, 3)
c = torch.randn(1)
# 形状不匹配时，自动broadcast扩展维度
print((a + b).shape)
print((a + c).shape)
#手动boradcast
print(b.expand_as(a).shape)
print(c.expand_as(a).shape)

torch.Size([2, 3])
torch.Size([2, 3])
torch.Size([2, 3])
torch.Size([2, 3])

Tensor splicing and splitting

a = torch.rand(4, 32, 8)
b = torch.rand(5, 32, 8)
#cat拼接,dim=0是指定要拼接的维度
print(torch.cat([a, b], dim=0).shape)  # 除了拼接的维度，其他维度完全相等
a = torch.rand(4, 32, 8)
b = torch.rand(4, 32, 8)
#stack组合,会创建一个新的维度,用以区分组合后的两个tensor
print(torch.stack([a, b], dim=0).shape)
a = torch.rand(4, 32, 8)
#split拆分,在0维度上拆分,每2个元素1拆
_1, _2 = a.split(2, dim=0)
print(_1.shape)
print(_2.shape)
#split拆分,在0维度上拆分,拆分后长度分别为1,2,1
_1, _2, _3 = a.split([1, 2, 1], dim=0)
print(_1.shape)
print(_2.shape)
print(_3.shape)
a = torch.rand(4, 32, 8)
#chunk拆分,在0维度上拆分,拆成2个
_1, _2 = a.chunk(2, dim=0)
print(_1.shape)
print(_2.shape)

torch.Size([9, 32, 8])
torch.Size([2, 4, 32, 8])
torch.Size([2, 32, 8])
torch.Size([2, 32, 8])
torch.Size([1, 32, 8])
torch.Size([2, 32, 8])
torch.Size([1, 32, 8])
torch.Size([2, 32, 8])
torch.Size([2, 32, 8])

computation

#测试数据
a = torch.FloatTensor([[0, 1, 2], [3, 4, 5]])
b = torch.FloatTensor([0, 1, 2])
print(a, b)
#四则运算
print(a + b)
print(a - b)
print(a * b)
print(a / b)
#矩阵乘法
print(a @ b)
print(a.matmul(b))
#计算过程
0 * 0 + 1 * 1 + 2 * 2, 0 * 3 + 1 * 4 + 2 * 5
#指数,对数运算
#求指数
print(a**2)
#开根号
print(a**0.5)
#求e的n次方
print(a.exp())
#以e为底,求对数
print(a.log())
#以2为底,求对数
print(a.log2())
#裁剪,限制数据的上下限
a.clamp(2, 4)

#逻辑运算:返回一个形状相同的bool类型张量
#大于
print(a > b)
#小于
print(a < b)
#等于
print(a == b)
#不等于
print(a != b)

#四舍五入
c = torch.FloatTensor([3.14])
#向下取整
print(c.floor())
#向上取整
print(c.ceil())
#四舍五入
print(c.round())

attribute statistics

#测试数据
a = torch.FloatTensor([[0., 1., 2.], [3., 4., 5.]])
# 求最小(对每列的多行求最小值) 行dim=0
print(a.min(dim=0))
# 求最大(对每列的多行求最大值) 行dim=0
print(a.max(dim=0))
# 求平均(对每列的多行求平均值) 行dim=0
print(a.mean(dim=0))
# 求积(对每列的多行求乘积) 行dim=0
print(a.prod(dim=0))
# 求和(对每列的多行求和) 行dim=0
print(a.sum(dim=0))
# 求最大值下标(对每列的多行求最大值下标) 行dim=0
print(a.argmax(dim=0))
# 求最小值下标(对每列的多行求最小值下标) 行dim=0
print(a.argmin(dim=0))
# 求1范数
print(a.norm(1))
print(a.norm(1, dim=0))  # 对每列的多行求L1范数
# 求2范数
print(a.norm(2))
print(a.norm(2, dim=0))  # 对每列的多行求L2范数
# 求前2个最小值
print(a.topk(2, dim=1, largest=False))
# 求第2个小的值
print(a.kthvalue(2, dim=1))

torch.return_types.min(
values=tensor([0., 1., 2.]),
indices=tensor([0, 0, 0]))
torch.return_types.max(
values=tensor([3., 4., 5.]),
indices=tensor([1, 1, 1]))
tensor([1.5000, 2.5000, 3.5000])
tensor([ 0., 4., 10.])
tensor([3., 5., 7.])
tensor([1, 1, 1])
tensor([0, 0, 0])
tensor(15.)
tensor([3., 5., 7.])
tensor(7.4162)
tensor([3.0000, 4.1231, 5.3852])
torch.return_types.topk(
values=tensor([[0., 1.],
[3., 4.]]),
indices=tensor([[0, 1],
[0, 1]]))
torch.return_types.kthvalue(
values=tensor([1., 4.]),
indices=tensor([1, 1]))