[pyTorch Study Notes ②] Numpy Basics Part 2

Five, Numpy arithmetic operations

1. Elements are multiplied correspondingly

A = np.array([[1, 2], [-1, 4]])
B = np.array([[2, 0], [3, 4]])
print(A)
>>>[[ 1  2] 
 	[-1  4]]
print(B)
>>>[[2 0]   
 	[3 4]] 
print(A*B)
>>>[[ 2  0] 
 	[-3 16]]
print(np.multiply(A,B))
>>>[[ 2  0] 
 	[-3 16]]

2. Array and scalar operations

A = np.array([[1, 2], [-1, 4]])
print(A)
>>>[[ 1  2] 
 	[-1  4]]
print(A/2.0)
>>>[[ 0.5  1. ] 
 	[-0.5  2. ]]
print(A*2.0)
>>>[[ 2.  4.]
 	[-2.  8.]]

3. Dot product (inner product of elements)

X1 = np.array([[1,2],[3,4]])
X2 = np.array([[1,2,3],[4,5,6]])
X3 = np.dot(X1,X2)
print(X3)
>>>[[ 9 12 15]
 	[19 26 33]]

Six, array deformation

In matrix or array operations, it is often encountered that multiple vectors or matrices need to be merged and expanded along a certain axis. For example, in a convolutional or recurrent neural network, the matrix needs to be flattened before the fully connected layer.

(1) Change shape

1.reshape

change the dimensions of a vector without modifying the vector itself

# reshape
arr = np.arange(10)
print(arr)
>>>[0 1 2 3 4 5 6 7 8 9]
# 将arr变换为2*5
print(arr.reshape(2,5))
>>>[[0 1 2 3 4]
 	[5 6 7 8 9]]
# 指定列数或行数，其他用-1代替
print(arr.reshape(5,-1))
>>>[[0 1]
 	[2 3]
 	[4 5]
 	[6 7]
 	[8 9]]
print(arr.reshape(-1,5))
>>>[[0 1 2 3 4]
 	[5 6 7 8 9]]

2.resize

change the dimensions of a vector, and modify the vector itself

# resize
arr = np.arange(10)
print(arr)
>>>[0 1 2 3 4 5 6 7 8 9]
# 将向量arr维度变换为2行5列
arr.resize(2,5)
print(arr)
>>>[[0 1 2 3 4]
 	[5 6 7 8 9]]

3. T (transpose)

# T(转置)
arr = np.arange(12).reshape(3,4)
print(arr)
>>>[[ 0  1  2  3]
 	[ 4  5  6  7]
 	[ 8  9 10 11]]
print(arr.T)
>>>[[ 0  4  8]
 	[ 1  5  9]
 	[ 2  6 10]
 	[ 3  7 11]]

4.ravel (flatten)

# ravel(展平)
arr = np.arange(6).reshape(2,-1)
print(arr)
>>>[[0 1 2]
 	[3 4 5]]
# 按列优先展平
print(arr.ravel('F'))
>>>[0 3 1 4 2 5]
# 按行优先展平
print(arr.ravel())
>>>[0 1 2 3 4 5]

5.flatten

convert matrix to vector

# flatten
a = np.floor(10*np.random.random((3,4)))
print(a)
>>>[[0. 0. 6. 8.]
 	[3. 1. 8. 8.]
 	[6. 4. 1. 8.]]
print(a.flatten())
>>>[0. 0. 6. 8. 3. 1. 8. 8. 6. 4. 1. 8.]

6.squeeze

The function used to reduce the dimension, remove the dimension containing 1 in the matrix.

arr = np.arange(3).reshape(3,1)
print(arr)
>>>[[0]
 	[1]
 	[2]]
print(arr.squeeze().shape)
>>>(3,)
arr1 = np.arange(6).reshape(3,1,2,1)
print(arr1.shape)
>>>(3, 1, 2, 1)
print(arr1.squeeze().shape)
>>>(3, 2)

7.transpose

Axis-swap the high-risk matrix. For example, change RGB to GBR

arr = np.arange(24).reshape(2,3,4)
print(arr.shape)
>>>(2, 3, 4)
print(arr.transpose(1,2,0).shape)
>>>(3, 4, 2)

(2) Merge arrays

1.append

There is an axis parameter to control merging by row/column, which takes up a lot of memory.

# 合并一维数组
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
c = np.append(a,b)
print(c)
>>>[1 2 3 4 5 6]
# 合并多维数组
a = np.arange(4).reshape(2,2)
b = np.arange(4).reshape(2,2)
print(np.append(a,b,axis = 0))
>>>[[0 1]
 	[2 3]
 	[0 1]
 	[2 3]]
print(np.append(a,b,axis = 1))
>>>[[0 1 0 1]
 	[2 3 2 3]]

2.concatenate

a = np.arange(4).reshape(2,2)
b = np.arange(4).reshape(2,2)
print(np.concatenate((a,b),axis = 0))
>>>[[0 1]
 	[2 3]
 	[0 1]
 	[2 3]]
print(np.concatenate((a,b),axis = 1))
>>>[[0 1 0 1]
 	[2 3 2 3]]

3.stack

Stack arrays/matrices along the specified axis
requiring the same shape

a = np.arange(4).reshape(2,2)
b = np.arange(4,8).reshape(2,2)
print(np.stack((a,b),axis = 0))
>>>[[[0 1]
  	 [2 3]]

 	[[4 5]
  	 [6 7]]]
print(np.stack((a,b),axis = 1))
>>>[[[0 1]
  	 [4 5]]

 	[[2 3]
  	 [6 7]]]

4.hstack 、vstack 和 dstack

a = np.arange(4).reshape(2,2)
b = np.arange(4,8).reshape(2,2)
print(np.hstack((a,b)))
>>>[[0 1 4 5]
 	[2 3 6 7]]
print(np.vstack((a,b)))
>>>[[0 1]
 	[2 3]
 	[4 5]
 	[6 7]]
print(np.dstack((a,b)))
>>>[[[0 4]
  	 [1 5]]

 	[[2 6]
  	 [3 7]]]

5. vsplit and hsplit

Split by row and by column

a = np.arange(12).reshape(3,4)
print(a)
>>>[[ 0  1  2  3]
 	[ 4  5  6  7]
 	[ 8  9 10 11]]
print(np.vsplit(a,[1,2]))
>>>[array([[0, 1, 2, 3]]), array([[4, 5, 6, 7]]), array([[ 8,  9, 10, 11]])]
print(np.hsplit(a,[1,2]))
>>>[array([[0],
       		[4],
       		[8]]), 
     array([[1],
       		[5],
       		[9]]), 
     array([[ 2,  3],
       		[ 6,  7],
       		[10, 11]])]

7. Batch processing

General steps:
1. Shuffle data randomly
2. Define batch size
3. Batch data

# 生成10000个形状为2*3的矩阵(一个10000*2*3形状的矩阵，第1维为样本数，后2维是数据)
data_train = np.random.randn(10000,2,3)

# 打乱数据
np.random.shuffle(data_train)

# 定义批大小
batch_size = 1000

# 进行批处理数据
for i in range(0,len(data_train)//batch_size):
    x_batch_sum = np.sum(data_train[i:i+batch_size])
    print("第{}批次，该批次数据和为：{}".format(i+1,x_batch_sum))
>>>第1批次，该批次数据和为：19.831597230692044
	第2批次，该批次数据和为：25.740728092864465
	第3批次，该批次数据和为：27.055236935523748
	第4批次，该批次数据和为：33.117813938724495
	第5批次，该批次数据和为：25.877849245176712
	第6批次，该批次数据和为：28.51526070095471
	第7批次，该批次数据和为：23.45418417276757
	第8批次，该批次数据和为：29.85505288703944
	第9批次，该批次数据和为：32.270674668876
	第10批次，该批次数据和为：34.17904037831163

8. Universal function (ufunc)

Many ufunc functions are written in C language, which is relatively fast.
More flexible than math. Math is generally a scalar, and Numpy can be a vector and a matrix, reducing the use of loop statements.

function name	Function
sqrt	Calculate the square root of serialized data
sin、cos	Trigonometric functions
abs	Calculate the absolute value of serialized data
dot	Matrix calculations (dot product, vector inner product)
log，log10，log2	Logarithmic function
exp	exponential function
cumsum，cumproduct	cumulative sum, product
sum	sum serialized data
mean	Calculate mean
median	Calculate the median
std	Calculate standard deviation
was	Calculate the variance
corrcoef	Calculate the correlation coefficient

a = np.arange(10).reshape(2,5)
b = np.arange(-5,5).reshape(5,2)
print(a)
>>>[[0 1 2 3 4] 
 	[5 6 7 8 9]]
print(b)
>>>[[-5 -4]
 	[-3 -2]
 	[-1  0]
 	[ 1  2]
 	[ 3  4]]
print(np.sqrt(a))
>>>[[0.         1.         1.41421356 1.73205081 2.        ]      
 	[2.23606798 2.44948974 2.64575131 2.82842712 3.        ]]
print(np.sin(a))
>>>[[0.         1.         1.41421356 1.73205081 2.        ]      
 	[2.23606798 2.44948974 2.64575131 2.82842712 3.        ]]
print(np.cos(a))
>>>[[ 1.          0.54030231 -0.41614684 -0.9899925  -0.65364362] 
 	[ 0.28366219  0.96017029  0.75390225 -0.14550003 -0.91113026]]
print(np.abs(b))
>>>[[5 4]
 	[3 2]
 	[1 0]
 	[1 2]
 	[3 4]]
print(np.dot(a,b))
>>>[[ 10  20]
 	[-15  20]]
print(np.log2(a))
>>>[[      -inf 0.         1.         1.5849625  2.        ]
 	[2.32192809 2.5849625  2.80735492 3.         3.169925  ]]
print(np.exp(a))
>>>[[1.00000000e+00 2.71828183e+00 7.38905610e+00 2.00855369e+01
  5.45981500e+01]
 [1.48413159e+02 4.03428793e+02 1.09663316e+03 2.98095799e+03
  8.10308393e+03]]
print(np.cumsum(a))
>>>[ 0  1  3  6 10 15 21 28 36 45]
print(np.cumproduct(a))
>>>[0 0 0 0 0 0 0 0 0 0]
print(np.sum(a))
>>>45
print(np.mean(a))
>>>4.5
print(np.median(a))
>>>4.5
print(np.std(a))
>>>2.8722813232690143
print(np.var(a))
>>>8.25
print(np.corrcoef(a))
>>>[[1. 1.]
 	[1. 1.]]

9. Broadcast mechanism

Numpy's Universal functions require that the shape of the input array be consistent. When inconsistent, the broadcast mechanism is used.
There are the following rules:
(1) Align with the longest array of shape, and add 1 if it is insufficient;
(2) Take the maximum value of each axis
(3) When the length of a certain axis of the input array and the corresponding axis of the output array are the same or 1 , used for calculation, otherwise, an error occurs.
(4) When the length of a certain axis of the input array is 1, the operations along this axis all use the first set of values.

a = np.arange(0, 40, 10).reshape(4, 1)
b = np.arange(0, 3)
c = a+b
print(a)
>>>[[ 0]
 	[10]
 	[20]
 	[30]]
print(b)
>>>[0 1 2]
print(c)
>>>[[ 0  1  2]
 	[10 11 12]
 	[20 21 22]
 	[30 31 32]]

According to rule 2, the output should be 4*3
According to rule 4, a should be: [[ 0 1 2] , b should be: [[ 0 0 0]
[ 0 1 2] , [10 10 10]
[ 0 1 2 ] , [20 20 20]
[ 0 1 2]] , [30 30 30]]

related suggestion

[pyTorch Study Notes ①] Numpy Basics Part 1
[pyTorch Study Notes ②] Numpy Basics Part 2