Numpy array: join, flatten, and add dimensions

up to now , We have learned how to create an array and how to set up an array in the tutorial numpy Arrays apply numerical operations . If we use numpy Programming , We will reach this point sooner or later , We will need functions to manipulate the shape or dimension of the array . We will also learn how to join arrays . Besides , We will demonstrate the possibility of adding dimensions to existing arrays and how to stack multiple arrays . We will conclude this chapter by showing an easy way to construct a new array by repeating an existing array .

1 Flatten and reshape the array

There are two ways to flatten multidimensional arrays ：flatten() and ravel().

1.1 flatten()

flatten Is a parameter with optional keywords “order” Of ndarry Method . order It can be worth “C”、“F” and “A”. The default value for the sequence is “C”. “C” Indicates flattening in row priority C style , The rightmost index “ Change the fastest ”, Or to put it another way ： In row priority , The row index changes the slowest , Column index changes the fastest , therefore a[0,1] With the a[0,0] after .“F” representative Fortran Column prioritization . “A” Express reservation C/Fortran The order .

import numpy as np

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       import numpy as np
       
       

       
       
A = np.array([[[0,  1],
       
       
               [2,  3],
       
       
               [4,  5],
       
       
               [6,  7]],
       
       
              [[8,  9],
       
       
               [10, 11],
       
       
               [12, 13],
       
       
               [14, 15]],
       
       
              [[16, 17],
       
       
               [18, 19],
       
       
               [20, 21],
       
       
               [22, 23]]])
       
       

       
       
Flattened_X = A.flatten()
       
       
print(Flattened_X)
       
       
print(A.flatten(order="C"))
       
       
print(A.flatten(order="F"))
       
       
print(A.flatten(order="A"))
      
      
      
      

       
       
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1.2 ravel()

ravel Returns a flat one-dimensional array . Make copies only when needed . Optional keyword parameters “order” It can be “C”、“F”、“A” or “K”

• 'C'： class C The order of , The last axis index changes the fastest , Back to the first axis, the index changes the slowest . “C” Is the default value ！
• 'F'： similar Fortran Index order of , The first index changes the fastest , The last index changes the slowest .
• 'A'： If the array “a” In memory is Fortran Successive , It's like Fortran Index order of , Otherwise, it's like C The order of .
• 'K'： Read the elements in the order they appear in memory , Except to reverse the data when the stride is negative .

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       print(A.ravel(order="A"))
       
       
print(A.ravel(order="F"))
       
       
print(A.ravel(order="A"))
       
       
print(A.ravel(order="K"))
      
      
      
      

       
       
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1.3 reshape()

      reshape() Method provides a new shape for the array without changing its data , That is, it returns a new array with a new shape .

reshape(a, newshape, order='C')

• ‘a’： An array that needs to be reshaped .
• ‘newshape’： Integer or integer tuple .
• ‘order’：'C', 'F', ‘A’, And flatten And ravel The same parameters as .

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       X = np.array(range(24))
       
       
Y = X.reshape((3, 4, 2))
      
      
      
      

       
       
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2 Linked array

In the following example , We concatenate three one-dimensional arrays into an array . The elements of the second array are appended to the first array . After that, append the elements of the third array ：

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       x = np.array([11, 22])
       
       
y = np.array([18, 7, 6])
       
       
z = np.array([1, 3, 5])
       
       
c = np.concatenate((x, y, z))
       
       
print(c)
      
      
      
      

       
       
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If we join multidimensional arrays , We can connect arrays by axis . An array must have the same shape to match concatenate() Connect . In the case of multidimensional arrays , We can arrange them by axis . The default value is axis = 0：

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       x = np.array(range(24))
       
       
x = x.reshape((3, 4, 2))
       
       
y = np.array(range(100, 124))
       
       
y = y.reshape((3, 4, 2))
       
       
z = np.concatenate((x, y))
       
       
print(z)
      
      
      
      

       
       
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We use now axis=1 Make the same connection ：

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       z = np.concatenate((x, y), axis=1)
      
      
      
      

       
       
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3 Add new dimension

You can use slicing and np.newaxis Add a new dimension to the array . We use an example to illustrate this technique ：

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       x = np.array([2, 5, 18, 14, 4])
       
       
y = x[:, np.newaxis]
       
       
print(y)
      
      
      
      

       
       
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4 Vector stacking

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       A = np.array([3, 4, 5])
       
       
B = np.array([1, 9, 0])
       
       
print(np.row_stack((A, B)))
       
       
print(np.column_stack((A, B)))
      
      
      
      

       
       
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       A = np.array([[3, 4, 5],
       
       
              [1, 9, 0],
       
       
              [4, 6, 8]])
       
       
print(np.column_stack((A, A, A)))
       
       
print(np.column_stack(A))
      
      
      
      

       
       
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       print(A[0])
       
       
print(np.column_stack((A[0], A[0], A[0])))
      
      
      
      

       
       
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       print(np.dstack((A, A, A)))
      
      
      
      

       
       
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5 Repetition mode ,“ tile ” Method

Sometimes , You want or must create a new matrix by repeating the existing matrix many times , To create new matrices with different shapes and even sizes . for example , You might have a one-dimensional array array([ 3.4]) And you want to convert it to an array array([ 3.4, 3.4, 3.4, 3.4, 3.4]). In another use case , You might have a two-dimensional array , for example np.array([ [1, 2], [3, 4]]), You intend to use it as a building block to construct shapes as (6, 8):

array([[1, 2, 1, 2, 1, 2, 1, 2],

       [3, 4, 3, 4, 3, 4, 3, 4],

       [1, 2, 1, 2, 1, 2, 1, 2],

       [3, 4, 3, 4, 3, 4, 3, 4],

       [1, 2, 1, 2, 1, 2, 1, 2],

       [3, 4, 3, 4, 3, 4, 3, 4]])

The construction idea is shown in the figure below ：

If this reminds you of tiling the bathroom or kitchen , Then you are on the right track ：Numpy The functionality provided for this task is called “ ceramic tile ”.tile The formal syntax for is as follows ：

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       np.tile(A, reps)
      
      
      
      

       
       
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By way of A The number of repetitions is determined by reps Given the number of times to construct an array .

“reps” It's usually a tuple （ Or list ）, It defines along the corresponding axis / The number of repetitions of the direction . for example , If we were to reps Set to (3, 4), be A Will target “ That's ok ” repeat 3 Time , Repeat in the direction of the column 4 Time . We demonstrate this in the following example ：

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       import numpy as np
       
       
x = np.array([[1, 2], [3, 4]])
       
       
print(np.tile(x, (3, 4)))
      
      
      
      

       
       
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       x = np.array([3.4])
       
       
y = np.tile(x, (5,))
       
       
print(y)
      
      
      
      

       
       
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In front of tile Example , We can also write y = np.tile(x, 5).

If “reps” The length of is n, Then the dimension of the result array will be n and A.ndim The maximum of .

If 'A.ndim < n, By adding a new axis 'A' Upgrade to n dimension . So shape (5,) The array is promoted to (1, 5) be used for 2-D Copy , Or shape (1, 1, 5) be used for 3-D Copy . If this is not the behavior required , Please manually set... Before calling this function “A” Upgrade to n dimension .

If 'A.ndim > d','reps' Promoted to 'A'.ndim, The method is to add 1. So for the shape (2, 3, 4, 5) Array of 'A','reps' ' Of (2, 2) Be regarded as (1, 1, 2, 2). Further examples ：

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       x = np.array([[1, 2], [3, 4]])
       
       
print(np.tile(x, 2))
      
      
      
      

       
       
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       x = np.array([[1, 2], [3, 4]])
       
       
print(np.tile(x, (2, 1)))
      
      
      
      

       
       
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       x = np.array([[1, 2], [3, 4]])
       
       
print(np.tile(x, (2, 2)))
      
      
      
      

       
       
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