Python matrix operations: dimension transformation, matrix combination, matrix division

1. Matrix dimension transformation

1.1 numpy.reshape(a, newshape, order=’C’)

The reshape() function is often used to change the dimension of a one-dimensional array, that is, to change a one-dimensional array into a matrix of the specified dimension. Order refers to different indexing rules, generally defaulting to C, and operating according to the row.
Example:

print np.reshape(np.arange(10), (2, 5))

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

1.2 numpy.ravel(a, order=’C’)

The ravel function is a dimensionality reduction operation for matrix data, for example, reducing two-dimensional data to one-dimensional
Example :

data = np.reshape(np.arange(10), (2, 5))
print data.reshape(-1)
print data.ravel()

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

1.3 flatten([order])

This member function is also used for dimensionality reduction, and works similarly to the ravel function
Example :

data = np.reshape(np.arange(10), (2, 5))
print data.flatten()

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

The difference from the ravel function: ravel is a view of the original data, and the original data will be modified after it is modified; while the flatten function returns a copy of the original data, and modifying it will not affect the original data.
Example:

# ravel函数
data = np.reshape(np.arange(10), (2, 5))
data1 = data.ravel()
data1[0] = 100
print data

[[100   1   2   3   4]
 [  5   6   7   8   9]]

# flatten函数
data = np.reshape(np.arange(10), (2, 5))
data1 = data.flatten()
data1[0] = 100
print data

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

2. Matrix combination

Two test matrices are used here:

a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6], [7, 8]])

2.1 Horizontal Combination

Example:

print np.hstack((a, b))
print np.concatenate((a, b), axis=1)

[[1 2 5 6]
 [3 4 7 8]]

2.2 Vertical combination

Example:

print np.vstack((a, b))
print np.concatenate((a, b), axis=0)

[[1 2]
 [3 4]
 [5 6]
 [7 8]]

2.3 Deep Combination

Example:

print np.dstack((a, b))

[[[1 5]
  [2 6]]

 [[3 7]
  [4 8]]]

3. Matrix partition

Here is the test with the following data:

a = np.array([[1, 2, 3],
             [4, 5, 6],
             [7, 8, 9]])

3.1 Horizontal split

After understanding the level combination in Section 2.1, its inverse process is easy to understand.
Example: Divide the example matrix into three equal parts

print np.hsplit(a, 3)

[array([[1],
       [4],
       [7]]), array([[2],
       [5],
       [8]]), array([[3],
       [6],
       [9]])]

3.2 Vertical division

The process is similar to the process above
Example :

print np.vsplit(a, 3)

[array([[1, 2, 3]]), array([[4, 5, 6]]), array([[7, 8, 9]])]

3.3 Depth segmentation

Example: Note that depth segmentation is only valid for matrices with more than three dimensions

print np.dsplit(np.arange(27).reshape((3, 3, 3)), 3)

[array([[[ 0],
        [ 3],
        [ 6]],

       [[ 9],
        [12],
        [15]],

       [[18],
        [21],
        [24]]]), array([[[ 1],
        [ 4],
        [ 7]],

       [[10],
        [13],
        [16]],

       [[19],
        [22],
        [25]]]), array([[[ 2],
        [ 5],
        [ 8]],

       [[11],
        [14],
        [17]],

       [[20],
        [23],
        [26]]])]

4. Properties of Matrix

The data used for testing here is still the data in Section 3

4.1 Matrix dimensions

print np.shape(a)

(3, 3)

4.2 Matrix data type

print a.dtype

int64

4.3 Number of Matrix Elements

print a.size

9

4.4 Number of bytes occupied by matrix elements

print a.itemsize

8

4.5 The total number of bytes occupied by the matrix

print a.nbytes

72

5. Reference

Python array splicing, combination, connection