Numpy ndarray learning ＜ I ＞ Foundation

0. ndarray structure ：

numpy One of its characteristics is N Dimension group --ndarray.  

ndarray Is a collection of data of the same type , Each of these elements has the same storage size area in memory .

ndarray Inside , It consists of the following parts ：

A. A pointer to data .

B. Element data type or dtype. Used to determine the size of each element in memory .

C. A said ndarray shape (shape) tuples . Used to determine the size of each dimension .

D. One span (stride) Tuples . Used to determine the step size to span to the next element .

1. ndarray establish ：

To create a ndarray. Just call np.array():

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

name	describe
object	An array or nested sequence of numbers
dtype	Data type of array element , Optional
copy	Whether the object needs to be copied , Optional
order	Create an array style ,C In the direction of the line ,F For column direction ,A In any direction （ Default ）
subok	By default, it returns an array consistent with the base class type
ndmin	Specifies the minimum dimension of the generated array

import numpy as np

arr1 = np.array([3,4,5])
print("arr1:",arr1)
print("type:",type(arr1))
print("shape:",arr1.shape)

arr2 = np.array([[1, 2, 3],[4, 5, 6],[7, 8, 9],[10, 11, 12]])
print("arr2:",arr2)
print("type:",type(arr2))
print("shape:",arr2.shape)

arr3 = np.array([1, 2, 3], ndmin= 3)
print("arr3:",arr3)
print("type:",type(arr3))
print("shape:",arr3.shape)

arr1: [3 4 5]
type: <class 'numpy.ndarray'>
shape: (3,)

arr2: [[ 1  2  3]
 [ 4  5  6]
 [ 7  8  9]
 [10 11 12]]
type: <class 'numpy.ndarray'>
shape: (4, 3)

arr3: [[[1 2 3]]]
type: <class 'numpy.ndarray'>
shape: (1, 1, 3)

2. ndarry The index of ：

The index is obtained through an unsigned integer ndarray Value .

Yes, one-dimensional ndarray, A single index value represents an element scalar .

For two-dimensional ndarray, A single index value represents the corresponding one-dimensional ndarray.

Yes N dimension ndarray, A single index value represents the corresponding （N-1） dimension ndarray.

arr1 = np.array([3,4,5])\
print(arr1[1],"\n")

4 

arr2 = np.array([[1, 2, 3],[4, 5, 6],[7, 8, 9],[10, 11, 12]])
print(arr2[1], "\n")

[4 5 6] 

print(arr2[1][2])

6

Because since arr2[1] It's a one-dimensional ndarray. that arr2[1][2] It's this one-dimensional array [4,5,6] Of the index=2 individual . That is to say 6.

The more common method is ：

print(arr2[1,2])

6

3.  ndarry The section of ：

4. ndarray Of min(), max(), sum() etc. ：

ndarray.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)

ndarray.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)

ndarray.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)

They are equivalent to ：

numpy.amin(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)

numpy.amax(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)

numpy.sum(a, axis=None, dtype=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)

They are :

Return minimum -- Along the given axis

Return maximum -- Along the given axis.

Returns the sum of elements -- Along the given axis.

arr4 = np.array([[1, 2, 3], [4, 5, 6]])
print("min()", arr4.min())
print("min(0)", arr4.min(0))
print("min(1)", arr4.min(1))

axis: 

If you don't choose . Is to find the minimum value in the whole field , Maximum , And the value .

If elected 0. Then it means to find the minimum value on this axis , Maximum , And the value .

If it is shape=(m, n). The result is shape(1,n) Of ndarray.

arr4 = np.array([[1, 2, 3], [4, 5, 6]])
print("min()", arr4.min())
print("min(0)", arr4.min(0))
print("min(1)", arr4.min(1))

min() 1
min(0) [1 2 3]
min(1) [1 4]

print("max() :", arr4.max())
print("max(0):", arr4.max(0))
print("max(1):", arr4.max(1))

max() : 6
max(0): [4 5 6]
max(1): [3 6]

5. ndarray Addition, subtraction, multiplication and division ：

  Arithmetic functions contain simple addition, subtraction, multiplication and division : add(),subtract(),multiply()  and  divide()

  It can also be used directly “+” , “-” , “*” , "/" To calculate .

such , be ndarray Add, subtract, multiply and divide the corresponding elements of .

arr5 = np.array([[0, 1, 2], [3, 4, 5]])
arr6 = np.array([[2, 2, 2], [2, 2, 2]])

print("Add:")
print(arr5 + arr6)
print(np.add(arr5, arr6))

print("Sub:")
print(arr5 - arr6)
print(np.subtract(arr5, arr6))

print("Mul:")
print(arr5 * arr6)
print(np.multiply(arr5, arr6))

print("Div：")
print(arr5 / arr6)
print(np.divide(arr5, arr6))

Add:
[[2 3 4]
 [5 6 7]]
[[2 3 4]
 [5 6 7]]
Sub:
[[-2 -1  0]
 [ 1  2  3]]
[[-2 -1  0]
 [ 1  2  3]]
Mul:
[[ 0  2  4]
 [ 6  8 10]]
[[ 0  2  4]
 [ 6  8 10]]
Div：
[[0.  0.5 1. ]
 [1.5 2.  2.5]]
[[0.  0.5 1. ]
 [1.5 2.  2.5]]

5.1： After the broadcast ndarray Calculation .

5.2：ndarray And integer calculation ：

First broadcast integers , Convert it into and ndarray Of shape identical . Calculate again .

6. Matrix multiplication ：

stay numpy in , have access to numpy.ndarray Two dimensional pattern representation matrix . You can also use matrix According to matrix . But recommended ndarray.

Matrix multiplication ：

If ndarray by 2 Dimensional , be numpy.dot() and np.matmul() The result of the function is the same . Are matrix multiplication .

from Python 3.5 and Numpy 1.10 in the future , You can use infix operators  @  Calculation ndarray Matrix multiplication between , It's easier to write .

The following is a detailed introduction to np.dot()

numpy.dot(a, b, out=None)

If a and b They're all one-dimensional arrays , Then it is the inner product of the vector . （ Corresponding bit multiplication , Then I add ）

If a and b It's all two-dimensional arrays , Matrix multiplication , But preferred matmul or .a @ b

If a or b yes 0-D（ Scalar ）, Equivalent to multiply . And we recommend numpy.multiply(a, b) or a * b.（ see 5.2）

Examples of matrix multiplication rules ：

a = np.array([[1,2],[3,4]]) b = np.array([[11,12],[13,14]]) print(np.dot(a,b))

The output is ：

[[37  40] 
 [85  92]]

The formula is ：

[[1*11+2*13, 1*12+2*14],[3*11+4*13, 3*12+4*14]]