1. Dimensions of the data
- Dimension: The organizational form of a set of data.
(Data dimension is a very important basic concept to form a specific relationship between data and express the meaning of various data.)
- One-dimensional data: It is composed of ordered or unordered data in a peer-to-peer relationship, and is organized in a linear manner . Corresponds to concepts such as lists, arrays, and sets.
Lists and arrays are ordered structures of a set of data, and they are distinguished :
List: data types can be different
Arrays: same data type
- Two-dimensional data: It is composed of multiple one-dimensional data and is a combination of one-dimensional data.
A table is a typical two-dimensional data, where the header is a part of the two-dimensional data
- Multidimensional data: formed by extending one-dimensional or two-dimensional data in new dimensions.
- High-dimensional data: use only the most basic binary relationship to show the complex structure between data.
- Python representation of data dimensions
One-dimensional data: list (ordered) and set (unordered) types
Two-dimensional data: list type
Multidimensional Data: List Type
High-dimensional data: dictionary type or data representation format
2. NumPy array object: ndarray
NumPy is an open source Python scientific computing base library.
- A powerful n-dimensional array object ndarray
- broadcast function
- Tools for integrating C/C++/Fortran code
- Linear algebra, Fourier transform, random number generation and other functions
NumPy is the basis for data processing or scientific computing libraries such as SciPy and Pandas.
NumPy application: import numpy as np Although aliases can be omitted or changed, it is recommended to use aliases with the above conventions.
In the Python language, there is already a list type, why do we need an array type?
- Array objects can remove the loops required for operations between elements, making a one-dimensional vector more like a single piece of data.
- Setting a special array object, after optimization, can improve the operation speed of this type of application.
Observation : In scientific computing, the types of all data in a dimension are often the same.
- Array objects use the same data type, which helps to save operation and storage space.
ndarray is a multidimensional array object consisting of two parts:
- actual data
- Metadata describing these data (data dimensions, data types, etc.)
The ndarray array generally requires that all elements are of the same type (homogeneous), and the array subscript starts from 0.
| Attributes | illustrate |
|---|---|
| .it's me |
rank, i.e. number of axes or number of dimensions |
| .shape | The scale of the ndarray object, for a matrix, n rows and m columns |
| .size | The number of ndarray object elements, which is equivalent to the value of n*m in .shape |
| .dtype | The element type of the ndarray object |
| .itemsize | The size of each element in the ndarray object, in bytes |
Why does ndarray support so many element types?
Contrast : Python syntax only supports 3 types of integers, floating point numbers and complex numbers
- Scientific computing involves a lot of data and has high requirements for storage and performance
- Fine definition of element types helps NumPy use storage space reasonably and optimize performance.
- The fine definition of element types helps programmers to have a reasonable assessment of the program size.
3. Creation and transformation of ndarray array
How to create an ndarray array:
- Create ndarray arrays from lists, tuples, etc. in Python.
- Use functions in NumPy to create ndarray arrays, such as: arange, ones, zeros, etc.
- Create ndarray array from byte stream (raw bytes).
- Read a specific format from a file, creating an ndarray array.
1) Create ndarray arrays from lists, tuples, etc. in Python
x = np.array(list/tuple)
x = np.array(list/tuple, dtype=np.float32)
When np.array() does not specify a dtype, NumPy will associate a dtype according to the data.
corresponding to:
2) Use functions in NumPy to create ndarray arrays, such as arange, ones, zeros, etc.
| function | illustrate |
| np.arange(n) | Similar to the range() function, returns ndarray type, with elements from 0 to n-1 |
| np.ones(shape) | Generate an array of all 1s according to shape, shape is a tuple type |
| np.zeros(shape) | Generate an array of all 0s according to shape, shape is a tuple type |
| np.full(shape,val) | Generate an array according to shape, each element value is val |
| np.eye(n) |
Create a square n*n identity matrix with 1s on the diagonal and 0s on the rest |
| np.ones_like(a) | Generate an array of all 1s according to the shape of the array a |
| np.zeros_like(a) | Generate an array of all 0s according to the shape of the array a |
| np.full_like(a,val) | Generate an array according to the shape of the array a, each element value is val |
| np.linspace() | Fill data at equal intervals according to the start and end data to form an array |
| np.concatenate() | Merges two or more arrays into a new array |
Transformation of ndarray arrays:
For the created ndarray array, dimension transformation and element type transformation can be performed on it.
- dimension transformation
| method | illustrate |
|---|---|
| .reshape(shape) | Returns an array of shape without changing the array elements, and the original array remains unchanged |
| .resize(shape) | Same function as .reshape(), but modify the original array |
| .swapaxes(ax1,ax2) | Swap two dimensions in the n dimensions of the array |
| .flatten() | Reduce the dimension of the array, return the folded one-dimensional array, and keep the original array unchanged |
- type conversion
new_a = a.astype(new_type)
The astype() method always creates a new array (a copy of the original array), even if the two types are the same.
Conversion of ndarray array to list: ls = a.tolist()
4. Operation of ndarray array
Array indexing and slicing
Indexing: the process of getting an element at a specific position in an array
Slicing: the process of obtaining a subset of array elements
Indexing and slicing of one-dimensional arrays : similar to Python's lists
start number: end number (not included); step size
Indexing of multidimensional arrays :
Slicing of multidimensional arrays :
5. Operation of ndarray array
Operations between arrays and scalars
Operations between arrays and scalars act on each element of the array
| function | illustrate |
|---|---|
| np.abs(x) np.fabs(x) | Calculate the absolute value of each element of an array |
| np.sqrt(x) | Calculates the square root of each element of an array |
| np.square(x) | Calculates the square of each element of an array |
| np.log(x) np.log10(x) np.log2(x) | Calculate the natural logarithm, base 10 logarithm, and base 2 logarithm of each element of an array |
| np.ceil(x) np.floor(x) | Calculate the ceiling value or floor value of each element of the array |
| np.rint(x) | Calculates the rounded value of each element of an array |
| np.modf(x) | Returns the fractional and integer parts of each element of an array as two separate arrays |
| np.cos(x) np.cosh(x) np.sin(x) np.sinh(x) np.tan(x) np.tanh(x) |
Computes ordinary and hyperbolic trigonometric functions for the elements of an array |
| np.exp(x) | Calculate the index value of each element of the array |
| np.sign(x) | Calculate the sign value of each element of the array, 1(+), 0, -1(-) |
| function | illustrate |
|---|---|
| + - * / ** | The corresponding operation is performed on the elements of the two arrays |
| np.maximum() np.fmax() np.minmum() np.fmin() |
Element-wise max/min calculations |
| np.mod(x,y) | element-wise modulo |
| np.copysign(x,y) | Assign the symbol of each element in the array y to the corresponding element of the array x |
| > < >= <= == != | Arithmetic comparison, yielding an array of booleans |
The content of the article comes from: Chinese University MOOC - Teacher Songtian