PyPyNum 1.9.2

A multifunctional mathematical calculation package written in pure Python programming language [Python>=3.4]

PyPyNum

A multifunctional mathematical calculation package written in pure Python programming language [Python>=3.4]

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\ \  \|\  \\ \  \/  / /\ \  \|\  \\ \  \/  / /\ \  \\ \  \\ \  \\\  \\ \  \\\__\ \  \
 \ \   ____\\ \    / /  \ \   ____\\ \    / /  \ \  \\ \  \\ \  \\\  \\ \  \\|__| \  \
  \ \  \___| \/  /  /    \ \  \___| \/  /  /    \ \  \\ \  \\ \  \\\  \\ \  \    \ \  \
   \ \__\  __/  / /       \ \__\  __/  / /       \ \__\\ \__\\ \_______\\ \__\    \ \__\
    \|__| |\___/ /         \|__| |\___/ /         \|__| \|__| \|_______| \|__|     \|__|
          \|___|/                \|___|/

Version -> 1.9.2 | PyPI -> https://pypi.org/project/PyPyNum/ | Gitee -> https://www.gitee.com/PythonSJL/PyPyNum | GitHub -> https://github.com/PythonSJL/PyPyNum

PyPI上无法显示logo，可以在Gitee或者GitHub中查看。

The logo cannot be displayed on PyPI, it can be viewed in Gitee or GitHub.

介绍

Introduction

• 多功能数学库，类似于numpy、scipy等，专为PyPy解释器制作，亦支持其他类型的Python解释器
• Multi functional math library, similar to numpy, scipy, etc., designed specifically for PyPy interpreters and also supports other types of Python interpreters
• 不定期更新版本，增加更多实用功能
• Update versions periodically to add more practical features
• 如需联系，请添加QQ号2261748025 （Py𝙿𝚢𝚝𝚑𝚘𝚗-水晶兰）
• If you need to contact, please add QQ number 2261748025 (Py𝙿𝚢𝚝𝚑𝚘𝚗-水晶兰)

子模块的名称与功能简介

Name and Function Introduction of Submodules

子模块名称 Submodule Name	功能简介 Function Introduction
pypynum.Array	多维数组 Multidimensional array
pypynum.chars	特殊数学符号 Special mathematical symbols
pypynum.cipher	加密解密算法 Encryption and decryption algorithm
pypynum.constants	数学常数集合 Set of mathematical constants
pypynum.equations	方程求解 Solving equations
pypynum.errors	异常对象 Exception object
pypynum.file	文件读写 File read and write
pypynum.FourierT	傅里叶变换 Fourier transform
pypynum.Geometry	几何形状 Geometric shape
pypynum.Graph	图论算法 Graph Theory Algorithm
pypynum.Group	群论算法 Group Theory Algorithm
pypynum.Logic	逻辑电路设计 Logic circuit design
pypynum.maths	通用数学函数 General mathematical functions
pypynum.Matrix	矩阵运算 Matrix operation
pypynum.NeuralN	神经网络训练 Neural network training
pypynum.numbers	数字处理 Number processing
pypynum.plotting	数据可视化 Data visualization
pypynum.polynomial	多项式运算 Polynomial operation
pypynum.probability	概率统计 Probability statistics
pypynum.Quaternion	四元数运算 Quaternion operation
pypynum.random	随机数生成 Random number generation
pypynum.regression	回归分析 Regression analysis
pypynum.sequence	数列计算 Sequence calculation
pypynum.Symbolics	符号计算 Symbol calculation
pypynum.Tensor	张量运算 Tensor operation
pypynum.test	简易测试 Easy test
pypynum.this	项目之禅 Zen of Projects
pypynum.tools	辅助函数 Auxiliary functions
pypynum.Tree	树形数据结构 Tree data structure
pypynum.types	特殊类型 Special types
pypynum.ufuncs	通用函数 Universal functions
pypynum.utils	实用工具 Utility
pypynum.Vector	向量运算 Vector operation

PyPyNum的Zen（预览）

The Zen of PyPyNum (Preview)

    The Zen of PyPyNum, by Shen Jiayi

This is a math package written purely in Python.

Elegant is superior to clunky.
Clarity trumps obscurity.
Straightforwardness is preferred over convolution.
Sophisticated is better than overcomplicated.
Flat structure beats nested hierarchies.
Sparse code wins over bloated ones.

...

Do you want to view all the content?

Enter "from pypynum import this" in your

Python interpreter and run it!

                                        February 27, 2024

与上一个版本相比新增功能

New features compared to the previous version

!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=

新增代码行数大约三百行

Approximately 300 new lines of
code added

!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=

修改过的函数

Modified functions

├── Array
fill(shape: Any, sequence: Any, repeat: Any, pad: Any, rtype: Any) -> Any
zeros(shape: Any, rtype: Any) -> Any
zeros_like(a: Any, rtype: Any) -> Any

!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=

新增加的函数

Newly added functions

class Polynomial(builtins.object)
    <以下为新增加的方法>
    <The following are the newly added methods>
    __divmod__ = __truediv__(self, other)
    __float__(self)
    __int__(self)
    __round__(self, n=None)
    coeffs(self, reverse=False)
    degs(self, reverse=False)
    deriv(self)
    evaluate(self, x)
    gcd(self, other)
    integ(self, constant=0)
    is_zero(self)
    latex(self)
    lcm(self, other)
    roots(self)
    sqrt(self)

PyPyNum
├── Array
│   └── FUNCTION
│       ├── full(shape: Any, fill_value: Any, rtype: Any) -> Any
│       ├── full_like(a: Any, fill_value: Any, rtype: Any) -> Any
│       ├── ones(shape: Any, rtype: Any) -> Any
│       ├── ones_like(a: Any, rtype: Any) -> Any
├── maths
│   └── FUNCTION
│       ├── sumprod(arrays: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
├── polynomial
│   └── FUNCTION
│       ├── from_coeffs(coeffs: Any) -> Any
│       ├── leggauss(polynomial: Any) -> Any
│       ├── legpoly(n: Any) -> Any
├── ufuncs
│   ├── CLASS
│   └── FUNCTION
│       ├── add(x: Any, y: Any) -> Any
│       ├── base_ufunc(arrays: Any, func: Any, args: Any, rtype: Any) -> Any
│       ├── divide(x: Any, y: Any) -> Any
│       ├── floor_divide(x: Any, y: Any) -> Any
│       ├── modulo(x: Any, y: Any) -> Any
│       ├── multiply(x: Any, y: Any) -> Any
│       ├── power(x: Any, y: Any, m: Any) -> Any
│       ├── subtract(x: Any, y: Any) -> Any
│       └── ufunc_helper(x: Any, y: Any, func: Any) -> Any

运行用时测试

Run Time Test

矩阵用时测试 Matrix Time Test	NumPy+CPython（seconds）	排名 Ranking	PyPyNum+PyPy（seconds）	排名 Ranking	Mpmath_+_PyPy_（_seconds_）	排名 Ranking	SymPy_+_PyPy_（_seconds_）	排名 Ranking
创建一百阶随机数矩阵 Create a hundred order random number matrix	0.000083	1	0.005374	2	0.075253	3	0.230530	4
创建一千阶随机数矩阵 Create a thousand order random number matrix	0.006740	1	0.035666	2	1.200950	3	4.370265	4
一百阶矩阵相加 Addition of matrices of order one hundred	0.000029	1	0.002163	2	0.045641	4	0.035700	3
一千阶矩阵相加 Adding matrices of order one thousand	0.002647	1	0.019111	2	1.746957	4	0.771542	3
一百阶矩阵行列式 Determinant of a hundred order matrix	0.087209	2	0.016331	1	4.354507	3	5.157206	4
一千阶矩阵行列式 Determinant of a thousand order matrix	0.616113	1	3.509747	2	速度极慢	3	无法计算	4
一百阶矩阵求逆 Finding the inverse of a hundred order matrix	0.162770	1	31.088849	4	8.162948	2	21.437424	3
一千阶矩阵求逆 Finding the inverse of a thousand order matrix	0.598905	1	速度较慢	4	速度较慢	2	速度较慢	3
数组输出效果 Array output effect	[[[[ -7 -67] [-78  29]] [[-86 -97] [ 68  -3]]] [[[ 11  42] [ 24 -65]] [[-60  72] [ 73   2]]]]	/	[[[[ 37  83] [ 40   2]] [[ -5 -34] [ -7  72]]] [[[ 13 -64] [  6  90]] [[ 68  57] [ 78  11]]]]	/	[-80.0   -8.0  80.0  -88.0] [-99.0  -43.0  87.0   81.0] [ 20.0  -55.0  98.0    8.0] [  8.0   44.0  64.0  -35.0] (只支持矩阵) (Only supports matrices)	/	⎡⎡16   -56⎤  ⎡ 8   -28⎤⎤ ⎢⎢        ⎥  ⎢        ⎥⎥ ⎢⎣-56  56 ⎦  ⎣-28  28 ⎦⎥ ⎢                      ⎥ ⎢ ⎡-2  7 ⎤   ⎡-18  63 ⎤⎥ ⎢ ⎢      ⎥   ⎢        ⎥⎥ ⎣ ⎣7   -7⎦   ⎣63   -63⎦⎦	/

基本结构

Basic structure

PyPyNum
├── Array
│   ├── CLASS
│   │   └── Array(object)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       ├── array(data: Any) -> Any
│       ├── fill(shape: Any, sequence: Any, repeat: Any, pad: Any, rtype: Any) -> Any
│       ├── full(shape: Any, fill_value: Any, rtype: Any) -> Any
│       ├── full_like(a: Any, fill_value: Any, rtype: Any) -> Any
│       ├── get_shape(data: Any) -> Any
│       ├── is_valid_array(_array: Any, _shape: Any) -> Any
│       ├── ones(shape: Any, rtype: Any) -> Any
│       ├── ones_like(a: Any, rtype: Any) -> Any
│       ├── zeros(shape: Any, rtype: Any) -> Any
│       └── zeros_like(a: Any, rtype: Any) -> Any
├── FourierT
│   ├── CLASS
│   │   └── FT1D(object)/__init__(self: Any, data: Any) -> Any
│   └── FUNCTION
├── Geometry
│   ├── CLASS
│   │   ├── Circle(object)/__init__(self: Any, center: typing.Union[list, tuple], radius: typing.Union[int, float]) -> Any
│   │   ├── Line(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> Any
│   │   ├── Point(object)/__init__(self: Any, p: typing.Union[list, tuple]) -> Any
│   │   ├── Polygon(object)/__init__(self: Any, p: typing.Union[list, tuple]) -> Any
│   │   ├── Quadrilateral(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple], c: typing.Union[list, tuple], d: typing.Union[list, tuple]) -> Any
│   │   └── Triangle(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple], c: typing.Union[list, tuple]) -> Any
│   └── FUNCTION
│       └── distance(g1: Any, g2: Any, error: typing.Union[int, float]) -> float
├── Graph
│   ├── CLASS
│   │   ├── BaseGraph(object)/__init__(self: Any) -> Any
│   │   ├── BaseWeGraph(pypynum.Graph.BaseGraph)/__init__(self: Any) -> Any
│   │   ├── DiGraph(pypynum.Graph.BaseGraph)/__init__(self: Any) -> Any
│   │   ├── UnGraph(pypynum.Graph.BaseGraph)/__init__(self: Any) -> Any
│   │   ├── WeDiGraph(pypynum.Graph.BaseWeGraph)/__init__(self: Any) -> Any
│   │   └── WeUnGraph(pypynum.Graph.BaseWeGraph)/__init__(self: Any) -> Any
│   └── FUNCTION
├── Group
│   ├── CLASS
│   │   └── Group(object)/__init__(self: Any, data: Any) -> Any
│   └── FUNCTION
│       ├── add(x: Any, y: Any) -> Any
│       ├── divide(x: Any, y: Any) -> Any
│       ├── group(data: Any) -> Any
│       ├── multiply(x: Any, y: Any) -> Any
│       └── subtract(x: Any, y: Any) -> Any
├── Logic
│   ├── CLASS
│   │   ├── AND(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── Basic(object)/__init__(self: Any, label: Any) -> Any
│   │   ├── Binary(pypynum.Logic.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── COMP(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── DFF(pypynum.Logic.Unary)/__init__(self: Any, label: Any, pin0: Any, state: Any) -> Any
│   │   ├── FullAdder(pypynum.Logic.Ternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any
│   │   ├── FullSuber(pypynum.Logic.Ternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any
│   │   ├── HalfAdder(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── HalfSuber(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── JKFF(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, state: Any) -> Any
│   │   ├── NAND(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── NOR(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── NOT(pypynum.Logic.Unary)/__init__(self: Any, label: Any, pin0: Any) -> Any
│   │   ├── OR(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── Quaternary(pypynum.Logic.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any
│   │   ├── TFF(pypynum.Logic.Unary)/__init__(self: Any, label: Any, pin0: Any, state: Any) -> Any
│   │   ├── Ternary(pypynum.Logic.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any
│   │   ├── TwoBDiver(pypynum.Logic.Quaternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any
│   │   ├── TwoBMuler(pypynum.Logic.Quaternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any
│   │   ├── Unary(pypynum.Logic.Basic)/__init__(self: Any, label: Any, pin0: Any) -> Any
│   │   ├── XNOR(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   └── XOR(pypynum.Logic.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   └── FUNCTION
│       └── connector(previous: Any, latter: Any) -> Any
├── Matrix
│   ├── CLASS
│   │   └── Matrix(pypynum.Array.Array)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       ├── eigen(matrix: pypynum.Matrix.Matrix) -> tuple
│       ├── hessenberg(matrix: pypynum.Matrix.Matrix) -> tuple
│       ├── identity(n: int) -> pypynum.Matrix.Matrix
│       ├── lu(matrix: pypynum.Matrix.Matrix) -> tuple
│       ├── mat(data: Any) -> Any
│       ├── qr(matrix: pypynum.Matrix.Matrix) -> tuple
│       ├── rotate90(matrix: pypynum.Matrix.Matrix, times: int) -> pypynum.Matrix.Matrix
│       ├── same(rows: Any, cols: Any, value: Any) -> Any
│       ├── svd(matrix: pypynum.Matrix.Matrix) -> tuple
│       ├── tril_indices(n: int, k: int, m: int) -> tuple
│       ├── zeros(_dimensions: Any) -> Any
│       └── zeros_like(_nested_list: Any) -> Any
├── NeuralN
│   ├── CLASS
│   │   └── NeuralNetwork(object)/__init__(self: Any, _input: Any, _hidden: Any, _output: Any) -> Any
│   └── FUNCTION
│       └── neuraln(_input: Any, _hidden: Any, _output: Any) -> Any
├── Quaternion
│   ├── CLASS
│   │   ├── Euler(object)/__init__(self: Any, y: typing.Union[int, float], p: typing.Union[int, float], r: typing.Union[int, float]) -> Any
│   │   └── Quaternion(object)/__init__(self: Any, w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> Any
│   └── FUNCTION
│       ├── change(data: typing.Union[pypynum.Quaternion.Quaternion, pypynum.Matrix.Matrix, pypynum.Quaternion.Euler], to: str) -> typing.Union[pypynum.Quaternion.Quaternion, pypynum.Matrix.Matrix, pypynum.Quaternion.Euler]
│       ├── euler(yaw: typing.Union[int, float], pitch: typing.Union[int, float], roll: typing.Union[int, float]) -> pypynum.Quaternion.Euler
│       └── quat(w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> pypynum.Quaternion.Quaternion
├── Symbolics
│   ├── CLASS
│   └── FUNCTION
│       └── parse_expr(expr: str) -> list
├── Tensor
│   ├── CLASS
│   │   └── Tensor(pypynum.Array.Array)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       ├── ten(data: list) -> pypynum.Tensor.Tensor
│       ├── tensor_and_number(tensor: Any, operator: Any, number: Any) -> Any
│       ├── tensorproduct(tensors: pypynum.Tensor.Tensor) -> pypynum.Tensor.Tensor
│       ├── zeros(_dimensions: Any) -> Any
│       └── zeros_like(_nested_list: Any) -> Any
├── Tree
│   ├── CLASS
│   │   ├── MultiTree(object)/__init__(self: Any, root: Any) -> Any
│   │   └── MultiTreeNode(object)/__init__(self: Any, data: Any) -> Any
│   └── FUNCTION
├── Vector
│   ├── CLASS
│   │   └── Vector(pypynum.Array.Array)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       ├── same(length: Any, value: Any) -> Any
│       ├── vec(data: Any) -> Any
│       ├── zeros(_dimensions: Any) -> Any
│       └── zeros_like(_nested_list: Any) -> Any
├── chars
│   ├── CLASS
│   └── FUNCTION
├── cipher
│   ├── CLASS
│   └── FUNCTION
│       ├── atbash(text: str) -> str
│       ├── base_64(text: str, decrypt: bool) -> str
│       ├── caesar(text: str, shift: int, decrypt: bool) -> str
│       ├── hill256(text: bytes, key: list, decrypt: bool) -> bytes
│       ├── ksa(key: bytes) -> list
│       ├── morse(text: str, decrypt: bool) -> str
│       ├── playfair(text: str, key: str, decrypt: bool) -> str
│       ├── prga(s: list) -> Any
│       ├── rc4(text: bytes, key: bytes) -> bytes
│       ├── rot13(text: str) -> str
│       ├── substitution(text: str, sub_map: dict, decrypt: bool) -> str
│       └── vigenere(text: str, key: str, decrypt: bool) -> str
├── constants
│   ├── CLASS
│   └── FUNCTION
├── equations
│   ├── CLASS
│   └── FUNCTION
│       ├── linear_equation(left: list, right: list) -> list
│       └── polynomial_equation(coefficients: list) -> list
├── errors
│   ├── CLASS
│   └── FUNCTION
├── file
│   ├── CLASS
│   └── FUNCTION
│       ├── read(file: str) -> list
│       └── write(file: str, cls: object) -> Any
├── maths
│   ├── CLASS
│   └── FUNCTION
│       ├── arrangement(n: int, r: int) -> int
│       ├── combination(n: int, r: int) -> int
│       ├── acos(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acosh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acot(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acoth(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acsc(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acsch(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── arrangement(n: int, r: int) -> int
│       ├── asec(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── asech(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── asin(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── asinh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── atan(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── atanh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── average(data: Any, weights: Any, expected: Any) -> Any
│       ├── beta(p: typing.Union[int, float], q: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── central_moment(data: typing.Union[list, tuple], order: int) -> float
│       ├── coeff_det(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── combination(n: int, r: int) -> int
│       ├── corr_coeff(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── cos(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cosh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cot(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── coth(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cov(x: typing.Union[list, tuple], y: typing.Union[list, tuple], dof: int) -> typing.Union[int, float, complex]
│       ├── crt(n: typing.Union[list, tuple], a: typing.Union[list, tuple]) -> int
│       ├── csc(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── csch(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cumprod(lst: typing.Union[list, tuple]) -> list
│       ├── cumsum(lst: typing.Union[list, tuple]) -> list
│       ├── definite_integral(f: Any, x_start: typing.Union[int, float], x_end: typing.Union[int, float], n: int, args: Any, kwargs: Any) -> float
│       ├── derivative(f: Any, x: typing.Union[int, float], h: typing.Union[int, float], args: Any, kwargs: Any) -> float
│       ├── erf(x: typing.Union[int, float]) -> float
│       ├── exgcd(a: int, b: int) -> tuple
│       ├── exp(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── factorial(n: int) -> int
│       ├── freq(data: typing.Union[list, tuple]) -> dict
│       ├── gamma(alpha: typing.Union[int, float]) -> float
│       ├── gaussian(x: typing.Union[int, float], _mu: typing.Union[int, float], _sigma: typing.Union[int, float]) -> float
│       ├── gcd(args: int) -> int
│       ├── geom_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── harm_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── iroot(y: int, n: int) -> int
│       ├── is_possibly_square(n: int) -> bool
│       ├── is_square(n: int) -> bool
│       ├── isqrt(x: int) -> int
│       ├── kurt(data: typing.Union[list, tuple]) -> float
│       ├── lcm(args: int) -> int
│       ├── ln(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── median(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── mod_order(a: int, n: int, b: int) -> int
│       ├── mode(data: typing.Union[list, tuple]) -> Any
│       ├── normalize(data: typing.Union[list, tuple], target: typing.Union[int, float, complex]) -> typing.Union[list, tuple]
│       ├── parity(x: int) -> int
│       ├── pi(i: int, n: int, f: Any) -> typing.Union[int, float, complex]
│       ├── poisson(x: int, _lambda: typing.Union[int, float]) -> float
│       ├── primitive_root(a: int, single: bool) -> typing.Union[int, list]
│       ├── product(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── ptp(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── raw_moment(data: typing.Union[list, tuple], order: int) -> float
│       ├── root(x: typing.Union[int, float, complex], y: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── sec(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── sech(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── sigma(i: int, n: int, f: Any) -> typing.Union[int, float, complex]
│       ├── sigmoid(x: typing.Union[int, float]) -> float
│       ├── sign(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── sin(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── sinh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── skew(data: typing.Union[list, tuple]) -> float
│       ├── square_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── std(numbers: typing.Union[list, tuple], dof: int) -> typing.Union[int, float, complex]
│       ├── sumprod(arrays: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── tan(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── tanh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── totient(n: int) -> int
│       ├── var(numbers: typing.Union[list, tuple], dof: int) -> typing.Union[int, float, complex]
│       └── zeta(alpha: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
├── numbers
│   ├── CLASS
│   └── FUNCTION
│       ├── float2fraction(number: float, mixed: bool, error: float) -> tuple
│       ├── int2roman(integer: int, overline: bool) -> str
│       ├── int2words(integer: int) -> str
│       ├── roman2int(roman_num: str) -> int
│       └── str2int(string: str) -> int
├── plotting
│   ├── CLASS
│   └── FUNCTION
│       ├── background(right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool) -> typing.Union[list, str]
│       ├── binary(function: Any, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], error: Any, compare: Any, string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]
│       ├── c_unary(function: Any, projection: str, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]
│       ├── change(data: typing.Union[list, str]) -> typing.Union[list, str]
│       ├── color(text: str, rgb: typing.Union[list, tuple]) -> str
│       └── unary(function: Any, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]
├── polynomial
│   ├── CLASS
│   │   └── Polynomial(object)/__init__(self: Any, terms: Any) -> Any
│   └── FUNCTION
│       ├── from_coeffs(coeffs: Any) -> Any
│       ├── leggauss(polynomial: Any) -> Any
│       ├── legpoly(n: Any) -> Any
│       └── poly(terms: Any) -> Any
├── probability
│   ├── CLASS
│   └── FUNCTION
│       ├── binomial(sample_size: int, successes: int, success_probability: typing.Union[int, float]) -> float
│       ├── chi2_cont(contingency: list, calc_p: bool, corr: bool) -> tuple
│       ├── chi2_pdf(x: typing.Union[int, float], k: typing.Union[int, float]) -> float
│       └── hypergeometric(total_items: int, success_items: int, sample_size: int, successes_in_sample: int) -> float
├── random
│   ├── CLASS
│   └── FUNCTION
│       ├── choice(seq: typing.Union[list, tuple, str], shape: typing.Union[list, tuple]) -> Any
│       ├── gauss(mu: typing.Union[int, float], sigma: typing.Union[int, float], shape: typing.Union[list, tuple]) -> typing.Union[float, list]
│       ├── gauss_error(original: typing.Union[list, tuple], mu: typing.Union[int, float], sigma: typing.Union[int, float]) -> list
│       ├── rand(shape: typing.Union[list, tuple]) -> typing.Union[float, list]
│       ├── randint(a: int, b: int, shape: typing.Union[list, tuple]) -> typing.Union[int, list]
│       └── uniform(a: typing.Union[int, float], b: typing.Union[int, float], shape: typing.Union[list, tuple]) -> typing.Union[float, list]
├── regression
│   ├── CLASS
│   └── FUNCTION
│       ├── linear_regression(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> list
│       ├── parabolic_regression(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> list
│       └── polynomial_regression(x: typing.Union[list, tuple], y: typing.Union[list, tuple], n: int) -> list
├── sequence
│   ├── CLASS
│   └── FUNCTION
│       ├── arithmetic_sequence(a1: typing.Union[int, float], an: typing.Union[int, float], d: typing.Union[int, float], n: typing.Union[int, float], s: typing.Union[int, float]) -> dict
│       ├── bernoulli(n: int, single: bool) -> list
│       ├── catalan(n: int, single: bool) -> typing.Union[int, list]
│       ├── farey(n: int) -> list
│       ├── fibonacci(n: int, single: bool) -> typing.Union[int, list]
│       ├── geometric_sequence(a1: typing.Union[int, float], an: typing.Union[int, float], r: typing.Union[int, float], n: typing.Union[int, float], s: typing.Union[int, float]) -> dict
│       └── recaman(n: int, single: bool) -> typing.Union[int, list]
├── test
│   ├── CLASS
│   └── FUNCTION
├── this
│   ├── CLASS
│   └── FUNCTION
├── tools
│   ├── CLASS
│   └── FUNCTION
│       ├── classify(array: typing.Union[list, tuple]) -> dict
│       ├── dedup(iterable: typing.Union[list, tuple, str]) -> typing.Union[list, tuple, str]
│       ├── frange(start: typing.Union[int, float], stop: typing.Union[int, float], step: float) -> list
│       ├── generate_primes(limit: int) -> list
│       ├── generate_semiprimes(limit: int) -> list
│       ├── geomspace(start: typing.Union[int, float], stop: typing.Union[int, float], number: int) -> list
│       ├── interp(data: typing.Union[list, tuple], length: int) -> list
│       ├── linspace(start: typing.Union[int, float], stop: typing.Union[int, float], number: int) -> list
│       ├── magic_square(n: Any) -> Any
│       ├── primality(n: int, iter_num: int) -> bool
│       ├── prime_factors(integer: int, dictionary: bool, pollard_rho: bool) -> typing.Union[list, dict]
│       └── split(iterable: typing.Union[list, tuple, str], key: typing.Union[list, tuple], retain: bool) -> list
├── types
│   ├── CLASS
│   └── FUNCTION
├── ufuncs
│   ├── CLASS
│   └── FUNCTION
│       ├── add(x: Any, y: Any) -> Any
│       ├── base_ufunc(arrays: Any, func: Any, args: Any, rtype: Any) -> Any
│       ├── divide(x: Any, y: Any) -> Any
│       ├── floor_divide(x: Any, y: Any) -> Any
│       ├── modulo(x: Any, y: Any) -> Any
│       ├── multiply(x: Any, y: Any) -> Any
│       ├── power(x: Any, y: Any, m: Any) -> Any
│       ├── subtract(x: Any, y: Any) -> Any
│       └── ufunc_helper(x: Any, y: Any, func: Any) -> Any
└── utils
    ├── CLASS
    │   ├── InfIterator(object)/__init__(self: Any, start: typing.Union[int, float, complex], mode: str, common: typing.Union[int, float, complex]) -> Any
    │   ├── LinkedList(object)/__init__(self: Any) -> Any
    │   ├── LinkedListNode(object)/__init__(self: Any, value: Any, next_node: Any) -> Any
    │   └── OrderedSet(object)/__init__(self: Any, sequence: Any) -> Any
    └── FUNCTION

代码测试

Code testing

from pypynum import (Array, Geometry, Logic, Matrix, Quaternion, Symbolics, Tensor, Vector,
                     cipher, constants, equations, maths, plotting, random, regression, tools)

...

print(Array.array())
print(Array.array([1, 2, 3, 4, 5, 6, 7, 8]))
print(Array.array([[1, 2, 3, 4], [5, 6, 7, 8]]))
print(Array.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]))

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

 [[5 6]
  [7 8]]]
"""

triangle = Geometry.Triangle((0, 0), (2, 2), (3, 0))
print(triangle.perimeter())
print(triangle.area())
print(triangle.centroid())

"""
8.06449510224598
3.0
(1.6666666666666667, 0.6666666666666666)
"""

a, b, c = 1, 1, 1
adder0, adder1 = Logic.HalfAdder("alpha", a, b), Logic.HalfAdder("beta", c, None)
xor0 = Logic.XOR("alpha")
ff0, ff1 = Logic.DFF("alpha"), Logic.DFF("beta")
xor0.set_order0(1)
xor0.set_order1(1)
Logic.connector(adder0, adder1)
Logic.connector(adder0, xor0)
Logic.connector(adder1, xor0)
Logic.connector(adder1, ff0)
Logic.connector(xor0, ff1)
print("sum: {}, carry: {}".format(ff0.out(), ff1.out()))

"""
sum: [1], carry: [1]
"""

m0 = Matrix.mat([[1, 2], [3, 4]])
m1 = Matrix.mat([[5, 6], [7, 8]])
print(m0)
print(m1)
print(m0 + m1)
print(m0 @ m1)
print(m0.inv())
print(m1.rank())

"""
[[1 2]
 [3 4]]
[[5 6]
 [7 8]]
[[ 6  8]
 [10 12]]
[[19 22]
 [43 50]]
[[-2.0  1.0]
 [ 1.5 -0.5]]
2
"""

q0 = Quaternion.quat(1, 2, 3, 4)
q1 = Quaternion.quat(5, 6, 7, 8)
print(q0)
print(q1)
print(q0 + q1)
print(q0 * q1)
print(q0.inverse())
print(q1.conjugate())

"""
(1+2i+3j+4k)
(5+6i+7j+8k)
(6+8i+10j+12k)
(-60+12i+30j+24k)
(0.18257418583505536+-0.3651483716701107i+-0.5477225575051661j+-0.7302967433402214k)
(5+-6i+-7j+-8k)
"""

print(Symbolics.BASIC)
print(Symbolics.ENGLISH)
print(Symbolics.GREEK)
print(Symbolics.parse_expr("-(10+a-(3.14+b0)*(-5))**(-ζn1-2.718/mΣ99)//9"))

"""
%()*+-./0123456789
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩαβγδεζηθικλμνξοπρστυφχψω
[['10', '+', 'a', '-', ['3.14', '+', 'b0'], '*', '-5'], '**', ['-ζn1', '-', '2.718', '/', 'mΣ99'], '//', '9']
"""

t0 = Tensor.ten([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
t1 = Tensor.ten([[[9, 10], [11, 12]], [[13, 14], [15, 16]]])
print(t0)
print(t1)
print(t0 + t1)
print(t0 @ t1)

"""
[[[1 2]
  [3 4]]

 [[5 6]
  [7 8]]]
[[[ 9 10]
  [11 12]]

 [[13 14]
  [15 16]]]
[[[10 12]
  [14 16]]

 [[18 20]
  [22 24]]]
[[[ 31  34]
  [ 71  78]]

 [[155 166]
  [211 226]]]
"""

string = "PyPyNum"
encrypted = cipher.caesar(string, 10)
print(string)
print(encrypted)
print(cipher.caesar(encrypted, 10, decrypt=True))
encrypted = cipher.vigenere(string, "cipher")
print(string)
print(encrypted)
print(cipher.vigenere(encrypted, "cipher", decrypt=True))
encrypted = cipher.morse(string)
print(string)
print(encrypted)
print(cipher.morse(encrypted, decrypt=True))

"""
PyPyNum
ZiZiXew
PyPyNum
PyPyNum
RgEfRlo
PyPyNum
PyPyNum
.--. -.-- .--. -.-- -. ..- --
PYPYNUM
"""

v0 = Vector.vec([1, 2, 3, 4])
v1 = Vector.vec([5, 6, 7, 8])
print(v0)
print(v1)
print(v0 + v1)
print(v0 @ v1)
print(v0.normalize())
print(v1.angles())

"""
[1 2 3 4]
[5 6 7 8]
[ 5 12 21 32]
70
[0.18257418583505536  0.3651483716701107  0.5477225575051661  0.7302967433402214]
[1.1820279130506308, 1.0985826410133916, 1.0114070854293842, 0.9191723423169716]
"""

print(constants.TB)
print(constants.e)
print(constants.h)
print(constants.phi)
print(constants.pi)
print(constants.tera)

"""
1099511627776
2.718281828459045
6.62607015e-34
1.618033988749895
3.141592653589793
1000000000000
"""

p = [1, -2, -3, 4]
m = [
    [
        [1, 2, 3],
        [6, 10, 12],
        [7, 16, 9]
    ],
    [-1, -2, -3]
]
print(equations.polynomial_equation(p))
print(equations.linear_equation(*m))

"""
[(-1.5615528128088307-6.5209667308287455e-24j)   (1.0000000000000007+3.241554513744382e-25j)   (2.5615528128088294+4.456233626665941e-24j)]
[ 1.6666666666666667 -0.6666666666666666 -0.4444444444444444]
"""

print(maths.cot(constants.pi / 3))
print(maths.gamma(1.5))
print(maths.pi(1, 10, lambda x: x ** 2))
print(maths.product([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))
print(maths.sigma(1, 10, lambda x: x ** 2))
print(maths.var([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))

"""
0.577350269189626
0.886226925452758
13168189440000
6469693230
385
73.29
"""

plt = plotting.unary(lambda x: x ** 2, top=10, bottom=0, character="+")
print(plt)
print(plotting.binary(lambda x, y: x ** 2 + y ** 2 - 10, right=10, left=0, compare="<=", basic=plotting.change(plt)))
print(plotting.c_unary(lambda x: x ** x, right=2, left=-2, top=2, bottom=-2, complexity=20, character="-"))

"""
  1.00e+01|         +                               +         
          |                                                   
          |          +                             +          
          |                                                   
          |           +                           +           
          |            +                         +            
          |                                                   
          |             +                       +             
  5.00e+00|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
          |              +                     +              
          |               +                   +               
          |                +                 +                
          |                 +               +                 
          |                  +             +                  
          |                   +           +                   
          |                    +         +                    
          |                     +++   +++                     
  0.00e+00|________________________+++________________________
           -5.00e+00             0.00e+00             5.00e+00
  1.00e+01|         +                               +         
          |                                                   
          |          +                             +          
          |                                                   
          |.........  +                           +           
          |.............                         +            
          |..............                                     
          |................                     +             
  5.00e+00|................_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
          |................                    +              
          |................                   +               
          |..............  +                 +                
          |.............    +               +                 
          |.........         +             +                  
          |                   +           +                   
          |                    +         +                    
          |                     +++   +++                     
  0.00e+00|________________________+++________________________
           -5.00e+00             0.00e+00             5.00e+00
  2.00e+00|           -                 -           -          -          -            -    
          |               -  -            -          -         -         -           -      
          |                     -           -         -        -        -          -        
          |-                       -          -       -       -        -         -          
          |     -   -                - -       --      -      -       -        -            
          |            -  -              -       -      -     -      -       -             -
          |                  -  - -       - --  - ---  -- -  --     -     - -         - -   
          |                         - -   -  --    --    -   -  - --     -       - -        
          |  -   -  - - -  -          - -- -   ---  ---  -   -   ---   --     - -           
          |             -    -  - - - --    ----- -- -- --- --  --  ---    --           -  -
          |               - -      -     ------------ ----  - --  -- - ---       - - -      
          |    -  -  -  - -  ----- - -- ----------------------- -- ----  - -- --            
          |   -  -   - -         - ---- ---------------------------------      - - - - -  - 
  0.00e+00|_ _ _ _ _ _ _ _-_-_-_-_---- ------------------------------------_-- _ _ _ _ _ _ _
          |            -  -   - - ----------------------------------------- -- - - - -      
          |   -  --  -  -       -- -  -  --------------------------------- -           -  - 
          |    -          - ---- - - -- --------------------- ----- ----    - -- -          
          |               -         - -- --------- -- -- -  -----  ---  -- -       - -  -   
          |             -  - -  - - - -    ---- --- --- --- --  --  ---     - -            -
          |  -   -  - -               - --     --   --   -   -    --   --       --          
          |                       - -     -  --    -    --   -- -  -     --        -  -     
          |                  -  -         - -   - - -  -- -   -     --      -           -   
          |            -  -            - -      --     --     -      -       - -           -
          |     -   -                -         -       -      -       -          -          
          |-                    -  -          -       -        -       -           -        
          |                  -              -         -        -        -            -      
          |               -               -          -         -         -                  
 -2.00e+00|___________-_________________-___________-_____________________-____________-____
           -2.00e+00                            0.00e+00                            2.00e+00
"""

print(random.gauss(0, 1, [2, 3, 4]))
print(random.rand([2, 3, 4]))
print(random.randint(0, 9, [2, 3, 4]))
print(random.uniform(0, 9, [2, 3, 4]))

"""
[[[2.0337109813389342, 0.07828151434838644, 0.5770175491332994, -0.45862437785903776], [-0.5647580909376742, 0.04013315334953438, -1.4415329001085142, 0.21063309355876483], [-0.13079032580688052, -0.12269092226721959, -1.0486596849517071, 0.33707912556088127]], [[1.0924880424965842, -0.2904666571377903, -0.8147193339820543, -0.12425697574808597], [-0.9431495143889028, 1.6993259508582454, 2.459143670684122, 0.6706774051649211], [-0.2067467760214054, -1.335666880934244, -0.06604610266464511, 1.4659516633001894]]]
[[[0.5056293647418786, 0.41138133426895374, 0.1116780669974381, 0.5421022799938007], [0.8529591223803364, 0.7967626494191837, 0.6778986058446654, 0.7966034784840031], [0.8226174224158366, 0.6882274477983558, 0.2043768498847348, 0.20649565416723548]], [[0.7858708880353261, 0.293208591223893, 0.9713037501099235, 0.1277647867709274], [0.5310738736523741, 0.3775394394569467, 0.6618665928287699, 0.7813821035754579], [0.41759114496811056, 0.8741519554894022, 0.8325056303107449, 0.8127323540413558]]]
[[[5, 9, 7, 5], [9, 9, 9, 8], [6, 2, 0, 3]], [[4, 7, 5, 8], [5, 7, 2, 4], [9, 9, 2, 2]]]
[[[7.666875196011509, 4.2629925536138815, 6.269304350870346, 6.1616482850575816], [8.736107228623906, 4.050564635824004, 8.719616126170123, 8.241460211008127], [2.2965292897567497, 2.3960057526618233, 2.406429664045121, 7.644380154396355]], [[3.8027437908649793, 5.075197041264121, 3.778237396690295, 0.9427794634466875], [1.9182768078467933, 6.926954119152528, 2.5353235396092666, 3.0648655668955422], [8.538065261473607, 7.652025295242501, 4.086320910353441, 7.457914057699455]]]
"""

print(regression.linear_regression(list(range(5)), [2, 4, 6, 7, 8]))
print(regression.parabolic_regression(list(range(5)), [2, 4, 6, 7, 8]))
print(regression.polynomial_regression(list(range(5)), [2, 4, 6, 7, 8], 4))

"""
[1.5, 2.4000000000000004]
[-0.21428571428571563, 2.3571428571428625, 1.971428571428569]
[0.0833333333480164, -0.6666666668091551, 1.416666667838451, 1.1666666648311779, 2.0000000002900586]
"""

print(tools.classify([1, 2.3, 4 + 5j, "string", list, True, 3.14, False, tuple, tools]))
print(tools.dedup(["Python", 6, "NumPy", int, "PyPyNum", 9, "pypynum", "NumPy", 6, True]))
print(tools.frange(0, 3, 0.4))
print(tools.linspace(0, 2.8, 8))

"""
{<class 'int'>: [1], <class 'float'>: [2.3, 3.14], <class 'complex'>: [(4+5j)], <class 'str'>: ['string'], <class 'type'>: [<class 'list'>, <class 'tuple'>], <class 'bool'>: [True, False], <class 'module'>: [<module 'pypynum.tools' from 'C:\\Users\\Administrator\\PycharmProjects\\pythonProject\\pypynum\\tools.py'>]}
['Python', 6, 'NumPy', <class 'int'>, 'PyPyNum', 9, 'pypynum', True]
[0.0, 0.4, 0.8, 1.2000000000000002, 1.6, 2.0, 2.4000000000000004, 2.8000000000000003]
[0.0, 0.39999999999999997, 0.7999999999999999, 1.2, 1.5999999999999999, 1.9999999999999998, 2.4, 2.8]
"""

# 提示：
# 
# 测试已成功通过并结束。
# 
# 这些测试只是这个包功能的一部分。
# 
# 更多的功能需要自己探索和尝试！
# 
# Tip:
# 
# The test has been successfully passed and ended.
# 
# These tests are only part of the functionality of this package.
# 
# More features need to be explored and tried by yourself!