A multifunctional mathematical calculation package written in pure Python programming language [Python>=3.4]
Project description
PyPyNum
A multifunctional mathematical calculation package written in pure Python programming language [Python>=3.4]
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\ \ \___| \/ / / \ \ \___| \/ / / \ \ \\ \ \\ \ \\\ \\ \ \ \ \ \
\ \__\ __/ / / \ \__\ __/ / / \ \__\\ \__\\ \_______\\ \__\ \ \__\
\|__| |\___/ / \|__| |\___/ / \|__| \|__| \|_______| \|__| \|__|
\|___|/ \|___|/
Version -> 1.9.0 | 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.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
!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=
新增的代码行数约三百行。
The number of new code lines is
about 300.
!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=
以下函数进行了改名，使用时请注意。
The following functions have
been renamed, please be careful
when using them.
interpreter -> parse_expr
deduplicate -> dedup
interpolation -> interp
!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=
“chi2_cont”是卡方检验函数，支持输入一
个列联表，返回(chi2，p，dof，
expected)，当自由度为1时可以设置是否
经过Yates校正。
"chi2_cont" is a chi-square
test function that supports
entering a contingency table and
returning (chi2, p, dof,
expected). When the degree of
freedom is 1, you can set
whether to perform Yates
correction.
!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=
PyPyNum
├── cipher
│ └── FUNCTION
│ ├── atbash(text: str) -> str
│ ├── base_64(text: str, decrypt: bool) -> str
│ ├── caesar(text: str, shift: int, decrypt: bool) -> str
│ ├── morse(text: str, decrypt: bool) -> str
│ ├── playfair(text: str, key: str, decrypt: bool) -> str
│ ├── rot13(text: str) -> str
│ ├── substitution(text: str, sub_map: dict, decrypt: bool) -> str
│ └── vigenere(text: str, key: str, decrypt: bool) -> str
├── probability
│ └── FUNCTION
│ ├── chi2_cont(contingency: list, calc_p: bool, corr: bool) -> tuple
│ ├── chi2_pdf(x: typing.Union[int, float], k: typing.Union[int, float]) -> float
└── utils
├── CLASS
│ ├── LinkedList(object)/__init__(self: Any) -> Any
│ ├── LinkedListNode(object)/__init__(self: Any, value: Any, next_node: 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) -> Any
│ ├── function(_array: Any, _function: Any, args: Any) -> Any
│ ├── get_shape(data: Any) -> Any
│ ├── is_valid_array(_array: Any, _shape: Any) -> Any
│ ├── zeros(shape: Any) -> Any
│ └── zeros_like(_nested_list: 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
│ ├── morse(text: str, decrypt: bool) -> str
│ ├── playfair(text: str, key: str, decrypt: bool) -> str
│ ├── 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]) -> int
│ ├── 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]
│ ├── 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]) -> float
├── numbers
│ ├── CLASS
│ └── FUNCTION
│ ├── float2fraction(number: float, mixed: bool, error: float) -> tuple
│ ├── int2roman(integer: int, overline: bool) -> 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, start: typing.Union[int, float], end: typing.Union[int, float], interval: typing.Union[int, float], 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
│ └── 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
└── 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) 0 0]
[ 0 (2.5615528128088294+4.456233626665941e-24j) 0]
[ 0 0 (1.0000000000000007+3.241554513744382e-25j)]]
[ 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, start=-10, end=10, interval=100, 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]))
"""
[[[1.5224810365398622, -0.3957309179046998, 0.22865800022960608, 0.69458992002954], [1.2796914880445907, -0.9963205507196862, -1.035672172661647, 0.6685698624811087], [0.7966036403993993, 1.4728609716690575, 1.4271945372122727, 1.1346636992788732]], [[-1.5167315121066547, 0.5337355746221562, -0.3856209788535444, 0.9933311189027801], [-0.3000451683620412, 1.985371100287406, 1.0044445415210081, -0.160547602340231], [-1.4024800661532726, -0.2943388293424122, 0.39426575084974064, -0.1788920335787877]]]
[[[0.5832734051570118, 0.12709072960713108, 0.8460371711928255, 0.7732502834495745], [0.1337174418330055, 0.20214133151753821, 0.11501155244785399, 0.945090241309287], [0.784115524194132, 0.5008953798117651, 0.3514598489060844, 0.2730882163660271]], [[0.8536525608965406, 0.03101021951426164, 0.8904423549934418, 0.30844019778976395], [0.6686071112680847, 0.8622569244011669, 0.5624751157425253, 0.25138337174684133], [0.28360470724085995, 0.31597491199666694, 0.8115190344839784, 0.2685895801115009]]]
[[[7, 1, 2, 5], [0, 7, 9, 9], [3, 0, 5, 6]], [[2, 2, 4, 3], [9, 7, 2, 0], [2, 5, 6, 6]]]
[[[3.2674331705558304, 8.794845124593792, 8.48281482952606, 4.071439810303413], [3.525937325174985, 8.353244015747865, 5.167113956700689, 8.200558536323298], [0.5729366698493622, 4.49113422389227, 7.736245315815029, 1.9082811620380302]], [[4.889120931109369, 1.6037956737307013, 7.983047897048623, 1.3817112552960102], [5.866208284533167, 0.5963242816793028, 6.17792540726971, 8.415093555918986], [0.2560629015262261, 1.9094767046602064, 5.647362624435581, 4.042400239970636]]]
"""
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]
[-0.21428571428571183, 2.3571428571428474, 1.9714285714285764]
[0.08333333334800574, -0.6666666668092494, 1.4166666678382942, 1.1666666648311956, 2.0000000002900613]
"""
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 'F:\\PyPyproject\\PyPyproject1\\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!
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