A Python math package written in pure Python programming language
Project description
PyPyNum
Version -> 1.0.2
PyPI -> https://pypi.org/project/PyPyNum/
Gitee -> https://gitee.com/PythonSJL/PyPyNum
介绍
Introduction
- DIY数学库，类似于numpy、scipy等，专为PyPy解释器制作
- DIY math library, similar to numpy, scipy, etc., specifically designed for PyPy 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，QQ 2261748025 （Py𝙿𝚢𝚝𝚑𝚘𝚗-水晶兰）
- If you need to contact, QQ 2261748025 (Py𝙿𝚢𝚝𝚑𝚘𝚗-水晶兰)
PyPyNum的Zen
The Zen of PyPyNum
The Zen of PyPyNum, by Shen Jiayi
This is a math package written purely in Python.
...(Do you want to see the entire content?
Then enter "from pypynum import this" on your
Python interpreter and run it!)
December 27, 2023
与上一个版本相比新增功能
New features compared to the previous version
Symbolics (符号计算)
FUNCTIONS
interpreter(expr: str) -> list
DATA
basic = '%()*+-./0123456789'
english = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'
greek = 'ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟ∏ΡΣΤΥΦΧΨΩβγδεζηθικλμνξοπρστυφχψω'
operators = ['**', '*', '//', '/', '%', '+', '-']
valid = '%()*+-./0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcd...yzΑΒΓΔΕΖΗΘ...'
(More features need to be added)
下一个版本预期新增功能
Expected new features in the next version
[Vector module]
基本结构
Basic structure
PyPyNum
test
[A Code Test File]
Geometry
CLASSES
Circle
Line
Point
Polygon
Quadrilateral
Triangle
FUNCTIONS
distance(g1: <built-in function any>, g2: <built-in function any>, error: int | float = 0) -> float
Matrix
CLASSES
Matrix
FUNCTIONS
eig(matrix)
hypot(a, b)
identity(n)
lu(matrix)
mat(data)
qr(matrix)
svd(matrix)
tril_indices(n, k=0, m=None)
zeros(_dimensions)
zeros_like(_nested_list)
Quaternion
CLASSES
Euler
Quaternion
FUNCTIONS
change(data: Euler | Quaternion) -> Quaternion | Euler
euler(yaw: int | float = 0, pitch: int | float = 0, roll: int | float = 0) -> Euler
quat(w: int | float = 0, x: int | float = 0, y: int | float = 0, z: int | float = 0) -> Quaternion
Symbolics
FUNCTIONS
interpreter(expr: str) -> list
DATA
basic = '%()*+-./0123456789'
english = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'
greek = 'ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟ∏ΡΣΤΥΦΧΨΩβγδεζηθικλμνξοπρστυφχψω'
operators = ['**', '*', '//', '/', '%', '+', '-']
valid = '%()*+-./0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcd...yzΑΒΓΔΕΖΗΘ...'
Tensor
CLASSES
Tensor
FUNCTIONS
get_shape(_tensor)
is_valid_tensor(_tensor, _shape)
ten(data)
tensor_and_number(tensor, operator, number)
tolist(_nested_list)
constants
DATA
AMU = 1.6605402e-27
EB = 1152921504606846976
G = 6.6743e-11
GB = 1073741824
KB = 1024
MB = 1048576
NA = 6.02214076e+23
PB = 1125899906842624
TB = 1099511627776
YB = 1208925819614629174706176
ZB = 1180591620717411303424
atto = 1e-18
c = 299792458
centi = 0.01
deci = 0.1
deka = 10.0
e = 2.718281828459045
exa = 1e+18
femto = 1e-15
gamma = 0.5772156649015329
giga = 1000000000.0
h = 6.62607015e-34
hecto = 100.0
inf = inf
kilo = 1000.0
mega = 1000000.0
micro = 1e-06
milli = 0.001
nan = nan
nano = 1e-09
peta = 1000000000000000.0
phi = 1.618033988749895
pi = 3.141592653589793
pico = 1e-12
qe = 1.60217733e-19
tera = 1000000000000.0
yocto = 1e-24
yotta = 1e+24
zepto = 1e-21
zetta = 1e+21
equations
FUNCTIONS
mles = multivariate_linear_equation_system(left: list, right: list) -> None | list
multivariate_linear_equation_system(left: list, right: list) -> None | list
pe = polynomial_equation(coefficients: list) -> list
polynomial_equation(coefficients: list) -> list
mathematics
FUNCTIONS
A = arrangement(n: int, r: int) -> int
C = combination(n: int, r: int) -> int
acos(x: int | float) -> int | float
acosh(x: int | float) -> int | float
acot(x: int | float) -> int | float
acoth(x: int | float) -> int | float
acsc(x: int | float) -> int | float
acsch(x: int | float) -> int | float
arrangement(n: int, r: int) -> int
asec(x: int | float) -> int | float
asech(x: int | float) -> int | float
asin(x: int | float) -> int | float
asinh(x: int | float) -> int | float
atan(x: int | float) -> int | float
atanh(x: int | float) -> int | float
beta(p: int | float, q: int | float) -> int | float
combination(n: int, r: int) -> int
cos(x: int | float) -> int | float
cosh(x: int | float) -> int | float
cot(x: int | float) -> int | float
coth(x: int | float) -> int | float
csc(x: int | float) -> int | float
csch(x: int | float) -> int | float
definite_integral(f, x_start: int | float, x_end: int | float, n: int = 10000000) -> float
derivative(f, x: int | float, h: int | float = 1e-07) -> float
erf(x: int | float) -> float
exp(x: int | float) -> int | float
factorial(n: int) -> int
freq(data: list | tuple) -> dict
gamma(alpha: int | float) -> float
gaussian(x: int | float, _mu: int | float = 0, _sigma: int | float = 1) -> float
ln(x: int | float) -> int | float
mean(numbers: list | tuple) -> int | float | complex
median(numbers: list | tuple) -> int | float | complex
mode(data: list | tuple) -> <built-in function any>
pi(i: int, n: int, f) -> int | float | complex
product(numbers: list | tuple) -> int | float | complex
ptp(numbers: list | tuple) -> int | float | complex
root(x: int | float | complex, y: int | float | complex) -> int | float | complex
sec(x: int | float) -> int | float
sech(x: int | float) -> int | float
sigma(i: int, n: int, f) -> int | float | complex
sigmoid(x: int | float) -> float
sign(x: int | float) -> int
sin(x: int | float) -> int | float
sinh(x: int | float) -> int | float
std(numbers: list | tuple) -> int | float | complex
tan(x: int | float) -> int | float
tanh(x: int | float) -> int | float
var(numbers: list | tuple) -> int | float | complex
zeta(alpha: int | float) -> float
plotting
FUNCTIONS
background(right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, merge: bool = False) -> list | str
binary(function, right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, error=0, compare='==', merge: bool = True, basic: list = None, character: str = '.', data: bool = False) -> list | str
c_unary(function, start: int | float, end: int | float, interval: int | float = 5, projection: str = 'ri', right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, merge: bool = True, basic: list = None, character: str = '.', data: bool = False) -> list | str
change(data: list | str) -> list | str
unary(function, right: int | float = 5, left: int | float = -5, top: int | float = 5, bottom: int | float = -5, complexity: int | float = 5, ratio: int | float = 3, merge: bool = True, basic: list = None, character: str = '.', data: bool = False) -> list | str
regression
FUNCTIONS
__covariance_matrix(_x, _y)
linear_regression(x_values, y_values)
parabolic_regression(x, y)
__solve_equations(a1, b1, c1, a2, b2, c2)
tools
FUNCTIONS
classify(array: list | tuple) -> dict
deduplicate(iterable: list | tuple | str) -> list | tuple | str
frange(start: int | float, stop: int | float, step: float = 1.0) -> list
linspace(start: int | float, stop: int | float, number: int) -> list
代码测试
Code testing
>>> from pypynum import Geometry, Matrix, Quaternion, Symbolics, Tensor, constants, equations, mathematics, regression, plotting, tools
...
>>> 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)
>>> 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.interpreter("-(10+a-(3.14+b0)*(-5))**(-ζn1-2.718/mΣ99)//9"))
%()*+-./0123456789
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟ∏ΡΣΤΥΦΧΨΩβγδεζηθικλμνξοπρστυφχψω
[['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]]]
>>> 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
1000000000000.0
>>> p = [1, -2, -3, 4]
>>> m = [
[
[1, 2, 3],
[6, 10, 12],
[7, 16, 9]
],
[-1, -2, -3]
]
>>> print(equations.pe(p))
>>> print(equations.mles(*m))
[2.561552812809, -1.561552812809, 1.0]
[1.666666666667, -0.666666666667, -0.444444444444]
>>> print(mathematics.cot(constants.pi / 3))
>>> print(mathematics.gamma(1.5))
>>> print(mathematics.pi(1, 10, lambda x: x ** 2))
>>> print(mathematics.product([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))
>>> print(mathematics.sigma(1, 10, lambda x: x ** 2))
>>> print(mathematics.var([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))
0.577350269189626
0.886226925452758
13168189440000
6469693230
385
73.29
>>> print(regression.linear_regression(range(5), [2, 4, 6, 7, 8]))
>>> print(regression.parabolic_regression(range(5), [2, 4, 6, 7, 8]))
f(x) = 1.5 * x + 2.4
[1.5, 2.4]
f(x) = -0.214285714 * x ** 2 + 2.357142857 * x + 1.971428571
[-0.214285714, 2.357142857, 1.971428571]
>>> 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(tools.classify([1, 2.3, 4 + 5j, "string", list, True, 3.14, False, tuple, tools]))
>>> print(tools.deduplicate(["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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