https://github.com/stelar-labs/opis-rs
Opis is a library for rational number and matrix arithmetic.
https://github.com/stelar-labs/opis-rs
arithmetic dynamic dynamic-size fractions integers matrix rational-numbers
Last synced: 4 months ago
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Opis is a library for rational number and matrix arithmetic.
- Host: GitHub
- URL: https://github.com/stelar-labs/opis-rs
- Owner: stelar-labs
- License: mit
- Created: 2021-09-26T09:46:53.000Z (almost 5 years ago)
- Default Branch: main
- Last Pushed: 2024-06-20T14:39:09.000Z (about 2 years ago)
- Last Synced: 2026-01-02T11:05:54.771Z (7 months ago)
- Topics: arithmetic, dynamic, dynamic-size, fractions, integers, matrix, rational-numbers
- Language: Rust
- Homepage:
- Size: 149 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 20
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Opis
Opis is a library for rational number and matrix arithmetic.
## Author
- Roy R. O. Okello: [Email](mailto:royokello@protonmail.com) & [GitHub](https://github.com/royokello)
## Features
- Arbitrary Precision Integer Representation and Arithmetic
- Fractions Arithmetic
- Matrix Arithmetic & Linear Regression
## Usage
### Import
```text
use opis::{ Bit, Integer, Fraction, Matrix };
```
### Bit
Add `a + b`
And `a & b`
Eq `a == a`
Not `!a`
Or `a | b`
Xor `a ^ b`
### Integer
pub struct Integer(pub Vec)
- Hash
- Display
- Debug (:?, :#, :x, :b)
Addition `a + b, a += b`
And `a & b`
Base2 `Integer::from_bin("1010101"), a.to_bin()`
Base10 `Integer::from_dec("674755"), a.to_dec()`
Base16 `Integer::from_hex("00ABC012"), a.to_hex()`
Bytes `Integer::from(&bytes), a.into()`
Comparision `a < b, a <= b, a > b, a >= b`
Division `a / b?`
Equality `a == b`
Extended Euclidean Algorithm `a.ext_gcd(&b)`
Extended Bits `a.to_ext_bits(256)`
Extended Bytes `a.to_ext_bytes(32)`
Linear Feedback Shift Register `a.lfsr(1)?`
Modulo: `a.modulo(&m)`
Modular Exponentiation: `base.mod_pow(&exponent, &modulus)`
Multiply `a * b, a *= b`
Negate `a.negate()`
Not `!a`
Or `a | b`
Exponentiation `a.pow(e)?`
Remainder: `a % b?`
Shifts `a << 1, a <<= 1, a >> 1, a >>= 1`
#### String Conversion
`fn try_from(value: &str) -> Result>`
- Binary (b'11, b'00, b'01)
- Decimal (-1, 0, 1)
- Hexadecimal (0xFF, 0x00, 0x01)
Subtraction `a - b, a -= b`
#### Type Conversion
- From: &[Bits], &[u8], u8, u16, u32, u64, u128, usize
- Into: Vec
#### String Conversion
Support: Binary, Decimal, Hexadecimal, Floating Literal
### Fraction
pub struct Fraction(pub Integer, pub Integer)
- Clone
- Hash
- Display
- Debug (:?, :#, :x, :b)
#### Addition
(a,b) + (c,d) = (ad + bc, bd)
- Add (+)
- AddAssign (+=)
#### Subtraction
(a,b) - (c,d) = (ad - bc, bd)
- Sub (-)
- SubAssign (-=)
#### Multiplication
(a,b) * (c,d) = (ac, bd)
- Mul (*)
- MulAssign (*=)
#### Division
(a,b) / (c,d) = (ad, bc) with c != 0
- Div (/) -> `Result>`
#### Comparison & Equality
#### Additive Inverse / Opposite
-(a,b) = (-a,b)
- `fraction.opposite() -> Fraction`
#### Multiplicative Inverse / Reciprocal
(a,b)^-1 = (b,a)
- `fraction.reciprocal() -> Result>`
#### Reduce
- `pub fn reduce(&mut self)`
- `pub fn reduction(&self) -> Fraction`
#### String Conversion
Support: Binary, Decimal, Hexadecimal, Floating Point Literal
#### Type Conversion
From: Integer, u8, u16, u32, u64, u128, usize
### Matrix
#### Addition
`fn add(self, b: Self) -> Result, Box>`
#### Cofactors
`fn cofactors(&self, neg_one: T) -> Result, Box>`
```
A = [ 3 -1 -2] C = [ 3 1 -2]
[ 3 1 -1] [-3 1 1]
[ 3 4 2] [ 3 -4 2]
```
#### Determinant
`fn determinant(&self, neg_one: T) -> Result>`
#### Dimensions
`fn dimensions(&self) -> Result<(usize, usize), Box>`
#### Equality
`fn eq(&self, b: &Self) -> bool`
#### Identity
`fn identity(size: usize, zero: T, one: T) -> Matrix`
#### inverse
`fn inverse(&self, neg_one: T, zero: T, one: T) -> Result, Box>`
#### Linear Regression
`fn linear_regression(&self, variables: &Matrix, neg_one: T, zero: T, one: T) -> Result, Box>`
#### Minors
`fn minors(&self, neg_one: T) -> Result, Box>`
#### Multiplication
`fn mul(self, b: Self) -> Result, Box>`
`fn mul(self, b: T) -> Matrix`
#### Subtraction
`fn sub(self, b: Self) -> Result, Box>`
#### Trace
```
A = [-1 2 7 0] Tr(A) = (-1 + 5 + 7 + 0) = 11
[ 3 5 -8 4]
[ 1 2 7 -3]
[ 4 -2 1 0]
```
`fn trace(&self) -> Result>`
#### Transpose
`fn transpose(&self) -> Result, Box>`
```
A = [2 0] A' = [2 1 4]
[1 1] [0 1 3]
[4 3]
```
## License
MIT License
Copyright Stelar Labs
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
## Disclaimer
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.