Opis

Opis is a library for rational number and matrix arithmetic.

Author

• Roy R. O. Okello: Email & GitHub

Features

• Arbitrary Precision Integer Representation and Arithmetic
• Fractions Arithmetic
• Matrix Arithmetic & Linear Regression

Usage

Import

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<Self, Box<dyn Error>>

• 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<Fraction, Box<dyn Error>>

Comparison & Equality

Additive Inverse / Opposite

-(a,b) = (-a,b)

• fraction.opposite() -> Fraction

Multiplicative Inverse / Reciprocal

(a,b)^-1 = (b,a)

• fraction.reciprocal() -> Result<Fraction, Box<dyn Error>>

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<Matrix<T>, Box<dyn Error>>

Cofactors

fn cofactors(&self, neg_one: T) -> Result<Matrix<T>, Box<dyn Error>>

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<T, Box<dyn std::error::Error>>

Dimensions

fn dimensions(&self) -> Result<(usize, usize), Box<dyn Error>>

Equality

fn eq(&self, b: &Self) -> bool

Identity

fn identity(size: usize, zero: T, one: T) -> Matrix<T>

inverse

fn inverse(&self, neg_one: T, zero: T, one: T) -> Result<Matrix<T>, Box<dyn Error>>

Linear Regression

fn linear_regression(&self, variables: &Matrix<T>, neg_one: T, zero: T, one: T) -> Result<Matrix<T>, Box<dyn Error>>

Minors

fn minors(&self, neg_one: T) -> Result<Matrix<T>, Box<dyn Error>>

Multiplication

fn mul(self, b: Self) -> Result<Matrix<T>, Box<dyn Error>> fn mul(self, b: T) -> Matrix<T>

Subtraction

fn sub(self, b: Self) -> Result<Matrix<T>, Box<dyn Error>>

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<T, Box<dyn Error>>

Transpose

fn transpose(&self) -> Result<Matrix<T>, Box<dyn Error>>

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.