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

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

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

Subtraction a - b, a -= b

Type Conversion 2_u8.into()

Fraction

Addition a + b, a += b

Comparison a < b, a <= b, a > b, a >= b

Division a / b?

Equality a == b

Multiplication a * b, a *= b

Reciprocal a.reciprocal()

Reduce a.reduce()

String Conversion Fraction::try_from("1/2")

Subtraction a - b, a -= b

Type Conversion 2_u8.into()

Matrix

Addition

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

Cofactors

A = [ 3 -1 -2] C = [ 3 1 -2] [ 3 1 -1] [-3 1 1] [ 3 4 2] [ 3 -4 2] fn cofactors(&self, neg_one: T) -> Result<Matrix<T>, Box<dyn Error>>

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

A = [2 0] A' = [2 1 4] [1 1] [0 1 3] [4 3] fn transpose(&self) -> Result<Matrix<T>, Box<dyn Error>>

License

MIT License

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.