# Crate totsu

Expand description

Totsu ( in Japanese) means convex.

This crate for Rust provides convex optimization problems LP/QP/QCQP/SOCP/SDP that can be solved by totsu_core.

## General usage

1. An optimization problem you want to solve is assumed to be expressed in the standard form of LP, QP, QCQP, SOCP or SDP. Refer to ProbLP, ProbQP, ProbQCQP, ProbSOCP and ProbSDP about their mathematical formulations.
2. Choose a totsu_core::LinAlgEx implementation to use:
3. Construct your problem with matrices using MatBuild.
4. Create a prelude::Solver instance and optionally set its parameters.
5. Feed the problem to the solver and invoke prelude::Solver::solve to get a resulted solution.

## Examples

A simple QP problem: $\begin{array}{ll} {\rm minimize} & {(x_0 - (-1))^2 + (x_1 - (-2))^2 \over 2} \\ {\rm subject \ to} & 1 - {x_0 \over 2} - {x_1 \over 3} <= 0 \end{array}$

You will notice that a perpendicular drawn from $$(-1, -2)$$ to the line $$1 - {x_0 \over 2} - {x_1 \over 3} = 0$$ intersects at point $$(2, 0)$$ which is the optimal solution of the problem.

use float_eq::assert_float_eq;
use totsu::prelude::*;
use totsu::*;

//env_logger::init(); // Use any logger crate as totsu uses log crate.

type La = FloatGeneric<f64>;
type AMatBuild = MatBuild<La>;
type AProbQP = ProbQP<La>;
type ASolver = Solver<La>;

let n = 2; // x0, x1
let m = 1;
let p = 0;

// (1/2)(x - a)^2 + const
let mut sym_p = AMatBuild::new(MatType::SymPack(n));
sym_p[(0, 0)] = 1.;
sym_p[(1, 1)] = 1.;

let mut vec_q = AMatBuild::new(MatType::General(n, 1));
vec_q[(0, 0)] = -(-1.); // -a0
vec_q[(1, 0)] = -(-2.); // -a1

// 1 - x0/b0 - x1/b1 <= 0
let mut mat_g = AMatBuild::new(MatType::General(m, n));
mat_g[(0, 0)] = -1. / 2.; // -1/b0
mat_g[(0, 1)] = -1. / 3.; // -1/b1

let mut vec_h = AMatBuild::new(MatType::General(m, 1));
vec_h[(0, 0)] = -1.;

let mat_a = AMatBuild::new(MatType::General(p, n));

let vec_b = AMatBuild::new(MatType::General(p, 1));

let s = ASolver::new().par(|p| {
p.max_iter = Some(100_000);
});
let mut qp = AProbQP::new(sym_p, vec_q, mat_g, vec_h, mat_a, vec_b, s.par.eps_zero);
let rslt = s.solve(qp.problem()).unwrap();

assert_float_eq!(rslt.0[0..2], [2., 0.].as_ref(), abs_all <= 1e-3);

### Other examples

You can find other tests of the problems. More practical examples are also available.

## Re-exports

pub use totsu_core;

Prelude

Matrix builder
Linear program