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extern crate nalgebra as na;
use na::{OMatrix, OVector, DMatrix, DVector, Scalar, Dim, DimName, default_allocator::DefaultAllocator, allocator::Allocator, convert, RealField, DimMin, DimSub, Const};
#[allow(non_snake_case)]
pub fn solve<T, M, N>(A: &OMatrix<T,M,N>, b: &OVector<T,M>, c: &OVector<T,N>, eps: T, theta: T, gamma: T, max_it: usize) -> (OVector<T, N>,OVector<T,M>)
where
T: Scalar + RealField + Copy,
M: Dim + DimName + DimMin<M, Output = M> + DimSub<Const<1>>,
N: Dim + DimName + DimMin<N, Output = N>,
DefaultAllocator: Allocator<T, M> + Allocator<T, M, N> + Allocator<T, N, M> + Allocator<T, N, N> + Allocator<T, N> + Allocator<T, M, M> + Allocator<(T, usize), M> + Allocator<(usize, usize), M> + Allocator<T, <M as DimSub<Const<1>>>::Output> {
let one: T = convert(1.0);
let max_val = T::max_value().unwrap();
let svd_eps: T = convert(1e-20);
let A_transpose = A.transpose();
let mut gamma_mu = OVector::<T,N>::from_element(one);
let mut x = OVector::<T,N>::from_element(one);
let mut s = OVector::<T,N>::from_element(one);
let mut y = OVector::<T,M>::zeros();
let mut r_primal = OVector::<T,M>::from_element(max_val);
let mut r_dual = OVector::<T,N>::from_element(max_val);
let mut k = 0;
let mut S_inv = OMatrix::<T,N,N>::zeros();
let mut X = OMatrix::<T,N,N>::zeros();
let n : T = convert(N::USIZE as f64);
while k < max_it && (r_primal.norm() > eps || r_dual.norm() > eps || x.dot(&s) > eps) {
r_primal = b - A*(&x);
r_dual = c - (&A_transpose)*(&y) - (&s);
let mu = x.dot(&s)/n;
for i in 0..N::USIZE {
S_inv[(i,i)] = one/s[i];
X[(i,i)] = x[i];
gamma_mu[i] = gamma*mu;
}
let M = A*(&S_inv)*(&X)*(&A_transpose);
let r = b + A*(&S_inv)*((&X)*(&r_dual) - (&gamma_mu));
let d_y = M.svd(true,true).solve(&r, svd_eps).expect("direction y failed");
let d_s = (&r_dual) - (&A_transpose)*(&d_y);
let d_x = -(&x) + (&S_inv)*((&gamma_mu)-(&X)*(&d_s));
let mut step_primal = max_val;
let mut step_dual = max_val;
for i in 0..N::USIZE {
let dx_i = d_x[i];
let ds_i = d_s[i];
if dx_i < T::zero() {
let v = -x[i]/dx_i;
step_primal = step_primal.min(v);
}
if ds_i < T::zero() {
let v = -s[i]/ds_i;
step_dual = step_dual.min(v);
}
}
let step_max = step_primal.min(step_dual);
let step = one.min(theta*step_max);
x = x+d_x.scale(step);
y = y+d_y.scale(step);
s = s+d_s.scale(step);
k = k+1;
}
(x,y)
}
#[allow(non_snake_case)]
pub fn solve_dyn<T>(A: &DMatrix<T>, b: &DVector<T>, c: &DVector<T>, eps: T, theta: T, gamma: T, max_it: usize) -> (DVector<T>, DVector<T>)
where T: Scalar + RealField + Copy{
let one: T = convert(1.0);
let max_val = T::max_value().unwrap();
let svd_eps: T = convert(1e-20);
let N = A.ncols();
let M = A.nrows();
let A_transpose = A.transpose();
let mut gamma_mu = DVector::<T>::from_element(N, one);
let mut x = DVector::<T>::from_element(N, one);
let mut s = DVector::<T>::from_element(N, one);
let mut y = DVector::<T>::zeros(M);
let mut r_primal = DVector::<T>::from_element(M, max_val);
let mut r_dual = DVector::<T>::from_element(N, max_val);
let mut k = 0;
let mut S_inv = DMatrix::<T>::zeros(N,N);
let mut X = DMatrix::<T>::zeros(N,N);
let n : T = convert(N as f64);
while k < max_it && (r_primal.norm() > eps || r_dual.norm() > eps || x.dot(&s) > eps) {
r_primal = b - A*(&x);
r_dual = c - (&A_transpose)*(&y) - (&s);
let mu = x.dot(&s)/n;
for i in 0..N {
S_inv[(i,i)] = one/s[i];
X[(i,i)] = x[i];
gamma_mu[i] = gamma*mu;
}
let M = A*(&S_inv)*(&X)*(&A_transpose);
let r = b + A*(&S_inv)*((&X)*(&r_dual) - (&gamma_mu));
let d_y = M.svd(true,true).solve(&r, svd_eps).expect("direction y failed");
let d_s = (&r_dual) - (&A_transpose)*(&d_y);
let d_x = -(&x) + (&S_inv)*((&gamma_mu)-(&X)*(&d_s));
let mut step_primal = max_val;
let mut step_dual = max_val;
for i in 0..N {
let dx_i = d_x[i];
let ds_i = d_s[i];
if dx_i < T::zero() {
let v = -x[i]/dx_i;
step_primal = step_primal.min(v);
}
if ds_i < T::zero() {
let v = -s[i]/ds_i;
step_dual = step_dual.min(v);
}
}
let step_max = step_primal.min(step_dual);
let step = one.min(theta*step_max);
x = x+d_x.scale(step);
y = y+d_y.scale(step);
s = s+d_s.scale(step);
k = k+1;
}
(x,y)
}